0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.13 % Command : run_vampire %s %d THM 0.13/0.34 % Computer : n004.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1920 0.13/0.34 % WCLimit : 240 0.13/0.34 % DateTime : Wed Jul 30 06:10:49 EDT 2025 0.13/0.34 % CPUTime : 0.13/0.36 This is a THF_ problem 0.13/0.37 Running higher-order theorem proving 0.23/0.43 Running /export/starexec/sandbox2/solver/bin/vampire-hol --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --print_def_sorts on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.3DV3eBGPqy/E---3.1_30784.p -m 16384 -t 240 0.23/0.47 % (30987)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/275Mi) 0.29/0.48 % (30988)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/18Mi) 0.29/0.48 % (30983)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/4Mi) 0.29/0.48 % (30982)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/183Mi) 0.29/0.48 % (30984)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/27Mi) 0.29/0.48 % (30983)Instruction limit reached! 0.29/0.48 % (30983)------------------------------ 0.29/0.48 % (30983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.48 % (30983)Termination reason: Unknown 0.29/0.48 % (30983)Termination phase: shuffling 0.29/0.48 0.29/0.48 % (30983)Memory used [KB]: 1535 0.29/0.48 % (30983)Time elapsed: 0.004 s 0.29/0.48 % (30983)Instructions burned: 4 (million) 0.29/0.48 % (30983)------------------------------ 0.29/0.48 % (30983)------------------------------ 0.29/0.49 % (30988)Instruction limit reached! 0.29/0.49 % (30988)------------------------------ 0.29/0.49 % (30988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.49 % (30988)Termination reason: Unknown 0.29/0.49 % (30988)Termination phase: shuffling 0.29/0.49 0.29/0.49 % (30988)Memory used [KB]: 1791 0.29/0.49 % (30988)Time elapsed: 0.011 s 0.29/0.49 % (30988)Instructions burned: 18 (million) 0.29/0.49 % (30988)------------------------------ 0.29/0.49 % (30988)------------------------------ 0.29/0.49 % (30985)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/2Mi) 0.29/0.49 % (30985)Instruction limit reached! 0.29/0.49 % (30985)------------------------------ 0.29/0.49 % (30985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.49 % (30985)Termination reason: Unknown 0.29/0.49 % (30985)Termination phase: shuffling 0.29/0.49 0.29/0.49 % (30985)Memory used [KB]: 1535 0.29/0.49 % (30985)Time elapsed: 0.003 s 0.29/0.49 % (30985)Instructions burned: 2 (million) 0.29/0.49 % (30985)------------------------------ 0.29/0.49 % (30985)------------------------------ 0.29/0.49 % (30986)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/2Mi) 0.29/0.49 % (30984)Instruction limit reached! 0.29/0.49 % (30984)------------------------------ 0.29/0.49 % (30984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.49 % (30984)Termination reason: Unknown 0.29/0.49 % (30986)Instruction limit reached! 0.29/0.49 % (30986)------------------------------ 0.29/0.49 % (30986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.49 % (30986)Termination reason: Unknown 0.29/0.49 % (30984)Termination phase: shuffling 0.29/0.49 0.29/0.49 % (30986)Termination phase: shuffling 0.29/0.49 % (30984)Memory used [KB]: 2046 0.29/0.49 0.29/0.49 % (30984)Time elapsed: 0.016 s 0.29/0.49 % (30986)Memory used [KB]: 1535 0.29/0.49 % (30984)Instructions burned: 27 (million) 0.29/0.49 % (30986)Time elapsed: 0.003 s 0.29/0.49 % (30984)------------------------------ 0.29/0.49 % (30984)------------------------------ 0.29/0.49 % (30986)Instructions burned: 2 (million) 0.29/0.49 % (30986)------------------------------ 0.29/0.49 % (30986)------------------------------ 0.29/0.50 % (31000)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/3Mi) 0.29/0.50 % (31003)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/37Mi) 0.29/0.50 % (31000)Instruction limit reached! 0.29/0.50 % (31000)------------------------------ 0.29/0.50 % (31000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.50 % (31000)Termination reason: Unknown 0.29/0.50 % (31000)Termination phase: shuffling 0.29/0.50 0.29/0.50 % (31000)Memory used [KB]: 1535 0.29/0.50 % (31000)Time elapsed: 0.004 s 0.29/0.50 % (31000)Instructions burned: 4 (million) 0.29/0.50 % (31000)------------------------------ 0.29/0.50 % (31000)------------------------------ 0.29/0.51 % (31007)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/15Mi) 0.29/0.51 % (31008)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/3Mi) 0.29/0.51 % (31009)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/1041Mi) 0.29/0.51 % (31008)Instruction limit reached! 0.29/0.51 % (31008)------------------------------ 0.29/0.51 % (31008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.51 % (31008)Termination reason: Unknown 0.29/0.51 % (31008)Termination phase: shuffling 0.29/0.51 0.29/0.51 % (31008)Memory used [KB]: 1535 0.29/0.51 % (31008)Time elapsed: 0.005 s 0.29/0.51 % (31008)Instructions burned: 4 (million) 0.29/0.51 % (31008)------------------------------ 0.29/0.51 % (31008)------------------------------ 0.29/0.51 % (31007)Instruction limit reached! 0.29/0.51 % (31007)------------------------------ 0.29/0.51 % (31007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.51 % (31007)Termination reason: Unknown 0.29/0.51 % (31007)Termination phase: shuffling 0.29/0.51 0.29/0.51 % (31007)Memory used [KB]: 1791 0.29/0.51 % (31007)Time elapsed: 0.010 s 0.29/0.51 % (31007)Instructions burned: 16 (million) 0.29/0.51 % (31007)------------------------------ 0.29/0.51 % (31007)------------------------------ 0.29/0.52 % (31003)Instruction limit reached! 0.29/0.52 % (31003)------------------------------ 0.29/0.52 % (31003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.52 % (31003)Termination reason: Unknown 0.29/0.52 % (31003)Termination phase: shuffling 0.29/0.52 0.29/0.52 % (31003)Memory used [KB]: 2302 0.29/0.52 % (31003)Time elapsed: 0.018 s 0.29/0.52 % (31003)Instructions burned: 37 (million) 0.29/0.52 % (31003)------------------------------ 0.29/0.52 % (31003)------------------------------ 0.29/0.52 % (31016)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/7Mi) 0.29/0.52 % (31016)Instruction limit reached! 0.29/0.52 % (31016)------------------------------ 0.29/0.52 % (31016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.52 % (31016)Termination reason: Unknown 0.29/0.52 % (31016)Termination phase: shuffling 0.29/0.52 0.29/0.52 % (31016)Memory used [KB]: 1535 0.29/0.52 % (31016)Time elapsed: 0.006 s 0.29/0.52 % (31016)Instructions burned: 7 (million) 0.29/0.52 % (31016)------------------------------ 0.29/0.52 % (31016)------------------------------ 0.29/0.53 % (31020)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/3Mi) 0.29/0.53 % (31019)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/16Mi) 0.29/0.53 % (31020)Instruction limit reached! 0.29/0.53 % (31020)------------------------------ 0.29/0.53 % (31020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.53 % (31020)Termination reason: Unknown 0.29/0.53 % (31020)Termination phase: shuffling 0.29/0.53 0.29/0.53 % (31020)Memory used [KB]: 1535 0.29/0.53 % (31020)Time elapsed: 0.004 s 0.29/0.53 % (31020)Instructions burned: 4 (million) 0.29/0.53 % (31020)------------------------------ 0.29/0.53 % (31020)------------------------------ 0.29/0.53 % (31021)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/3Mi) 0.29/0.53 % (31021)Instruction limit reached! 0.29/0.53 % (31021)------------------------------ 0.29/0.53 % (31021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.53 % (31021)Termination reason: Unknown 0.29/0.53 % (31021)Termination phase: shuffling 0.29/0.53 0.29/0.53 % (31021)Memory used [KB]: 1535 0.29/0.53 % (31021)Time elapsed: 0.004 s 0.29/0.53 % (31021)Instructions burned: 5 (million) 0.29/0.53 % (31021)------------------------------ 0.29/0.53 % (31021)------------------------------ 0.29/0.54 % (31019)Instruction limit reached! 0.29/0.54 % (31019)------------------------------ 0.29/0.54 % (31019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.54 % (31019)Termination reason: Unknown 0.29/0.54 % (31019)Termination phase: shuffling 0.29/0.54 0.29/0.54 % (31019)Memory used [KB]: 1791 0.29/0.54 % (31019)Time elapsed: 0.011 s 0.29/0.54 % (31019)Instructions burned: 16 (million) 0.29/0.54 % (31019)------------------------------ 0.29/0.54 % (31019)------------------------------ 0.29/0.54 % (31023)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/7Mi) 0.29/0.55 % (31023)Instruction limit reached! 0.29/0.55 % (31023)------------------------------ 0.29/0.55 % (31023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.55 % (31023)Termination reason: Unknown 0.29/0.55 % (31023)Termination phase: shuffling 0.29/0.55 0.29/0.55 % (31023)Memory used [KB]: 1663 0.29/0.55 % (31023)Time elapsed: 0.007 s 0.29/0.55 % (31023)Instructions burned: 8 (million) 0.29/0.55 % (31023)------------------------------ 0.29/0.55 % (31023)------------------------------ 0.29/0.55 % (31033)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/3Mi) 0.29/0.55 % (31033)Instruction limit reached! 0.29/0.55 % (31033)------------------------------ 0.29/0.55 % (31033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.55 % (31033)Termination reason: Unknown 0.29/0.55 % (31033)Termination phase: shuffling 0.29/0.55 0.29/0.55 % (31033)Memory used [KB]: 1535 0.29/0.55 % (31033)Time elapsed: 0.004 s 0.29/0.55 % (31033)Instructions burned: 4 (million) 0.29/0.55 % (31033)------------------------------ 0.29/0.55 % (31033)------------------------------ 0.29/0.55 % (31035)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/4Mi) 0.29/0.55 % (31035)Instruction limit reached! 0.29/0.55 % (31035)------------------------------ 0.29/0.55 % (31035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.55 % (31035)Termination reason: Unknown 0.29/0.55 % (31035)Termination phase: shuffling 0.29/0.55 0.29/0.55 % (31035)Memory used [KB]: 1535 0.29/0.55 % (31035)Time elapsed: 0.004 s 0.29/0.55 % (31035)Instructions burned: 5 (million) 0.29/0.55 % (31035)------------------------------ 0.29/0.55 % (31035)------------------------------ 0.29/0.56 % (31040)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/18Mi) 0.29/0.56 % (30987)Instruction limit reached! 0.29/0.56 % (30987)------------------------------ 0.29/0.56 % (30987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.56 % (30987)Termination reason: Unknown 0.29/0.56 % (30987)Termination phase: Saturation 0.29/0.56 0.29/0.56 % (30987)Memory used [KB]: 10106 0.29/0.56 % (30987)Time elapsed: 0.089 s 0.29/0.56 % (30987)Instructions burned: 277 (million) 0.29/0.56 % (30987)------------------------------ 0.29/0.56 % (30987)------------------------------ 0.29/0.56 % (31041)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_30784 for (2399ds/710Mi) 0.29/0.57 % (31042)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/6Mi) 0.29/0.57 % (31040)Instruction limit reached! 0.29/0.57 % (31040)------------------------------ 0.29/0.57 % (31040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.57 % (31040)Termination reason: Unknown 0.29/0.57 % (31040)Termination phase: shuffling 0.29/0.57 0.29/0.57 % (31040)Memory used [KB]: 1791 0.29/0.57 % (31040)Time elapsed: 0.011 s 0.29/0.57 % (31040)Instructions burned: 18 (million) 0.29/0.57 % (31040)------------------------------ 0.29/0.57 % (31040)------------------------------ 0.29/0.57 % (31042)Instruction limit reached! 0.29/0.57 % (31042)------------------------------ 0.29/0.57 % (31042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.57 % (31042)Termination reason: Unknown 0.29/0.57 % (31042)Termination phase: shuffling 0.29/0.57 0.29/0.57 % (31042)Memory used [KB]: 1535 0.29/0.57 % (31042)Time elapsed: 0.004 s 0.29/0.57 % (31042)Instructions burned: 7 (million) 0.29/0.57 % (31042)------------------------------ 0.29/0.57 % (31042)------------------------------ 0.29/0.57 % (31045)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/902Mi) 0.29/0.57 % (30982)Instruction limit reached! 0.29/0.57 % (30982)------------------------------ 0.29/0.57 % (30982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.57 % (30982)Termination reason: Unknown 0.29/0.57 % (30982)Termination phase: Saturation 0.29/0.57 0.29/0.57 % (30982)Memory used [KB]: 7419 0.29/0.57 % (30982)Time elapsed: 0.091 s 0.29/0.57 % (30982)Instructions burned: 183 (million) 0.29/0.57 % (30982)------------------------------ 0.29/0.57 % (30982)------------------------------ 0.29/0.57 % (31049)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/21Mi) 0.29/0.58 % (31049)Instruction limit reached! 0.29/0.58 % (31049)------------------------------ 0.29/0.58 % (31049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.58 % (31049)Termination reason: Unknown 0.29/0.58 % (31049)Termination phase: shuffling 0.29/0.58 0.29/0.58 % (31049)Memory used [KB]: 1918 0.29/0.58 % (31049)Time elapsed: 0.008 s 0.29/0.58 % (31049)Instructions burned: 22 (million) 0.29/0.58 % (31049)------------------------------ 0.29/0.58 % (31049)------------------------------ 0.29/0.58 % (31055)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/6Mi) 0.29/0.58 % (31054)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/5Mi) 0.29/0.58 % (31055)Instruction limit reached! 0.29/0.58 % (31055)------------------------------ 0.29/0.58 % (31055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.58 % (31055)Termination reason: Unknown 0.29/0.58 % (31055)Termination phase: shuffling 0.29/0.58 0.29/0.58 % (31055)Memory used [KB]: 1535 0.29/0.58 % (31055)Time elapsed: 0.003 s 0.29/0.58 % (31055)Instructions burned: 6 (million) 0.29/0.58 % (31055)------------------------------ 0.29/0.58 % (31055)------------------------------ 0.29/0.58 % (31054)Instruction limit reached! 0.29/0.58 % (31054)------------------------------ 0.29/0.58 % (31054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.58 % (31054)Termination reason: Unknown 0.29/0.58 % (31054)Termination phase: shuffling 0.29/0.58 0.29/0.58 % (31054)Memory used [KB]: 1535 0.29/0.58 % (31054)Time elapsed: 0.003 s 0.29/0.58 % (31054)Instructions burned: 5 (million) 0.29/0.58 % (31054)------------------------------ 0.29/0.58 % (31054)------------------------------ 0.29/0.58 % (31056)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/377Mi) 0.29/0.59 % (31062)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/779Mi) 0.29/0.59 % (31063)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/19Mi) 0.29/0.59 % (31064)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/879Mi) 0.29/0.60 % (31063)Instruction limit reached! 0.29/0.60 % (31063)------------------------------ 0.29/0.60 % (31063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.29/0.60 % (31063)Termination reason: Unknown 0.29/0.60 % (31063)Termination phase: shuffling 0.29/0.60 0.29/0.60 % (31063)Memory used [KB]: 1791 0.29/0.60 % (31063)Time elapsed: 0.007 s 0.29/0.60 % (31063)Instructions burned: 20 (million) 0.29/0.60 % (31063)------------------------------ 0.29/0.60 % (31063)------------------------------ 1.20/0.61 % (31070)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/17Mi) 1.20/0.61 % (31070)Instruction limit reached! 1.20/0.61 % (31070)------------------------------ 1.20/0.61 % (31070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.20/0.61 % (31070)Termination reason: Unknown 1.20/0.61 % (31070)Termination phase: shuffling 1.20/0.61 1.20/0.61 % (31070)Memory used [KB]: 1791 1.20/0.61 % (31070)Time elapsed: 0.007 s 1.20/0.61 % (31070)Instructions burned: 18 (million) 1.20/0.61 % (31070)------------------------------ 1.20/0.61 % (31070)------------------------------ 1.20/0.62 % (31077)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/3Mi) 1.20/0.63 % (31077)Instruction limit reached! 1.20/0.63 % (31077)------------------------------ 1.20/0.63 % (31077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.20/0.63 % (31077)Termination reason: Unknown 1.20/0.63 % (31077)Termination phase: shuffling 1.20/0.63 1.20/0.63 % (31077)Memory used [KB]: 1535 1.20/0.63 % (31077)Time elapsed: 0.003 s 1.20/0.63 % (31077)Instructions burned: 5 (million) 1.20/0.63 % (31077)------------------------------ 1.20/0.63 % (31077)------------------------------ 1.42/0.64 % (31081)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/30Mi) 1.42/0.65 % (31081)Instruction limit reached! 1.42/0.65 % (31081)------------------------------ 1.42/0.65 % (31081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.42/0.65 % (31081)Termination reason: Unknown 1.42/0.65 % (31081)Termination phase: shuffling 1.42/0.65 1.42/0.65 % (31081)Memory used [KB]: 2174 1.42/0.65 % (31081)Time elapsed: 0.011 s 1.42/0.65 % (31081)Instructions burned: 32 (million) 1.42/0.65 % (31081)------------------------------ 1.42/0.65 % (31081)------------------------------ 1.42/0.66 % (31089)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on E---3.1_30784 for (2398ds/127Mi) 1.42/0.69 % (31056)Instruction limit reached! 1.42/0.69 % (31056)------------------------------ 1.42/0.69 % (31056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.42/0.69 % (31056)Termination reason: Unknown 1.42/0.69 % (31056)Termination phase: Saturation 1.42/0.69 1.42/0.69 % (31056)Memory used [KB]: 9466 1.42/0.69 % (31056)Time elapsed: 0.106 s 1.42/0.69 % (31056)Instructions burned: 379 (million) 1.42/0.69 % (31056)------------------------------ 1.42/0.69 % (31056)------------------------------ 1.42/0.69 % (31089)Instruction limit reached! 1.42/0.69 % (31089)------------------------------ 1.42/0.69 % (31089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.42/0.69 % (31089)Termination reason: Unknown 1.42/0.69 % (31089)Termination phase: Property scanning 1.42/0.69 1.42/0.69 % (31089)Memory used [KB]: 2814 1.42/0.69 % (31089)Time elapsed: 0.038 s 1.42/0.69 % (31089)Instructions burned: 130 (million) 1.42/0.69 % (31089)------------------------------ 1.42/0.69 % (31089)------------------------------ 1.42/0.70 % (31101)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on E---3.1_30784 for (2397ds/100Mi) 1.87/0.71 % (31103)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on E---3.1_30784 for (2397ds/3Mi) 1.87/0.71 % (31103)Instruction limit reached! 1.87/0.71 % (31103)------------------------------ 1.87/0.71 % (31103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.87/0.71 % (31103)Termination reason: Unknown 1.87/0.71 % (31103)Termination phase: shuffling 1.87/0.71 1.87/0.71 % (31103)Memory used [KB]: 1535 1.87/0.71 % (31103)Time elapsed: 0.003 s 1.87/0.71 % (31103)Instructions burned: 5 (million) 1.87/0.71 % (31103)------------------------------ 1.87/0.71 % (31103)------------------------------ 1.87/0.72 % (31108)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on E---3.1_30784 for (2397ds/20Mi) 1.87/0.72 % (31101)Instruction limit reached! 1.87/0.72 % (31101)------------------------------ 1.87/0.72 % (31101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.87/0.72 % (31101)Termination reason: Unknown 1.87/0.72 % (31101)Termination phase: Property scanning 1.87/0.72 1.87/0.72 % (31101)Memory used [KB]: 2686 1.87/0.72 % (31101)Time elapsed: 0.028 s 1.87/0.72 % (31101)Instructions burned: 102 (million) 1.87/0.72 % (31101)------------------------------ 1.87/0.72 % (31101)------------------------------ 1.87/0.72 % (31108)Instruction limit reached! 1.87/0.72 % (31108)------------------------------ 1.87/0.72 % (31108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.87/0.72 % (31108)Termination reason: Unknown 1.87/0.72 % (31108)Termination phase: shuffling 1.87/0.72 1.87/0.72 % (31108)Memory used [KB]: 1791 1.87/0.72 % (31108)Time elapsed: 0.008 s 1.87/0.72 % (31108)Instructions burned: 20 (million) 1.87/0.72 % (31108)------------------------------ 1.87/0.72 % (31108)------------------------------ 1.87/0.73 % (31113)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on E---3.1_30784 for (2397ds/86Mi) 1.87/0.73 % (31114)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on E---3.1_30784 for (2397ds/107Mi) 1.87/0.76 % (31113)Instruction limit reached! 1.87/0.76 % (31113)------------------------------ 1.87/0.76 % (31113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.87/0.76 % (31113)Termination reason: Unknown 1.87/0.76 % (31113)Termination phase: Property scanning 1.87/0.76 1.87/0.76 % (31113)Memory used [KB]: 2558 1.87/0.76 % (31113)Time elapsed: 0.024 s 1.87/0.76 % (31113)Instructions burned: 88 (million) 1.87/0.76 % (31113)------------------------------ 1.87/0.76 % (31113)------------------------------ 2.27/0.76 % (31114)Instruction limit reached! 2.27/0.76 % (31114)------------------------------ 2.27/0.76 % (31114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.27/0.76 % (31114)Termination reason: Unknown 2.27/0.76 % (31114)Termination phase: SInE selection 2.27/0.76 2.27/0.76 % (31114)Memory used [KB]: 2558 2.27/0.76 % (31114)Time elapsed: 0.031 s 2.27/0.76 % (31114)Instructions burned: 109 (million) 2.27/0.76 % (31114)------------------------------ 2.27/0.76 % (31114)------------------------------ 2.27/0.77 % (31118)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on E---3.1_30784 for (2396ds/39Mi) 2.27/0.78 % (31119)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on E---3.1_30784 for (2396ds/448Mi) 2.27/0.78 % (31118)Instruction limit reached! 2.27/0.78 % (31118)------------------------------ 2.27/0.78 % (31118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.27/0.78 % (31118)Termination reason: Unknown 2.27/0.78 % (31118)Termination phase: shuffling 2.27/0.78 2.27/0.78 % (31118)Memory used [KB]: 2302 2.27/0.78 % (31118)Time elapsed: 0.012 s 2.27/0.78 % (31118)Instructions burned: 41 (million) 2.27/0.78 % (31118)------------------------------ 2.27/0.78 % (31118)------------------------------ 2.27/0.79 % (31125)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on E---3.1_30784 for (2396ds/46Mi) 2.27/0.80 % (31125)Instruction limit reached! 2.27/0.80 % (31125)------------------------------ 2.27/0.80 % (31125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.27/0.80 % (31125)Termination reason: Unknown 2.27/0.80 % (31125)Termination phase: shuffling 2.27/0.80 2.27/0.80 % (31125)Memory used [KB]: 2430 2.27/0.80 % (31125)Time elapsed: 0.015 s 2.27/0.80 % (31125)Instructions burned: 48 (million) 2.27/0.80 % (31125)------------------------------ 2.27/0.80 % (31125)------------------------------ 2.27/0.81 % (31127)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on E---3.1_30784 for (2396ds/98Mi) 2.27/0.81 % (31041)Instruction limit reached! 2.27/0.81 % (31041)------------------------------ 2.27/0.81 % (31041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.27/0.81 % (31041)Termination reason: Unknown 2.27/0.81 % (31041)Termination phase: Saturation 2.27/0.81 2.27/0.81 % (31041)Memory used [KB]: 12025 2.27/0.81 % (31041)Time elapsed: 0.250 s 2.27/0.81 % (31041)Instructions burned: 711 (million) 2.27/0.81 % (31041)------------------------------ 2.27/0.81 % (31041)------------------------------ 2.27/0.81 % (31062)Instruction limit reached! 2.27/0.81 % (31062)------------------------------ 2.27/0.81 % (31062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.27/0.81 % (31062)Termination reason: Unknown 2.27/0.81 % (31062)Termination phase: Saturation 2.27/0.81 2.27/0.81 % (31062)Memory used [KB]: 7675 2.27/0.81 % (31062)Time elapsed: 0.215 s 2.27/0.81 % (31062)Instructions burned: 782 (million) 2.27/0.81 % (31062)------------------------------ 2.27/0.81 % (31062)------------------------------ 2.27/0.82 % (31129)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on E---3.1_30784 for (2396ds/149Mi) 2.27/0.82 % (31128)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on E---3.1_30784 for (2396ds/507Mi) 2.27/0.83 % (31127)Instruction limit reached! 2.27/0.83 % (31127)------------------------------ 2.27/0.83 % (31127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.27/0.83 % (31127)Termination reason: Unknown 2.27/0.83 % (31127)Termination phase: Property scanning 2.27/0.83 2.27/0.83 % (31127)Memory used [KB]: 2558 2.27/0.83 % (31127)Time elapsed: 0.026 s 2.27/0.83 % (31127)Instructions burned: 99 (million) 2.27/0.83 % (31127)------------------------------ 2.27/0.83 % (31127)------------------------------ 2.27/0.84 % (31130)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on E---3.1_30784 for (2396ds/39Mi) 2.27/0.85 % (31009)Instruction limit reached! 2.27/0.85 % (31009)------------------------------ 2.27/0.85 % (31009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.27/0.85 % (31009)Termination reason: Unknown 2.27/0.85 % (31009)Termination phase: Saturation 2.27/0.85 2.27/0.85 % (31009)Memory used [KB]: 16375 2.27/0.85 % (31009)Time elapsed: 0.336 s 2.27/0.85 % (31009)Instructions burned: 1043 (million) 2.27/0.85 % (31009)------------------------------ 2.27/0.85 % (31009)------------------------------ 2.78/0.86 % (31130)Instruction limit reached! 2.78/0.86 % (31130)------------------------------ 2.78/0.86 % (31130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.78/0.86 % (31130)Termination reason: Unknown 2.78/0.86 % (31130)Termination phase: shuffling 2.78/0.86 2.78/0.86 % (31130)Memory used [KB]: 2302 2.78/0.86 % (31130)Time elapsed: 0.013 s 2.78/0.86 % (31130)Instructions burned: 42 (million) 2.78/0.86 % (31130)------------------------------ 2.78/0.86 % (31130)------------------------------ 2.78/0.86 % (31131)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/6Mi) 2.78/0.86 % (31131)Instruction limit reached! 2.78/0.86 % (31131)------------------------------ 2.78/0.86 % (31131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.78/0.86 % (31131)Termination reason: Unknown 2.78/0.86 % (31131)Termination phase: shuffling 2.78/0.86 2.78/0.86 % (31131)Memory used [KB]: 1535 2.78/0.86 % (31131)Time elapsed: 0.003 s 2.78/0.86 % (31131)Instructions burned: 6 (million) 2.78/0.86 % (31131)------------------------------ 2.78/0.86 % (31131)------------------------------ 2.78/0.86 % (31129)Instruction limit reached! 2.78/0.86 % (31129)------------------------------ 2.78/0.86 % (31129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.78/0.86 % (31129)Termination reason: Unknown 2.78/0.86 % (31129)Termination phase: Twee Goal Transformation 2.78/0.86 2.78/0.86 % (31129)Memory used [KB]: 3070 2.78/0.86 % (31129)Time elapsed: 0.041 s 2.78/0.86 % (31129)Instructions burned: 152 (million) 2.78/0.86 % (31129)------------------------------ 2.78/0.86 % (31129)------------------------------ 2.78/0.87 % (31132)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/1087Mi) 2.78/0.87 % (31133)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/47Mi) 2.78/0.87 % (31134)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/44Mi) 2.78/0.88 % (31064)Instruction limit reached! 2.78/0.88 % (31064)------------------------------ 2.78/0.88 % (31064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.78/0.88 % (31064)Termination reason: Unknown 2.78/0.88 % (31064)Termination phase: Saturation 2.78/0.88 2.78/0.88 % (31064)Memory used [KB]: 10106 2.78/0.88 % (31064)Time elapsed: 0.286 s 2.78/0.88 % (31064)Instructions burned: 880 (million) 2.78/0.88 % (31064)------------------------------ 2.78/0.88 % (31064)------------------------------ 2.78/0.88 % (31133)Instruction limit reached! 2.78/0.88 % (31133)------------------------------ 2.78/0.88 % (31133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.78/0.88 % (31133)Termination reason: Unknown 2.78/0.88 % (31133)Termination phase: shuffling 2.78/0.88 2.78/0.88 % (31133)Memory used [KB]: 2430 2.78/0.88 % (31133)Time elapsed: 0.014 s 2.78/0.88 % (31133)Instructions burned: 48 (million) 2.78/0.88 % (31133)------------------------------ 2.78/0.88 % (31133)------------------------------ 2.78/0.88 % (31134)Instruction limit reached! 2.78/0.88 % (31134)------------------------------ 2.78/0.88 % (31134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.78/0.88 % (31134)Termination reason: Unknown 2.78/0.88 % (31134)Termination phase: shuffling 2.78/0.88 2.78/0.88 % (31134)Memory used [KB]: 2430 2.78/0.88 % (31134)Time elapsed: 0.013 s 2.78/0.88 % (31134)Instructions burned: 44 (million) 2.78/0.88 % (31134)------------------------------ 2.78/0.88 % (31134)------------------------------ 2.78/0.89 % (31045)Instruction limit reached! 2.78/0.89 % (31045)------------------------------ 2.78/0.89 % (31045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 2.78/0.89 % (31045)Termination reason: Unknown 2.78/0.89 % (31045)Termination phase: Saturation 2.78/0.89 2.78/0.89 % (31045)Memory used [KB]: 12025 2.78/0.89 % (31045)Time elapsed: 0.319 s 2.78/0.89 % (31045)Instructions burned: 903 (million) 2.78/0.89 % (31045)------------------------------ 2.78/0.89 % (31045)------------------------------ 3.00/0.89 % (31140)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/432Mi) 3.00/0.89 % (31142)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/62Mi) 3.00/0.89 % (31143)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/31Mi) 3.00/0.90 % (31144)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/96Mi) 3.00/0.90 % (31119)Instruction limit reached! 3.00/0.90 % (31119)------------------------------ 3.00/0.90 % (31119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.00/0.90 % (31119)Termination reason: Unknown 3.00/0.90 % (31119)Termination phase: Saturation 3.00/0.90 3.00/0.90 % (31119)Memory used [KB]: 7547 3.00/0.90 % (31119)Time elapsed: 0.122 s 3.00/0.90 % (31119)Instructions burned: 450 (million) 3.00/0.90 % (31119)------------------------------ 3.00/0.90 % (31119)------------------------------ 3.00/0.90 % (31143)Instruction limit reached! 3.00/0.90 % (31143)------------------------------ 3.00/0.90 % (31143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.00/0.90 % (31143)Termination reason: Unknown 3.00/0.90 % (31143)Termination phase: shuffling 3.00/0.90 3.00/0.90 % (31143)Memory used [KB]: 2174 3.00/0.90 % (31143)Time elapsed: 0.010 s 3.00/0.90 % (31143)Instructions burned: 31 (million) 3.00/0.90 % (31143)------------------------------ 3.00/0.90 % (31143)------------------------------ 3.00/0.91 % (31142)Instruction limit reached! 3.00/0.91 % (31142)------------------------------ 3.00/0.91 % (31142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.00/0.91 % (31142)Termination reason: Unknown 3.00/0.91 % (31142)Termination phase: Property scanning 3.00/0.91 3.00/0.91 % (31142)Memory used [KB]: 2558 3.00/0.91 % (31142)Time elapsed: 0.018 s 3.00/0.91 % (31142)Instructions burned: 63 (million) 3.00/0.91 % (31142)------------------------------ 3.00/0.91 % (31142)------------------------------ 3.00/0.91 % (31148)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/453Mi) 3.00/0.91 % (31150)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/71Mi) 3.00/0.92 % (31152)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/83Mi) 3.00/0.92 % (31144)Instruction limit reached! 3.00/0.92 % (31144)------------------------------ 3.00/0.92 % (31144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.00/0.92 % (31144)Termination reason: Unknown 3.00/0.92 % (31144)Termination phase: Property scanning 3.00/0.92 3.00/0.92 % (31144)Memory used [KB]: 2686 3.00/0.92 % (31144)Time elapsed: 0.027 s 3.00/0.92 % (31144)Instructions burned: 98 (million) 3.00/0.92 % (31144)------------------------------ 3.00/0.92 % (31144)------------------------------ 3.21/0.93 % (31164)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/11Mi) 3.21/0.93 % (31150)Instruction limit reached! 3.21/0.93 % (31150)------------------------------ 3.21/0.93 % (31150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.21/0.93 % (31150)Termination reason: Unknown 3.21/0.93 % (31150)Termination phase: Property scanning 3.21/0.93 3.21/0.93 % (31150)Memory used [KB]: 2558 3.21/0.93 % (31150)Time elapsed: 0.020 s 3.21/0.93 % (31150)Instructions burned: 71 (million) 3.21/0.93 % (31150)------------------------------ 3.21/0.93 % (31150)------------------------------ 3.21/0.93 % (31164)Instruction limit reached! 3.21/0.93 % (31164)------------------------------ 3.21/0.93 % (31164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.21/0.93 % (31164)Termination reason: Unknown 3.21/0.93 % (31164)Termination phase: shuffling 3.21/0.93 3.21/0.93 % (31164)Memory used [KB]: 1791 3.21/0.93 % (31164)Time elapsed: 0.005 s 3.21/0.93 % (31164)Instructions burned: 14 (million) 3.21/0.93 % (31164)------------------------------ 3.21/0.93 % (31164)------------------------------ 3.26/0.94 % (31152)Instruction limit reached! 3.26/0.94 % (31152)------------------------------ 3.26/0.94 % (31152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.26/0.94 % (31152)Termination reason: Unknown 3.26/0.94 % (31152)Termination phase: Property scanning 3.26/0.94 3.26/0.94 % (31152)Memory used [KB]: 2558 3.26/0.94 % (31152)Time elapsed: 0.023 s 3.26/0.94 % (31152)Instructions burned: 84 (million) 3.26/0.94 % (31152)------------------------------ 3.26/0.94 % (31152)------------------------------ 3.26/0.94 % (31173)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/41Mi) 3.26/0.94 % (31176)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/6Mi) 3.26/0.95 % (31176)Instruction limit reached! 3.26/0.95 % (31176)------------------------------ 3.26/0.95 % (31176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.26/0.95 % (31176)Termination reason: Unknown 3.26/0.95 % (31176)Termination phase: shuffling 3.26/0.95 3.26/0.95 % (31176)Memory used [KB]: 1535 3.26/0.95 % (31176)Time elapsed: 0.003 s 3.26/0.95 % (31176)Instructions burned: 6 (million) 3.26/0.95 % (31176)------------------------------ 3.26/0.95 % (31176)------------------------------ 3.26/0.95 % (31179)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/150Mi) 3.26/0.95 % (31173)Instruction limit reached! 3.26/0.95 % (31173)------------------------------ 3.26/0.95 % (31173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.26/0.95 % (31173)Termination reason: Unknown 3.26/0.95 % (31173)Termination phase: shuffling 3.26/0.95 3.26/0.95 % (31173)Memory used [KB]: 2302 3.26/0.95 % (31173)Time elapsed: 0.013 s 3.26/0.95 % (31173)Instructions burned: 43 (million) 3.26/0.95 % (31173)------------------------------ 3.26/0.95 % (31173)------------------------------ 3.26/0.96 % (31186)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on E---3.1_30784 for (2395ds/343Mi) 3.26/0.96 % (31191)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on E---3.1_30784 for (2394ds/109Mi) 3.26/0.98 % (31128)Instruction limit reached! 3.26/0.98 % (31128)------------------------------ 3.26/0.98 % (31128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.26/0.98 % (31128)Termination reason: Unknown 3.26/0.98 % (31128)Termination phase: Saturation 3.26/0.98 3.26/0.98 % (31128)Memory used [KB]: 8187 3.26/0.98 % (31128)Time elapsed: 0.160 s 3.26/0.98 % (31128)Instructions burned: 509 (million) 3.26/0.98 % (31128)------------------------------ 3.26/0.98 % (31128)------------------------------ 3.26/0.99 % (31191)Instruction limit reached! 3.26/0.99 % (31191)------------------------------ 3.26/0.99 % (31191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.26/0.99 % (31191)Termination reason: Unknown 3.26/0.99 % (31191)Termination phase: SInE selection 3.26/0.99 3.26/0.99 % (31191)Memory used [KB]: 2558 3.26/0.99 % (31191)Time elapsed: 0.030 s 3.26/0.99 % (31191)Instructions burned: 110 (million) 3.26/0.99 % (31191)------------------------------ 3.26/0.99 % (31191)------------------------------ 3.26/0.99 % (31179)Instruction limit reached! 3.26/0.99 % (31179)------------------------------ 3.26/0.99 % (31179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.26/0.99 % (31179)Termination reason: Unknown 3.26/0.99 % (31179)Termination phase: Property scanning 3.26/0.99 3.26/0.99 % (31179)Memory used [KB]: 4989 3.26/0.99 % (31179)Time elapsed: 0.046 s 3.26/0.99 % (31179)Instructions burned: 151 (million) 3.26/0.99 % (31179)------------------------------ 3.26/0.99 % (31179)------------------------------ 3.26/0.99 % (31196)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on E---3.1_30784 for (2394ds/253Mi) 3.26/1.00 % (31197)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on E---3.1_30784 for (2394ds/140Mi) 3.59/1.00 % (31198)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on E---3.1_30784 for (2394ds/614Mi) 3.59/1.00 % (31140)Instruction limit reached! 3.59/1.00 % (31140)------------------------------ 3.59/1.00 % (31140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.59/1.00 % (31140)Termination reason: Unknown 3.59/1.00 % (31140)Termination phase: Saturation 3.59/1.00 3.59/1.00 % (31140)Memory used [KB]: 3070 3.59/1.00 % (31140)Time elapsed: 0.116 s 3.59/1.00 % (31140)Instructions burned: 435 (million) 3.59/1.00 % (31140)------------------------------ 3.59/1.00 % (31140)------------------------------ 3.59/1.01 % (31199)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on E---3.1_30784 for (2394ds/202Mi) 3.59/1.02 % (31148)Instruction limit reached! 3.59/1.02 % (31148)------------------------------ 3.59/1.02 % (31148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.59/1.02 % (31148)Termination reason: Unknown 3.59/1.02 % (31148)Termination phase: Saturation 3.59/1.02 3.59/1.02 % (31148)Memory used [KB]: 7547 3.59/1.02 % (31148)Time elapsed: 0.118 s 3.59/1.02 % (31148)Instructions burned: 453 (million) 3.59/1.02 % (31148)------------------------------ 3.59/1.02 % (31148)------------------------------ 3.59/1.03 % (31200)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on E---3.1_30784 for (2394ds/339Mi) 3.59/1.04 % (31197)Instruction limit reached! 3.59/1.04 % (31197)------------------------------ 3.59/1.04 % (31197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.59/1.04 % (31197)Termination reason: Unknown 3.59/1.04 % (31197)Termination phase: Function definition elimination 3.59/1.04 3.59/1.04 % (31197)Memory used [KB]: 2814 3.59/1.04 % (31197)Time elapsed: 0.037 s 3.59/1.04 % (31197)Instructions burned: 140 (million) 3.59/1.04 % (31197)------------------------------ 3.59/1.04 % (31197)------------------------------ 3.59/1.05 % (31186)Instruction limit reached! 3.59/1.05 % (31186)------------------------------ 3.59/1.05 % (31186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.59/1.05 % (31186)Termination reason: Unknown 3.59/1.05 % (31186)Termination phase: Saturation 3.59/1.05 3.59/1.05 % (31186)Memory used [KB]: 8315 3.59/1.05 % (31186)Time elapsed: 0.091 s 3.59/1.05 % (31186)Instructions burned: 344 (million) 3.59/1.05 % (31186)------------------------------ 3.59/1.05 % (31186)------------------------------ 3.59/1.05 % (31201)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on E---3.1_30784 for (2394ds/283Mi) 3.98/1.06 % (31202)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on E---3.1_30784 for (2394ds/134Mi) 3.98/1.07 % (31196)Instruction limit reached! 3.98/1.07 % (31196)------------------------------ 3.98/1.07 % (31196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.98/1.07 % (31196)Termination reason: Unknown 3.98/1.07 % (31196)Termination phase: Saturation 3.98/1.07 3.98/1.07 % (31196)Memory used [KB]: 5628 3.98/1.07 % (31196)Time elapsed: 0.073 s 3.98/1.07 % (31196)Instructions burned: 256 (million) 3.98/1.07 % (31196)------------------------------ 3.98/1.07 % (31196)------------------------------ 3.98/1.07 % (31199)Instruction limit reached! 3.98/1.07 % (31199)------------------------------ 3.98/1.07 % (31199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.98/1.07 % (31199)Termination reason: Unknown 3.98/1.07 % (31199)Termination phase: Property scanning 3.98/1.07 3.98/1.07 % (31199)Memory used [KB]: 5245 3.98/1.07 % (31199)Time elapsed: 0.058 s 3.98/1.07 % (31199)Instructions burned: 204 (million) 3.98/1.07 % (31199)------------------------------ 3.98/1.07 % (31199)------------------------------ 3.98/1.08 % (31203)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on E---3.1_30784 for (2393ds/298Mi) 3.98/1.08 % (31204)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on E---3.1_30784 for (2393ds/192Mi) 3.98/1.12 % (31201)Instruction limit reached! 3.98/1.12 % (31201)------------------------------ 3.98/1.12 % (31201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.98/1.12 % (31201)Termination reason: Unknown 3.98/1.12 % (31201)Termination phase: Saturation 3.98/1.12 3.98/1.12 % (31201)Memory used [KB]: 7547 3.98/1.12 % (31201)Time elapsed: 0.072 s 3.98/1.12 % (31201)Instructions burned: 283 (million) 3.98/1.12 % (31201)------------------------------ 3.98/1.12 % (31201)------------------------------ 3.98/1.13 % (31200)Instruction limit reached! 3.98/1.13 % (31200)------------------------------ 3.98/1.13 % (31200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.98/1.13 % (31200)Termination reason: Unknown 3.98/1.13 % (31200)Termination phase: Saturation 3.98/1.13 3.98/1.13 % (31200)Memory used [KB]: 7931 3.98/1.13 % (31200)Time elapsed: 0.093 s 3.98/1.13 % (31200)Instructions burned: 339 (million) 3.98/1.13 % (31200)------------------------------ 3.98/1.13 % (31200)------------------------------ 3.98/1.13 % (31205)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on E---3.1_30784 for (2393ds/258Mi) 3.98/1.13 % (31202)Instruction limit reached! 3.98/1.13 % (31202)------------------------------ 3.98/1.13 % (31202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.98/1.13 % (31202)Termination reason: Unknown 3.98/1.13 % (31202)Termination phase: Function definition elimination 3.98/1.13 3.98/1.13 % (31202)Memory used [KB]: 2814 3.98/1.13 % (31202)Time elapsed: 0.068 s 3.98/1.13 % (31202)Instructions burned: 135 (million) 3.98/1.13 % (31202)------------------------------ 3.98/1.13 % (31202)------------------------------ 3.98/1.13 % (31204)Instruction limit reached! 3.98/1.13 % (31204)------------------------------ 3.98/1.13 % (31204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.98/1.13 % (31204)Termination reason: Unknown 3.98/1.13 % (31204)Termination phase: Saturation 3.98/1.13 3.98/1.13 % (31204)Memory used [KB]: 7547 3.98/1.13 % (31204)Time elapsed: 0.051 s 3.98/1.13 % (31204)Instructions burned: 194 (million) 3.98/1.13 % (31204)------------------------------ 3.98/1.13 % (31204)------------------------------ 3.98/1.14 % (31206)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on E---3.1_30784 for (2393ds/90Mi) 3.98/1.14 % (31208)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on E---3.1_30784 for (2393ds/458Mi) 3.98/1.15 % (31207)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on E---3.1_30784 for (2393ds/231Mi) 3.98/1.15 % (31203)Instruction limit reached! 3.98/1.15 % (31203)------------------------------ 3.98/1.15 % (31203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.98/1.15 % (31203)Termination reason: Unknown 3.98/1.15 % (31203)Termination phase: Saturation 3.98/1.15 3.98/1.15 % (31203)Memory used [KB]: 7547 3.98/1.15 % (31203)Time elapsed: 0.077 s 3.98/1.15 % (31203)Instructions burned: 299 (million) 3.98/1.15 % (31203)------------------------------ 3.98/1.15 % (31203)------------------------------ 3.98/1.16 % (31206)Instruction limit reached! 3.98/1.16 % (31206)------------------------------ 3.98/1.16 % (31206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 3.98/1.16 % (31206)Termination reason: Unknown 3.98/1.16 % (31206)Termination phase: Property scanning 3.98/1.16 3.98/1.16 % (31206)Memory used [KB]: 2686 3.98/1.16 % (31206)Time elapsed: 0.026 s 3.98/1.16 % (31206)Instructions burned: 92 (million) 3.98/1.16 % (31206)------------------------------ 3.98/1.16 % (31206)------------------------------ 3.98/1.16 % (31209)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_30784 for (2393ds/31Mi) 5.14/1.17 % (31210)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on E---3.1_30784 for (2392ds/297Mi) 5.14/1.17 % (31209)Instruction limit reached! 5.14/1.17 % (31209)------------------------------ 5.14/1.17 % (31209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.14/1.17 % (31209)Termination reason: Unknown 5.14/1.17 % (31209)Termination phase: shuffling 5.14/1.17 5.14/1.17 % (31209)Memory used [KB]: 2046 5.14/1.17 % (31209)Time elapsed: 0.011 s 5.14/1.17 % (31209)Instructions burned: 32 (million) 5.14/1.17 % (31209)------------------------------ 5.14/1.17 % (31209)------------------------------ 5.14/1.18 % (31198)Instruction limit reached! 5.14/1.18 % (31198)------------------------------ 5.14/1.18 % (31198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.14/1.18 % (31198)Termination reason: Unknown 5.14/1.18 % (31198)Termination phase: Saturation 5.14/1.18 5.14/1.18 % (31198)Memory used [KB]: 10106 5.14/1.18 % (31198)Time elapsed: 0.178 s 5.14/1.18 % (31198)Instructions burned: 614 (million) 5.14/1.18 % (31198)------------------------------ 5.14/1.18 % (31198)------------------------------ 5.14/1.18 % (31211)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on E---3.1_30784 for (2392ds/987Mi) 5.14/1.19 % (31212)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on E---3.1_30784 for (2392ds/182Mi) 5.29/1.21 % (31205)Instruction limit reached! 5.29/1.21 % (31205)------------------------------ 5.29/1.21 % (31205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.29/1.21 % (31205)Termination reason: Unknown 5.29/1.21 % (31205)Termination phase: Saturation 5.29/1.21 5.29/1.21 % (31205)Memory used [KB]: 7931 5.29/1.21 % (31205)Time elapsed: 0.070 s 5.29/1.21 % (31205)Instructions burned: 259 (million) 5.29/1.21 % (31205)------------------------------ 5.29/1.21 % (31205)------------------------------ 5.29/1.21 % (31207)Instruction limit reached! 5.29/1.21 % (31207)------------------------------ 5.29/1.21 % (31207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.29/1.21 % (31207)Termination reason: Unknown 5.29/1.21 % (31207)Termination phase: Saturation 5.29/1.21 5.29/1.21 % (31207)Memory used [KB]: 8443 5.29/1.21 % (31207)Time elapsed: 0.067 s 5.29/1.21 % (31207)Instructions burned: 233 (million) 5.29/1.21 % (31207)------------------------------ 5.29/1.21 % (31207)------------------------------ 5.29/1.22 % (31213)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on E---3.1_30784 for (2392ds/182Mi) 5.29/1.22 % (31214)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on E---3.1_30784 for (2392ds/154Mi) 5.29/1.24 % (31212)Instruction limit reached! 5.29/1.24 % (31212)------------------------------ 5.29/1.24 % (31212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.29/1.24 % (31212)Termination reason: Unknown 5.29/1.24 % (31212)Termination phase: Saturation 5.29/1.24 5.29/1.24 % (31212)Memory used [KB]: 7419 5.29/1.24 % (31212)Time elapsed: 0.048 s 5.29/1.24 % (31212)Instructions burned: 183 (million) 5.29/1.24 % (31212)------------------------------ 5.29/1.24 % (31212)------------------------------ 5.47/1.24 % (31210)Instruction limit reached! 5.47/1.24 % (31210)------------------------------ 5.47/1.24 % (31210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.24 % (31210)Termination reason: Unknown 5.47/1.24 % (31210)Termination phase: Saturation 5.47/1.24 5.47/1.24 % (31210)Memory used [KB]: 7547 5.47/1.24 % (31210)Time elapsed: 0.076 s 5.47/1.24 % (31210)Instructions burned: 301 (million) 5.47/1.24 % (31210)------------------------------ 5.47/1.24 % (31210)------------------------------ 5.47/1.25 % (31215)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on E---3.1_30784 for (2392ds/79Mi) 5.47/1.25 % (31216)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/216Mi) 5.47/1.26 % (31214)Instruction limit reached! 5.47/1.26 % (31214)------------------------------ 5.47/1.26 % (31214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.26 % (31214)Termination reason: Unknown 5.47/1.26 % (31214)Termination phase: Property scanning 5.47/1.26 5.47/1.26 % (31214)Memory used [KB]: 2686 5.47/1.26 % (31214)Time elapsed: 0.040 s 5.47/1.26 % (31214)Instructions burned: 157 (million) 5.47/1.26 % (31214)------------------------------ 5.47/1.26 % (31214)------------------------------ 5.47/1.26 % (31132)Instruction limit reached! 5.47/1.26 % (31132)------------------------------ 5.47/1.26 % (31132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.26 % (31132)Termination reason: Unknown 5.47/1.26 % (31132)Termination phase: Saturation 5.47/1.26 5.47/1.26 % (31132)Memory used [KB]: 12665 5.47/1.26 % (31132)Time elapsed: 0.400 s 5.47/1.26 % (31132)Instructions burned: 1088 (million) 5.47/1.26 % (31132)------------------------------ 5.47/1.26 % (31132)------------------------------ 5.47/1.27 % (31208)Instruction limit reached! 5.47/1.27 % (31208)------------------------------ 5.47/1.27 % (31208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.27 % (31208)Termination reason: Unknown 5.47/1.27 % (31208)Termination phase: Saturation 5.47/1.27 5.47/1.27 % (31208)Memory used [KB]: 9722 5.47/1.27 % (31208)Time elapsed: 0.127 s 5.47/1.27 % (31208)Instructions burned: 459 (million) 5.47/1.27 % (31208)------------------------------ 5.47/1.27 % (31208)------------------------------ 5.47/1.27 % (31215)Instruction limit reached! 5.47/1.27 % (31215)------------------------------ 5.47/1.27 % (31215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.27 % (31215)Termination reason: Unknown 5.47/1.27 % (31215)Termination phase: Property scanning 5.47/1.27 5.47/1.27 % (31215)Memory used [KB]: 2558 5.47/1.27 % (31215)Time elapsed: 0.023 s 5.47/1.27 % (31215)Instructions burned: 81 (million) 5.47/1.27 % (31215)------------------------------ 5.47/1.27 % (31215)------------------------------ 5.47/1.27 % (31217)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/114Mi) 5.47/1.27 % (31213)Instruction limit reached! 5.47/1.27 % (31213)------------------------------ 5.47/1.27 % (31213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.27 % (31213)Termination reason: Unknown 5.47/1.27 % (31213)Termination phase: Property scanning 5.47/1.27 5.47/1.27 % (31213)Memory used [KB]: 5117 5.47/1.27 % (31213)Time elapsed: 0.054 s 5.47/1.27 % (31213)Instructions burned: 184 (million) 5.47/1.27 % (31213)------------------------------ 5.47/1.27 % (31213)------------------------------ 5.47/1.28 % (31219)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/182Mi) 5.47/1.28 % (31220)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/164Mi) 5.47/1.28 % (31221)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/50Mi) 5.47/1.28 % (31218)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/922Mi) 5.47/1.29 % (31221)Instruction limit reached! 5.47/1.29 % (31221)------------------------------ 5.47/1.29 % (31221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.29 % (31221)Termination reason: Unknown 5.47/1.29 % (31221)Termination phase: shuffling 5.47/1.29 5.47/1.29 % (31221)Memory used [KB]: 2430 5.47/1.29 % (31221)Time elapsed: 0.015 s 5.47/1.29 % (31221)Instructions burned: 51 (million) 5.47/1.29 % (31221)------------------------------ 5.47/1.29 % (31221)------------------------------ 5.47/1.30 % (31217)Instruction limit reached! 5.47/1.30 % (31217)------------------------------ 5.47/1.30 % (31217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.30 % (31217)Termination reason: Unknown 5.47/1.30 % (31217)Termination phase: Property scanning 5.47/1.30 5.47/1.30 % (31217)Memory used [KB]: 2686 5.47/1.30 % (31217)Time elapsed: 0.031 s 5.47/1.30 % (31217)Instructions burned: 115 (million) 5.47/1.30 % (31217)------------------------------ 5.47/1.30 % (31217)------------------------------ 5.47/1.30 % (31222)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/368Mi) 5.47/1.31 % (31216)Instruction limit reached! 5.47/1.31 % (31216)------------------------------ 5.47/1.31 % (31216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.31 % (31216)Termination reason: Unknown 5.47/1.31 % (31216)Termination phase: Property scanning 5.47/1.31 5.47/1.31 % (31216)Memory used [KB]: 2814 5.47/1.31 % (31216)Time elapsed: 0.054 s 5.47/1.31 % (31216)Instructions burned: 217 (million) 5.47/1.31 % (31216)------------------------------ 5.47/1.31 % (31216)------------------------------ 5.47/1.31 % (31223)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/1021Mi) 5.47/1.32 % (31224)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/267Mi) 5.47/1.32 % (31220)Instruction limit reached! 5.47/1.32 % (31220)------------------------------ 5.47/1.32 % (31220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.32 % (31220)Termination reason: Unknown 5.47/1.32 % (31220)Termination phase: Function definition elimination 5.47/1.32 5.47/1.32 % (31220)Memory used [KB]: 2814 5.47/1.32 % (31220)Time elapsed: 0.042 s 5.47/1.32 % (31220)Instructions burned: 165 (million) 5.47/1.32 % (31220)------------------------------ 5.47/1.32 % (31220)------------------------------ 5.47/1.32 % (31219)Instruction limit reached! 5.47/1.32 % (31219)------------------------------ 5.47/1.32 % (31219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 5.47/1.32 % (31219)Termination reason: Unknown 5.47/1.32 % (31219)Termination phase: Saturation 5.47/1.32 5.47/1.32 % (31219)Memory used [KB]: 7547 5.47/1.32 % (31219)Time elapsed: 0.047 s 5.47/1.32 % (31219)Instructions burned: 183 (million) 5.47/1.32 % (31219)------------------------------ 5.47/1.32 % (31219)------------------------------ 5.47/1.33 % (31225)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/204Mi) 5.47/1.33 % (31226)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/26Mi) 6.01/1.34 % (31226)Instruction limit reached! 6.01/1.34 % (31226)------------------------------ 6.01/1.34 % (31226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.01/1.34 % (31226)Termination reason: Unknown 6.01/1.34 % (31226)Termination phase: shuffling 6.01/1.34 6.01/1.34 % (31226)Memory used [KB]: 2046 6.01/1.34 % (31226)Time elapsed: 0.009 s 6.01/1.34 % (31226)Instructions burned: 29 (million) 6.01/1.34 % (31226)------------------------------ 6.01/1.34 % (31226)------------------------------ 6.01/1.35 % (31227)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on E---3.1_30784 for (2391ds/53Mi) 6.01/1.36 % (31227)Instruction limit reached! 6.01/1.36 % (31227)------------------------------ 6.01/1.36 % (31227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.01/1.36 % (31227)Termination reason: Unknown 6.01/1.36 % (31227)Termination phase: shuffling 6.01/1.36 6.01/1.36 % (31227)Memory used [KB]: 2558 6.01/1.36 % (31227)Time elapsed: 0.016 s 6.01/1.36 % (31227)Instructions burned: 54 (million) 6.01/1.36 % (31227)------------------------------ 6.01/1.36 % (31227)------------------------------ 6.01/1.37 % (31228)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on E---3.1_30784 for (2390ds/4436Mi) 6.01/1.38 % (31225)Instruction limit reached! 6.01/1.38 % (31225)------------------------------ 6.01/1.38 % (31225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.01/1.38 % (31225)Termination reason: Unknown 6.01/1.38 % (31225)Termination phase: Property scanning 6.01/1.38 6.01/1.38 % (31225)Memory used [KB]: 2814 6.01/1.38 % (31225)Time elapsed: 0.052 s 6.01/1.38 % (31225)Instructions burned: 206 (million) 6.01/1.38 % (31225)------------------------------ 6.01/1.38 % (31225)------------------------------ 6.01/1.38 % (31224)Instruction limit reached! 6.01/1.38 % (31224)------------------------------ 6.01/1.38 % (31224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.01/1.38 % (31224)Termination reason: Unknown 6.01/1.38 % (31224)Termination phase: Saturation 6.01/1.38 6.01/1.38 % (31224)Memory used [KB]: 7547 6.01/1.38 % (31224)Time elapsed: 0.068 s 6.01/1.38 % (31224)Instructions burned: 267 (million) 6.01/1.38 % (31224)------------------------------ 6.01/1.38 % (31224)------------------------------ 6.01/1.39 % (31229)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on E---3.1_30784 for (2390ds/1539Mi) 6.18/1.39 % (31230)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on E---3.1_30784 for (2390ds/408Mi) 6.18/1.40 % (31222)Instruction limit reached! 6.18/1.40 % (31222)------------------------------ 6.18/1.40 % (31222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.18/1.40 % (31222)Termination reason: Unknown 6.18/1.40 % (31222)Termination phase: Saturation 6.18/1.40 6.18/1.40 % (31222)Memory used [KB]: 9338 6.18/1.40 % (31222)Time elapsed: 0.100 s 6.18/1.40 % (31222)Instructions burned: 370 (million) 6.18/1.40 % (31222)------------------------------ 6.18/1.40 % (31222)------------------------------ 6.18/1.41 % (31231)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on E---3.1_30784 for (2390ds/5205Mi) 6.18/1.43 % (31211)Instruction limit reached! 6.18/1.43 % (31211)------------------------------ 6.18/1.43 % (31211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.18/1.43 % (31211)Termination reason: Unknown 6.18/1.43 % (31211)Termination phase: Saturation 6.18/1.43 6.18/1.43 % (31211)Memory used [KB]: 16502 6.18/1.43 % (31211)Time elapsed: 0.250 s 6.18/1.43 % (31211)Instructions burned: 989 (million) 6.18/1.43 % (31211)------------------------------ 6.18/1.43 % (31211)------------------------------ 6.18/1.44 % (31232)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on E---3.1_30784 for (2390ds/1913Mi) 6.55/1.51 % (31230)Instruction limit reached! 6.55/1.51 % (31230)------------------------------ 6.55/1.51 % (31230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.55/1.51 % (31230)Termination reason: Unknown 6.55/1.51 % (31230)Termination phase: Saturation 6.55/1.51 6.55/1.51 % (31230)Memory used [KB]: 11257 6.55/1.51 % (31230)Time elapsed: 0.122 s 6.55/1.51 % (31230)Instructions burned: 408 (million) 6.55/1.51 % (31230)------------------------------ 6.55/1.51 % (31230)------------------------------ 6.55/1.53 % (31233)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on E---3.1_30784 for (2389ds/4350Mi) 6.68/1.58 % (31218)Instruction limit reached! 6.68/1.58 % (31218)------------------------------ 6.68/1.58 % (31218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.68/1.58 % (31218)Termination reason: Unknown 6.68/1.58 % (31218)Termination phase: Saturation 6.68/1.58 6.68/1.58 % (31218)Memory used [KB]: 12281 6.68/1.58 % (31218)Time elapsed: 0.297 s 6.68/1.58 % (31218)Instructions burned: 924 (million) 6.68/1.58 % (31218)------------------------------ 6.68/1.58 % (31218)------------------------------ 6.68/1.59 % (31234)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on E---3.1_30784 for (2388ds/68Mi) 6.68/1.61 % (31234)Instruction limit reached! 6.68/1.61 % (31234)------------------------------ 6.68/1.61 % (31234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.68/1.61 % (31234)Termination reason: Unknown 6.68/1.61 % (31234)Termination phase: Property scanning 6.68/1.61 6.68/1.61 % (31234)Memory used [KB]: 2558 6.68/1.61 % (31234)Time elapsed: 0.020 s 6.68/1.61 % (31234)Instructions burned: 68 (million) 6.68/1.61 % (31234)------------------------------ 6.68/1.61 % (31234)------------------------------ 6.68/1.62 % (31235)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on E---3.1_30784 for (2388ds/358Mi) 6.68/1.62 % (31223)Instruction limit reached! 6.68/1.62 % (31223)------------------------------ 6.68/1.62 % (31223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 6.68/1.62 % (31223)Termination reason: Unknown 6.68/1.62 % (31223)Termination phase: Saturation 6.68/1.62 6.68/1.62 % (31223)Memory used [KB]: 12792 6.68/1.62 % (31223)Time elapsed: 0.316 s 6.68/1.62 % (31223)Instructions burned: 1022 (million) 6.68/1.62 % (31223)------------------------------ 6.68/1.62 % (31223)------------------------------ 6.68/1.64 % (31236)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on E---3.1_30784 for (2388ds/31Mi) 7.36/1.64 % (31236)Instruction limit reached! 7.36/1.64 % (31236)------------------------------ 7.36/1.64 % (31236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 7.36/1.64 % (31236)Termination reason: Unknown 7.36/1.64 % (31236)Termination phase: shuffling 7.36/1.64 7.36/1.64 % (31236)Memory used [KB]: 2174 7.36/1.64 % (31236)Time elapsed: 0.010 s 7.36/1.64 % (31236)Instructions burned: 32 (million) 7.36/1.64 % (31236)------------------------------ 7.36/1.64 % (31236)------------------------------ 7.36/1.65 % (31237)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on E---3.1_30784 for (2388ds/279Mi) 7.38/1.71 % (31235)Instruction limit reached! 7.38/1.71 % (31235)------------------------------ 7.38/1.71 % (31235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 7.38/1.71 % (31235)Termination reason: Unknown 7.38/1.71 % (31235)Termination phase: Saturation 7.38/1.71 7.38/1.71 % (31235)Memory used [KB]: 8315 7.38/1.71 % (31235)Time elapsed: 0.094 s 7.38/1.71 % (31235)Instructions burned: 358 (million) 7.38/1.71 % (31235)------------------------------ 7.38/1.71 % (31235)------------------------------ 7.38/1.72 % (31238)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on E---3.1_30784 for (2387ds/258Mi) 7.38/1.72 % (31237)Instruction limit reached! 7.38/1.72 % (31237)------------------------------ 7.38/1.72 % (31237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 7.38/1.72 % (31237)Termination reason: Unknown 7.38/1.72 % (31237)Termination phase: Saturation 7.38/1.72 7.38/1.72 % (31237)Memory used [KB]: 7547 7.38/1.72 % (31237)Time elapsed: 0.069 s 7.38/1.72 % (31237)Instructions burned: 279 (million) 7.38/1.72 % (31237)------------------------------ 7.38/1.72 % (31237)------------------------------ 7.38/1.73 % (31239)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on E---3.1_30784 for (2387ds/26Mi) 7.38/1.74 % (31239)Instruction limit reached! 7.38/1.74 % (31239)------------------------------ 7.38/1.74 % (31239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 7.38/1.74 % (31239)Termination reason: Unknown 7.38/1.74 % (31239)Termination phase: shuffling 7.38/1.74 7.38/1.74 % (31239)Memory used [KB]: 1918 7.38/1.74 % (31239)Time elapsed: 0.009 s 7.38/1.74 % (31239)Instructions burned: 28 (million) 7.38/1.74 % (31239)------------------------------ 7.38/1.74 % (31239)------------------------------ 7.38/1.75 % (31240)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on E---3.1_30784 for (2387ds/995Mi) 9.33/1.79 % (31238)Instruction limit reached! 9.33/1.79 % (31238)------------------------------ 9.33/1.79 % (31238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 9.33/1.79 % (31238)Termination reason: Unknown 9.33/1.79 % (31238)Termination phase: Saturation 9.33/1.79 9.33/1.79 % (31238)Memory used [KB]: 8059 9.33/1.79 % (31238)Time elapsed: 0.070 s 9.33/1.79 % (31238)Instructions burned: 258 (million) 9.33/1.79 % (31238)------------------------------ 9.33/1.79 % (31238)------------------------------ 9.33/1.80 % (31241)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on E---3.1_30784 for (2386ds/373Mi) 9.80/1.87 % (31229)Instruction limit reached! 9.80/1.87 % (31229)------------------------------ 9.80/1.87 % (31229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 9.80/1.87 % (31229)Termination reason: Unknown 9.80/1.87 % (31229)Termination phase: Saturation 9.80/1.87 9.80/1.87 % (31229)Memory used [KB]: 10874 9.80/1.87 % (31229)Time elapsed: 0.477 s 9.80/1.87 % (31229)Instructions burned: 1541 (million) 9.80/1.87 % (31229)------------------------------ 9.80/1.87 % (31229)------------------------------ 9.80/1.88 % (31242)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on E---3.1_30784 for (2385ds/253Mi) 9.80/1.90 % (31241)Instruction limit reached! 9.80/1.90 % (31241)------------------------------ 9.80/1.90 % (31241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 9.80/1.90 % (31241)Termination reason: Unknown 9.80/1.90 % (31241)Termination phase: Saturation 9.80/1.90 9.80/1.90 % (31241)Memory used [KB]: 9466 9.80/1.90 % (31241)Time elapsed: 0.103 s 9.80/1.90 % (31241)Instructions burned: 373 (million) 9.80/1.90 % (31241)------------------------------ 9.80/1.90 % (31241)------------------------------ 9.80/1.91 % (31243)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on E---3.1_30784 for (2385ds/832Mi) 10.38/1.94 % (31242)Instruction limit reached! 10.38/1.94 % (31242)------------------------------ 10.38/1.94 % (31242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 10.38/1.94 % (31242)Termination reason: Unknown 10.38/1.94 % (31242)Termination phase: Saturation 10.38/1.94 10.38/1.94 % (31242)Memory used [KB]: 7547 10.38/1.94 % (31242)Time elapsed: 0.066 s 10.38/1.94 % (31242)Instructions burned: 254 (million) 10.38/1.94 % (31242)------------------------------ 10.38/1.94 % (31242)------------------------------ 10.38/1.95 % (31244)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on E---3.1_30784 for (2385ds/668Mi) 10.74/2.00 % (31240)Instruction limit reached! 10.74/2.00 % (31240)------------------------------ 10.74/2.00 % (31240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 10.74/2.00 % (31240)Termination reason: Unknown 10.74/2.00 % (31240)Termination phase: Saturation 10.74/2.00 10.74/2.00 % (31240)Memory used [KB]: 16375 10.74/2.00 % (31240)Time elapsed: 0.254 s 10.74/2.00 % (31240)Instructions burned: 995 (million) 10.74/2.00 % (31240)------------------------------ 10.74/2.00 % (31240)------------------------------ 10.74/2.01 % (31245)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on E---3.1_30784 for (2384ds/40Mi) 10.74/2.02 % (31245)Instruction limit reached! 10.74/2.02 % (31245)------------------------------ 10.74/2.02 % (31245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 10.74/2.02 % (31245)Termination reason: Unknown 10.74/2.02 % (31245)Termination phase: shuffling 10.74/2.02 10.74/2.02 % (31245)Memory used [KB]: 2302 10.74/2.02 % (31245)Time elapsed: 0.013 s 10.74/2.02 % (31245)Instructions burned: 43 (million) 10.74/2.02 % (31245)------------------------------ 10.74/2.02 % (31245)------------------------------ 10.74/2.03 % (31232)Instruction limit reached! 10.74/2.03 % (31232)------------------------------ 10.74/2.03 % (31232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 10.74/2.03 % (31232)Termination reason: Unknown 10.74/2.03 % (31232)Termination phase: Saturation 10.74/2.03 10.74/2.03 % (31232)Memory used [KB]: 6268 10.74/2.03 % (31232)Time elapsed: 0.587 s 10.74/2.03 % (31232)Instructions burned: 1915 (million) 10.74/2.03 % (31232)------------------------------ 10.74/2.03 % (31232)------------------------------ 10.74/2.03 % (31246)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on E---3.1_30784 for (2384ds/294Mi) 10.74/2.04 % (31247)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on E---3.1_30784 for (2384ds/187Mi) 11.09/2.08 % (31247)Instruction limit reached! 11.09/2.08 % (31247)------------------------------ 11.09/2.08 % (31247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 11.09/2.08 % (31247)Termination reason: Unknown 11.09/2.08 % (31247)Termination phase: Saturation 11.09/2.08 11.09/2.08 % (31247)Memory used [KB]: 7419 11.09/2.08 % (31247)Time elapsed: 0.049 s 11.09/2.08 % (31247)Instructions burned: 189 (million) 11.09/2.08 % (31247)------------------------------ 11.09/2.08 % (31247)------------------------------ 11.09/2.09 % (31248)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on E---3.1_30784 for (2383ds/371Mi) 11.09/2.11 % (31246)Instruction limit reached! 11.09/2.11 % (31246)------------------------------ 11.09/2.11 % (31246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 11.09/2.11 % (31246)Termination reason: Unknown 11.09/2.11 % (31246)Termination phase: Saturation 11.09/2.11 11.09/2.11 % (31246)Memory used [KB]: 7547 11.09/2.11 % (31246)Time elapsed: 0.074 s 11.09/2.11 % (31246)Instructions burned: 294 (million) 11.09/2.11 % (31246)------------------------------ 11.09/2.11 % (31246)------------------------------ 11.36/2.12 % (31249)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on E---3.1_30784 for (2383ds/1827Mi) 11.36/2.12 % (31244)Instruction limit reached! 11.36/2.12 % (31244)------------------------------ 11.36/2.12 % (31244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 11.36/2.12 % (31244)Termination reason: Unknown 11.36/2.12 % (31244)Termination phase: Saturation 11.36/2.12 11.36/2.12 % (31244)Memory used [KB]: 14456 11.36/2.12 % (31244)Time elapsed: 0.169 s 11.36/2.12 % (31244)Instructions burned: 671 (million) 11.36/2.12 % (31244)------------------------------ 11.36/2.12 % (31244)------------------------------ 11.36/2.13 % (31250)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on E---3.1_30784 for (2383ds/70Mi) 11.65/2.15 % (31250)Instruction limit reached! 11.65/2.15 % (31250)------------------------------ 11.65/2.15 % (31250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 11.65/2.15 % (31250)Termination reason: Unknown 11.65/2.15 % (31250)Termination phase: Property scanning 11.65/2.15 11.65/2.15 % (31250)Memory used [KB]: 2558 11.65/2.15 % (31250)Time elapsed: 0.020 s 11.65/2.15 % (31250)Instructions burned: 73 (million) 11.65/2.15 % (31250)------------------------------ 11.65/2.15 % (31250)------------------------------ 11.65/2.16 % (31251)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on E---3.1_30784 for (2382ds/316Mi) 11.65/2.16 % (31243)Instruction limit reached! 11.65/2.16 % (31243)------------------------------ 11.65/2.16 % (31243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 11.65/2.16 % (31243)Termination reason: Unknown 11.65/2.16 % (31243)Termination phase: Saturation 11.65/2.16 11.65/2.16 % (31243)Memory used [KB]: 11641 11.65/2.16 % (31243)Time elapsed: 0.276 s 11.65/2.16 % (31243)Instructions burned: 835 (million) 11.65/2.16 % (31243)------------------------------ 11.65/2.16 % (31243)------------------------------ 11.65/2.18 % (31252)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on E---3.1_30784 for (2382ds/932Mi) 11.65/2.19 % (31248)Instruction limit reached! 11.65/2.19 % (31248)------------------------------ 11.65/2.19 % (31248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 11.65/2.19 % (31248)Termination reason: Unknown 11.65/2.19 % (31248)Termination phase: Saturation 11.65/2.19 11.65/2.19 % (31248)Memory used [KB]: 9210 11.65/2.19 % (31248)Time elapsed: 0.100 s 11.65/2.19 % (31248)Instructions burned: 373 (million) 11.65/2.19 % (31248)------------------------------ 11.65/2.19 % (31248)------------------------------ 11.65/2.20 % (31253)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on E---3.1_30784 for (2382ds/4714Mi) 12.31/2.24 % (31251)Instruction limit reached! 12.31/2.24 % (31251)------------------------------ 12.31/2.24 % (31251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 12.31/2.24 % (31251)Termination reason: Unknown 12.31/2.24 % (31251)Termination phase: Saturation 12.31/2.24 12.31/2.24 % (31251)Memory used [KB]: 7547 12.31/2.24 % (31251)Time elapsed: 0.083 s 12.31/2.24 % (31251)Instructions burned: 320 (million) 12.31/2.24 % (31251)------------------------------ 12.31/2.24 % (31251)------------------------------ 12.31/2.25 % (31254)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on E---3.1_30784 for (2382ds/8250Mi) 13.84/2.41 % (31252)Instruction limit reached! 13.84/2.41 % (31252)------------------------------ 13.84/2.41 % (31252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 13.84/2.41 % (31252)Termination reason: Unknown 13.84/2.41 % (31252)Termination phase: Saturation 13.84/2.41 13.84/2.41 % (31252)Memory used [KB]: 16375 13.84/2.41 % (31252)Time elapsed: 0.237 s 13.84/2.41 % (31252)Instructions burned: 932 (million) 13.84/2.41 % (31252)------------------------------ 13.84/2.41 % (31252)------------------------------ 13.84/2.42 % (31255)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on E---3.1_30784 for (2380ds/770Mi) 14.88/2.63 % (31255)Instruction limit reached! 14.88/2.63 % (31255)------------------------------ 14.88/2.63 % (31255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 14.88/2.63 % (31255)Termination reason: Unknown 14.88/2.63 % (31255)Termination phase: Saturation 14.88/2.63 14.88/2.63 % (31255)Memory used [KB]: 7675 14.88/2.63 % (31255)Time elapsed: 0.208 s 14.88/2.63 % (31255)Instructions burned: 771 (million) 14.88/2.63 % (31255)------------------------------ 14.88/2.63 % (31255)------------------------------ 14.88/2.63 % (31249)Instruction limit reached! 14.88/2.63 % (31249)------------------------------ 14.88/2.63 % (31249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 14.88/2.63 % (31249)Termination reason: Unknown 14.88/2.63 % (31249)Termination phase: Saturation 14.88/2.63 14.88/2.63 % (31249)Memory used [KB]: 20980 14.88/2.63 % (31249)Time elapsed: 0.515 s 14.88/2.63 % (31249)Instructions burned: 1828 (million) 14.88/2.63 % (31249)------------------------------ 14.88/2.63 % (31249)------------------------------ 14.88/2.64 % (31256)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on E---3.1_30784 for (2378ds/794Mi) 14.88/2.64 % (31257)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on E---3.1_30784 for (2378ds/464Mi) 15.86/2.75 % (31231)Instruction limit reached! 15.86/2.75 % (31231)------------------------------ 15.86/2.75 % (31231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 15.86/2.75 % (31231)Termination reason: Unknown 15.86/2.75 % (31231)Termination phase: Saturation 15.86/2.75 15.86/2.75 % (31231)Memory used [KB]: 17270 15.86/2.75 % (31231)Time elapsed: 1.337 s 15.86/2.75 % (31231)Instructions burned: 5208 (million) 15.86/2.75 % (31231)------------------------------ 15.86/2.75 % (31231)------------------------------ 15.86/2.76 % (31228)Instruction limit reached! 15.86/2.76 % (31228)------------------------------ 15.86/2.76 % (31228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 15.86/2.76 % (31228)Termination reason: Unknown 15.86/2.76 % (31228)Termination phase: Saturation 15.86/2.76 15.86/2.76 % (31228)Memory used [KB]: 15351 15.86/2.76 % (31228)Time elapsed: 1.386 s 15.86/2.76 % (31228)Instructions burned: 4436 (million) 15.86/2.76 % (31228)------------------------------ 15.86/2.76 % (31228)------------------------------ 15.86/2.76 % (31258)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on E---3.1_30784 for (2377ds/1376Mi) 15.86/2.77 % (31257)Instruction limit reached! 15.86/2.77 % (31257)------------------------------ 15.86/2.77 % (31257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 15.86/2.77 % (31257)Termination reason: Unknown 15.86/2.77 % (31257)Termination phase: Saturation 15.86/2.77 15.86/2.77 % (31257)Memory used [KB]: 9594 15.86/2.77 % (31257)Time elapsed: 0.126 s 15.86/2.77 % (31257)Instructions burned: 465 (million) 15.86/2.77 % (31257)------------------------------ 15.86/2.77 % (31257)------------------------------ 15.86/2.77 % (31259)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on E---3.1_30784 for (2376ds/906Mi) 15.86/2.78 % (31260)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on E---3.1_30784 for (2376ds/434Mi) 16.79/2.87 % (31233)Instruction limit reached! 16.79/2.87 % (31233)------------------------------ 16.79/2.87 % (31233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 16.79/2.87 % (31233)Termination reason: Unknown 16.79/2.87 % (31233)Termination phase: Saturation 16.79/2.87 16.79/2.87 % (31233)Memory used [KB]: 13816 16.79/2.87 % (31233)Time elapsed: 1.343 s 16.79/2.87 % (31233)Instructions burned: 4350 (million) 16.79/2.87 % (31233)------------------------------ 16.79/2.87 % (31233)------------------------------ 16.79/2.87 % (31256)Instruction limit reached! 16.79/2.87 % (31256)------------------------------ 16.79/2.87 % (31256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 16.79/2.87 % (31256)Termination reason: Unknown 16.79/2.87 % (31256)Termination phase: Saturation 16.79/2.87 16.79/2.87 % (31256)Memory used [KB]: 6140 16.79/2.87 % (31256)Time elapsed: 0.235 s 16.79/2.87 % (31256)Instructions burned: 795 (million) 16.79/2.87 % (31256)------------------------------ 16.79/2.87 % (31256)------------------------------ 16.79/2.88 % (31261)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on E---3.1_30784 for (2375ds/865Mi) 16.79/2.88 % (31262)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on E---3.1_30784 for (2375ds/593Mi) 17.25/2.90 % (31260)Instruction limit reached! 17.25/2.90 % (31260)------------------------------ 17.25/2.90 % (31260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 17.25/2.90 % (31260)Termination reason: Unknown 17.25/2.90 % (31260)Termination phase: Saturation 17.25/2.90 17.25/2.90 % (31260)Memory used [KB]: 11385 17.25/2.90 % (31260)Time elapsed: 0.149 s 17.25/2.90 % (31260)Instructions burned: 436 (million) 17.25/2.90 % (31260)------------------------------ 17.25/2.90 % (31260)------------------------------ 17.25/2.91 % (31263)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on E---3.1_30784 for (2375ds/443Mi) 17.60/3.03 % (31262)Instruction limit reached! 17.60/3.03 % (31262)------------------------------ 17.60/3.03 % (31262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 17.60/3.03 % (31262)Termination reason: Unknown 17.60/3.03 % (31262)Termination phase: Saturation 17.60/3.03 17.60/3.03 % (31262)Memory used [KB]: 7675 17.60/3.03 % (31262)Time elapsed: 0.148 s 17.60/3.03 % (31262)Instructions burned: 594 (million) 17.60/3.03 % (31262)------------------------------ 17.60/3.03 % (31262)------------------------------ 17.60/3.03 % (31263)Instruction limit reached! 17.60/3.03 % (31263)------------------------------ 17.60/3.03 % (31263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 17.60/3.03 % (31263)Termination reason: Unknown 17.60/3.03 % (31263)Termination phase: Saturation 17.60/3.03 17.60/3.03 % (31263)Memory used [KB]: 9722 17.60/3.03 % (31263)Time elapsed: 0.145 s 17.60/3.03 % (31263)Instructions burned: 444 (million) 17.60/3.03 % (31263)------------------------------ 17.60/3.03 % (31263)------------------------------ 17.60/3.04 % (31264)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on E---3.1_30784 for (2374ds/594Mi) 17.60/3.04 % (31265)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on E---3.1_30784 for (2374ds/327Mi) 17.60/3.04 % (31259)Instruction limit reached! 17.60/3.04 % (31259)------------------------------ 17.60/3.04 % (31259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 17.60/3.04 % (31259)Termination reason: Unknown 17.60/3.04 % (31259)Termination phase: Saturation 17.60/3.04 17.60/3.04 % (31259)Memory used [KB]: 11385 17.60/3.04 % (31259)Time elapsed: 0.296 s 17.60/3.04 % (31259)Instructions burned: 906 (million) 17.60/3.04 % (31259)------------------------------ 17.60/3.04 % (31259)------------------------------ 17.60/3.05 % (31266)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on E---3.1_30784 for (2374ds/5411Mi) 18.33/3.11 % (31258)Instruction limit reached! 18.33/3.11 % (31258)------------------------------ 18.33/3.11 % (31258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 18.33/3.11 % (31258)Termination reason: Unknown 18.33/3.11 % (31258)Termination phase: Saturation 18.33/3.11 18.33/3.11 % (31258)Memory used [KB]: 9466 18.33/3.11 % (31258)Time elapsed: 0.352 s 18.33/3.11 % (31258)Instructions burned: 1377 (million) 18.33/3.11 % (31258)------------------------------ 18.33/3.11 % (31258)------------------------------ 18.33/3.12 % (31267)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on E---3.1_30784 for (2373ds/1762Mi) 18.33/3.13 % (31261)Instruction limit reached! 18.33/3.13 % (31261)------------------------------ 18.33/3.13 % (31261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 18.33/3.13 % (31261)Termination reason: Unknown 18.33/3.13 % (31261)Termination phase: Saturation 18.33/3.13 18.33/3.13 % (31261)Memory used [KB]: 9978 18.33/3.13 % (31261)Time elapsed: 0.256 s 18.33/3.13 % (31261)Instructions burned: 865 (million) 18.33/3.13 % (31261)------------------------------ 18.33/3.13 % (31261)------------------------------ 18.33/3.14 % (31265)Instruction limit reached! 18.33/3.14 % (31265)------------------------------ 18.33/3.14 % (31265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 18.33/3.14 % (31265)Termination reason: Unknown 18.33/3.14 % (31265)Termination phase: Saturation 18.33/3.14 18.33/3.14 % (31265)Memory used [KB]: 11385 18.33/3.14 % (31265)Time elapsed: 0.096 s 18.33/3.14 % (31265)Instructions burned: 328 (million) 18.33/3.14 % (31265)------------------------------ 18.33/3.14 % (31265)------------------------------ 18.33/3.14 % (31268)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on E---3.1_30784 for (2373ds/96Mi) 18.33/3.15 % (31269)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on E---3.1_30784 for (2373ds/503Mi) 18.33/3.17 % (31268)Instruction limit reached! 18.33/3.17 % (31268)------------------------------ 18.33/3.17 % (31268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 18.33/3.17 % (31268)Termination reason: Unknown 18.33/3.17 % (31268)Termination phase: Property scanning 18.33/3.17 18.33/3.17 % (31268)Memory used [KB]: 2558 18.33/3.17 % (31268)Time elapsed: 0.026 s 18.33/3.17 % (31268)Instructions burned: 97 (million) 18.33/3.17 % (31268)------------------------------ 18.33/3.17 % (31268)------------------------------ 18.33/3.18 % (31270)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on E---3.1_30784 for (2372ds/90Mi) 18.92/3.20 % (31270)Instruction limit reached! 18.92/3.20 % (31270)------------------------------ 18.92/3.20 % (31270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 18.92/3.20 % (31270)Termination reason: Unknown 18.92/3.20 % (31270)Termination phase: Property scanning 18.92/3.20 18.92/3.20 % (31270)Memory used [KB]: 2686 18.92/3.20 % (31270)Time elapsed: 0.025 s 18.92/3.20 % (31270)Instructions burned: 92 (million) 18.92/3.20 % (31270)------------------------------ 18.92/3.20 % (31270)------------------------------ 18.92/3.21 % (31264)Instruction limit reached! 18.92/3.21 % (31264)------------------------------ 18.92/3.21 % (31264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 18.92/3.21 % (31264)Termination reason: Unknown 18.92/3.21 % (31264)Termination phase: Saturation 18.92/3.21 18.92/3.21 % (31264)Memory used [KB]: 9850 18.92/3.21 % (31264)Time elapsed: 0.193 s 18.92/3.21 % (31264)Instructions burned: 595 (million) 18.92/3.21 % (31264)------------------------------ 18.92/3.21 % (31264)------------------------------ 18.92/3.21 % (31271)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on E---3.1_30784 for (2372ds/593Mi) 18.92/3.22 % (31272)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on E---3.1_30784 for (2372ds/1512Mi) 19.30/3.29 % (31269)Instruction limit reached! 19.30/3.29 % (31269)------------------------------ 19.30/3.29 % (31269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 19.30/3.29 % (31269)Termination reason: Unknown 19.30/3.29 % (31269)Termination phase: Saturation 19.30/3.29 19.30/3.29 % (31269)Memory used [KB]: 9850 19.30/3.29 % (31269)Time elapsed: 0.141 s 19.30/3.29 % (31269)Instructions burned: 505 (million) 19.30/3.29 % (31269)------------------------------ 19.30/3.29 % (31269)------------------------------ 19.30/3.30 % (31273)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on E---3.1_30784 for (2371ds/569Mi) 19.30/3.37 % (31253)Instruction limit reached! 19.30/3.37 % (31253)------------------------------ 19.30/3.37 % (31253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 19.30/3.37 % (31253)Termination reason: Unknown 19.30/3.37 % (31253)Termination phase: Saturation 19.30/3.37 19.30/3.37 % (31253)Memory used [KB]: 7675 19.30/3.37 % (31253)Time elapsed: 1.169 s 19.30/3.37 % (31253)Instructions burned: 4714 (million) 19.30/3.37 % (31253)------------------------------ 19.30/3.37 % (31253)------------------------------ 19.30/3.38 % (31271)Instruction limit reached! 19.30/3.38 % (31271)------------------------------ 19.30/3.38 % (31271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 19.30/3.38 % (31271)Termination reason: Unknown 19.30/3.38 % (31271)Termination phase: Saturation 19.30/3.38 19.30/3.38 % (31271)Memory used [KB]: 10106 19.30/3.38 % (31271)Time elapsed: 0.171 s 19.30/3.38 % (31271)Instructions burned: 596 (million) 19.30/3.38 % (31271)------------------------------ 19.30/3.38 % (31271)------------------------------ 19.30/3.38 % (31274)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on E---3.1_30784 for (2370ds/501Mi) 19.83/3.40 % (31275)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on E---3.1_30784 for (2370ds/562Mi) 20.96/3.44 % (31273)Instruction limit reached! 20.96/3.44 % (31273)------------------------------ 20.96/3.44 % (31273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 20.96/3.44 % (31273)Termination reason: Unknown 20.96/3.44 % (31273)Termination phase: Saturation 20.96/3.44 20.96/3.44 % (31273)Memory used [KB]: 7675 20.96/3.44 % (31273)Time elapsed: 0.143 s 20.96/3.44 % (31273)Instructions burned: 570 (million) 20.96/3.44 % (31273)------------------------------ 20.96/3.44 % (31273)------------------------------ 20.96/3.45 % (31276)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on E---3.1_30784 for (2370ds/406Mi) 21.52/3.53 % (31274)Instruction limit reached! 21.52/3.53 % (31274)------------------------------ 21.52/3.53 % (31274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 21.52/3.53 % (31274)Termination reason: Unknown 21.52/3.53 % (31274)Termination phase: Saturation 21.52/3.53 21.52/3.53 % (31274)Memory used [KB]: 10618 21.52/3.53 % (31274)Time elapsed: 0.152 s 21.52/3.53 % (31274)Instructions burned: 502 (million) 21.52/3.53 % (31274)------------------------------ 21.52/3.53 % (31274)------------------------------ 21.52/3.54 % (31277)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on E---3.1_30784 for (2369ds/582Mi) 21.52/3.56 % (31275)Instruction limit reached! 21.52/3.56 % (31275)------------------------------ 21.52/3.56 % (31275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 21.52/3.56 % (31275)Termination reason: Unknown 21.52/3.56 % (31275)Termination phase: Saturation 21.52/3.56 21.52/3.56 % (31275)Memory used [KB]: 8315 21.52/3.56 % (31275)Time elapsed: 0.161 s 21.52/3.56 % (31275)Instructions burned: 562 (million) 21.52/3.56 % (31275)------------------------------ 21.52/3.56 % (31275)------------------------------ 21.52/3.56 % (31267)Instruction limit reached! 21.52/3.56 % (31267)------------------------------ 21.52/3.56 % (31267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 21.52/3.56 % (31267)Termination reason: Unknown 21.52/3.56 % (31267)Termination phase: Saturation 21.52/3.56 21.52/3.56 % (31267)Memory used [KB]: 23027 21.52/3.56 % (31267)Time elapsed: 0.439 s 21.52/3.56 % (31267)Instructions burned: 1762 (million) 21.52/3.56 % (31267)------------------------------ 21.52/3.56 % (31267)------------------------------ 21.52/3.56 % (31276)Instruction limit reached! 21.52/3.56 % (31276)------------------------------ 21.52/3.56 % (31276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 21.52/3.56 % (31276)Termination reason: Unknown 21.52/3.56 % (31276)Termination phase: Saturation 21.52/3.56 21.52/3.56 % (31276)Memory used [KB]: 7803 21.52/3.56 % (31276)Time elapsed: 0.114 s 21.52/3.56 % (31276)Instructions burned: 406 (million) 21.52/3.56 % (31276)------------------------------ 21.52/3.56 % (31276)------------------------------ 21.52/3.57 % (31279)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on E---3.1_30784 for (2368ds/393Mi) 21.52/3.57 % (31280)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on E---3.1_30784 for (2368ds/1335Mi) 21.52/3.58 % (31278)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on E---3.1_30784 for (2368ds/456Mi) 22.27/3.68 % (31279)Instruction limit reached! 22.27/3.68 % (31279)------------------------------ 22.27/3.68 % (31279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 22.27/3.68 % (31279)Termination reason: Unknown 22.27/3.68 % (31279)Termination phase: Saturation 22.27/3.68 22.27/3.68 % (31279)Memory used [KB]: 9978 22.27/3.68 % (31279)Time elapsed: 0.109 s 22.27/3.68 % (31279)Instructions burned: 396 (million) 22.27/3.68 % (31279)------------------------------ 22.27/3.68 % (31279)------------------------------ 22.27/3.69 % (31281)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on E---3.1_30784 for (2367ds/3373Mi) 22.27/3.69 % (31272)Instruction limit reached! 22.27/3.69 % (31272)------------------------------ 22.27/3.69 % (31272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 22.27/3.69 % (31272)Termination reason: Unknown 22.27/3.69 % (31272)Termination phase: Saturation 22.27/3.69 22.27/3.69 % (31272)Memory used [KB]: 13560 22.27/3.69 % (31272)Time elapsed: 0.477 s 22.27/3.69 % (31272)Instructions burned: 1514 (million) 22.27/3.69 % (31272)------------------------------ 22.27/3.69 % (31272)------------------------------ 22.27/3.70 % (31282)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on E---3.1_30784 for (2367ds/474Mi) 22.48/3.72 % (31277)Instruction limit reached! 22.48/3.72 % (31277)------------------------------ 22.48/3.72 % (31277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 22.48/3.72 % (31277)Termination reason: Unknown 22.48/3.72 % (31277)Termination phase: Saturation 22.48/3.72 22.48/3.72 % (31277)Memory used [KB]: 10874 22.48/3.72 % (31277)Time elapsed: 0.198 s 22.48/3.72 % (31277)Instructions burned: 585 (million) 22.48/3.72 % (31277)------------------------------ 22.48/3.72 % (31277)------------------------------ 22.69/3.73 % (31283)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on E---3.1_30784 for (2367ds/157Mi) 22.69/3.75 % (31278)Instruction limit reached! 22.69/3.75 % (31278)------------------------------ 22.69/3.75 % (31278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 22.69/3.75 % (31278)Termination reason: Unknown 22.69/3.75 % (31278)Termination phase: Saturation 22.69/3.75 22.69/3.75 % (31278)Memory used [KB]: 9722 22.69/3.75 % (31278)Time elapsed: 0.173 s 22.69/3.75 % (31278)Instructions burned: 458 (million) 22.69/3.75 % (31278)------------------------------ 22.69/3.75 % (31278)------------------------------ 22.69/3.76 % (31284)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on E---3.1_30784 for (2367ds/590Mi) 22.69/3.77 % (31283)Instruction limit reached! 22.69/3.77 % (31283)------------------------------ 22.69/3.77 % (31283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 22.69/3.77 % (31283)Termination reason: Unknown 22.69/3.77 % (31283)Termination phase: Property scanning 22.69/3.77 22.69/3.77 % (31283)Memory used [KB]: 2686 22.69/3.77 % (31283)Time elapsed: 0.040 s 22.69/3.77 % (31283)Instructions burned: 157 (million) 22.69/3.77 % (31283)------------------------------ 22.69/3.77 % (31283)------------------------------ 22.69/3.78 % (31285)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on E---3.1_30784 for (2366ds/104Mi) 22.69/3.80 % (31285)Instruction limit reached! 22.69/3.80 % (31285)------------------------------ 22.69/3.80 % (31285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 22.69/3.80 % (31285)Termination reason: Unknown 22.69/3.80 % (31285)Termination phase: Property scanning 22.69/3.80 22.69/3.80 % (31285)Memory used [KB]: 2686 22.69/3.80 % (31285)Time elapsed: 0.028 s 22.69/3.80 % (31285)Instructions burned: 106 (million) 22.69/3.80 % (31285)------------------------------ 22.69/3.80 % (31285)------------------------------ 22.69/3.81 % (31286)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on E---3.1_30784 for (2366ds/414Mi) 23.15/3.82 % (31282)Instruction limit reached! 23.15/3.82 % (31282)------------------------------ 23.15/3.82 % (31282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 23.15/3.82 % (31282)Termination reason: Unknown 23.15/3.82 % (31282)Termination phase: Saturation 23.15/3.82 23.15/3.82 % (31282)Memory used [KB]: 7547 23.15/3.82 % (31282)Time elapsed: 0.118 s 23.15/3.82 % (31282)Instructions burned: 474 (million) 23.15/3.82 % (31282)------------------------------ 23.15/3.82 % (31282)------------------------------ 23.15/3.83 % (31287)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on E---3.1_30784 for (2366ds/715Mi) 23.42/3.92 % (31286)Instruction limit reached! 23.42/3.92 % (31286)------------------------------ 23.42/3.92 % (31286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 23.42/3.92 % (31286)Termination reason: Unknown 23.42/3.92 % (31286)Termination phase: Saturation 23.42/3.92 23.42/3.92 % (31286)Memory used [KB]: 7547 23.42/3.92 % (31286)Time elapsed: 0.107 s 23.42/3.92 % (31286)Instructions burned: 417 (million) 23.42/3.92 % (31286)------------------------------ 23.42/3.92 % (31286)------------------------------ 23.42/3.93 % (31288)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on E---3.1_30784 for (2365ds/961Mi) 23.42/3.94 % (31284)Instruction limit reached! 23.42/3.94 % (31284)------------------------------ 23.42/3.94 % (31284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 23.42/3.94 % (31284)Termination reason: Unknown 23.42/3.94 % (31284)Termination phase: Saturation 23.42/3.94 23.42/3.94 % (31284)Memory used [KB]: 8699 23.42/3.94 % (31284)Time elapsed: 0.182 s 23.42/3.94 % (31284)Instructions burned: 592 (million) 23.42/3.94 % (31284)------------------------------ 23.42/3.94 % (31284)------------------------------ 23.42/3.95 % (31289)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on E---3.1_30784 for (2364ds/1213Mi) 23.42/3.96 % (31280)Instruction limit reached! 23.42/3.96 % (31280)------------------------------ 23.42/3.96 % (31280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 23.42/3.96 % (31280)Termination reason: Unknown 23.42/3.96 % (31280)Termination phase: Saturation 23.42/3.96 23.42/3.96 % (31280)Memory used [KB]: 10362 23.42/3.96 % (31280)Time elapsed: 0.389 s 23.42/3.96 % (31280)Instructions burned: 1336 (million) 23.42/3.96 % (31280)------------------------------ 23.42/3.96 % (31280)------------------------------ 24.28/3.97 % (31290)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on E---3.1_30784 for (2364ds/1979Mi) 25.24/4.04 % (31287)Instruction limit reached! 25.24/4.04 % (31287)------------------------------ 25.24/4.04 % (31287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 25.24/4.04 % (31287)Termination reason: Unknown 25.24/4.04 % (31287)Termination phase: Saturation 25.24/4.04 25.24/4.04 % (31287)Memory used [KB]: 5628 25.24/4.04 % (31287)Time elapsed: 0.211 s 25.24/4.04 % (31287)Instructions burned: 716 (million) 25.24/4.04 % (31287)------------------------------ 25.24/4.04 % (31287)------------------------------ 25.24/4.05 % (31291)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on E---3.1_30784 for (2364ds/481Mi) 25.73/4.17 % (31291)Instruction limit reached! 25.73/4.17 % (31291)------------------------------ 25.73/4.17 % (31291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 25.73/4.17 % (31291)Termination reason: Unknown 25.73/4.17 % (31291)Termination phase: Saturation 25.73/4.17 26.10/4.17 % (31291)Memory used [KB]: 7547 26.10/4.17 % (31291)Time elapsed: 0.124 s 26.10/4.17 % (31291)Instructions burned: 482 (million) 26.10/4.17 % (31291)------------------------------ 26.10/4.17 % (31291)------------------------------ 26.10/4.18 % (31292)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on E---3.1_30784 for (2362ds/783Mi) 26.10/4.22 % (31288)Instruction limit reached! 26.10/4.22 % (31288)------------------------------ 26.10/4.22 % (31288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 26.10/4.22 % (31288)Termination reason: Unknown 26.10/4.22 % (31288)Termination phase: Saturation 26.10/4.22 26.10/4.22 % (31288)Memory used [KB]: 10234 26.10/4.22 % (31288)Time elapsed: 0.290 s 26.10/4.22 % (31288)Instructions burned: 962 (million) 26.10/4.22 % (31288)------------------------------ 26.10/4.22 % (31288)------------------------------ 26.10/4.23 % (31293)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on E---3.1_30784 for (2362ds/432Mi) 27.09/4.35 % (31293)Instruction limit reached! 27.09/4.35 % (31293)------------------------------ 27.09/4.35 % (31293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 27.09/4.35 % (31293)Termination reason: Unknown 27.09/4.35 % (31293)Termination phase: Saturation 27.09/4.35 27.09/4.35 % (31293)Memory used [KB]: 9594 27.09/4.35 % (31293)Time elapsed: 0.119 s 27.09/4.35 % (31293)Instructions burned: 434 (million) 27.09/4.35 % (31293)------------------------------ 27.09/4.35 % (31293)------------------------------ 27.09/4.36 % (31294)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on E---3.1_30784 for (2361ds/1670Mi) 27.09/4.38 % (31289)Instruction limit reached! 27.09/4.38 % (31289)------------------------------ 27.09/4.38 % (31289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 27.09/4.38 % (31289)Termination reason: Unknown 27.09/4.38 % (31289)Termination phase: Saturation 27.09/4.38 27.09/4.38 % (31289)Memory used [KB]: 15351 27.09/4.38 % (31289)Time elapsed: 0.428 s 27.09/4.38 % (31289)Instructions burned: 1213 (million) 27.09/4.38 % (31289)------------------------------ 27.09/4.38 % (31289)------------------------------ 27.09/4.39 % (31295)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on E---3.1_30784 for (2360ds/90Mi) 27.09/4.41 % (31295)Instruction limit reached! 27.09/4.41 % (31295)------------------------------ 27.09/4.41 % (31295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 27.09/4.41 % (31295)Termination reason: Unknown 27.09/4.41 % (31295)Termination phase: Clausification 27.09/4.41 27.09/4.41 % (31295)Memory used [KB]: 2686 27.09/4.41 % (31295)Time elapsed: 0.025 s 27.09/4.41 % (31295)Instructions burned: 92 (million) 27.09/4.41 % (31295)------------------------------ 27.09/4.41 % (31295)------------------------------ 27.63/4.42 % (31296)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on E---3.1_30784 for (2360ds/346Mi) 27.63/4.42 % (31292)Instruction limit reached! 27.63/4.42 % (31292)------------------------------ 27.63/4.42 % (31292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 27.63/4.42 % (31292)Termination reason: Unknown 27.63/4.42 % (31292)Termination phase: Saturation 27.63/4.42 27.63/4.42 % (31292)Memory used [KB]: 11897 27.63/4.42 % (31292)Time elapsed: 0.242 s 27.63/4.42 % (31292)Instructions burned: 783 (million) 27.63/4.42 % (31292)------------------------------ 27.63/4.42 % (31292)------------------------------ 27.63/4.44 % (31297)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on E---3.1_30784 for (2360ds/401Mi) 28.12/4.51 % (31296)Instruction limit reached! 28.12/4.51 % (31296)------------------------------ 28.12/4.51 % (31296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 28.12/4.51 % (31296)Termination reason: Unknown 28.12/4.51 % (31296)Termination phase: Saturation 28.12/4.51 28.12/4.51 % (31296)Memory used [KB]: 7547 28.12/4.51 % (31296)Time elapsed: 0.089 s 28.12/4.51 % (31296)Instructions burned: 346 (million) 28.12/4.51 % (31296)------------------------------ 28.12/4.51 % (31296)------------------------------ 28.12/4.52 % (31298)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on E---3.1_30784 for (2359ds/6454Mi) 28.12/4.54 % (31297)Instruction limit reached! 28.12/4.54 % (31297)------------------------------ 28.12/4.54 % (31297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 28.12/4.54 % (31297)Termination reason: Unknown 28.12/4.54 % (31297)Termination phase: Saturation 28.12/4.54 28.12/4.54 % (31297)Memory used [KB]: 7547 28.12/4.54 % (31297)Time elapsed: 0.104 s 28.12/4.54 % (31297)Instructions burned: 404 (million) 28.12/4.54 % (31297)------------------------------ 28.12/4.54 % (31297)------------------------------ 28.12/4.55 % (31299)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on E---3.1_30784 for (2359ds/283Mi) 29.01/4.57 % (31290)Instruction limit reached! 29.01/4.57 % (31290)------------------------------ 29.01/4.57 % (31290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 29.01/4.57 % (31290)Termination reason: Unknown 29.01/4.57 % (31290)Termination phase: Saturation 29.01/4.57 29.01/4.57 % (31290)Memory used [KB]: 10618 29.01/4.57 % (31290)Time elapsed: 0.607 s 29.01/4.57 % (31290)Instructions burned: 1980 (million) 29.01/4.57 % (31290)------------------------------ 29.01/4.57 % (31290)------------------------------ 29.01/4.58 % (31300)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on E---3.1_30784 for (2358ds/865Mi) 29.16/4.62 % (31299)Instruction limit reached! 29.16/4.62 % (31299)------------------------------ 29.16/4.62 % (31299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 29.16/4.62 % (31299)Termination reason: Unknown 29.16/4.62 % (31299)Termination phase: Saturation 29.16/4.62 29.16/4.62 % (31299)Memory used [KB]: 8315 29.16/4.62 % (31299)Time elapsed: 0.076 s 29.16/4.62 % (31299)Instructions burned: 286 (million) 29.16/4.62 % (31299)------------------------------ 29.16/4.62 % (31299)------------------------------ 29.16/4.63 % (31301)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on E---3.1_30784 for (2358ds/4528Mi) 29.73/4.71 % (31281)Instruction limit reached! 29.73/4.71 % (31281)------------------------------ 29.73/4.71 % (31281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 29.73/4.71 % (31281)Termination reason: Unknown 29.73/4.71 % (31281)Termination phase: Saturation 29.73/4.71 29.73/4.71 % (31281)Memory used [KB]: 12537 29.73/4.71 % (31281)Time elapsed: 1.048 s 29.73/4.71 % (31281)Instructions burned: 3374 (million) 29.73/4.71 % (31281)------------------------------ 29.73/4.71 % (31281)------------------------------ 29.73/4.72 % (31302)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on E---3.1_30784 for (2357ds/1001Mi) 29.73/4.73 % (31266)Instruction limit reached! 29.73/4.73 % (31266)------------------------------ 29.73/4.73 % (31266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 29.73/4.73 % (31266)Termination reason: Unknown 29.73/4.73 % (31266)Termination phase: Saturation 29.73/4.73 29.73/4.73 % (31266)Memory used [KB]: 16247 29.73/4.73 % (31266)Time elapsed: 1.704 s 29.73/4.73 % (31266)Instructions burned: 5412 (million) 29.73/4.73 % (31266)------------------------------ 29.73/4.73 % (31266)------------------------------ 29.73/4.74 % (31303)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on E---3.1_30784 for (2357ds/102Mi) 29.97/4.77 % (31303)Instruction limit reached! 29.97/4.77 % (31303)------------------------------ 29.97/4.77 % (31303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 29.97/4.77 % (31303)Termination reason: Unknown 29.97/4.77 % (31303)Termination phase: Property scanning 29.97/4.77 29.97/4.77 % (31303)Memory used [KB]: 2686 29.97/4.77 % (31303)Time elapsed: 0.029 s 29.97/4.77 % (31303)Instructions burned: 104 (million) 29.97/4.77 % (31303)------------------------------ 29.97/4.77 % (31303)------------------------------ 29.97/4.78 % (31304)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on E---3.1_30784 for (2356ds/952Mi) 29.97/4.78 % (31294)Instruction limit reached! 29.97/4.78 % (31294)------------------------------ 29.97/4.78 % (31294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 29.97/4.78 % (31294)Termination reason: Unknown 29.97/4.78 % (31294)Termination phase: Saturation 29.97/4.78 29.97/4.78 % (31294)Memory used [KB]: 18166 29.97/4.78 % (31294)Time elapsed: 0.427 s 29.97/4.78 % (31294)Instructions burned: 1672 (million) 29.97/4.78 % (31294)------------------------------ 29.97/4.78 % (31294)------------------------------ 29.97/4.79 % (31305)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on E---3.1_30784 for (2356ds/578Mi) 29.97/4.82 % (31300)Instruction limit reached! 29.97/4.82 % (31300)------------------------------ 29.97/4.82 % (31300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 29.97/4.82 % (31300)Termination reason: Unknown 29.97/4.82 % (31300)Termination phase: Saturation 29.97/4.82 29.97/4.82 % (31300)Memory used [KB]: 8059 29.97/4.82 % (31300)Time elapsed: 0.233 s 29.97/4.82 % (31300)Instructions burned: 867 (million) 29.97/4.82 % (31300)------------------------------ 29.97/4.82 % (31300)------------------------------ 29.97/4.83 % (31306)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on E---3.1_30784 for (2356ds/643Mi) 29.97/4.83 % (31301)Refutation not found, incomplete strategy 29.97/4.83 % (31301)------------------------------ 29.97/4.83 % (31301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 29.97/4.83 % (31301)Termination reason: Refutation not found, incomplete strategy 29.97/4.83 29.97/4.83 29.97/4.83 % (31301)Memory used [KB]: 3070 29.97/4.83 % (31301)Time elapsed: 0.198 s 29.97/4.83 % (31301)Instructions burned: 777 (million) 29.97/4.83 % (31301)------------------------------ 29.97/4.83 % (31301)------------------------------ 29.97/4.84 % (31307)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on E---3.1_30784 for (2356ds/865Mi) 30.78/4.92 % (31254)Instruction limit reached! 30.78/4.92 % (31254)------------------------------ 30.78/4.92 % (31254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 30.78/4.92 % (31254)Termination reason: Unknown 30.78/4.92 % (31254)Termination phase: Saturation 30.78/4.92 30.78/4.92 % (31254)Memory used [KB]: 29040 30.78/4.92 % (31254)Time elapsed: 2.670 s 30.78/4.92 % (31254)Instructions burned: 8251 (million) 30.78/4.92 % (31254)------------------------------ 30.78/4.92 % (31254)------------------------------ 30.78/4.93 % (31305)Instruction limit reached! 30.78/4.93 % (31305)------------------------------ 30.78/4.93 % (31305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 30.78/4.93 % (31305)Termination reason: Unknown 30.78/4.93 % (31305)Termination phase: Saturation 30.78/4.93 30.78/4.93 % (31305)Memory used [KB]: 11001 30.78/4.93 % (31305)Time elapsed: 0.138 s 30.78/4.93 % (31305)Instructions burned: 579 (million) 30.78/4.93 % (31305)------------------------------ 30.78/4.93 % (31305)------------------------------ 30.78/4.93 % (31308)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on E---3.1_30784 for (2355ds/1174Mi) 31.00/4.94 % (31309)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on E---3.1_30784 for (2355ds/644Mi) 31.00/4.99 % (31306)Instruction limit reached! 31.00/4.99 % (31306)------------------------------ 31.00/4.99 % (31306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 31.00/4.99 % (31306)Termination reason: Unknown 31.00/4.99 % (31306)Termination phase: Saturation 31.00/4.99 31.00/4.99 % (31306)Memory used [KB]: 7675 31.00/4.99 % (31306)Time elapsed: 0.160 s 31.00/4.99 % (31306)Instructions burned: 645 (million) 31.00/4.99 % (31306)------------------------------ 31.00/4.99 % (31306)------------------------------ 31.00/5.00 % (31310)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on E---3.1_30784 for (2354ds/1201Mi) 31.22/5.03 % (31302)Instruction limit reached! 31.22/5.03 % (31302)------------------------------ 31.22/5.03 % (31302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 31.22/5.03 % (31302)Termination reason: Unknown 31.22/5.03 % (31302)Termination phase: Saturation 31.22/5.03 31.22/5.03 % (31302)Memory used [KB]: 11385 31.22/5.03 % (31302)Time elapsed: 0.304 s 31.22/5.03 % (31302)Instructions burned: 1002 (million) 31.22/5.03 % (31302)------------------------------ 31.22/5.03 % (31302)------------------------------ 31.22/5.04 % (31311)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on E---3.1_30784 for (2354ds/1046Mi) 31.22/5.06 % (31304)Instruction limit reached! 31.22/5.06 % (31304)------------------------------ 31.22/5.06 % (31304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 31.22/5.06 % (31304)Termination reason: Unknown 31.22/5.06 % (31304)Termination phase: Saturation 31.22/5.06 31.22/5.06 % (31304)Memory used [KB]: 10362 31.22/5.06 % (31304)Time elapsed: 0.282 s 31.22/5.06 % (31304)Instructions burned: 953 (million) 31.22/5.06 % (31304)------------------------------ 31.22/5.06 % (31304)------------------------------ 31.22/5.07 % (31312)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on E---3.1_30784 for (2353ds/222Mi) 31.22/5.07 % (31307)Instruction limit reached! 31.22/5.07 % (31307)------------------------------ 31.22/5.07 % (31307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 31.22/5.07 % (31307)Termination reason: Unknown 31.22/5.07 % (31307)Termination phase: Saturation 31.22/5.07 31.22/5.07 % (31307)Memory used [KB]: 7931 31.22/5.07 % (31307)Time elapsed: 0.234 s 31.22/5.07 % (31307)Instructions burned: 867 (million) 31.22/5.07 % (31307)------------------------------ 31.22/5.07 % (31307)------------------------------ 32.55/5.08 % (31313)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on E---3.1_30784 for (2353ds/68Mi) 32.55/5.10 % (31313)Instruction limit reached! 32.55/5.10 % (31313)------------------------------ 32.55/5.10 % (31313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 32.55/5.10 % (31313)Termination reason: Unknown 32.55/5.10 % (31313)Termination phase: Property scanning 32.55/5.10 32.55/5.10 % (31313)Memory used [KB]: 2558 32.55/5.10 % (31313)Time elapsed: 0.021 s 32.55/5.10 % (31313)Instructions burned: 71 (million) 32.55/5.10 % (31313)------------------------------ 32.55/5.10 % (31313)------------------------------ 32.55/5.11 % (31314)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on E---3.1_30784 for (2353ds/454Mi) 32.55/5.12 % (31309)Instruction limit reached! 32.55/5.12 % (31309)------------------------------ 32.55/5.12 % (31309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 32.55/5.12 % (31309)Termination reason: Unknown 32.55/5.12 % (31309)Termination phase: Saturation 32.55/5.12 32.55/5.12 % (31309)Memory used [KB]: 8443 32.55/5.12 % (31309)Time elapsed: 0.186 s 32.55/5.12 % (31309)Instructions burned: 645 (million) 32.55/5.12 % (31309)------------------------------ 32.55/5.12 % (31309)------------------------------ 32.55/5.13 % (31312)Instruction limit reached! 32.55/5.13 % (31312)------------------------------ 32.55/5.13 % (31312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 32.55/5.13 % (31312)Termination reason: Unknown 32.55/5.13 % (31312)Termination phase: Saturation 32.55/5.13 32.55/5.13 % (31312)Memory used [KB]: 7547 32.55/5.13 % (31312)Time elapsed: 0.059 s 32.55/5.13 % (31312)Instructions burned: 225 (million) 32.55/5.13 % (31312)------------------------------ 32.55/5.13 % (31312)------------------------------ 32.55/5.13 % (31315)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on E---3.1_30784 for (2353ds/360Mi) 32.55/5.14 % (31316)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on E---3.1_30784 for (2353ds/157Mi) 33.09/5.18 % (31316)Instruction limit reached! 33.09/5.18 % (31316)------------------------------ 33.09/5.18 % (31316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 33.09/5.18 % (31316)Termination reason: Unknown 33.09/5.18 % (31316)Termination phase: Property scanning 33.09/5.18 33.09/5.18 % (31316)Memory used [KB]: 2814 33.09/5.18 % (31316)Time elapsed: 0.041 s 33.09/5.18 % (31316)Instructions burned: 160 (million) 33.09/5.18 % (31316)------------------------------ 33.09/5.18 % (31316)------------------------------ 33.09/5.19 % (31317)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on E---3.1_30784 for (2352ds/5061Mi) 33.29/5.22 % (31315)Instruction limit reached! 33.29/5.22 % (31315)------------------------------ 33.29/5.22 % (31315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 33.29/5.22 % (31315)Termination reason: Unknown 33.29/5.22 % (31315)Termination phase: Saturation 33.29/5.22 33.29/5.22 % (31315)Memory used [KB]: 7547 33.29/5.22 % (31315)Time elapsed: 0.091 s 33.29/5.22 % (31315)Instructions burned: 363 (million) 33.29/5.22 % (31315)------------------------------ 33.29/5.22 % (31315)------------------------------ 33.29/5.23 % (31314)Instruction limit reached! 33.29/5.23 % (31314)------------------------------ 33.29/5.23 % (31314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 33.29/5.23 % (31314)Termination reason: Unknown 33.29/5.23 % (31314)Termination phase: Saturation 33.29/5.23 33.29/5.23 % (31314)Memory used [KB]: 12025 33.29/5.23 % (31314)Time elapsed: 0.114 s 33.29/5.23 % (31314)Instructions burned: 457 (million) 33.29/5.23 % (31314)------------------------------ 33.29/5.23 % (31314)------------------------------ 33.29/5.23 % (31318)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on E---3.1_30784 for (2352ds/2401Mi) 33.63/5.24 % (31319)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on E---3.1_30784 for (2352ds/5798Mi) 33.63/5.28 % (31308)Instruction limit reached! 33.63/5.28 % (31308)------------------------------ 33.63/5.28 % (31308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 33.63/5.28 % (31308)Termination reason: Unknown 33.63/5.28 % (31308)Termination phase: Saturation 33.63/5.28 33.63/5.28 % (31308)Memory used [KB]: 10490 33.63/5.28 % (31308)Time elapsed: 0.356 s 33.63/5.28 % (31308)Instructions burned: 1177 (million) 33.63/5.28 % (31308)------------------------------ 33.63/5.28 % (31308)------------------------------ 33.63/5.29 % (31320)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on E---3.1_30784 for (2351ds/346Mi) 33.63/5.30 % (31311)Instruction limit reached! 33.63/5.30 % (31311)------------------------------ 33.63/5.30 % (31311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 33.63/5.30 % (31311)Termination reason: Unknown 33.63/5.30 % (31311)Termination phase: Saturation 33.63/5.30 33.63/5.30 % (31311)Memory used [KB]: 7675 33.63/5.30 % (31311)Time elapsed: 0.263 s 33.63/5.30 % (31311)Instructions burned: 1048 (million) 33.63/5.30 % (31311)------------------------------ 33.63/5.30 % (31311)------------------------------ 33.63/5.31 % (31321)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on E---3.1_30784 for (2351ds/1321Mi) 33.92/5.33 % (31310)Instruction limit reached! 33.92/5.33 % (31310)------------------------------ 33.92/5.33 % (31310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 33.92/5.33 % (31310)Termination reason: Unknown 33.92/5.33 % (31310)Termination phase: Saturation 33.92/5.33 33.92/5.33 % (31310)Memory used [KB]: 11769 33.92/5.33 % (31310)Time elapsed: 0.340 s 33.92/5.33 % (31310)Instructions burned: 1201 (million) 33.92/5.33 % (31310)------------------------------ 33.92/5.33 % (31310)------------------------------ 33.92/5.34 % (31322)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on E---3.1_30784 for (2351ds/1312Mi) 33.92/5.38 % (31320)Instruction limit reached! 33.92/5.38 % (31320)------------------------------ 33.92/5.38 % (31320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 33.92/5.38 % (31320)Termination reason: Unknown 33.92/5.38 % (31320)Termination phase: Saturation 33.92/5.38 33.92/5.38 % (31320)Memory used [KB]: 7547 33.92/5.38 % (31320)Time elapsed: 0.087 s 33.92/5.38 % (31320)Instructions burned: 347 (million) 33.92/5.38 % (31320)------------------------------ 33.92/5.38 % (31320)------------------------------ 34.10/5.39 % (31323)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on E---3.1_30784 for (2350ds/672Mi) 34.27/5.60 % (31323)Instruction limit reached! 34.27/5.60 % (31323)------------------------------ 34.27/5.60 % (31323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 34.27/5.60 % (31323)Termination reason: Unknown 34.27/5.60 % (31323)Termination phase: Saturation 34.27/5.60 34.27/5.60 % (31323)Memory used [KB]: 11129 34.27/5.60 % (31323)Time elapsed: 0.207 s 34.27/5.60 % (31323)Instructions burned: 674 (million) 34.27/5.60 % (31323)------------------------------ 34.27/5.60 % (31323)------------------------------ 34.27/5.61 % (31324)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on E---3.1_30784 for (2348ds/1897Mi) 34.57/5.68 % (31322)Instruction limit reached! 34.57/5.68 % (31322)------------------------------ 34.57/5.68 % (31322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 34.57/5.68 % (31322)Termination reason: Unknown 34.57/5.68 % (31322)Termination phase: Saturation 34.57/5.68 34.57/5.68 % (31322)Memory used [KB]: 17142 34.57/5.68 % (31322)Time elapsed: 0.335 s 34.57/5.68 % (31322)Instructions burned: 1314 (million) 34.57/5.68 % (31322)------------------------------ 34.57/5.68 % (31322)------------------------------ 34.57/5.69 % (31325)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on E---3.1_30784 for (2347ds/1202Mi) 36.91/5.71 % (31321)Instruction limit reached! 36.91/5.71 % (31321)------------------------------ 36.91/5.71 % (31321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 36.91/5.71 % (31321)Termination reason: Unknown 36.91/5.71 % (31321)Termination phase: Saturation 36.91/5.71 36.91/5.71 % (31321)Memory used [KB]: 9850 36.91/5.71 % (31321)Time elapsed: 0.398 s 36.91/5.71 % (31321)Instructions burned: 1323 (million) 36.91/5.71 % (31321)------------------------------ 36.91/5.71 % (31321)------------------------------ 36.91/5.72 % (31326)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on E---3.1_30784 for (2347ds/1493Mi) 38.18/5.96 % (31318)Instruction limit reached! 38.18/5.96 % (31318)------------------------------ 38.18/5.96 % (31318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 38.18/5.96 % (31318)Termination reason: Unknown 38.18/5.96 % (31318)Termination phase: Saturation 38.18/5.96 38.18/5.96 % (31318)Memory used [KB]: 10106 38.18/5.96 % (31318)Time elapsed: 0.726 s 38.18/5.96 % (31318)Instructions burned: 2403 (million) 38.18/5.96 % (31318)------------------------------ 38.18/5.96 % (31318)------------------------------ 38.18/5.97 % (31327)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on E---3.1_30784 for (2344ds/7679Mi) 38.63/6.03 % (31325)Instruction limit reached! 38.63/6.03 % (31325)------------------------------ 38.63/6.03 % (31325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 38.63/6.03 % (31325)Termination reason: Unknown 38.63/6.03 % (31325)Termination phase: Saturation 38.63/6.03 38.63/6.03 % (31325)Memory used [KB]: 9594 38.63/6.03 % (31325)Time elapsed: 0.341 s 38.63/6.03 % (31325)Instructions burned: 1203 (million) 38.63/6.03 % (31325)------------------------------ 38.63/6.03 % (31325)------------------------------ 38.63/6.04 % (31328)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on E---3.1_30784 for (2344ds/340Mi) 39.12/6.09 % (31326)Instruction limit reached! 39.12/6.09 % (31326)------------------------------ 39.12/6.09 % (31326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 39.12/6.09 % (31326)Termination reason: Unknown 39.12/6.09 % (31326)Termination phase: Saturation 39.12/6.09 39.12/6.09 % (31326)Memory used [KB]: 8059 39.12/6.09 % (31326)Time elapsed: 0.375 s 39.12/6.09 % (31326)Instructions burned: 1493 (million) 39.12/6.09 % (31326)------------------------------ 39.12/6.09 % (31326)------------------------------ 39.12/6.10 % (31329)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on E---3.1_30784 for (2343ds/3672Mi) 39.62/6.13 % (31328)Instruction limit reached! 39.62/6.13 % (31328)------------------------------ 39.62/6.13 % (31328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 39.62/6.13 % (31328)Termination reason: Unknown 39.62/6.13 % (31328)Termination phase: Saturation 39.62/6.13 39.62/6.13 % (31328)Memory used [KB]: 11129 39.62/6.13 % (31328)Time elapsed: 0.095 s 39.62/6.13 % (31328)Instructions burned: 340 (million) 39.62/6.13 % (31328)------------------------------ 39.62/6.13 % (31328)------------------------------ 39.62/6.14 % (31330)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on E---3.1_30784 for (2343ds/1535Mi) 39.62/6.21 % (31324)Instruction limit reached! 39.62/6.21 % (31324)------------------------------ 39.62/6.21 % (31324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 39.62/6.21 % (31324)Termination reason: Unknown 39.62/6.21 % (31324)Termination phase: Saturation 39.62/6.21 39.62/6.21 % (31324)Memory used [KB]: 13816 39.62/6.21 % (31324)Time elapsed: 0.600 s 39.62/6.21 % (31324)Instructions burned: 1898 (million) 39.62/6.21 % (31324)------------------------------ 39.62/6.21 % (31324)------------------------------ 39.62/6.22 % (31331)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on E---3.1_30784 for (2342ds/4637Mi) 41.62/6.45 % (31317)Instruction limit reached! 41.62/6.45 % (31317)------------------------------ 41.62/6.45 % (31317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 41.62/6.45 % (31317)Termination reason: Unknown 41.62/6.45 % (31317)Termination phase: Saturation 41.62/6.45 41.62/6.45 % (31317)Memory used [KB]: 7803 41.62/6.45 % (31317)Time elapsed: 1.264 s 41.62/6.45 % (31317)Instructions burned: 5062 (million) 41.62/6.45 % (31317)------------------------------ 41.62/6.45 % (31317)------------------------------ 41.62/6.46 % (31332)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on E---3.1_30784 for (2339ds/3174Mi) 42.23/6.52 % (31330)Instruction limit reached! 42.23/6.52 % (31330)------------------------------ 42.23/6.52 % (31330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 42.23/6.52 % (31330)Termination reason: Unknown 42.23/6.52 % (31330)Termination phase: Saturation 42.23/6.52 42.23/6.52 % (31330)Memory used [KB]: 16247 42.23/6.52 % (31330)Time elapsed: 0.381 s 42.23/6.52 % (31330)Instructions burned: 1537 (million) 42.23/6.52 % (31330)------------------------------ 42.23/6.52 % (31330)------------------------------ 42.23/6.53 % (31333)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on E---3.1_30784 for (2339ds/307Mi) 42.23/6.53 % (31298)Instruction limit reached! 42.23/6.53 % (31298)------------------------------ 42.23/6.53 % (31298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 42.23/6.53 % (31298)Termination reason: Unknown 42.23/6.53 % (31298)Termination phase: Saturation 42.23/6.53 42.23/6.53 % (31298)Memory used [KB]: 14200 42.23/6.53 % (31298)Time elapsed: 2.016 s 42.23/6.53 % (31298)Instructions burned: 6455 (million) 42.23/6.53 % (31298)------------------------------ 42.23/6.53 % (31298)------------------------------ 42.23/6.55 % (31334)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on E---3.1_30784 for (2339ds/3619Mi) 42.60/6.61 % (31333)Instruction limit reached! 42.60/6.61 % (31333)------------------------------ 42.60/6.61 % (31333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 42.60/6.61 % (31333)Termination reason: Unknown 42.60/6.61 % (31333)Termination phase: Saturation 42.60/6.61 42.60/6.61 % (31333)Memory used [KB]: 7547 42.60/6.61 % (31333)Time elapsed: 0.077 s 42.60/6.61 % (31333)Instructions burned: 307 (million) 42.60/6.61 % (31333)------------------------------ 42.60/6.61 % (31333)------------------------------ 42.60/6.62 % (31335)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on E---3.1_30784 for (2338ds/2325Mi) 46.01/7.05 % (31319)Instruction limit reached! 46.01/7.05 % (31319)------------------------------ 46.01/7.05 % (31319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 46.01/7.05 % (31319)Termination reason: Unknown 46.01/7.05 % (31319)Termination phase: Saturation 46.01/7.05 46.01/7.05 % (31319)Memory used [KB]: 13944 46.01/7.05 % (31319)Time elapsed: 1.818 s 46.01/7.05 % (31319)Instructions burned: 5798 (million) 46.01/7.05 % (31319)------------------------------ 46.01/7.05 % (31319)------------------------------ 46.01/7.06 % (31336)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on E---3.1_30784 for (2334ds/2341Mi) 46.84/7.18 % (31335)Refutation not found, non-redundant clauses discarded% (31335)------------------------------ 46.84/7.18 % (31335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 46.84/7.18 % (31335)Termination reason: Refutation not found, non-redundant clauses discarded 46.84/7.18 46.84/7.18 % (31335)Memory used [KB]: 17142 46.84/7.18 % (31335)Time elapsed: 0.556 s 46.84/7.18 % (31335)Instructions burned: 1819 (million) 46.84/7.18 % (31335)------------------------------ 46.84/7.18 % (31335)------------------------------ 46.84/7.19 % (31337)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on E---3.1_30784 for (2332ds/7257Mi) 47.38/7.23 % (31332)Refutation not found, non-redundant clauses discarded% (31332)------------------------------ 47.38/7.23 % (31332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 47.38/7.23 % (31332)Termination reason: Refutation not found, non-redundant clauses discarded 47.38/7.23 47.38/7.23 % (31332)Memory used [KB]: 19317 47.38/7.23 % (31332)Time elapsed: 0.768 s 47.38/7.23 % (31332)Instructions burned: 2511 (million) 47.38/7.23 % (31332)------------------------------ 47.38/7.23 % (31332)------------------------------ 47.38/7.24 % (31338)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on E---3.1_30784 for (2332ds/3710Mi) 47.38/7.24 % (31329)Instruction limit reached! 47.38/7.24 % (31329)------------------------------ 47.38/7.24 % (31329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 47.38/7.24 % (31329)Termination reason: Unknown 47.38/7.24 % (31329)Termination phase: Saturation 47.38/7.24 47.38/7.24 % (31329)Memory used [KB]: 12665 47.38/7.24 % (31329)Time elapsed: 1.140 s 47.38/7.24 % (31329)Instructions burned: 3672 (million) 47.38/7.24 % (31329)------------------------------ 47.38/7.24 % (31329)------------------------------ 47.38/7.25 % (31339)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on E---3.1_30784 for (2332ds/326Mi) 47.68/7.34 % (31339)Instruction limit reached! 47.68/7.34 % (31339)------------------------------ 47.68/7.34 % (31339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 47.68/7.34 % (31339)Termination reason: Unknown 47.68/7.34 % (31339)Termination phase: Saturation 47.68/7.34 47.68/7.34 % (31339)Memory used [KB]: 8571 47.68/7.34 % (31339)Time elapsed: 0.090 s 47.68/7.34 % (31339)Instructions burned: 329 (million) 47.68/7.34 % (31339)------------------------------ 47.68/7.34 % (31339)------------------------------ 47.68/7.35 % (31340)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on E---3.1_30784 for (2331ds/1100Mi) 50.09/7.64 % (31334)Instruction limit reached! 50.09/7.64 % (31334)------------------------------ 50.09/7.64 % (31334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 50.09/7.64 % (31334)Termination reason: Unknown 50.09/7.64 % (31334)Termination phase: Saturation 50.09/7.64 50.09/7.64 % (31334)Memory used [KB]: 18421 50.09/7.64 % (31334)Time elapsed: 1.099 s 50.09/7.64 % (31334)Instructions burned: 3621 (million) 50.09/7.64 % (31334)------------------------------ 50.09/7.64 % (31334)------------------------------ 50.09/7.65 % (31341)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on E---3.1_30784 for (2327ds/406Mi) 50.67/7.66 % (31331)Instruction limit reached! 50.67/7.66 % (31331)------------------------------ 50.67/7.66 % (31331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 50.67/7.66 % (31331)Termination reason: Unknown 50.67/7.66 % (31331)Termination phase: Saturation 50.67/7.66 50.67/7.66 % (31331)Memory used [KB]: 11769 50.67/7.66 % (31331)Time elapsed: 1.449 s 50.67/7.66 % (31331)Instructions burned: 4639 (million) 50.67/7.66 % (31331)------------------------------ 50.67/7.66 % (31331)------------------------------ 50.67/7.67 % (31342)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on E---3.1_30784 for (2327ds/1871Mi) 50.80/7.69 % (31340)Instruction limit reached! 50.80/7.69 % (31340)------------------------------ 50.80/7.69 % (31340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 50.80/7.69 % (31340)Termination reason: Unknown 50.80/7.69 % (31340)Termination phase: Saturation 50.80/7.69 50.80/7.69 % (31340)Memory used [KB]: 15351 50.80/7.69 % (31340)Time elapsed: 0.342 s 50.80/7.69 % (31340)Instructions burned: 1101 (million) 50.80/7.69 % (31340)------------------------------ 50.80/7.69 % (31340)------------------------------ 50.80/7.70 % (31343)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on E---3.1_30784 for (2327ds/1194Mi) 51.04/7.76 % (31341)Instruction limit reached! 51.04/7.76 % (31341)------------------------------ 51.04/7.76 % (31341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 51.04/7.76 % (31341)Termination reason: Unknown 51.04/7.76 % (31341)Termination phase: Saturation 51.04/7.76 51.04/7.76 % (31341)Memory used [KB]: 7675 51.04/7.76 % (31341)Time elapsed: 0.109 s 51.04/7.76 % (31341)Instructions burned: 407 (million) 51.04/7.76 % (31341)------------------------------ 51.04/7.76 % (31341)------------------------------ 51.04/7.77 % (31344)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on E---3.1_30784 for (2326ds/474Mi) 51.04/7.78 % (31336)Instruction limit reached! 51.04/7.78 % (31336)------------------------------ 51.04/7.78 % (31336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 51.04/7.78 % (31336)Termination reason: Unknown 51.04/7.78 % (31336)Termination phase: Saturation 51.04/7.78 51.04/7.78 % (31336)Memory used [KB]: 11257 51.04/7.78 % (31336)Time elapsed: 0.736 s 51.04/7.78 % (31336)Instructions burned: 2342 (million) 51.04/7.78 % (31336)------------------------------ 51.04/7.78 % (31336)------------------------------ 51.04/7.79 % (31345)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on E---3.1_30784 for (2326ds/3115Mi) 51.63/7.89 % (31344)Instruction limit reached! 51.63/7.89 % (31344)------------------------------ 51.63/7.89 % (31344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 51.63/7.89 % (31344)Termination reason: Unknown 51.63/7.89 % (31344)Termination phase: Saturation 51.63/7.89 51.63/7.89 % (31344)Memory used [KB]: 7547 51.63/7.89 % (31344)Time elapsed: 0.118 s 51.63/7.89 % (31344)Instructions burned: 474 (million) 51.63/7.89 % (31344)------------------------------ 51.63/7.89 % (31344)------------------------------ 51.63/7.90 % (31346)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on E---3.1_30784 for (2325ds/831Mi) 53.34/8.08 % (31343)Instruction limit reached! 53.34/8.08 % (31343)------------------------------ 53.34/8.08 % (31343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 53.34/8.08 % (31343)Termination reason: Unknown 53.34/8.08 % (31343)Termination phase: Saturation 53.34/8.08 53.34/8.08 % (31343)Memory used [KB]: 13048 53.34/8.08 % (31343)Time elapsed: 0.376 s 53.34/8.08 % (31343)Instructions burned: 1195 (million) 53.34/8.08 % (31343)------------------------------ 53.34/8.08 % (31343)------------------------------ 53.34/8.09 % (31347)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on E---3.1_30784 for (2323ds/1188Mi) 53.74/8.15 % (31346)Instruction limit reached! 53.74/8.15 % (31346)------------------------------ 53.74/8.15 % (31346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 53.74/8.15 % (31346)Termination reason: Unknown 53.74/8.15 % (31346)Termination phase: Saturation 53.74/8.15 53.74/8.15 % (31346)Memory used [KB]: 10234 53.74/8.15 % (31346)Time elapsed: 0.253 s 53.74/8.15 % (31346)Instructions burned: 832 (million) 53.74/8.15 % (31346)------------------------------ 53.74/8.15 % (31346)------------------------------ 54.12/8.16 % (31348)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on E---3.1_30784 for (2322ds/2868Mi) 54.12/8.19 % (31338)Instruction limit reached! 54.12/8.19 % (31338)------------------------------ 54.12/8.19 % (31338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 54.12/8.19 % (31338)Termination reason: Unknown 54.12/8.19 % (31338)Termination phase: Saturation 54.12/8.19 54.12/8.19 % (31338)Memory used [KB]: 18549 54.12/8.19 % (31338)Time elapsed: 0.980 s 54.12/8.19 % (31338)Instructions burned: 3713 (million) 54.12/8.19 % (31338)------------------------------ 54.12/8.19 % (31338)------------------------------ 54.12/8.21 % (31349)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on E---3.1_30784 for (2322ds/1516Mi) 54.57/8.26 % (31342)Instruction limit reached! 54.57/8.26 % (31342)------------------------------ 54.57/8.26 % (31342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 54.57/8.26 % (31342)Termination reason: Unknown 54.57/8.26 % (31342)Termination phase: Saturation 54.57/8.26 54.57/8.26 % (31342)Memory used [KB]: 20340 54.57/8.26 % (31342)Time elapsed: 0.584 s 54.57/8.26 % (31342)Instructions burned: 1871 (million) 54.57/8.26 % (31342)------------------------------ 54.57/8.26 % (31342)------------------------------ 54.57/8.27 % (31350)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on E---3.1_30784 for (2321ds/2321Mi) 54.57/8.29 % (31327)Instruction limit reached! 54.57/8.29 % (31327)------------------------------ 54.57/8.29 % (31327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 54.57/8.29 % (31327)Termination reason: Unknown 54.57/8.29 % (31327)Termination phase: Saturation 54.57/8.29 54.57/8.29 % (31327)Memory used [KB]: 23666 54.57/8.29 % (31327)Time elapsed: 2.317 s 54.57/8.29 % (31327)Instructions burned: 7680 (million) 54.57/8.29 % (31327)------------------------------ 54.57/8.29 % (31327)------------------------------ 54.70/8.30 % (31351)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on E---3.1_30784 for (2321ds/2812Mi) 56.35/8.48 % (31347)Instruction limit reached! 56.35/8.48 % (31347)------------------------------ 56.35/8.48 % (31347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 56.35/8.48 % (31347)Termination reason: Unknown 56.35/8.48 % (31347)Termination phase: Saturation 56.35/8.48 56.35/8.48 % (31347)Memory used [KB]: 17142 56.35/8.48 % (31347)Time elapsed: 0.373 s 56.35/8.48 % (31347)Instructions burned: 1190 (million) 56.35/8.48 % (31347)------------------------------ 56.35/8.48 % (31347)------------------------------ 56.35/8.49 % (31352)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on E---3.1_30784 for (2319ds/4604Mi) 56.96/8.57 % (31345)Instruction limit reached! 56.96/8.57 % (31345)------------------------------ 56.96/8.57 % (31345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 56.96/8.57 % (31345)Termination reason: Unknown 56.96/8.57 % (31345)Termination phase: Saturation 56.96/8.57 56.96/8.57 % (31345)Memory used [KB]: 17270 56.96/8.57 % (31345)Time elapsed: 0.786 s 56.96/8.57 % (31345)Instructions burned: 3115 (million) 56.96/8.57 % (31345)------------------------------ 56.96/8.57 % (31345)------------------------------ 56.96/8.58 % (31353)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on E---3.1_30784 for (2318ds/2678Mi) 57.32/8.67 % (31349)Instruction limit reached! 57.32/8.67 % (31349)------------------------------ 57.32/8.67 % (31349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 57.32/8.67 % (31349)Termination reason: Unknown 57.32/8.67 % (31349)Termination phase: Saturation 57.32/8.67 57.32/8.67 % (31349)Memory used [KB]: 12537 57.32/8.67 % (31349)Time elapsed: 0.468 s 57.32/8.67 % (31349)Instructions burned: 1517 (million) 57.32/8.67 % (31349)------------------------------ 57.32/8.67 % (31349)------------------------------ 57.32/8.68 % (31354)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on E---3.1_30784 for (2317ds/643Mi) 57.97/8.84 % (31354)Instruction limit reached! 57.97/8.84 % (31354)------------------------------ 57.97/8.84 % (31354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 57.97/8.84 % (31354)Termination reason: Unknown 57.97/8.84 % (31354)Termination phase: Saturation 57.97/8.84 57.97/8.84 % (31354)Memory used [KB]: 7675 57.97/8.84 % (31354)Time elapsed: 0.162 s 57.97/8.84 % (31354)Instructions burned: 646 (million) 57.97/8.84 % (31354)------------------------------ 57.97/8.84 % (31354)------------------------------ 57.97/8.85 % (31355)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on E---3.1_30784 for (2316ds/458Mi) 57.97/8.86 % (31350)Instruction limit reached! 57.97/8.86 % (31350)------------------------------ 57.97/8.86 % (31350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 57.97/8.86 % (31350)Termination reason: Unknown 57.97/8.86 % (31350)Termination phase: Saturation 57.97/8.86 57.97/8.86 % (31350)Memory used [KB]: 16375 57.97/8.86 % (31350)Time elapsed: 0.590 s 57.97/8.86 % (31350)Instructions burned: 2324 (million) 57.97/8.86 % (31350)------------------------------ 57.97/8.86 % (31350)------------------------------ 58.48/8.87 % (31356)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on E---3.1_30784 for (2315ds/2546Mi) 58.48/8.88 % (31348)Instruction limit reached! 58.48/8.88 % (31348)------------------------------ 58.48/8.88 % (31348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 58.48/8.88 % (31348)Termination reason: Unknown 58.48/8.88 % (31348)Termination phase: Saturation 58.48/8.88 58.48/8.88 % (31348)Memory used [KB]: 7675 58.48/8.88 % (31348)Time elapsed: 0.717 s 58.48/8.88 % (31348)Instructions burned: 2869 (million) 58.48/8.88 % (31348)------------------------------ 58.48/8.88 % (31348)------------------------------ 58.48/8.89 % (31357)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on E---3.1_30784 for (2315ds/1432Mi) 58.64/8.97 % (31355)Instruction limit reached! 58.64/8.97 % (31355)------------------------------ 58.64/8.97 % (31355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 58.64/8.97 % (31355)Termination reason: Unknown 58.64/8.97 % (31355)Termination phase: Saturation 58.64/8.97 58.64/8.97 % (31355)Memory used [KB]: 7547 58.64/8.97 % (31355)Time elapsed: 0.114 s 58.64/8.97 % (31355)Instructions burned: 459 (million) 58.64/8.97 % (31355)------------------------------ 58.64/8.97 % (31355)------------------------------ 58.64/8.98 % (31358)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on E---3.1_30784 for (2314ds/386Mi) 58.94/9.07 % (31358)Instruction limit reached! 58.94/9.07 % (31358)------------------------------ 58.94/9.07 % (31358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 58.94/9.07 % (31358)Termination reason: Unknown 58.94/9.07 % (31358)Termination phase: Saturation 58.94/9.07 58.94/9.07 % (31358)Memory used [KB]: 7547 58.94/9.07 % (31358)Time elapsed: 0.097 s 58.94/9.07 % (31358)Instructions burned: 389 (million) 58.94/9.07 % (31358)------------------------------ 58.94/9.07 % (31358)------------------------------ 58.94/9.08 % (31359)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on E---3.1_30784 for (2313ds/360Mi) 60.75/9.16 % (31351)Instruction limit reached! 60.75/9.16 % (31351)------------------------------ 60.75/9.16 % (31351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 60.75/9.16 % (31351)Termination reason: Unknown 60.75/9.16 % (31351)Termination phase: Saturation 60.75/9.16 60.75/9.16 % (31351)Memory used [KB]: 13432 60.75/9.16 % (31351)Time elapsed: 0.864 s 60.75/9.16 % (31351)Instructions burned: 2814 (million) 60.75/9.16 % (31351)------------------------------ 60.75/9.16 % (31351)------------------------------ 61.27/9.17 % (31360)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on E---3.1_30784 for (2312ds/5446Mi) 61.27/9.17 % (31359)Instruction limit reached! 61.27/9.17 % (31359)------------------------------ 61.27/9.17 % (31359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 61.27/9.17 % (31359)Termination reason: Unknown 61.27/9.17 % (31359)Termination phase: Saturation 61.27/9.17 61.27/9.17 % (31359)Memory used [KB]: 7547 61.27/9.17 % (31359)Time elapsed: 0.091 s 61.27/9.17 % (31359)Instructions burned: 362 (million) 61.27/9.17 % (31359)------------------------------ 61.27/9.17 % (31359)------------------------------ 61.33/9.18 % (31361)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on E---3.1_30784 for (2312ds/2573Mi) 61.56/9.23 % (31353)Instruction limit reached! 61.56/9.23 % (31353)------------------------------ 61.56/9.23 % (31353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 61.56/9.23 % (31353)Termination reason: Unknown 61.56/9.23 % (31353)Termination phase: Saturation 61.56/9.23 61.56/9.23 % (31353)Memory used [KB]: 25969 61.56/9.23 % (31353)Time elapsed: 0.654 s 61.56/9.23 % (31353)Instructions burned: 2679 (million) 61.56/9.23 % (31353)------------------------------ 61.56/9.23 % (31353)------------------------------ 61.56/9.24 % (31357)Instruction limit reached! 61.56/9.24 % (31357)------------------------------ 61.56/9.24 % (31357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 61.56/9.24 % (31357)Termination reason: Unknown 61.56/9.24 % (31357)Termination phase: Saturation 61.56/9.24 61.56/9.24 % (31357)Memory used [KB]: 21108 61.56/9.24 % (31357)Time elapsed: 0.348 s 61.56/9.24 % (31357)Instructions burned: 1432 (million) 61.56/9.24 % (31357)------------------------------ 61.56/9.24 % (31357)------------------------------ 61.56/9.25 % (31363)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on E---3.1_30784 for (2312ds/2781Mi) 61.56/9.25 % (31362)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on E---3.1_30784 for (2312ds/2655Mi) 62.09/9.45 % (31337)Instruction limit reached! 62.09/9.45 % (31337)------------------------------ 62.09/9.45 % (31337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 62.09/9.45 % (31337)Termination reason: Unknown 62.09/9.45 % (31337)Termination phase: Saturation 62.09/9.45 62.09/9.45 % (31337)Memory used [KB]: 10362 62.09/9.45 % (31337)Time elapsed: 2.283 s 62.09/9.45 % (31337)Instructions burned: 7258 (million) 62.09/9.45 % (31337)------------------------------ 62.09/9.45 % (31337)------------------------------ 62.09/9.46 % (31364)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on E---3.1_30784 for (2310ds/307Mi) 62.45/9.53 % (31364)Instruction limit reached! 62.45/9.53 % (31364)------------------------------ 62.45/9.53 % (31364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 62.45/9.53 % (31364)Termination reason: Unknown 62.45/9.53 % (31364)Termination phase: Saturation 62.45/9.53 62.45/9.53 % (31364)Memory used [KB]: 7547 62.45/9.53 % (31364)Time elapsed: 0.077 s 62.45/9.53 % (31364)Instructions burned: 308 (million) 62.45/9.53 % (31364)------------------------------ 62.45/9.53 % (31364)------------------------------ 62.45/9.54 % (31365)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on E---3.1_30784 for (2309ds/1548Mi) 62.45/9.62 % (31356)Instruction limit reached! 62.45/9.62 % (31356)------------------------------ 62.45/9.62 % (31356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 62.45/9.62 % (31356)Termination reason: Unknown 62.45/9.62 % (31356)Termination phase: Saturation 62.45/9.62 62.45/9.62 % (31356)Memory used [KB]: 10618 62.45/9.62 % (31356)Time elapsed: 0.752 s 62.45/9.62 % (31356)Instructions burned: 2546 (million) 62.45/9.62 % (31356)------------------------------ 62.45/9.62 % (31356)------------------------------ 62.45/9.63 % (31366)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on E---3.1_30784 for (2308ds/5214Mi) 65.43/9.85 % (31361)Instruction limit reached! 65.43/9.85 % (31361)------------------------------ 65.43/9.85 % (31361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 65.43/9.85 % (31361)Termination reason: Unknown 65.43/9.85 % (31361)Termination phase: Saturation 65.43/9.85 65.43/9.85 % (31361)Memory used [KB]: 18677 65.43/9.85 % (31361)Time elapsed: 0.688 s 65.43/9.85 % (31361)Instructions burned: 2574 (million) 65.43/9.85 % (31361)------------------------------ 65.43/9.85 % (31361)------------------------------ 65.43/9.86 % (31367)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on E---3.1_30784 for (2305ds/3201Mi) 66.16/9.94 % (31362)Instruction limit reached! 66.16/9.94 % (31362)------------------------------ 66.16/9.94 % (31362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 66.16/9.94 % (31362)Termination reason: Unknown 66.16/9.94 % (31362)Termination phase: Saturation 66.16/9.94 66.16/9.94 % (31362)Memory used [KB]: 6140 66.16/9.94 % (31362)Time elapsed: 0.711 s 66.16/9.94 % (31362)Instructions burned: 2655 (million) 66.16/9.94 % (31362)------------------------------ 66.16/9.94 % (31362)------------------------------ 66.16/9.95 % (31368)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on E---3.1_30784 for (2305ds/454Mi) 66.16/9.98 % (31352)Instruction limit reached! 66.16/9.98 % (31352)------------------------------ 66.16/9.98 % (31352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 66.16/9.98 % (31352)Termination reason: Unknown 66.16/9.98 % (31352)Termination phase: Saturation 66.16/9.98 66.16/9.98 % (31352)Memory used [KB]: 14200 66.16/9.98 % (31352)Time elapsed: 1.493 s 66.16/9.98 % (31352)Instructions burned: 4605 (million) 66.16/9.98 % (31352)------------------------------ 66.16/9.98 % (31352)------------------------------ 66.16/9.99 % (31369)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on E---3.1_30784 for (2304ds/3049Mi) 66.55/10.03 % (31365)Instruction limit reached! 66.55/10.03 % (31365)------------------------------ 66.55/10.03 % (31365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 66.55/10.03 % (31365)Termination reason: Unknown 66.55/10.03 % (31365)Termination phase: Saturation 66.55/10.03 66.55/10.03 % (31365)Memory used [KB]: 10618 66.55/10.03 % (31365)Time elapsed: 0.510 s 66.55/10.03 % (31365)Instructions burned: 1550 (million) 66.55/10.03 % (31365)------------------------------ 66.55/10.03 % (31365)------------------------------ 66.55/10.04 % (31370)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on E---3.1_30784 for (2304ds/7311Mi) 66.55/10.06 % (31368)Instruction limit reached! 66.55/10.06 % (31368)------------------------------ 66.55/10.06 % (31368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 66.55/10.06 % (31368)Termination reason: Unknown 66.55/10.06 % (31368)Termination phase: Saturation 66.55/10.06 66.55/10.06 % (31368)Memory used [KB]: 12025 66.55/10.06 % (31368)Time elapsed: 0.115 s 66.55/10.06 % (31368)Instructions burned: 456 (million) 66.55/10.06 % (31368)------------------------------ 66.55/10.06 % (31368)------------------------------ 66.55/10.07 % (31371)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on E---3.1_30784 for (2303ds/6804Mi) 66.86/10.10 % (31363)Instruction limit reached! 66.86/10.10 % (31363)------------------------------ 66.86/10.10 % (31363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 66.86/10.10 % (31363)Termination reason: Unknown 66.86/10.10 % (31363)Termination phase: Saturation 66.86/10.10 66.86/10.10 % (31363)Memory used [KB]: 9338 66.86/10.10 % (31363)Time elapsed: 0.875 s 66.86/10.10 % (31363)Instructions burned: 2781 (million) 66.86/10.10 % (31363)------------------------------ 66.86/10.10 % (31363)------------------------------ 66.86/10.11 % (31372)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on E---3.1_30784 for (2303ds/1683Mi) 70.83/10.58 % (31372)Instruction limit reached! 70.83/10.58 % (31372)------------------------------ 70.83/10.58 % (31372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 70.83/10.58 % (31372)Termination reason: Unknown 70.83/10.58 % (31372)Termination phase: Saturation 70.83/10.58 70.83/10.58 % (31372)Memory used [KB]: 20596 70.83/10.58 % (31372)Time elapsed: 0.473 s 70.83/10.58 % (31372)Instructions burned: 1686 (million) 70.83/10.58 % (31372)------------------------------ 70.83/10.58 % (31372)------------------------------ 70.83/10.59 % (31373)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on E---3.1_30784 for (2298ds/4688Mi) 72.87/10.84 % (31367)Instruction limit reached! 72.87/10.84 % (31367)------------------------------ 72.87/10.84 % (31367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 72.87/10.84 % (31367)Termination reason: Unknown 72.87/10.84 % (31367)Termination phase: Saturation 72.87/10.84 72.87/10.84 % (31367)Memory used [KB]: 12537 72.87/10.84 % (31367)Time elapsed: 0.978 s 72.87/10.84 % (31367)Instructions burned: 3202 (million) 72.87/10.84 % (31367)------------------------------ 72.87/10.84 % (31367)------------------------------ 73.03/10.85 % (31374)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on E---3.1_30784 for (2296ds/2207Mi) 73.03/10.90 % (31360)Instruction limit reached! 73.03/10.90 % (31360)------------------------------ 73.03/10.90 % (31360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 73.03/10.90 % (31360)Termination reason: Unknown 73.03/10.90 % (31360)Termination phase: Saturation 73.03/10.90 73.03/10.90 % (31360)Memory used [KB]: 16758 73.03/10.90 % (31360)Time elapsed: 1.751 s 73.03/10.90 % (31360)Instructions burned: 5447 (million) 73.03/10.90 % (31360)------------------------------ 73.03/10.90 % (31360)------------------------------ 73.03/10.91 % (31375)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on E---3.1_30784 for (2295ds/8216Mi) 73.47/10.93 % (31369)Instruction limit reached! 73.47/10.93 % (31369)------------------------------ 73.47/10.93 % (31369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 73.47/10.93 % (31369)Termination reason: Unknown 73.47/10.93 % (31369)Termination phase: Saturation 73.47/10.93 73.47/10.93 % (31369)Memory used [KB]: 11129 73.47/10.93 % (31369)Time elapsed: 0.937 s 73.47/10.93 % (31369)Instructions burned: 3049 (million) 73.47/10.93 % (31369)------------------------------ 73.47/10.93 % (31369)------------------------------ 73.47/10.94 % (31376)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on E---3.1_30784 for (2295ds/430Mi) 73.99/11.05 % (31376)Instruction limit reached! 73.99/11.05 % (31376)------------------------------ 73.99/11.05 % (31376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 73.99/11.05 % (31376)Termination reason: Unknown 73.99/11.05 % (31376)Termination phase: Saturation 73.99/11.05 73.99/11.05 % (31376)Memory used [KB]: 7547 73.99/11.05 % (31376)Time elapsed: 0.111 s 73.99/11.05 % (31376)Instructions burned: 431 (million) 73.99/11.05 % (31376)------------------------------ 73.99/11.05 % (31376)------------------------------ 73.99/11.06 % (31377)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on E---3.1_30784 for (2293ds/2012Mi) 74.82/11.23 % (31366)Instruction limit reached! 74.82/11.23 % (31366)------------------------------ 74.82/11.23 % (31366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 74.82/11.23 % (31366)Termination reason: Unknown 74.82/11.23 % (31366)Termination phase: Saturation 74.82/11.23 74.82/11.23 % (31366)Memory used [KB]: 11641 74.82/11.23 % (31366)Time elapsed: 1.606 s 74.82/11.23 % (31366)Instructions burned: 5214 (million) 74.82/11.23 % (31366)------------------------------ 74.82/11.23 % (31366)------------------------------ 74.82/11.24 % (31378)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on E---3.1_30784 for (2292ds/631Mi) 76.85/11.43 % (31378)Instruction limit reached! 76.85/11.43 % (31378)------------------------------ 76.85/11.43 % (31378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 76.85/11.43 % (31378)Termination reason: Unknown 76.85/11.43 % (31378)Termination phase: Saturation 76.85/11.43 76.85/11.43 % (31378)Memory used [KB]: 8443 76.85/11.43 % (31378)Time elapsed: 0.184 s 76.85/11.43 % (31378)Instructions burned: 634 (million) 76.85/11.43 % (31378)------------------------------ 76.85/11.43 % (31378)------------------------------ 76.85/11.44 % (31379)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on E---3.1_30784 for (2290ds/8785Mi) 77.59/11.52 % (31374)Instruction limit reached! 77.59/11.52 % (31374)------------------------------ 77.59/11.52 % (31374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 77.59/11.52 % (31374)Termination reason: Unknown 77.59/11.52 % (31374)Termination phase: Saturation 77.59/11.52 77.59/11.52 % (31374)Memory used [KB]: 11513 77.59/11.52 % (31374)Time elapsed: 0.680 s 77.59/11.52 % (31374)Instructions burned: 2207 (million) 77.59/11.52 % (31374)------------------------------ 77.59/11.52 % (31374)------------------------------ 77.59/11.54 % (31380)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on E---3.1_30784 for (2289ds/739Mi) 77.87/11.56 % (31377)Instruction limit reached! 77.87/11.56 % (31377)------------------------------ 77.87/11.56 % (31377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 77.87/11.56 % (31377)Termination reason: Unknown 77.87/11.56 % (31377)Termination phase: Saturation 77.87/11.56 77.87/11.56 % (31377)Memory used [KB]: 12153 77.87/11.56 % (31377)Time elapsed: 0.509 s 77.87/11.56 % (31377)Instructions burned: 2013 (million) 77.87/11.56 % (31377)------------------------------ 77.87/11.56 % (31377)------------------------------ 77.87/11.57 % (31381)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on E---3.1_30784 for (2288ds/5473Mi) 78.67/11.76 % (31380)Instruction limit reached! 78.67/11.76 % (31380)------------------------------ 78.67/11.76 % (31380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 78.67/11.76 % (31380)Termination reason: Unknown 78.67/11.76 % (31380)Termination phase: Saturation 78.67/11.76 78.67/11.76 % (31380)Memory used [KB]: 13816 78.67/11.76 % (31380)Time elapsed: 0.229 s 78.67/11.76 % (31380)Instructions burned: 740 (million) 78.67/11.76 % (31380)------------------------------ 78.67/11.76 % (31380)------------------------------ 78.67/11.77 % (31382)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on E---3.1_30784 for (2286ds/43570Mi) 80.91/11.99 % (31373)Instruction limit reached! 80.91/11.99 % (31373)------------------------------ 80.91/11.99 % (31373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 80.91/11.99 % (31373)Termination reason: Unknown 80.91/11.99 % (31373)Termination phase: Saturation 80.91/11.99 80.91/11.99 % (31373)Memory used [KB]: 14583 80.91/11.99 % (31373)Time elapsed: 1.400 s 80.91/11.99 % (31373)Instructions burned: 4689 (million) 80.91/11.99 % (31373)------------------------------ 80.91/11.99 % (31373)------------------------------ 80.91/12.00 % (31383)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on E---3.1_30784 for (2284ds/8382Mi) 82.28/12.20 % (31371)Instruction limit reached! 82.28/12.20 % (31371)------------------------------ 82.28/12.20 % (31371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 82.28/12.20 % (31371)Termination reason: Unknown 82.28/12.20 % (31371)Termination phase: Saturation 82.28/12.20 82.28/12.20 % (31371)Memory used [KB]: 19573 82.28/12.20 % (31371)Time elapsed: 2.134 s 82.28/12.20 % (31371)Instructions burned: 6804 (million) 82.28/12.20 % (31371)------------------------------ 82.28/12.20 % (31371)------------------------------ 82.28/12.21 % (31384)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on E---3.1_30784 for (2282ds/407Mi) 82.90/12.32 % (31384)Instruction limit reached! 82.90/12.32 % (31384)------------------------------ 82.90/12.32 % (31384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 82.90/12.32 % (31384)Termination reason: Unknown 82.90/12.32 % (31384)Termination phase: Saturation 82.90/12.32 82.90/12.32 % (31384)Memory used [KB]: 9722 82.90/12.32 % (31384)Time elapsed: 0.111 s 82.90/12.32 % (31384)Instructions burned: 407 (million) 82.90/12.32 % (31384)------------------------------ 82.90/12.32 % (31384)------------------------------ 82.90/12.33 % (31385)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on E---3.1_30784 for (2281ds/2971Mi) 83.19/12.37 % (31370)Instruction limit reached! 83.19/12.37 % (31370)------------------------------ 83.19/12.37 % (31370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 83.19/12.37 % (31370)Termination reason: Unknown 83.19/12.37 % (31370)Termination phase: Saturation 83.19/12.37 83.19/12.37 % (31370)Memory used [KB]: 21492 83.19/12.37 % (31370)Time elapsed: 2.337 s 83.19/12.37 % (31370)Instructions burned: 7311 (million) 83.19/12.37 % (31370)------------------------------ 83.19/12.37 % (31370)------------------------------ 83.19/12.39 % (31387)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on E---3.1_30784 for (2280ds/9822Mi) 87.33/12.89 % (31375)Instruction limit reached! 87.33/12.89 % (31375)------------------------------ 87.33/12.89 % (31375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 87.33/12.89 % (31375)Termination reason: Unknown 87.33/12.89 % (31375)Termination phase: Saturation 87.33/12.89 87.33/12.89 % (31375)Memory used [KB]: 7931 87.33/12.89 % (31375)Time elapsed: 1.977 s 87.33/12.89 % (31375)Instructions burned: 8218 (million) 87.33/12.89 % (31375)------------------------------ 87.33/12.89 % (31375)------------------------------ 87.33/12.90 % (31388)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on E---3.1_30784 for (2275ds/8425Mi) 88.39/13.07 % (31385)Instruction limit reached! 88.39/13.07 % (31385)------------------------------ 88.39/13.07 % (31385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 88.39/13.07 % (31385)Termination reason: Unknown 88.39/13.07 % (31385)Termination phase: Saturation 88.39/13.07 88.39/13.07 % (31385)Memory used [KB]: 7675 88.39/13.07 % (31385)Time elapsed: 0.739 s 88.39/13.07 % (31385)Instructions burned: 2973 (million) 88.39/13.07 % (31385)------------------------------ 88.39/13.07 % (31385)------------------------------ 88.39/13.08 % (31389)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on E---3.1_30784 for (2273ds/3107Mi) 89.36/13.26 % (31381)Instruction limit reached! 89.36/13.26 % (31381)------------------------------ 89.36/13.26 % (31381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 89.36/13.26 % (31381)Termination reason: Unknown 89.36/13.26 % (31381)Termination phase: Saturation 89.36/13.26 89.36/13.26 % (31381)Memory used [KB]: 13944 89.36/13.26 % (31381)Time elapsed: 1.684 s 89.36/13.26 % (31381)Instructions burned: 5475 (million) 89.36/13.26 % (31381)------------------------------ 89.36/13.26 % (31381)------------------------------ 89.36/13.27 % (31390)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on E---3.1_30784 for (2271ds/7967Mi) 95.33/14.04 % (31389)Instruction limit reached! 95.33/14.04 % (31389)------------------------------ 95.33/14.04 % (31389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 95.33/14.04 % (31389)Termination reason: Unknown 95.33/14.04 % (31389)Termination phase: Saturation 95.33/14.04 95.33/14.04 % (31389)Memory used [KB]: 20596 95.33/14.04 % (31389)Time elapsed: 0.964 s 95.33/14.04 % (31389)Instructions burned: 3109 (million) 95.33/14.04 % (31389)------------------------------ 95.33/14.04 % (31389)------------------------------ 95.33/14.06 % (31391)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on E---3.1_30784 for (2263ds/3629Mi) 96.53/14.20 % (31379)Instruction limit reached! 96.53/14.20 % (31379)------------------------------ 96.53/14.20 % (31379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 96.53/14.20 % (31379)Termination reason: Unknown 96.53/14.20 % (31379)Termination phase: Saturation 96.53/14.20 96.53/14.20 % (31379)Memory used [KB]: 21364 96.53/14.20 % (31379)Time elapsed: 2.761 s 96.53/14.20 % (31379)Instructions burned: 8787 (million) 96.53/14.20 % (31379)------------------------------ 96.53/14.20 % (31379)------------------------------ 96.53/14.21 % (31410)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on E---3.1_30784 for (2262ds/939Mi) 96.88/14.28 % (31383)Instruction limit reached! 96.88/14.28 % (31383)------------------------------ 96.88/14.28 % (31383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 96.88/14.28 % (31383)Termination reason: Unknown 96.88/14.28 % (31383)Termination phase: Saturation 96.88/14.28 96.88/14.28 % (31383)Memory used [KB]: 14583 96.88/14.28 % (31383)Time elapsed: 2.282 s 96.88/14.28 % (31383)Instructions burned: 8384 (million) 96.88/14.28 % (31383)------------------------------ 96.88/14.28 % (31383)------------------------------ 96.88/14.30 % (31441)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on E---3.1_30784 for (2261ds/1188Mi) 98.07/14.49 % (31410)Instruction limit reached! 98.07/14.49 % (31410)------------------------------ 98.07/14.49 % (31410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 98.07/14.49 % (31410)Termination reason: Unknown 98.07/14.49 % (31410)Termination phase: Saturation 98.07/14.49 98.07/14.49 % (31410)Memory used [KB]: 10234 98.07/14.49 % (31410)Time elapsed: 0.282 s 98.07/14.49 % (31410)Instructions burned: 939 (million) 98.07/14.49 % (31410)------------------------------ 98.07/14.49 % (31410)------------------------------ 98.07/14.50 % (31527)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on E---3.1_30784 for (2259ds/3205Mi) 98.73/14.60 % (31441)Instruction limit reached! 98.73/14.60 % (31441)------------------------------ 98.73/14.60 % (31441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 98.73/14.60 % (31441)Termination reason: Unknown 98.73/14.60 % (31441)Termination phase: Saturation 98.73/14.60 98.73/14.60 % (31441)Memory used [KB]: 18293 98.73/14.60 % (31441)Time elapsed: 0.303 s 98.73/14.60 % (31441)Instructions burned: 1189 (million) 98.73/14.60 % (31441)------------------------------ 98.73/14.60 % (31441)------------------------------ 98.73/14.61 % (31555)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on E---3.1_30784 for (2258ds/865Mi) 101.10/14.84 % (31555)Instruction limit reached! 101.10/14.84 % (31555)------------------------------ 101.10/14.84 % (31555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 101.10/14.84 % (31555)Termination reason: Unknown 101.10/14.84 % (31555)Termination phase: Saturation 101.10/14.84 101.10/14.84 % (31555)Memory used [KB]: 7803 101.10/14.84 % (31555)Time elapsed: 0.235 s 101.10/14.84 % (31555)Instructions burned: 867 (million) 101.10/14.84 % (31555)------------------------------ 101.10/14.84 % (31555)------------------------------ 101.16/14.85 % (31647)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on E---3.1_30784 for (2256ds/7469Mi) 101.79/14.96 % (31391)Instruction limit reached! 101.79/14.96 % (31391)------------------------------ 101.79/14.96 % (31391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 101.79/14.96 % (31391)Termination reason: Unknown 101.79/14.96 % (31391)Termination phase: Saturation 101.79/14.96 101.79/14.96 % (31391)Memory used [KB]: 7803 101.79/14.96 % (31391)Time elapsed: 0.902 s 101.79/14.96 % (31391)Instructions burned: 3633 (million) 101.79/14.96 % (31391)------------------------------ 101.79/14.96 % (31391)------------------------------ 101.79/14.97 % (31713)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on E---3.1_30784 for (2254ds/4165Mi) 104.16/15.29 % (31390)Instruction limit reached! 104.16/15.29 % (31390)------------------------------ 104.16/15.29 % (31390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 104.16/15.29 % (31390)Termination reason: Unknown 104.16/15.29 % (31390)Termination phase: Saturation 104.16/15.29 104.16/15.29 % (31390)Memory used [KB]: 16630 104.16/15.29 % (31390)Time elapsed: 2.024 s 104.16/15.29 % (31390)Instructions burned: 7967 (million) 104.16/15.29 % (31390)------------------------------ 104.16/15.29 % (31390)------------------------------ 104.16/15.30 % (31781)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on E---3.1_30784 for (2251ds/13468Mi) 104.76/15.41 % (31387)Instruction limit reached! 104.76/15.41 % (31387)------------------------------ 104.76/15.41 % (31387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 104.76/15.41 % (31387)Termination reason: Unknown 104.76/15.41 % (31387)Termination phase: Saturation 104.76/15.41 104.76/15.41 % (31387)Memory used [KB]: 29679 104.76/15.41 % (31387)Time elapsed: 3.027 s 104.76/15.41 % (31387)Instructions burned: 9824 (million) 104.76/15.41 % (31387)------------------------------ 104.76/15.41 % (31387)------------------------------ 105.03/15.42 % (31782)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on E---3.1_30784 for (2250ds/2635Mi) 105.17/15.47 % (31388)Instruction limit reached! 105.17/15.47 % (31388)------------------------------ 105.17/15.47 % (31388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 105.17/15.47 % (31388)Termination reason: Unknown 105.17/15.47 % (31388)Termination phase: Saturation 105.17/15.47 105.17/15.47 % (31388)Memory used [KB]: 12281 105.17/15.47 % (31388)Time elapsed: 2.571 s 105.17/15.47 % (31388)Instructions burned: 8425 (million) 105.17/15.47 % (31388)------------------------------ 105.17/15.47 % (31388)------------------------------ 105.17/15.48 % (31783)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=631:si=on:rtra=on_0 on E---3.1_30784 for (2249ds/631Mi) 105.17/15.51 % (31527)Instruction limit reached! 105.17/15.51 % (31527)------------------------------ 105.17/15.51 % (31527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 105.17/15.51 % (31527)Termination reason: Unknown 105.17/15.51 % (31527)Termination phase: Saturation 105.17/15.51 105.17/15.51 % (31527)Memory used [KB]: 16119 105.17/15.51 % (31527)Time elapsed: 1.014 s 105.17/15.51 % (31527)Instructions burned: 3207 (million) 105.17/15.51 % (31527)------------------------------ 105.17/15.51 % (31527)------------------------------ 105.52/15.52 % (31784)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=15557:si=on:rtra=on_0 on E---3.1_30784 for (2249ds/15557Mi) 105.67/15.63 % (31783)Instruction limit reached! 105.67/15.63 % (31783)------------------------------ 105.67/15.63 % (31783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 105.67/15.63 % (31783)Termination reason: Unknown 105.67/15.63 % (31783)Termination phase: Saturation 105.67/15.63 105.67/15.63 % (31783)Memory used [KB]: 7675 105.67/15.63 % (31783)Time elapsed: 0.157 s 105.67/15.63 % (31783)Instructions burned: 632 (million) 105.67/15.63 % (31783)------------------------------ 105.67/15.63 % (31783)------------------------------ 105.67/15.64 % (31785)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on E---3.1_30784 for (2248ds/2142Mi) 110.44/16.23 % (31782)Instruction limit reached! 110.44/16.23 % (31782)------------------------------ 110.44/16.23 % (31782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 110.44/16.23 % (31782)Termination reason: Unknown 110.44/16.23 % (31782)Termination phase: Saturation 110.44/16.23 110.44/16.23 % (31782)Memory used [KB]: 12537 110.44/16.23 % (31782)Time elapsed: 0.826 s 110.44/16.23 % (31782)Instructions burned: 2636 (million) 110.44/16.23 % (31782)------------------------------ 110.44/16.23 % (31782)------------------------------ 110.44/16.24 % (31786)dis+1002_1:1_aac=none:au=on:bd=off:cnfonf=conj_eager:nwc=5.0:sgt=5:sp=reverse_arity:ss=axioms:i=5624:si=on:rtra=on_0 on E---3.1_30784 for (2242ds/5624Mi) 110.44/16.26 % (31713)Instruction limit reached! 110.44/16.26 % (31713)------------------------------ 110.44/16.26 % (31713)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 110.44/16.26 % (31713)Termination reason: Unknown 110.44/16.26 % (31713)Termination phase: Saturation 110.44/16.26 110.44/16.26 % (31713)Memory used [KB]: 24434 110.44/16.26 % (31713)Time elapsed: 1.316 s 110.44/16.26 % (31713)Instructions burned: 4167 (million) 110.44/16.26 % (31713)------------------------------ 110.44/16.26 % (31713)------------------------------ 111.06/16.27 % (31787)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=1665:si=on:rtra=on_0 on E---3.1_30784 for (2241ds/1665Mi) 111.06/16.29 % (31785)Instruction limit reached! 111.06/16.29 % (31785)------------------------------ 111.06/16.29 % (31785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 111.06/16.29 % (31785)Termination reason: Unknown 111.06/16.29 % (31785)Termination phase: Saturation 111.06/16.29 111.06/16.29 % (31785)Memory used [KB]: 11129 111.06/16.29 % (31785)Time elapsed: 0.644 s 111.06/16.29 % (31785)Instructions burned: 2143 (million) 111.06/16.29 % (31785)------------------------------ 111.06/16.29 % (31785)------------------------------ 111.18/16.30 % (31788)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=64912:si=on:rtra=on_0 on E---3.1_30784 for (2241ds/64912Mi) 113.48/16.69 % (31787)Instruction limit reached! 113.48/16.69 % (31787)------------------------------ 113.48/16.69 % (31787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 113.48/16.69 % (31787)Termination reason: Unknown 113.48/16.69 % (31787)Termination phase: Saturation 113.48/16.69 113.48/16.69 % (31787)Memory used [KB]: 16502 113.48/16.69 % (31787)Time elapsed: 0.421 s 113.48/16.69 % (31787)Instructions burned: 1667 (million) 113.48/16.69 % (31787)------------------------------ 113.48/16.69 % (31787)------------------------------ 113.48/16.70 % (31789)lrs+10_1:32_atotf=0.1:avsq=on:bsr=on:cnfonf=lazy_gen:fde=unused:i=7801:si=on:rtra=on_0 on E---3.1_30784 for (2237ds/7801Mi) 114.68/16.86 % (31647)Instruction limit reached! 114.68/16.86 % (31647)------------------------------ 114.68/16.86 % (31647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 114.68/16.86 % (31647)Termination reason: Unknown 114.68/16.86 % (31647)Termination phase: Saturation 114.68/16.86 114.68/16.86 % (31647)Memory used [KB]: 13048 114.68/16.86 % (31647)Time elapsed: 2.028 s 114.68/16.86 % (31647)Instructions burned: 7472 (million) 114.68/16.86 % (31647)------------------------------ 114.68/16.86 % (31647)------------------------------ 114.68/16.87 % (31790)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15194:si=on:rtra=on_0 on E---3.1_30784 for (2235ds/15194Mi) 122.78/17.93 % (31786)Instruction limit reached! 122.78/17.93 % (31786)------------------------------ 122.78/17.93 % (31786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 122.78/17.93 % (31786)Termination reason: Unknown 122.78/17.93 % (31786)Termination phase: Saturation 122.78/17.93 122.78/17.93 % (31786)Memory used [KB]: 14456 122.78/17.93 % (31786)Time elapsed: 1.700 s 122.78/17.93 % (31786)Instructions burned: 5625 (million) 122.78/17.93 % (31786)------------------------------ 122.78/17.93 % (31786)------------------------------ 122.78/17.95 % (31791)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=6753:si=on:rtra=on_0 on E---3.1_30784 for (2225ds/6753Mi) 126.42/18.49 % (31781)Instruction limit reached! 126.42/18.49 % (31781)------------------------------ 126.42/18.49 % (31781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 126.42/18.49 % (31781)Termination reason: Unknown 126.42/18.49 % (31781)Termination phase: Saturation 126.42/18.49 126.42/18.49 % (31781)Memory used [KB]: 10106 126.42/18.49 % (31781)Time elapsed: 3.209 s 126.42/18.49 % (31781)Instructions burned: 13469 (million) 126.42/18.49 % (31781)------------------------------ 126.42/18.49 % (31781)------------------------------ 126.42/18.50 % (31792)lrs+1002_1:28_bd=off:cnfonf=lazy_simp:plsq=on:plsqr=1,1:prag=on:i=1003:si=on:rtra=on_0 on E---3.1_30784 for (2219ds/1003Mi) 127.86/18.75 % (31792)Instruction limit reached! 127.86/18.75 % (31792)------------------------------ 127.86/18.75 % (31792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 127.86/18.75 % (31792)Termination reason: Unknown 127.86/18.75 % (31792)Termination phase: Saturation 127.86/18.75 127.86/18.75 % (31792)Memory used [KB]: 7675 127.86/18.75 % (31792)Time elapsed: 0.255 s 127.86/18.75 % (31792)Instructions burned: 1004 (million) 127.86/18.75 % (31792)------------------------------ 127.86/18.75 % (31792)------------------------------ 127.86/18.76 % (31793)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=13018:si=on:rtra=on_0 on E---3.1_30784 for (2216ds/13018Mi) 129.67/18.96 % (31789)Instruction limit reached! 129.67/18.96 % (31789)------------------------------ 129.67/18.96 % (31789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 129.67/18.96 % (31789)Termination reason: Unknown 129.67/18.96 % (31789)Termination phase: Saturation 129.67/18.96 129.67/18.96 % (31789)Memory used [KB]: 13560 129.67/18.96 % (31789)Time elapsed: 2.256 s 129.67/18.96 % (31789)Instructions burned: 7801 (million) 129.67/18.96 % (31789)------------------------------ 129.67/18.96 % (31789)------------------------------ 129.67/18.97 % (31794)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1267:si=on:rtra=on_0 on E---3.1_30784 for (2214ds/1267Mi) 131.52/19.27 % (31784)Instruction limit reached! 131.52/19.27 % (31784)------------------------------ 131.52/19.27 % (31784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 131.52/19.27 % (31784)Termination reason: Unknown 131.52/19.27 % (31784)Termination phase: Saturation 131.52/19.27 131.52/19.27 % (31784)Memory used [KB]: 17654 131.52/19.27 % (31784)Time elapsed: 3.752 s 131.52/19.27 % (31784)Instructions burned: 15559 (million) 131.52/19.27 % (31784)------------------------------ 131.52/19.27 % (31784)------------------------------ 131.52/19.29 % (31795)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=2570:si=on:rtra=on_0 on E---3.1_30784 for (2211ds/2570Mi) 132.27/19.36 % (31794)Instruction limit reached! 132.27/19.36 % (31794)------------------------------ 132.27/19.36 % (31794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 132.27/19.36 % (31794)Termination reason: Unknown 132.27/19.36 % (31794)Termination phase: Saturation 132.27/19.36 132.27/19.36 % (31794)Memory used [KB]: 12153 132.27/19.36 % (31794)Time elapsed: 0.391 s 132.27/19.36 % (31794)Instructions burned: 1268 (million) 132.27/19.36 % (31794)------------------------------ 132.27/19.36 % (31794)------------------------------ 132.83/19.37 % (31796)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=13163:si=on:rtra=on_0 on E---3.1_30784 for (2210ds/13163Mi) 136.49/19.91 % (31795)Instruction limit reached! 136.49/19.91 % (31795)------------------------------ 136.49/19.91 % (31795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 136.49/19.91 % (31795)Termination reason: Unknown 136.49/19.91 % (31795)Termination phase: Saturation 136.49/19.91 136.49/19.91 % (31795)Memory used [KB]: 25713 136.49/19.91 % (31795)Time elapsed: 0.629 s 136.49/19.91 % (31795)Instructions burned: 2571 (million) 136.49/19.91 % (31795)------------------------------ 136.49/19.91 % (31795)------------------------------ 136.49/19.93 % (31797)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=5087:si=on:rtra=on_0 on E---3.1_30784 for (2205ds/5087Mi) 137.24/20.05 % (31791)Instruction limit reached! 137.24/20.05 % (31791)------------------------------ 137.24/20.05 % (31791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 137.24/20.05 % (31791)Termination reason: Unknown 137.24/20.05 % (31791)Termination phase: Saturation 137.24/20.05 137.24/20.05 % (31791)Memory used [KB]: 21748 137.24/20.05 % (31791)Time elapsed: 2.108 s 137.24/20.05 % (31791)Instructions burned: 6754 (million) 137.24/20.05 % (31791)------------------------------ 137.24/20.05 % (31791)------------------------------ 137.24/20.06 % (31798)lrs+1002_1:1_aac=none:au=on:bd=off:cnfonf=lazy_pi_sigma_gen:s2a=on:sac=on:sd=1:sgt=20:ss=axioms:i=10380:si=on:rtra=on_0 on E---3.1_30784 for (2203ds/10380Mi) 146.61/21.37 % (31790)Instruction limit reached! 146.61/21.37 % (31790)------------------------------ 146.61/21.37 % (31790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 146.61/21.37 % (31790)Termination reason: Unknown 146.61/21.37 % (31790)Termination phase: Saturation 146.61/21.37 146.61/21.37 % (31790)Memory used [KB]: 20980 146.61/21.37 % (31790)Time elapsed: 4.500 s 146.61/21.37 % (31790)Instructions burned: 15195 (million) 146.61/21.37 % (31790)------------------------------ 146.61/21.37 % (31790)------------------------------ 146.61/21.38 % (31799)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4218:si=on:rtra=on_0 on E---3.1_30784 for (2190ds/4218Mi) 147.45/21.50 % (31797)Instruction limit reached! 147.45/21.50 % (31797)------------------------------ 147.45/21.50 % (31797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 147.45/21.50 % (31797)Termination reason: Unknown 147.45/21.50 % (31797)Termination phase: Saturation 147.45/21.50 147.45/21.50 % (31797)Memory used [KB]: 12665 147.45/21.50 % (31797)Time elapsed: 1.577 s 147.45/21.50 % (31797)Instructions burned: 5087 (million) 147.45/21.50 % (31797)------------------------------ 147.45/21.50 % (31797)------------------------------ 147.45/21.51 % (31800)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on E---3.1_30784 for (2189ds/3971Mi) 155.63/22.62 % (31798)Instruction limit reached! 155.63/22.62 % (31798)------------------------------ 155.63/22.62 % (31798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 155.63/22.62 % (31798)Termination reason: Unknown 155.63/22.62 % (31798)Termination phase: Saturation 155.63/22.62 155.63/22.62 % (31798)Memory used [KB]: 7803 155.63/22.62 % (31798)Time elapsed: 2.561 s 155.63/22.62 % (31798)Instructions burned: 10381 (million) 155.63/22.62 % (31798)------------------------------ 155.63/22.62 % (31798)------------------------------ 155.63/22.63 % (31801)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on E---3.1_30784 for (2178ds/14014Mi) 155.63/22.66 % (31799)Instruction limit reached! 155.63/22.66 % (31799)------------------------------ 155.63/22.66 % (31799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 155.63/22.66 % (31799)Termination reason: Unknown 155.63/22.66 % (31799)Termination phase: Saturation 155.63/22.66 155.63/22.66 % (31799)Memory used [KB]: 13560 155.63/22.66 % (31799)Time elapsed: 1.286 s 155.63/22.66 % (31799)Instructions burned: 4218 (million) 155.63/22.66 % (31799)------------------------------ 155.63/22.66 % (31799)------------------------------ 155.63/22.67 % (31802)lrs+10_1:1_ins=1:sgt=8:ss=axioms:i=8517:si=on:rtra=on_0 on E---3.1_30784 for (2177ds/8517Mi) 156.05/22.71 % (31800)Instruction limit reached! 156.05/22.71 % (31800)------------------------------ 156.05/22.71 % (31800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 156.05/22.71 % (31800)Termination reason: Unknown 156.05/22.71 % (31800)Termination phase: Saturation 156.05/22.71 156.05/22.71 % (31800)Memory used [KB]: 18549 156.05/22.71 % (31800)Time elapsed: 1.196 s 156.05/22.71 % (31800)Instructions burned: 3973 (million) 156.05/22.71 % (31800)------------------------------ 156.05/22.71 % (31800)------------------------------ 156.05/22.72 % (31803)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=10148:si=on:rtra=on_0 on E---3.1_30784 for (2177ds/10148Mi) 156.05/22.76 % (31793)Instruction limit reached! 156.05/22.76 % (31793)------------------------------ 156.05/22.76 % (31793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 156.05/22.76 % (31793)Termination reason: Unknown 156.05/22.76 % (31793)Termination phase: Saturation 156.05/22.76 156.05/22.76 % (31793)Memory used [KB]: 48229 156.05/22.76 % (31793)Time elapsed: 3.996 s 156.05/22.76 % (31793)Instructions burned: 13020 (million) 156.05/22.76 % (31793)------------------------------ 156.05/22.76 % (31793)------------------------------ 156.55/22.77 % (31804)lrs+10_1:2_ntd=on:nwc=10.0:plsq=on:plsqc=1:plsqr=2,1:ss=axioms:i=9078:si=on:rtra=on_0 on E---3.1_30784 for (2176ds/9078Mi) 161.16/23.42 % (31796)Instruction limit reached! 161.16/23.42 % (31796)------------------------------ 161.16/23.42 % (31796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 161.16/23.42 % (31796)Termination reason: Unknown 161.16/23.42 % (31796)Termination phase: Saturation 161.16/23.42 161.16/23.42 % (31796)Memory used [KB]: 25713 161.16/23.42 % (31796)Time elapsed: 4.048 s 161.16/23.42 % (31796)Instructions burned: 13164 (million) 161.16/23.42 % (31796)------------------------------ 161.16/23.42 % (31796)------------------------------ 161.22/23.43 % (31805)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=16164:si=on:rtra=on_0 on E---3.1_30784 for (2170ds/16164Mi) 170.44/24.77 % (31382)Refutation not found, non-redundant clauses discarded% (31382)------------------------------ 170.44/24.77 % (31382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 170.44/24.77 % (31382)Termination reason: Refutation not found, non-redundant clauses discarded 170.44/24.77 170.44/24.77 % (31382)Memory used [KB]: 36076 170.44/24.77 % (31382)Time elapsed: 12.998 s 170.44/24.77 % (31382)Instructions burned: 43152 (million) 170.44/24.77 % (31382)------------------------------ 170.44/24.77 % (31382)------------------------------ 170.44/24.78 % (31806)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on E---3.1_30784 for (2156ds/6102Mi) 174.04/25.28 % (31802)Instruction limit reached! 174.04/25.28 % (31802)------------------------------ 174.04/25.28 % (31802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 174.04/25.28 % (31802)Termination reason: Unknown 174.04/25.28 % (31802)Termination phase: Saturation 174.04/25.28 174.04/25.28 % (31802)Memory used [KB]: 15223 174.04/25.28 % (31802)Time elapsed: 2.608 s 174.04/25.28 % (31802)Instructions burned: 8517 (million) 174.04/25.28 % (31802)------------------------------ 174.04/25.28 % (31802)------------------------------ 174.04/25.29 % (31807)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=10308:si=on:rtra=on_0 on E---3.1_30784 for (2151ds/10308Mi) 176.00/25.54 % (31804)Instruction limit reached! 176.00/25.54 % (31804)------------------------------ 176.00/25.54 % (31804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 176.00/25.54 % (31804)Termination reason: Unknown 176.00/25.54 % (31804)Termination phase: Saturation 176.00/25.54 176.00/25.54 % (31804)Memory used [KB]: 13688 176.00/25.54 % (31804)Time elapsed: 2.769 s 176.00/25.54 % (31804)Instructions burned: 9079 (million) 176.00/25.54 % (31804)------------------------------ 176.00/25.54 % (31804)------------------------------ 176.00/25.55 % (31808)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=4041:si=on:rtra=on_0 on E---3.1_30784 for (2149ds/4041Mi) 177.96/25.89 % (31803)Instruction limit reached! 177.96/25.89 % (31803)------------------------------ 177.96/25.89 % (31803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 177.96/25.89 % (31803)Termination reason: Unknown 177.96/25.89 % (31803)Termination phase: Saturation 177.96/25.89 177.96/25.89 % (31803)Memory used [KB]: 19189 177.96/25.89 % (31803)Time elapsed: 3.174 s 177.96/25.89 % (31803)Instructions burned: 10150 (million) 177.96/25.89 % (31803)------------------------------ 177.96/25.89 % (31803)------------------------------ 177.96/25.90 % (31809)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=6901:si=on:rtra=on_0 on E---3.1_30784 for (2145ds/6901Mi) 183.38/26.63 % (31806)Instruction limit reached! 183.38/26.63 % (31806)------------------------------ 183.38/26.63 % (31806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 183.38/26.63 % (31806)Termination reason: Unknown 183.38/26.63 % (31806)Termination phase: Saturation 183.38/26.63 183.38/26.63 % (31806)Memory used [KB]: 36715 183.38/26.63 % (31806)Time elapsed: 1.845 s 183.38/26.63 % (31806)Instructions burned: 6103 (million) 183.38/26.63 % (31806)------------------------------ 183.38/26.63 % (31806)------------------------------ 183.38/26.64 % (31810)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on E---3.1_30784 for (2138ds/5576Mi) 184.08/26.71 % (31808)Instruction limit reached! 184.08/26.71 % (31808)------------------------------ 184.08/26.71 % (31808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 184.08/26.71 % (31808)Termination reason: Unknown 184.08/26.71 % (31808)Termination phase: Saturation 184.08/26.71 184.08/26.71 % (31808)Memory used [KB]: 11385 184.08/26.71 % (31808)Time elapsed: 1.164 s 184.08/26.71 % (31808)Instructions burned: 4042 (million) 184.08/26.71 % (31808)------------------------------ 184.08/26.71 % (31808)------------------------------ 184.27/26.72 % (31811)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=2014:si=on:rtra=on_0 on E---3.1_30784 for (2137ds/2014Mi) 185.08/26.92 % (31805)Refutation not found, non-redundant clauses discarded% (31805)------------------------------ 185.08/26.92 % (31805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 185.08/26.92 % (31805)Termination reason: Refutation not found, non-redundant clauses discarded 185.08/26.92 185.08/26.92 % (31805)Memory used [KB]: 8571 185.08/26.92 % (31805)Time elapsed: 3.489 s 185.08/26.92 % (31805)Instructions burned: 14463 (million) 185.08/26.92 % (31805)------------------------------ 185.08/26.92 % (31805)------------------------------ 185.08/26.93 % (31812)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=5115:si=on:rtra=on_0 on E---3.1_30784 for (2135ds/5115Mi) 185.65/27.02 % (31801)Instruction limit reached! 185.65/27.02 % (31801)------------------------------ 185.65/27.02 % (31801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 185.65/27.02 % (31801)Termination reason: Unknown 185.65/27.02 % (31801)Termination phase: Saturation 185.65/27.02 185.65/27.02 % (31801)Memory used [KB]: 24306 185.65/27.02 % (31801)Time elapsed: 4.387 s 185.65/27.02 % (31801)Instructions burned: 14014 (million) 185.65/27.02 % (31801)------------------------------ 185.65/27.02 % (31801)------------------------------ 185.65/27.03 % (31813)lrs+2_1:1_au=on:cnfonf=lazy_pi_sigma_gen:sos=on:ss=axioms:i=13001:si=on:rtra=on_0 on E---3.1_30784 for (2134ds/13001Mi) 188.26/27.32 % (31811)Instruction limit reached! 188.26/27.32 % (31811)------------------------------ 188.26/27.32 % (31811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 188.26/27.32 % (31811)Termination reason: Unknown 188.26/27.32 % (31811)Termination phase: Saturation 188.26/27.32 188.26/27.32 % (31811)Memory used [KB]: 13560 188.26/27.32 % (31811)Time elapsed: 0.622 s 188.26/27.32 % (31811)Instructions burned: 2014 (million) 188.26/27.32 % (31811)------------------------------ 188.26/27.32 % (31811)------------------------------ 188.26/27.33 % (31814)dis+10_1:2_aac=none:acc=on:atotf=0.1:au=on:fde=none:ins=1:ixr=off:nwc=5.0:i=11105:si=on:rtra=on_0 on E---3.1_30784 for (2131ds/11105Mi) 193.55/28.05 % (31809)Instruction limit reached! 193.55/28.05 % (31809)------------------------------ 193.55/28.05 % (31809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 193.55/28.05 % (31809)Termination reason: Unknown 193.55/28.05 % (31809)Termination phase: Saturation 193.55/28.05 193.55/28.05 % (31809)Memory used [KB]: 16758 193.55/28.05 % (31809)Time elapsed: 2.168 s 193.55/28.05 % (31809)Instructions burned: 6901 (million) 193.55/28.05 % (31809)------------------------------ 193.55/28.05 % (31809)------------------------------ 193.55/28.06 % (31815)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=13832:si=on:rtra=on_0 on E---3.1_30784 for (2124ds/13832Mi) 194.81/28.22 % (31812)Instruction limit reached! 194.81/28.22 % (31812)------------------------------ 194.81/28.22 % (31812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 194.81/28.22 % (31812)Termination reason: Unknown 194.81/28.22 % (31812)Termination phase: Saturation 194.81/28.22 194.81/28.22 % (31812)Memory used [KB]: 19189 194.81/28.22 % (31812)Time elapsed: 1.311 s 194.81/28.22 % (31812)Instructions burned: 5115 (million) 194.81/28.22 % (31812)------------------------------ 194.81/28.22 % (31812)------------------------------ 194.81/28.23 % (31816)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=32887:si=on:rtra=on_0 on E---3.1_30784 for (2122ds/32887Mi) 195.54/28.34 % (31810)Instruction limit reached! 195.54/28.34 % (31810)------------------------------ 195.54/28.34 % (31810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 195.54/28.34 % (31810)Termination reason: Unknown 195.54/28.34 % (31810)Termination phase: Saturation 195.54/28.34 195.54/28.34 % (31810)Memory used [KB]: 13816 195.54/28.34 % (31810)Time elapsed: 1.717 s 195.54/28.34 % (31810)Instructions burned: 5576 (million) 195.54/28.34 % (31810)------------------------------ 195.54/28.34 % (31810)------------------------------ 195.54/28.35 % (31817)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on E---3.1_30784 for (2121ds/3362Mi) 196.66/28.58 % (31807)Instruction limit reached! 196.66/28.58 % (31807)------------------------------ 196.66/28.58 % (31807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 196.66/28.58 % (31807)Termination reason: Unknown 196.66/28.58 % (31807)Termination phase: Saturation 196.66/28.58 196.66/28.58 % (31807)Memory used [KB]: 19445 196.66/28.58 % (31807)Time elapsed: 3.288 s 196.66/28.58 % (31807)Instructions burned: 10310 (million) 196.66/28.58 % (31807)------------------------------ 196.66/28.58 % (31807)------------------------------ 196.66/28.59 % (31818)ott+1002_1:1_au=on:cnfonf=lazy_simp:nwc=5.0:sgt=5:ss=axioms:st=1.5:i=24965:si=on:rtra=on_0 on E---3.1_30784 for (2118ds/24965Mi) 202.30/29.32 % (31817)Instruction limit reached! 202.30/29.32 % (31817)------------------------------ 202.30/29.32 % (31817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 202.30/29.32 % (31817)Termination reason: Unknown 202.30/29.32 % (31817)Termination phase: Saturation 202.30/29.32 202.30/29.32 % (31817)Memory used [KB]: 23922 202.30/29.32 % (31817)Time elapsed: 0.979 s 202.30/29.32 % (31817)Instructions burned: 3364 (million) 202.30/29.32 % (31817)------------------------------ 202.30/29.32 % (31817)------------------------------ 202.30/29.34 % (31819)lrs+1010_2:1_amm=off:avsq=on:c=on:cbe=off:e2e=on:fsr=off:ins=3:s2a=on:s2at=-1.0:i=15705:si=on:rtra=on_0 on E---3.1_30784 for (2111ds/15705Mi) 208.05/30.16 % (31813)Instruction limit reached! 208.05/30.16 % (31813)------------------------------ 208.05/30.16 % (31813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 208.05/30.16 % (31813)Termination reason: Unknown 208.05/30.16 % (31813)Termination phase: Saturation 208.05/30.16 208.05/30.16 % (31813)Memory used [KB]: 7803 208.05/30.16 % (31813)Time elapsed: 3.125 s 208.05/30.16 % (31813)Instructions burned: 13004 (million) 208.05/30.16 % (31813)------------------------------ 208.05/30.16 % (31813)------------------------------ 208.05/30.17 % (31820)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1536:si=on:rtra=on_0 on E---3.1_30784 for (2102ds/1536Mi) 211.72/30.63 % (31820)Instruction limit reached! 211.72/30.63 % (31820)------------------------------ 211.72/30.63 % (31820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 211.72/30.63 % (31820)Termination reason: Unknown 211.72/30.63 % (31820)Termination phase: Saturation 211.72/30.63 211.72/30.63 % (31820)Memory used [KB]: 10490 211.72/30.63 % (31820)Time elapsed: 0.464 s 211.72/30.63 % (31820)Instructions burned: 1538 (million) 211.72/30.63 % (31820)------------------------------ 211.72/30.63 % (31820)------------------------------ 211.72/30.64 % (31821)dis+10_1:1_fde=none:kws=precedence:piset=not:prag=on:slsq=on:slsqc=1:sp=unary_frequency:i=23684:si=on:rtra=on_0 on E---3.1_30784 for (2098ds/23684Mi) 212.24/30.73 % (31814)Instruction limit reached! 212.24/30.73 % (31814)------------------------------ 212.24/30.73 % (31814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 212.24/30.73 % (31814)Termination reason: Unknown 212.24/30.73 % (31814)Termination phase: Saturation 212.24/30.73 212.24/30.73 % (31814)Memory used [KB]: 33517 212.24/30.73 % (31814)Time elapsed: 3.425 s 212.24/30.73 % (31814)Instructions burned: 11108 (million) 212.24/30.73 % (31814)------------------------------ 212.24/30.73 % (31814)------------------------------ 212.24/30.74 % (31822)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=4925:si=on:rtra=on_0 on E---3.1_30784 for (2097ds/4925Mi) 217.99/31.55 % (31815)Instruction limit reached! 217.99/31.55 % (31815)------------------------------ 217.99/31.55 % (31815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 217.99/31.55 % (31815)Termination reason: Unknown 217.99/31.55 % (31815)Termination phase: Saturation 217.99/31.55 217.99/31.55 % (31815)Memory used [KB]: 18421 217.99/31.55 % (31815)Time elapsed: 3.510 s 217.99/31.55 % (31815)Instructions burned: 13833 (million) 217.99/31.55 % (31815)------------------------------ 217.99/31.55 % (31815)------------------------------ 218.18/31.56 % (31823)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=14666:si=on:rtra=on_0 on E---3.1_30784 for (2088ds/14666Mi) 220.42/31.96 % (31822)Instruction limit reached! 220.42/31.96 % (31822)------------------------------ 220.42/31.96 % (31822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 220.42/31.96 % (31822)Termination reason: Unknown 220.42/31.96 % (31822)Termination phase: Saturation 220.42/31.96 220.42/31.96 % (31822)Memory used [KB]: 7803 220.42/31.96 % (31822)Time elapsed: 1.220 s 220.42/31.96 % (31822)Instructions burned: 4926 (million) 220.42/31.96 % (31822)------------------------------ 220.42/31.96 % (31822)------------------------------ 220.70/31.97 % (31824)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=3322:si=on:rtra=on_0 on E---3.1_30784 for (2084ds/3322Mi) 226.52/32.84 % (31824)Instruction limit reached! 226.52/32.84 % (31824)------------------------------ 226.52/32.84 % (31824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 226.52/32.84 % (31824)Termination reason: Unknown 226.52/32.84 % (31824)Termination phase: Saturation 226.52/32.84 226.52/32.84 % (31824)Memory used [KB]: 7675 226.52/32.84 % (31824)Time elapsed: 0.867 s 226.52/32.84 % (31824)Instructions burned: 3323 (million) 226.52/32.84 % (31824)------------------------------ 226.52/32.84 % (31824)------------------------------ 227.24/32.85 % (31825)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1810:si=on:rtra=on_0 on E---3.1_30784 for (2076ds/1810Mi) 229.63/33.30 % (31825)Instruction limit reached! 229.63/33.30 % (31825)------------------------------ 229.63/33.30 % (31825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 229.63/33.30 % (31825)Termination reason: Unknown 229.63/33.30 % (31825)Termination phase: Saturation 229.63/33.30 229.63/33.30 % (31825)Memory used [KB]: 17014 229.63/33.30 % (31825)Time elapsed: 0.452 s 229.63/33.30 % (31825)Instructions burned: 1810 (million) 229.63/33.30 % (31825)------------------------------ 229.63/33.30 % (31825)------------------------------ 230.51/33.31 % (31826)dis+1666_1:1_anc=none:bs=on:cbe=off:cha=on:cnfonf=lazy_gen:fe=off:fsr=off:hud=5:kws=precedence:piset=pi_sigma:prag=on:sos=on:sp=frequency:i=2465:si=on:rtra=on_0 on E---3.1_30784 for (2071ds/2465Mi) 234.92/33.95 % (31826)Instruction limit reached! 234.92/33.95 % (31826)------------------------------ 234.92/33.95 % (31826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 234.92/33.95 % (31826)Termination reason: Unknown 234.92/33.95 % (31826)Termination phase: Saturation 234.92/33.95 234.92/33.95 % (31826)Memory used [KB]: 20340 234.92/33.95 % (31826)Time elapsed: 0.639 s 234.92/33.95 % (31826)Instructions burned: 2466 (million) 234.92/33.95 % (31826)------------------------------ 234.92/33.95 % (31826)------------------------------ 234.92/33.96 % (31827)dis+1002_1:1_cbe=off:cnfonf=lazy_pi_sigma_gen:fsr=off:ins=1:kws=inv_precedence:nwc=10.0:ss=axioms:st=2.0:i=41234:si=on:rtra=on_0 on E---3.1_30784 for (2064ds/41234Mi) 239.13/34.58 % (31819)Instruction limit reached! 239.13/34.58 % (31819)------------------------------ 239.13/34.58 % (31819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 239.13/34.58 % (31819)Termination reason: Unknown 239.13/34.58 % (31819)Termination phase: Saturation 239.13/34.58 239.13/34.58 % (31819)Memory used [KB]: 34796 239.13/34.58 % (31819)Time elapsed: 5.240 s 239.13/34.58 % (31819)Instructions burned: 15707 (million) 239.13/34.58 % (31819)------------------------------ 239.13/34.58 % (31819)------------------------------ 239.13/34.59 % (31828)dis+1002_1:1_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:nm=0:i=14027:si=on:rtra=on_0 on E---3.1_30784 for (2058ds/14027Mi) 241.84/35.02 % (31818)Instruction limit reached! 241.84/35.02 % (31818)------------------------------ 241.84/35.02 % (31818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 241.84/35.02 % (31818)Termination reason: Unknown 241.84/35.02 % (31818)Termination phase: Saturation 241.84/35.02 241.84/35.02 % (31818)Memory used [KB]: 17142 241.84/35.02 % (31818)Time elapsed: 6.426 s 241.84/35.02 % (31818)Instructions burned: 24967 (million) 241.84/35.02 % (31818)------------------------------ 241.84/35.02 % (31818)------------------------------ 241.84/35.03 % (31829)dis+1010_1:1_au=on:cnfonf=conj_eager:nwc=10.0:sac=on:i=27021:si=on:rtra=on_0 on E---3.1_30784 for (2054ds/27021Mi) 248.33/35.92 % (31788)Instruction limit reached! 248.33/35.92 % (31788)------------------------------ 248.33/35.92 % (31788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 248.33/35.92 % (31788)Termination reason: Unknown 248.33/35.92 % (31788)Termination phase: Saturation 248.33/35.92 248.33/35.92 % (31788)Memory used [KB]: 37867 248.33/35.92 % (31788)Time elapsed: 19.619 s 248.33/35.92 % (31788)Instructions burned: 64914 (million) 248.33/35.92 % (31788)------------------------------ 248.33/35.92 % (31788)------------------------------ 248.33/35.93 % (31830)dis-1666_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:i=5643:si=on:rtra=on_0 on E---3.1_30784 for (2045ds/5643Mi) 249.19/36.04 % (31823)Instruction limit reached! 249.19/36.04 % (31823)------------------------------ 249.19/36.04 % (31823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 249.19/36.04 % (31823)Termination reason: Unknown 249.19/36.04 % (31823)Termination phase: Saturation 249.19/36.04 249.19/36.04 % (31823)Memory used [KB]: 15479 249.19/36.04 % (31823)Time elapsed: 4.482 s 249.19/36.04 % (31823)Instructions burned: 14668 (million) 249.19/36.04 % (31823)------------------------------ 249.19/36.04 % (31823)------------------------------ 249.53/36.05 % (31831)dis+1002_1:1_apa=on:au=on:cnfonf=off:e2e=on:flr=on:nm=4:s2a=on:i=8612:si=on:rtra=on_0 on E---3.1_30784 for (2044ds/8612Mi) 257.94/37.31 % (31830)Instruction limit reached! 257.94/37.31 % (31830)------------------------------ 257.94/37.31 % (31830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 257.94/37.31 % (31830)Termination reason: Unknown 257.94/37.31 % (31830)Termination phase: Saturation 257.94/37.31 257.94/37.31 % (31830)Memory used [KB]: 16375 257.94/37.31 % (31830)Time elapsed: 1.383 s 257.94/37.31 % (31830)Instructions burned: 5646 (million) 257.94/37.31 % (31830)------------------------------ 257.94/37.31 % (31830)------------------------------ 257.94/37.32 % (31832)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=3743:si=on:rtra=on_0 on E---3.1_30784 for (2031ds/3743Mi) 262.55/37.90 % (31821)Instruction limit reached! 262.55/37.90 % (31821)------------------------------ 262.55/37.90 % (31821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 262.55/37.90 % (31821)Termination reason: Unknown 262.55/37.90 % (31821)Termination phase: Saturation 262.55/37.90 262.55/37.90 % (31821)Memory used [KB]: 44007 262.55/37.90 % (31821)Time elapsed: 7.263 s 262.55/37.90 % (31821)Instructions burned: 23686 (million) 262.55/37.90 % (31821)------------------------------ 262.55/37.90 % (31821)------------------------------ 262.55/37.91 % (31833)dis+10_1:2_amm=off:bd=preordered:cnfonf=off:e2e=on:fe=off:fsr=off:hud=5:nm=3:s2a=on:sos=on:i=2571:si=on:rtra=on_0 on E---3.1_30784 for (2025ds/2571Mi) 262.96/37.94 % (31828)Instruction limit reached! 262.96/37.94 % (31828)------------------------------ 262.96/37.94 % (31828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 262.96/37.94 % (31828)Termination reason: Unknown 262.96/37.94 % (31828)Termination phase: Saturation 262.96/37.94 262.96/37.94 % (31828)Memory used [KB]: 9466 262.96/37.94 % (31828)Time elapsed: 3.350 s 262.96/37.94 % (31828)Instructions burned: 14029 (million) 262.96/37.94 % (31828)------------------------------ 262.96/37.94 % (31828)------------------------------ 262.96/37.95 % (31834)dis+1010_1:16_cbe=off:cnfonf=conj_eager:fe=off:hud=15:nwc=3.0:piset=pi_sigma:prag=on:sd=5:sp=weighted_frequency:ss=axioms:st=2.0:i=35728:si=on:rtra=on_0 on E---3.1_30784 for (2025ds/35728Mi) 265.64/38.42 % (31816)Instruction limit reached! 265.64/38.42 % (31816)------------------------------ 265.64/38.42 % (31816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 265.64/38.42 % (31816)Termination reason: Unknown 265.64/38.42 % (31816)Termination phase: Saturation 265.64/38.42 265.64/38.42 % (31816)Memory used [KB]: 28272 265.64/38.42 % (31816)Time elapsed: 10.190 s 265.64/38.42 % (31816)Instructions burned: 32889 (million) 265.64/38.42 % (31816)------------------------------ 265.64/38.42 % (31816)------------------------------ 265.64/38.43 % (31835)lrs+1004_1:24_i=5433:si=on:rtra=on_0 on E---3.1_30784 for (2020ds/5433Mi) 266.75/38.49 % (31832)Instruction limit reached! 266.75/38.49 % (31832)------------------------------ 266.75/38.49 % (31832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 266.75/38.49 % (31832)Termination reason: Unknown 266.75/38.49 % (31832)Termination phase: Saturation 266.75/38.49 266.75/38.49 % (31832)Memory used [KB]: 21236 266.75/38.49 % (31832)Time elapsed: 1.172 s 266.75/38.49 % (31832)Instructions burned: 3745 (million) 266.75/38.49 % (31832)------------------------------ 266.75/38.49 % (31832)------------------------------ 266.75/38.51 % (31836)ott+1002_1:1_anc=all_dependent:au=on:avsq=on:cnfonf=lazy_pi_sigma_gen:piset=not:i=27944:si=on:rtra=on_0 on E---3.1_30784 for (2019ds/27944Mi) 267.90/38.70 % (31833)Instruction limit reached! 267.90/38.70 % (31833)------------------------------ 267.90/38.70 % (31833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 267.90/38.70 % (31833)Termination reason: Unknown 267.90/38.70 % (31833)Termination phase: Saturation 267.90/38.70 267.90/38.70 % (31833)Memory used [KB]: 16886 267.90/38.70 % (31833)Time elapsed: 0.788 s 267.90/38.70 % (31833)Instructions burned: 2571 (million) 267.90/38.70 % (31833)------------------------------ 267.90/38.70 % (31833)------------------------------ 267.90/38.71 % (31837)ott+10_1:10_cnfonf=lazy_gen:fde=none:sp=const_frequency:i=15814:si=on:rtra=on_0 on E---3.1_30784 for (2017ds/15814Mi) 268.29/38.75 % (31831)Instruction limit reached! 268.29/38.75 % (31831)------------------------------ 268.29/38.75 % (31831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 268.29/38.75 % (31831)Termination reason: Unknown 268.29/38.75 % (31831)Termination phase: Saturation 268.29/38.75 268.29/38.75 % (31831)Memory used [KB]: 20212 268.29/38.75 % (31831)Time elapsed: 2.698 s 268.29/38.75 % (31831)Instructions burned: 8613 (million) 268.29/38.75 % (31831)------------------------------ 268.29/38.75 % (31831)------------------------------ 268.29/38.76 % (31838)lrs+1002_1:128_atotf=0.1:au=on:cbe=off:ntd=on:sp=const_frequency:i=9867:si=on:rtra=on_0 on E---3.1_30784 for (2017ds/9867Mi) 277.66/40.09 % (31835)Instruction limit reached! 277.66/40.09 % (31835)------------------------------ 277.66/40.09 % (31835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 277.66/40.09 % (31835)Termination reason: Unknown 277.66/40.09 % (31835)Termination phase: Saturation 277.66/40.09 277.66/40.09 % (31835)Memory used [KB]: 11385 277.66/40.09 % (31835)Time elapsed: 1.654 s 277.66/40.09 % (31835)Instructions burned: 5433 (million) 277.66/40.09 % (31835)------------------------------ 277.66/40.09 % (31835)------------------------------ 277.66/40.10 % (31839)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=5419:si=on:rtra=on_0 on E---3.1_30784 for (2003ds/5419Mi) 287.35/41.44 % (31839)Instruction limit reached! 287.35/41.44 % (31839)------------------------------ 287.35/41.44 % (31839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 287.35/41.44 % (31839)Termination reason: Unknown 287.35/41.44 % (31839)Termination phase: Saturation 287.35/41.44 287.35/41.44 % (31839)Memory used [KB]: 17142 287.35/41.44 % (31839)Time elapsed: 1.344 s 287.35/41.44 % (31839)Instructions burned: 5419 (million) 287.35/41.44 % (31839)------------------------------ 287.35/41.44 % (31839)------------------------------ 287.35/41.45 % (31840)dis+1010_1:28_au=on:cnfonf=off:e2e=on:fde=none:nicw=on:s2a=on:s2at=5.0:tgt=full:i=15386:si=on:rtra=on_0 on E---3.1_30784 for (1990ds/15386Mi) 288.49/41.64 % (31838)Instruction limit reached! 288.49/41.64 % (31838)------------------------------ 288.49/41.64 % (31838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 288.49/41.64 % (31838)Termination reason: Unknown 288.49/41.64 % (31838)Termination phase: Saturation 288.49/41.64 288.49/41.64 % (31838)Memory used [KB]: 11897 288.49/41.64 % (31838)Time elapsed: 2.879 s 288.49/41.64 % (31838)Instructions burned: 9867 (million) 288.49/41.64 % (31838)------------------------------ 288.49/41.64 % (31838)------------------------------ 288.68/41.65 % (31841)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on E---3.1_30784 for (1988ds/4714Mi) 296.87/42.80 % (31837)Instruction limit reached! 296.87/42.80 % (31837)------------------------------ 296.87/42.80 % (31837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 296.87/42.80 % (31837)Termination reason: Unknown 296.87/42.80 % (31837)Termination phase: Saturation 296.87/42.80 296.87/42.80 % (31837)Memory used [KB]: 43112 296.87/42.80 % (31837)Time elapsed: 4.090 s 296.87/42.80 % (31837)Instructions burned: 15816 (million) 296.87/42.80 % (31837)------------------------------ 296.87/42.80 % (31837)------------------------------ 296.87/42.81 % (31841)Instruction limit reached! 296.87/42.81 % (31841)------------------------------ 296.87/42.81 % (31841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 296.87/42.81 % (31841)Termination reason: Unknown 296.87/42.81 % (31841)Termination phase: Saturation 296.87/42.81 296.87/42.81 % (31841)Memory used [KB]: 7675 296.87/42.81 % (31841)Time elapsed: 1.164 s 296.87/42.81 % (31841)Instructions burned: 4716 (million) 296.87/42.81 % (31841)------------------------------ 296.87/42.81 % (31841)------------------------------ 296.87/42.81 % (31842)lrs+10_1:1_bd=off:c=on:fsr=off:ntd=on:prag=on:sd=1:sos=all:ss=axioms:st=5.0:i=42749:si=on:rtra=on_0 on E---3.1_30784 for (1976ds/42749Mi) 296.87/42.82 % (31843)lrs+10_1:156_afp=4000:avsq=on:avsqr=4,1:fe=axiom:ss=axioms:tgt=ground:i=19001:si=on:rtra=on_0 on E---3.1_30784 for (1976ds/19001Mi) 300.05/43.29 % (31829)Instruction limit reached! 300.05/43.29 % (31829)------------------------------ 300.05/43.29 % (31829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 300.45/43.29 % (31829)Termination reason: Unknown 300.45/43.29 % (31829)Termination phase: Saturation 300.45/43.29 300.45/43.29 % (31829)Memory used [KB]: 29040 300.45/43.29 % (31829)Time elapsed: 8.269 s 300.45/43.29 % (31829)Instructions burned: 27022 (million) 300.45/43.29 % (31829)------------------------------ 300.45/43.29 % (31829)------------------------------ 300.45/43.31 % (31844)lrs+1_1:1_au=on:cbe=off:cs=on:nm=4:i=14341:si=on:rtra=on_0 on E---3.1_30784 for (1971ds/14341Mi) 315.68/45.50 % (31827)Instruction limit reached! 315.68/45.50 % (31827)------------------------------ 315.68/45.50 % (31827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 315.68/45.50 % (31827)Termination reason: Unknown 315.68/45.50 % (31827)Termination phase: Saturation 315.68/45.50 315.68/45.50 % (31827)Memory used [KB]: 40937 315.68/45.50 % (31827)Time elapsed: 11.539 s 315.68/45.50 % (31827)Instructions burned: 41234 (million) 315.68/45.50 % (31827)------------------------------ 315.68/45.50 % (31827)------------------------------ 315.68/45.51 % (31845)lrs+10_1:1_cnfonf=off:sd=1:ss=axioms:st=3.0:i=13159:si=on:rtra=on_0 on E---3.1_30784 for (1949ds/13159Mi) 320.38/46.14 % (31836)Instruction limit reached! 320.38/46.14 % (31836)------------------------------ 320.38/46.14 % (31836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 320.38/46.14 % (31836)Termination reason: Unknown 320.38/46.14 % (31836)Termination phase: Saturation 320.38/46.14 320.38/46.14 % (31836)Memory used [KB]: 24050 320.38/46.14 % (31836)Time elapsed: 7.655 s 320.38/46.14 % (31836)Instructions burned: 27945 (million) 320.38/46.14 % (31836)------------------------------ 320.38/46.14 % (31836)------------------------------ 320.38/46.16 % (31846)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=6604:si=on:rtra=on_0 on E---3.1_30784 for (1942ds/6604Mi) 321.98/46.45 % (31840)Instruction limit reached! 321.98/46.45 % (31840)------------------------------ 321.98/46.45 % (31840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 321.98/46.45 % (31840)Termination reason: Unknown 321.98/46.45 % (31840)Termination phase: Saturation 321.98/46.45 321.98/46.45 % (31840)Memory used [KB]: 43624 321.98/46.45 % (31840)Time elapsed: 5.024 s 321.98/46.45 % (31840)Instructions burned: 15388 (million) 321.98/46.45 % (31840)------------------------------ 321.98/46.45 % (31840)------------------------------ 322.58/46.47 % (31847)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on E---3.1_30784 for (1939ds/2635Mi) 327.97/47.28 % (31847)Instruction limit reached! 327.97/47.28 % (31847)------------------------------ 327.97/47.28 % (31847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 327.97/47.28 % (31847)Termination reason: Unknown 327.97/47.28 % (31847)Termination phase: Saturation 327.97/47.28 327.97/47.28 % (31847)Memory used [KB]: 12153 327.97/47.28 % (31847)Time elapsed: 0.812 s 327.97/47.28 % (31847)Instructions burned: 2637 (million) 327.97/47.28 % (31847)------------------------------ 327.97/47.28 % (31847)------------------------------ 327.97/47.29 % (31850)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=41131:si=on:rtra=on_0 on E---3.1_30784 for (1931ds/41131Mi) 328.49/47.36 % (31844)Instruction limit reached! 328.49/47.36 % (31844)------------------------------ 328.49/47.36 % (31844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 328.49/47.36 % (31844)Termination reason: Unknown 328.49/47.36 % (31844)Termination phase: Saturation 328.49/47.36 328.49/47.36 % (31844)Memory used [KB]: 50788 328.49/47.36 % (31844)Time elapsed: 4.053 s 328.49/47.36 % (31844)Instructions burned: 14344 (million) 328.49/47.36 % (31844)------------------------------ 328.49/47.36 % (31844)------------------------------ 328.94/47.37 % (31851)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on E---3.1_30784 for (1930ds/3971Mi) 334.30/48.13 % (31843)Instruction limit reached! 334.30/48.13 % (31843)------------------------------ 334.30/48.13 % (31843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 334.30/48.13 % (31843)Termination reason: Unknown 334.30/48.13 % (31843)Termination phase: Saturation 334.30/48.13 334.30/48.13 % (31843)Memory used [KB]: 26865 334.30/48.13 % (31843)Time elapsed: 5.313 s 334.30/48.13 % (31843)Instructions burned: 19002 (million) 334.30/48.13 % (31843)------------------------------ 334.30/48.13 % (31843)------------------------------ 334.40/48.14 % (31852)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2142:si=on:rtra=on_0 on E---3.1_30784 for (1923ds/2142Mi) 334.40/48.19 % (31846)Refutation not found, non-redundant clauses discarded% (31846)------------------------------ 334.40/48.19 % (31846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 334.40/48.19 % (31846)Termination reason: Refutation not found, non-redundant clauses discarded 334.40/48.19 334.40/48.19 % (31846)Memory used [KB]: 22771 334.40/48.19 % (31846)Time elapsed: 2.031 s 334.40/48.19 % (31846)Instructions burned: 6530 (million) 334.40/48.19 % (31846)------------------------------ 334.40/48.19 % (31846)------------------------------ 334.40/48.20 % (31853)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=1314:si=on:rtra=on_0 on E---3.1_30784 for (1922ds/1314Mi) 335.96/48.52 % (31834)Instruction limit reached! 335.96/48.52 % (31834)------------------------------ 335.96/48.52 % (31834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 335.96/48.52 % (31834)Termination reason: Unknown 335.96/48.52 % (31834)Termination phase: Saturation 335.96/48.52 335.96/48.52 % (31834)Memory used [KB]: 20084 335.96/48.52 % (31834)Time elapsed: 10.580 s 335.96/48.52 % (31834)Instructions burned: 35729 (million) 335.96/48.52 % (31834)------------------------------ 335.96/48.52 % (31834)------------------------------ 336.40/48.53 % (31851)Instruction limit reached! 336.40/48.53 % (31851)------------------------------ 336.40/48.53 % (31851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 336.40/48.53 % (31851)Termination reason: Unknown 336.40/48.53 % (31851)Termination phase: Saturation 336.40/48.53 336.40/48.53 % (31851)Memory used [KB]: 15863 336.40/48.53 % (31851)Time elapsed: 1.154 s 336.40/48.53 % (31851)Instructions burned: 3971 (million) 336.40/48.53 % (31851)------------------------------ 336.40/48.53 % (31851)------------------------------ 336.40/48.53 % (31854)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on E---3.1_30784 for (1919ds/3362Mi) 336.40/48.54 % (31855)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=5756:si=on:rtra=on_0 on E---3.1_30784 for (1919ds/5756Mi) 336.58/48.59 % (31853)Instruction limit reached! 336.58/48.59 % (31853)------------------------------ 336.58/48.59 % (31853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 336.58/48.59 % (31853)Termination reason: Unknown 336.58/48.59 % (31853)Termination phase: Saturation 336.58/48.59 336.58/48.59 % (31853)Memory used [KB]: 10618 336.58/48.59 % (31853)Time elapsed: 0.394 s 336.58/48.59 % (31853)Instructions burned: 1316 (million) 336.58/48.59 % (31853)------------------------------ 336.58/48.59 % (31853)------------------------------ 336.58/48.60 % (31856)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=2607:si=on:rtra=on_0 on E---3.1_30784 for (1918ds/2607Mi) 338.70/48.80 % (31852)Instruction limit reached! 338.70/48.80 % (31852)------------------------------ 338.70/48.80 % (31852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 338.70/48.80 % (31852)Termination reason: Unknown 338.70/48.80 % (31852)Termination phase: Saturation 338.70/48.80 338.70/48.80 % (31852)Memory used [KB]: 11129 338.70/48.80 % (31852)Time elapsed: 0.657 s 338.70/48.80 % (31852)Instructions burned: 2143 (million) 338.70/48.80 % (31852)------------------------------ 338.70/48.80 % (31852)------------------------------ 338.70/48.81 % (31857)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15187:si=on:rtra=on_0 on E---3.1_30784 for (1916ds/15187Mi) 340.54/49.08 % (31845)Instruction limit reached! 340.54/49.08 % (31845)------------------------------ 340.54/49.08 % (31845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 340.54/49.08 % (31845)Termination reason: Unknown 340.54/49.08 % (31845)Termination phase: Saturation 340.54/49.08 340.54/49.08 % (31845)Memory used [KB]: 10874 340.54/49.08 % (31845)Time elapsed: 3.573 s 340.54/49.08 % (31845)Instructions burned: 13161 (million) 340.54/49.08 % (31845)------------------------------ 340.54/49.08 % (31845)------------------------------ 340.54/49.09 % (31858)dis-1666_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:i=21027:si=on:rtra=on_0 on E---3.1_30784 for (1913ds/21027Mi) 341.16/49.25 % (31856)Instruction limit reached! 341.16/49.25 % (31856)------------------------------ 341.16/49.25 % (31856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 341.16/49.25 % (31856)Termination reason: Unknown 341.16/49.25 % (31856)Termination phase: Saturation 341.16/49.25 341.16/49.25 % (31856)Memory used [KB]: 17142 341.16/49.25 % (31856)Time elapsed: 0.649 s 341.16/49.25 % (31856)Instructions burned: 2609 (million) 341.16/49.25 % (31856)------------------------------ 341.16/49.25 % (31856)------------------------------ 342.20/49.26 % (31859)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=35698:si=on:rtra=on_0 on E---3.1_30784 for (1911ds/35698Mi) 343.40/49.51 % (31854)Instruction limit reached! 343.40/49.51 % (31854)------------------------------ 343.40/49.51 % (31854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 343.40/49.51 % (31854)Termination reason: Unknown 343.40/49.51 % (31854)Termination phase: Saturation 343.40/49.51 343.40/49.51 % (31854)Memory used [KB]: 23155 343.40/49.51 % (31854)Time elapsed: 0.981 s 343.40/49.51 % (31854)Instructions burned: 3364 (million) 343.40/49.51 % (31854)------------------------------ 343.40/49.51 % (31854)------------------------------ 343.40/49.52 % (31860)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=14573:si=on:rtra=on_0 on E---3.1_30784 for (1909ds/14573Mi) 349.11/50.31 % (31855)Refutation not found, non-redundant clauses discarded% (31855)------------------------------ 349.11/50.31 % (31855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 349.11/50.31 % (31855)Termination reason: Refutation not found, non-redundant clauses discarded 349.11/50.31 349.11/50.31 % (31855)Memory used [KB]: 19061 349.11/50.31 % (31855)Time elapsed: 1.776 s 349.11/50.31 % (31855)Instructions burned: 5740 (million) 349.11/50.31 % (31855)------------------------------ 349.11/50.31 % (31855)------------------------------ 349.11/50.32 % (31861)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=14014:si=on:rtra=on_0 on E---3.1_30784 for (1901ds/14014Mi) 370.41/53.33 % (31857)Instruction limit reached! 370.41/53.33 % (31857)------------------------------ 370.41/53.33 % (31857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 370.41/53.33 % (31857)Termination reason: Unknown 370.41/53.33 % (31857)Termination phase: Saturation 370.41/53.33 370.41/53.33 % (31857)Memory used [KB]: 21875 370.41/53.33 % (31857)Time elapsed: 4.520 s 370.41/53.33 % (31857)Instructions burned: 15190 (million) 370.41/53.33 % (31857)------------------------------ 370.41/53.33 % (31857)------------------------------ 370.68/53.34 % (31862)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on E---3.1_30784 for (1871ds/4165Mi) 374.84/53.98 % (31860)Instruction limit reached! 374.84/53.98 % (31860)------------------------------ 374.84/53.98 % (31860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 374.84/53.98 % (31860)Termination reason: Unknown 374.84/53.98 % (31860)Termination phase: Saturation 374.84/53.98 374.84/53.98 % (31860)Memory used [KB]: 15351 374.84/53.98 % (31860)Time elapsed: 4.452 s 374.84/53.98 % (31860)Instructions burned: 14574 (million) 374.84/53.98 % (31860)------------------------------ 374.84/53.98 % (31860)------------------------------ 374.84/53.99 % (31863)dis+1002_1:1_apa=on:au=on:cnfonf=off:e2e=on:flr=on:nm=4:s2a=on:i=8612:si=on:rtra=on_0 on E---3.1_30784 for (1864ds/8612Mi) 376.27/54.18 % (31858)Instruction limit reached! 376.27/54.18 % (31858)------------------------------ 376.27/54.18 % (31858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 376.27/54.18 % (31858)Termination reason: Unknown 376.27/54.18 % (31858)Termination phase: Saturation 376.27/54.18 376.27/54.18 % (31858)Memory used [KB]: 20596 376.27/54.18 % (31858)Time elapsed: 5.083 s 376.27/54.18 % (31858)Instructions burned: 21028 (million) 376.27/54.18 % (31858)------------------------------ 376.27/54.18 % (31858)------------------------------ 376.27/54.19 % (31864)lrs-1_1:1_au=on:cbe=off:ntd=on:i=5576:si=on:rtra=on_0 on E---3.1_30784 for (1862ds/5576Mi) 379.74/54.65 % (31862)Instruction limit reached! 379.74/54.65 % (31862)------------------------------ 379.74/54.65 % (31862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 379.74/54.65 % (31862)Termination reason: Unknown 379.74/54.65 % (31862)Termination phase: Saturation 379.74/54.65 379.74/54.65 % (31862)Memory used [KB]: 24562 379.74/54.65 % (31862)Time elapsed: 1.309 s 379.74/54.65 % (31862)Instructions burned: 4167 (million) 379.74/54.65 % (31862)------------------------------ 379.74/54.65 % (31862)------------------------------ 379.74/54.66 % (31865)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=4408:si=on:rtra=on_0 on E---3.1_30784 for (1857ds/4408Mi) 380.63/54.79 % (31861)Instruction limit reached! 380.63/54.79 % (31861)------------------------------ 380.63/54.79 % (31861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 380.63/54.79 % (31861)Termination reason: Unknown 380.63/54.79 % (31861)Termination phase: Saturation 380.63/54.79 380.63/54.79 % (31861)Memory used [KB]: 24562 380.63/54.79 % (31861)Time elapsed: 4.481 s 380.63/54.79 % (31861)Instructions burned: 14016 (million) 380.63/54.79 % (31861)------------------------------ 380.63/54.79 % (31861)------------------------------ 380.63/54.80 % (31866)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=13925:si=on:rtra=on_0 on E---3.1_30784 for (1856ds/13925Mi) 385.52/55.49 % (31842)Instruction limit reached! 385.52/55.49 % (31842)------------------------------ 385.52/55.49 % (31842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 385.52/55.49 % (31842)Termination reason: Unknown 385.52/55.49 % (31842)Termination phase: Saturation 385.52/55.49 385.52/55.49 % (31842)Memory used [KB]: 29295 385.52/55.49 % (31842)Time elapsed: 12.665 s 385.52/55.49 % (31842)Instructions burned: 42751 (million) 385.52/55.49 % (31842)------------------------------ 385.52/55.49 % (31842)------------------------------ 385.77/55.50 % (31867)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=117046:si=on:rtra=on_0 on E---3.1_30784 for (1849ds/117046Mi) 387.90/55.87 % (31864)Refutation not found, non-redundant clauses discarded% (31864)------------------------------ 387.90/55.87 % (31864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 387.90/55.87 % (31864)Termination reason: Refutation not found, non-redundant clauses discarded 387.90/55.87 387.90/55.87 % (31864)Memory used [KB]: 13944 387.90/55.87 % (31864)Time elapsed: 1.685 s 387.90/55.87 % (31864)Instructions burned: 5481 (million) 387.90/55.87 % (31864)------------------------------ 387.90/55.87 % (31864)------------------------------ 387.90/55.88 % (31868)lrs+1004_1:24_i=5433:si=on:rtra=on_0 on E---3.1_30784 for (1845ds/5433Mi) 388.54/56.04 % (31865)Instruction limit reached! 388.54/56.04 % (31865)------------------------------ 388.54/56.04 % (31865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 388.54/56.04 % (31865)Termination reason: Unknown 388.54/56.04 % (31865)Termination phase: Saturation 388.54/56.04 388.54/56.04 % (31865)Memory used [KB]: 22387 388.54/56.04 % (31865)Time elapsed: 1.380 s 388.54/56.04 % (31865)Instructions burned: 4408 (million) 388.54/56.04 % (31865)------------------------------ 388.54/56.04 % (31865)------------------------------ 388.54/56.05 % (31869)dis+1002_1:1_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:nm=0:i=8192:si=on:rtra=on_0 on E---3.1_30784 for (1844ds/8192Mi) 393.97/56.68 % (31863)Instruction limit reached! 393.97/56.68 % (31863)------------------------------ 393.97/56.68 % (31863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 393.97/56.68 % (31863)Termination reason: Unknown 393.97/56.68 % (31863)Termination phase: Saturation 393.97/56.68 393.97/56.68 % (31863)Memory used [KB]: 20468 393.97/56.68 % (31863)Time elapsed: 2.699 s 393.97/56.68 % (31863)Instructions burned: 8613 (million) 393.97/56.68 % (31863)------------------------------ 393.97/56.68 % (31863)------------------------------ 393.97/56.70 % (31870)lrs+32_1:1_au=on:bet=on:cbe=off:cs=on:ins=3:i=6102:si=on:rtra=on_0 on E---3.1_30784 for (1837ds/6102Mi) 399.99/57.53 % (31868)Instruction limit reached! 399.99/57.53 % (31868)------------------------------ 399.99/57.53 % (31868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 399.99/57.53 % (31868)Termination reason: Unknown 399.99/57.53 % (31868)Termination phase: Saturation 399.99/57.53 399.99/57.53 % (31868)Memory used [KB]: 11257 399.99/57.53 % (31868)Time elapsed: 1.653 s 399.99/57.53 % (31868)Instructions burned: 5434 (million) 399.99/57.53 % (31868)------------------------------ 399.99/57.53 % (31868)------------------------------ 399.99/57.54 % (31871)lrs+1002_8:1_au=on:cs=on:e2e=on:nm=10:s2a=on:i=35602:si=on:rtra=on_0 on E---3.1_30784 for (1829ds/35602Mi) 403.40/58.01 % (31869)Instruction limit reached! 403.40/58.01 % (31869)------------------------------ 403.40/58.01 % (31869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 403.40/58.01 % (31869)Termination reason: Unknown 403.40/58.01 % (31869)Termination phase: Saturation 403.40/58.01 403.40/58.01 % (31869)Memory used [KB]: 7675 403.40/58.01 % (31869)Time elapsed: 1.963 s 403.40/58.01 % (31869)Instructions burned: 8194 (million) 403.40/58.01 % (31869)------------------------------ 403.40/58.01 % (31869)------------------------------ 403.40/58.02 % (31872)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=6101:si=on:rtra=on_0 on E---3.1_30784 for (1824ds/6101Mi) 407.36/58.63 % (31870)Instruction limit reached! 407.36/58.63 % (31870)------------------------------ 407.36/58.63 % (31870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 407.36/58.63 % (31870)Termination reason: Unknown 407.36/58.63 % (31870)Termination phase: Saturation 407.36/58.63 407.36/58.63 % (31870)Memory used [KB]: 36715 407.36/58.63 % (31870)Time elapsed: 1.931 s 407.36/58.63 % (31870)Instructions burned: 6103 (million) 407.36/58.63 % (31870)------------------------------ 407.36/58.63 % (31870)------------------------------ 407.36/58.64 % (31873)dis+1010_3039923:1048576_bsr=unit_only:cbe=off:cha=on:cnfonf=off:e2e=on:fsr=off:hud=1:ixr=off:kws=precedence:lma=on:nm=4:piset=or:s2a=on:sp=frequency:spb=goal_then_units:i=28153:si=on:rtra=on_0 on E---3.1_30784 for (1818ds/28153Mi) 411.49/59.18 % (31866)Instruction limit reached! 411.49/59.18 % (31866)------------------------------ 411.49/59.18 % (31866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 411.49/59.18 % (31866)Termination reason: Unknown 411.49/59.18 % (31866)Termination phase: Saturation 411.49/59.18 411.49/59.18 % (31866)Memory used [KB]: 13304 411.49/59.18 % (31866)Time elapsed: 4.378 s 411.49/59.18 % (31866)Instructions burned: 13925 (million) 411.49/59.18 % (31866)------------------------------ 411.49/59.18 % (31866)------------------------------ 411.49/59.19 % (31874)lrs+10_1:1_cnfonf=off:sd=1:ss=axioms:st=3.0:i=13159:si=on:rtra=on_0 on E---3.1_30784 for (1812ds/13159Mi) 413.33/59.52 % (31872)Instruction limit reached! 413.33/59.52 % (31872)------------------------------ 413.33/59.52 % (31872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 413.33/59.52 % (31872)Termination reason: Unknown 413.33/59.52 % (31872)Termination phase: Saturation 413.33/59.52 413.33/59.52 % (31872)Memory used [KB]: 8059 413.33/59.52 % (31872)Time elapsed: 1.503 s 413.33/59.52 % (31872)Instructions burned: 6102 (million) 413.33/59.52 % (31872)------------------------------ 413.33/59.52 % (31872)------------------------------ 413.33/59.53 % (31875)lrs+2_1:1_bet=on:bsr=on:cnfonf=lazy_pi_sigma_gen:er=filter:kws=inv_frequency:ntd=on:sd=3:ss=axioms:i=12389:si=on:rtra=on_0 on E---3.1_30784 for (1809ds/12389Mi) 416.75/59.93 % (31859)Instruction limit reached! 416.75/59.93 % (31859)------------------------------ 416.75/59.93 % (31859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 416.75/59.93 % (31859)Termination reason: Unknown 416.75/59.93 % (31859)Termination phase: Saturation 416.75/59.93 416.75/59.93 % (31859)Memory used [KB]: 47333 416.75/59.93 % (31859)Time elapsed: 10.672 s 416.75/59.93 % (31859)Instructions burned: 35699 (million) 416.75/59.93 % (31859)------------------------------ 416.75/59.93 % (31859)------------------------------ 416.75/59.95 % (31876)dis+1002_16:1_au=on:nwc=5.0:i=37202:si=on:rtra=on_0 on E---3.1_30784 for (1805ds/37202Mi) 418.50/60.16 % (31850)Instruction limit reached! 418.50/60.16 % (31850)------------------------------ 418.50/60.16 % (31850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 418.50/60.16 % (31850)Termination reason: Unknown 418.50/60.16 % (31850)Termination phase: Saturation 418.50/60.16 418.50/60.16 % (31850)Memory used [KB]: 32110 418.50/60.16 % (31850)Time elapsed: 12.867 s 418.50/60.16 % (31850)Instructions burned: 41132 (million) 418.50/60.16 % (31850)------------------------------ 418.50/60.16 % (31850)------------------------------ 418.58/60.18 % (31877)ott+10_1:10_cnfonf=lazy_gen:fde=none:sp=const_frequency:i=15814:si=on:rtra=on_0 on E---3.1_30784 for (1802ds/15814Mi) 434.82/62.51 % (31875)Instruction limit reached! 434.82/62.51 % (31875)------------------------------ 434.82/62.51 % (31875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 434.82/62.51 % (31875)Termination reason: Unknown 434.82/62.51 % (31875)Termination phase: Saturation 434.82/62.51 434.82/62.51 % (31875)Memory used [KB]: 7803 434.82/62.51 % (31875)Time elapsed: 2.974 s 434.82/62.51 % (31875)Instructions burned: 12390 (million) 434.82/62.51 % (31875)------------------------------ 434.82/62.51 % (31875)------------------------------ 434.82/62.52 % (31878)dis+1010_1:28_add=off:cnfonf=lazy_not_gen:kws=frequency:piset=all:i=8801:si=on:rtra=on_0 on E---3.1_30784 for (1779ds/8801Mi) 436.34/62.74 % (31874)Instruction limit reached! 436.34/62.74 % (31874)------------------------------ 436.34/62.74 % (31874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 436.34/62.74 % (31874)Termination reason: Unknown 436.34/62.74 % (31874)Termination phase: Saturation 436.34/62.74 436.34/62.74 % (31874)Memory used [KB]: 10874 436.34/62.74 % (31874)Time elapsed: 3.553 s 436.34/62.74 % (31874)Instructions burned: 13162 (million) 436.34/62.74 % (31874)------------------------------ 436.34/62.74 % (31874)------------------------------ 436.34/62.76 % (31879)ott-21_5:4_atotf=0.3:e2e=on:hud=15:ins=1:plsq=on:plsqc=1:plsqr=32,1:sp=unary_frequency:tnu=2:i=12360:si=on:rtra=on_0 on E---3.1_30784 for (1776ds/12360Mi) 447.84/64.39 % (31877)Instruction limit reached! 447.84/64.39 % (31877)------------------------------ 447.84/64.39 % (31877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 447.84/64.39 % (31877)Termination reason: Unknown 447.84/64.39 % (31877)Termination phase: Saturation 447.84/64.39 447.84/64.39 % (31877)Memory used [KB]: 42984 447.84/64.39 % (31877)Time elapsed: 4.233 s 447.84/64.39 % (31877)Instructions burned: 15815 (million) 447.84/64.39 % (31877)------------------------------ 447.84/64.39 % (31877)------------------------------ 448.12/64.40 % (31880)lrs+10_1:156_afp=4000:avsq=on:avsqr=4,1:fe=axiom:ss=axioms:tgt=ground:i=19001:si=on:rtra=on_0 on E---3.1_30784 for (1760ds/19001Mi) 449.42/64.62 % (31878)Instruction limit reached! 449.42/64.62 % (31878)------------------------------ 449.42/64.62 % (31878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 449.42/64.62 % (31878)Termination reason: Unknown 449.42/64.62 % (31878)Termination phase: Saturation 449.42/64.62 449.42/64.62 % (31878)Memory used [KB]: 8059 449.42/64.62 % (31878)Time elapsed: 2.110 s 449.42/64.62 % (31878)Instructions burned: 8801 (million) 449.42/64.62 % (31878)------------------------------ 449.42/64.62 % (31878)------------------------------ 449.42/64.63 % (31881)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=28134:si=on:rtra=on_0 on E---3.1_30784 for (1758ds/28134Mi) 464.75/66.76 % (31879)Instruction limit reached! 464.75/66.76 % (31879)------------------------------ 464.75/66.76 % (31879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 464.75/66.76 % (31879)Termination reason: Unknown 464.75/66.76 % (31879)Termination phase: Saturation 464.75/66.76 464.75/66.76 % (31879)Memory used [KB]: 39914 464.75/66.76 % (31879)Time elapsed: 4.005 s 464.75/66.76 % (31879)Instructions burned: 12361 (million) 464.75/66.76 % (31879)------------------------------ 464.75/66.76 % (31879)------------------------------ 464.75/66.77 % (31882)dis+10_1:1_fde=none:kws=precedence:piset=not:prag=on:slsq=on:slsqc=1:sp=unary_frequency:i=23684:si=on:rtra=on_0 on E---3.1_30784 for (1736ds/23684Mi) 469.60/67.53 % (31873)Instruction limit reached! 469.60/67.53 % (31873)------------------------------ 469.60/67.53 % (31873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 469.60/67.53 % (31873)Termination reason: Unknown 469.60/67.53 % (31873)Termination phase: Saturation 469.60/67.53 469.60/67.53 % (31873)Memory used [KB]: 50148 469.60/67.53 % (31873)Time elapsed: 8.889 s 469.60/67.53 % (31873)Instructions burned: 28156 (million) 469.60/67.53 % (31873)------------------------------ 469.60/67.53 % (31873)------------------------------ 469.60/67.54 % (31883)ott+10_1:10_avsq=on:bd=off:cnfonf=lazy_gen:sd=2:sgt=16:sos=on:ss=axioms:i=56001:si=on:rtra=on_0 on E---3.1_30784 for (1729ds/56001Mi) 477.02/68.52 % (31871)Instruction limit reached! 477.02/68.52 % (31871)------------------------------ 477.02/68.52 % (31871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 477.02/68.52 % (31871)Termination reason: Unknown 477.02/68.52 % (31871)Termination phase: Saturation 477.02/68.52 477.02/68.52 % (31871)Memory used [KB]: 68058 477.02/68.52 % (31871)Time elapsed: 10.973 s 477.02/68.52 % (31871)Instructions burned: 35603 (million) 477.02/68.52 % (31871)------------------------------ 477.02/68.52 % (31871)------------------------------ 477.02/68.54 % (31884)dis+2_1:1_cbe=off:fe=off:i=13068:si=on:rtra=on_0 on E---3.1_30784 for (1719ds/13068Mi) 479.89/69.01 % (31881)Refutation not found, incomplete strategy 479.89/69.01 % (31881)------------------------------ 479.89/69.01 % (31881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 479.89/69.01 % (31881)Termination reason: Refutation not found, incomplete strategy 479.89/69.01 479.89/69.01 479.89/69.01 % (31881)Memory used [KB]: 11129 479.89/69.01 % (31881)Time elapsed: 4.373 s 479.89/69.01 % (31881)Instructions burned: 16045 (million) 479.89/69.01 % (31881)------------------------------ 479.89/69.01 % (31881)------------------------------ 479.89/69.02 % (31885)dis+10_3:1_anc=all:avsq=on:c=on:cnfonf=off:e2e=on:fd=off:fde=none:ins=3:nwc=5.0:plsq=on:plsqc=1:plsqr=4964065,131072:prag=on:s2a=on:s2agt=64:i=8801:si=on:rtra=on_0 on E---3.1_30784 for (1714ds/8801Mi) 486.28/69.84 % (31880)Instruction limit reached! 486.28/69.84 % (31880)------------------------------ 486.28/69.84 % (31880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 486.28/69.84 % (31880)Termination reason: Unknown 486.28/69.84 % (31880)Termination phase: Saturation 486.28/69.84 486.28/69.84 % (31880)Memory used [KB]: 26353 486.28/69.84 % (31880)Time elapsed: 5.441 s 486.28/69.84 % (31880)Instructions burned: 19003 (million) 486.28/69.84 % (31880)------------------------------ 486.28/69.84 % (31880)------------------------------ 486.28/69.85 % (31886)dis+1010_1:64_bet=on:cond=fast:e2e=on:fe=off:hud=5:nm=0:ntd=on:nwc=7.0:piset=and:prag=on:rawr=on:sgt=40:ss=included:uhcvi=on:i=42318:si=on:rtra=on_0 on E---3.1_30784 for (1706ds/42318Mi) 497.51/71.47 % (31876)Instruction limit reached! 497.51/71.47 % (31876)------------------------------ 497.51/71.47 % (31876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 497.51/71.47 % (31876)Termination reason: Unknown 497.51/71.47 % (31876)Termination phase: Saturation 497.51/71.47 497.51/71.47 % (31876)Memory used [KB]: 36843 497.51/71.47 % (31876)Time elapsed: 11.544 s 497.51/71.47 % (31876)Instructions burned: 37203 (million) 497.51/71.47 % (31876)------------------------------ 497.51/71.47 % (31876)------------------------------ 497.51/71.48 % (31887)dis+1010_1:1_au=on:avsq=on:bd=off:cbe=off:cnfonf=off:cs=on:hud=5:nm=0:plsq=on:plsqc=1:plsqr=7,1:ss=axioms:tgt=full:i=10924:si=on:rtra=on_0 on E---3.1_30784 for (1689ds/10924Mi) 498.94/71.66 % (31885)Instruction limit reached! 498.94/71.66 % (31885)------------------------------ 498.94/71.66 % (31885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 498.94/71.66 % (31885)Termination reason: Unknown 498.94/71.66 % (31885)Termination phase: Saturation 498.94/71.66 498.94/71.66 % (31885)Memory used [KB]: 44263 498.94/71.66 % (31885)Time elapsed: 2.649 s 498.94/71.66 % (31885)Instructions burned: 8802 (million) 498.94/71.66 % (31885)------------------------------ 498.94/71.66 % (31885)------------------------------ 498.94/71.68 % (31888)lrs+1010_1:1_anc=all_dependent:cnfonf=conj_eager:cond=fast:fe=axiom:nm=16:s2a=on:s2at=4.0:sd=2:ss=axioms:st=3.0:i=96745:si=on:rtra=on_0 on E---3.1_30784 for (1687ds/96745Mi) 504.60/72.51 % (31884)Instruction limit reached! 504.60/72.51 % (31884)------------------------------ 504.60/72.51 % (31884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 504.60/72.51 % (31884)Termination reason: Unknown 504.60/72.51 % (31884)Termination phase: Saturation 504.60/72.51 504.60/72.51 % (31884)Memory used [KB]: 20468 504.60/72.51 % (31884)Time elapsed: 3.976 s 504.60/72.51 % (31884)Instructions burned: 13069 (million) 504.60/72.51 % (31884)------------------------------ 504.60/72.51 % (31884)------------------------------ 504.60/72.52 % (31889)lrs-1010_8:1_au=on:c=on:ins=1:i=70437:si=on:rtra=on_0 on E---3.1_30784 for (1679ds/70437Mi) 506.49/72.79 % (31887)Refutation not found, incomplete strategy 506.49/72.79 % (31887)------------------------------ 506.49/72.79 % (31887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 506.49/72.79 % (31887)Termination reason: Refutation not found, incomplete strategy 506.49/72.79 506.49/72.79 506.49/72.79 % (31887)Memory used [KB]: 11513 506.49/72.79 % (31887)Time elapsed: 1.309 s 506.49/72.79 % (31887)Instructions burned: 4525 (million) 506.49/72.79 % (31887)------------------------------ 506.49/72.79 % (31887)------------------------------ 506.49/72.80 % (31890)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=11540:si=on:rtra=on_0 on E---3.1_30784 for (1676ds/11540Mi) 515.92/74.11 % (31882)Instruction limit reached! 515.92/74.11 % (31882)------------------------------ 515.92/74.11 % (31882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 515.92/74.11 % (31882)Termination reason: Unknown 515.92/74.11 % (31882)Termination phase: Saturation 515.92/74.11 515.92/74.11 % (31882)Memory used [KB]: 44007 515.92/74.11 % (31882)Time elapsed: 7.339 s 515.92/74.11 % (31882)Instructions burned: 23685 (million) 515.92/74.11 % (31882)------------------------------ 515.92/74.11 % (31882)------------------------------ 515.92/74.12 % (31891)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=32059:si=on:rtra=on_0 on E---3.1_30784 for (1663ds/32059Mi) 529.34/76.02 % (31890)Refutation not found, non-redundant clauses discarded% (31890)------------------------------ 529.34/76.02 % (31890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 529.34/76.02 % (31890)Termination reason: Refutation not found, non-redundant clauses discarded 529.34/76.02 529.34/76.02 % (31890)Memory used [KB]: 22387 529.34/76.02 % (31890)Time elapsed: 3.224 s 529.34/76.02 % (31890)Instructions burned: 10389 (million) 529.34/76.02 % (31890)------------------------------ 529.34/76.02 % (31890)------------------------------ 529.34/76.04 % (31892)lrs+1002_1:128_atotf=0.1:au=on:cbe=off:ntd=on:sp=const_frequency:i=14041:si=on:rtra=on_0 on E---3.1_30784 for (1644ds/14041Mi) 558.52/80.16 % (31892)Instruction limit reached! 558.52/80.16 % (31892)------------------------------ 558.52/80.16 % (31892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 558.52/80.16 % (31892)Termination reason: Unknown 558.52/80.16 % (31892)Termination phase: Saturation 558.52/80.16 558.52/80.16 % (31892)Memory used [KB]: 13432 558.52/80.16 % (31892)Time elapsed: 4.125 s 558.52/80.16 % (31892)Instructions burned: 14043 (million) 558.52/80.16 % (31892)------------------------------ 558.52/80.16 % (31892)------------------------------ 558.69/80.17 % (31893)dis+10_1:1_fe=axiom:fsr=off:hud=5:nwc=6.0:plsq=on:plsqc=2:plsqr=32,1:s2a=on:s2agt=40:sp=weighted_frequency:i=15424:si=on:rtra=on_0 on E---3.1_30784 for (1602ds/15424Mi) 571.89/82.10 % (31883)Instruction limit reached! 571.89/82.10 % (31883)------------------------------ 571.89/82.10 % (31883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 571.89/82.10 % (31883)Termination reason: Unknown 571.89/82.10 % (31883)Termination phase: Saturation 571.89/82.10 571.89/82.10 % (31883)Memory used [KB]: 17014 571.89/82.10 % (31883)Time elapsed: 14.560 s 571.89/82.10 % (31883)Instructions burned: 56001 (million) 571.89/82.10 % (31883)------------------------------ 571.89/82.10 % (31883)------------------------------ 572.35/82.11 % (31894)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3971:si=on:rtra=on_0 on E---3.1_30784 for (1583ds/3971Mi) 574.52/82.51 % (31891)Refutation not found, non-redundant clauses discarded% (31891)------------------------------ 574.52/82.51 % (31891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 574.52/82.51 % (31891)Termination reason: Refutation not found, non-redundant clauses discarded 574.52/82.51 574.52/82.51 % (31891)Memory used [KB]: 12537 574.52/82.51 % (31891)Time elapsed: 8.389 s 574.52/82.51 % (31891)Instructions burned: 31985 (million) 574.52/82.51 % (31891)------------------------------ 574.52/82.51 % (31891)------------------------------ 574.52/82.52 % (31895)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on E---3.1_30784 for (1579ds/2207Mi) 576.99/82.79 % (31886)Instruction limit reached! 576.99/82.79 % (31886)------------------------------ 576.99/82.79 % (31886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 576.99/82.79 % (31886)Termination reason: Unknown 576.99/82.79 % (31886)Termination phase: Saturation 576.99/82.79 576.99/82.79 % (31886)Memory used [KB]: 74327 576.99/82.79 % (31886)Time elapsed: 12.940 s 576.99/82.79 % (31886)Instructions burned: 42319 (million) 576.99/82.79 % (31886)------------------------------ 576.99/82.79 % (31886)------------------------------ 576.99/82.81 % (31896)dis+1002_1:1_au=on:bsr=unit_only:cbe=off:fe=off:fsr=off:nm=10:nwc=6.0:plsq=on:plsqc=1:plsqr=32,1:sos=all:i=2635:si=on:rtra=on_0 on E---3.1_30784 for (1576ds/2635Mi) 579.30/83.19 % (31895)Instruction limit reached! 579.30/83.19 % (31895)------------------------------ 579.30/83.19 % (31895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 579.30/83.19 % (31895)Termination reason: Unknown 579.30/83.19 % (31895)Termination phase: Saturation 579.30/83.19 579.30/83.19 % (31895)Memory used [KB]: 11513 579.30/83.19 % (31895)Time elapsed: 0.664 s 579.30/83.19 % (31895)Instructions burned: 2209 (million) 579.30/83.19 % (31895)------------------------------ 579.30/83.19 % (31895)------------------------------ 579.90/83.20 % (31897)dis+1010_2:1_avsq=on:fde=unused:prag=on:i=3362:si=on:rtra=on_0 on E---3.1_30784 for (1572ds/3362Mi) 580.35/83.29 % (31894)Instruction limit reached! 580.35/83.29 % (31894)------------------------------ 580.35/83.29 % (31894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 580.35/83.29 % (31894)Termination reason: Unknown 580.35/83.29 % (31894)Termination phase: Saturation 580.35/83.29 580.35/83.29 % (31894)Memory used [KB]: 15351 580.35/83.29 % (31894)Time elapsed: 1.202 s 580.35/83.29 % (31894)Instructions burned: 3971 (million) 580.35/83.29 % (31894)------------------------------ 580.35/83.29 % (31894)------------------------------ 580.35/83.30 % (31898)dis+1002_1:1_apa=on:au=on:cnfonf=off:e2e=on:flr=on:nm=4:s2a=on:i=8612:si=on:rtra=on_0 on E---3.1_30784 for (1571ds/8612Mi) 581.89/83.62 % (31896)Instruction limit reached! 581.89/83.62 % (31896)------------------------------ 581.89/83.62 % (31896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 581.89/83.62 % (31896)Termination reason: Unknown 581.89/83.62 % (31896)Termination phase: Saturation 581.89/83.62 581.89/83.62 % (31896)Memory used [KB]: 12153 581.89/83.62 % (31896)Time elapsed: 0.811 s 581.89/83.62 % (31896)Instructions burned: 2637 (million) 581.89/83.62 % (31896)------------------------------ 581.89/83.62 % (31896)------------------------------ 582.20/83.63 % (31899)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=129283:si=on:rtra=on_0 on E---3.1_30784 for (1568ds/129283Mi) 586.71/84.17 % (31897)Instruction limit reached! 586.71/84.17 % (31897)------------------------------ 586.71/84.17 % (31897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 586.71/84.17 % (31897)Termination reason: Unknown 586.71/84.17 % (31897)Termination phase: Saturation 586.71/84.17 586.71/84.17 % (31897)Memory used [KB]: 23539 586.71/84.17 % (31897)Time elapsed: 0.972 s 586.71/84.17 % (31897)Instructions burned: 3363 (million) 586.71/84.17 % (31897)------------------------------ 586.71/84.17 % (31897)------------------------------ 586.71/84.18 % (31900)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15187:si=on:rtra=on_0 on E---3.1_30784 for (1562ds/15187Mi) 592.62/85.01 % (31893)Instruction limit reached! 592.62/85.01 % (31893)------------------------------ 592.62/85.01 % (31893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 592.62/85.01 % (31893)Termination reason: Unknown 592.62/85.01 % (31893)Termination phase: Saturation 592.62/85.01 592.62/85.01 % (31893)Memory used [KB]: 25713 592.62/85.01 % (31893)Time elapsed: 4.842 s 592.62/85.01 % (31893)Instructions burned: 15426 (million) 592.62/85.01 % (31893)------------------------------ 592.62/85.01 % (31893)------------------------------ 592.62/85.02 % (31901)lrs+10_1:1_cnfonf=off:sd=1:ss=axioms:st=3.0:i=13159:si=on:rtra=on_0 on E---3.1_30784 for (1554ds/13159Mi) 598.71/85.96 % (31898)Instruction limit reached! 598.71/85.96 % (31898)------------------------------ 598.71/85.96 % (31898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 598.71/85.96 % (31898)Termination reason: Unknown 598.71/85.96 % (31898)Termination phase: Saturation 598.71/85.96 598.71/85.96 % (31898)Memory used [KB]: 20340 598.71/85.96 % (31898)Time elapsed: 2.657 s 598.71/85.96 % (31898)Instructions burned: 8614 (million) 598.71/85.96 % (31898)------------------------------ 598.71/85.96 % (31898)------------------------------ 599.35/85.97 % (31902)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=14573:si=on:rtra=on_0 on E---3.1_30784 for (1544ds/14573Mi) 617.74/88.60 % (31901)Instruction limit reached! 617.74/88.60 % (31901)------------------------------ 617.74/88.60 % (31901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 617.74/88.60 % (31901)Termination reason: Unknown 617.74/88.60 % (31901)Termination phase: Saturation 617.74/88.60 617.74/88.60 % (31901)Memory used [KB]: 10874 617.74/88.60 % (31901)Time elapsed: 3.574 s 617.74/88.60 % (31901)Instructions burned: 13161 (million) 617.74/88.60 % (31901)------------------------------ 617.74/88.60 % (31901)------------------------------ 617.74/88.61 % (31903)dis+1010_1:28_add=off:cnfonf=lazy_not_gen:kws=frequency:piset=all:i=8801:si=on:rtra=on_0 on E---3.1_30784 for (1518ds/8801Mi) 618.17/88.66 % (31900)Instruction limit reached! 618.17/88.66 % (31900)------------------------------ 618.17/88.66 % (31900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 618.17/88.66 % (31900)Termination reason: Unknown 618.17/88.66 % (31900)Termination phase: Saturation 618.17/88.66 618.17/88.66 % (31900)Memory used [KB]: 21492 618.17/88.66 % (31900)Time elapsed: 4.481 s 618.17/88.66 % (31900)Instructions burned: 15190 (million) 618.17/88.66 % (31900)------------------------------ 618.17/88.66 % (31900)------------------------------ 618.23/88.67 % (31904)dis-1666_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:i=50861:si=on:rtra=on_0 on E---3.1_30784 for (1517ds/50861Mi) 630.00/90.36 % (31902)Instruction limit reached! 630.00/90.36 % (31902)------------------------------ 630.00/90.36 % (31902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 630.00/90.36 % (31902)Termination reason: Unknown 630.00/90.36 % (31902)Termination phase: Saturation 630.00/90.36 630.00/90.36 % (31902)Memory used [KB]: 15223 630.00/90.36 % (31902)Time elapsed: 4.391 s 630.00/90.36 % (31902)Instructions burned: 14573 (million) 630.00/90.36 % (31902)------------------------------ 630.00/90.36 % (31902)------------------------------ 630.00/90.37 % (31905)lrs+1666_1:1_au=on:s2a=on:sd=2:ss=axioms:st=5.0:i=120493:si=on:rtra=on_0 on E---3.1_30784 for (1500ds/120493Mi) 636.47/90.69 % (31903)Instruction limit reached! 636.47/90.69 % (31903)------------------------------ 636.47/90.69 % (31903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 636.47/90.69 % (31903)Termination reason: Unknown 636.47/90.69 % (31903)Termination phase: Saturation 636.47/90.69 636.47/90.69 % (31903)Memory used [KB]: 8059 636.47/90.69 % (31903)Time elapsed: 2.086 s 636.47/90.69 % (31903)Instructions burned: 8801 (million) 636.47/90.69 % (31903)------------------------------ 636.47/90.69 % (31903)------------------------------ 636.47/90.70 % (31906)dis+1010_1:1_anc=all_dependent:au=on:bs=on:sd=5:sp=occurrence:ss=axioms:st=2.0:i=77525:si=on:rtra=on_0 on E---3.1_30784 for (1497ds/77525Mi) 646.80/92.19 % (31867)Instruction limit reached! 646.80/92.19 % (31867)------------------------------ 646.80/92.19 % (31867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 646.80/92.19 % (31867)Termination reason: Unknown 646.80/92.19 % (31867)Termination phase: Saturation 646.80/92.19 646.80/92.19 % (31867)Memory used [KB]: 66651 646.80/92.19 % (31867)Time elapsed: 36.702 s 646.80/92.19 % (31867)Instructions burned: 117047 (million) 646.80/92.19 % (31867)------------------------------ 646.80/92.19 % (31867)------------------------------ 646.80/92.20 % (31907)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=13432:si=on:rtra=on_0 on E---3.1_30784 for (1482ds/13432Mi) 665.41/94.81 % (31889)Instruction limit reached! 665.41/94.81 % (31889)------------------------------ 665.41/94.81 % (31889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 665.41/94.81 % (31889)Termination reason: Unknown 665.41/94.81 % (31889)Termination phase: Saturation 665.41/94.81 665.41/94.81 % (31889)Memory used [KB]: 48997 665.41/94.81 % (31889)Time elapsed: 22.287 s 665.41/94.81 % (31889)Instructions burned: 70437 (million) 665.41/94.81 % (31889)------------------------------ 665.41/94.81 % (31889)------------------------------ 665.41/94.82 % (31908)lrs+10_1:156_afp=4000:avsq=on:avsqr=4,1:fe=axiom:ss=axioms:tgt=ground:i=19001:si=on:rtra=on_0 on E---3.1_30784 for (1456ds/19001Mi) 673.10/95.89 % (31907)Instruction limit reached! 673.10/95.89 % (31907)------------------------------ 673.10/95.89 % (31907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 673.10/95.89 % (31907)Termination reason: Unknown 673.10/95.89 % (31907)Termination phase: Saturation 673.10/95.89 673.10/95.89 % (31907)Memory used [KB]: 11001 673.10/95.89 % (31907)Time elapsed: 3.690 s 673.10/95.89 % (31907)Instructions burned: 13433 (million) 673.10/95.89 % (31907)------------------------------ 673.10/95.89 % (31907)------------------------------ 673.10/95.90 % (31909)ott+1002_1:1_au=on:cnfonf=lazy_simp:nwc=5.0:sgt=5:ss=axioms:st=1.5:i=17538:si=on:rtra=on_0 on E---3.1_30784 for (1445ds/17538Mi) 703.84/100.31 % (31909)Instruction limit reached! 703.84/100.31 % (31909)------------------------------ 703.84/100.31 % (31909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 703.84/100.31 % (31909)Termination reason: Unknown 703.84/100.31 % (31909)Termination phase: Saturation 703.84/100.31 703.84/100.31 % (31909)Memory used [KB]: 13560 703.84/100.31 % (31909)Time elapsed: 4.412 s 703.84/100.31 % (31909)Instructions burned: 17539 (million) 703.84/100.31 % (31909)------------------------------ 703.84/100.31 % (31909)------------------------------ 704.18/100.32 % (31910)lrs+1010_1:1024_au=on:hud=10:ntd=on:ss=included:i=168763:si=on:rtra=on_0 on E---3.1_30784 for (1401ds/168763Mi) 704.32/100.42 % (31908)Instruction limit reached! 704.32/100.42 % (31908)------------------------------ 704.32/100.42 % (31908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 704.32/100.42 % (31908)Termination reason: Unknown 704.32/100.42 % (31908)Termination phase: Saturation 704.32/100.42 704.32/100.42 % (31908)Memory used [KB]: 23027 704.32/100.42 % (31908)Time elapsed: 5.596 s 704.32/100.42 % (31908)Instructions burned: 19004 (million) 704.32/100.42 % (31908)------------------------------ 704.32/100.42 % (31908)------------------------------ 704.76/100.43 % (31911)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=84973:si=on:rtra=on_0 on E---3.1_30784 for (1400ds/84973Mi) 710.15/101.19 % (31888)Instruction limit reached! 710.15/101.19 % (31888)------------------------------ 710.15/101.19 % (31888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 710.15/101.19 % (31888)Termination reason: Unknown 710.15/101.19 % (31888)Termination phase: Saturation 710.15/101.19 710.15/101.19 % (31888)Memory used [KB]: 59487 710.15/101.19 % (31888)Time elapsed: 29.511 s 710.15/101.19 % (31888)Instructions burned: 96745 (million) 710.15/101.19 % (31888)------------------------------ 710.15/101.19 % (31888)------------------------------ 710.15/101.21 % (31912)ott+10_1:10_cnfonf=lazy_gen:fde=none:sp=const_frequency:i=15814:si=on:rtra=on_0 on E---3.1_30784 for (1392ds/15814Mi) 711.73/101.42 % (31904)Instruction limit reached! 711.73/101.42 % (31904)------------------------------ 711.73/101.42 % (31904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 711.73/101.42 % (31904)Termination reason: Unknown 711.73/101.42 % (31904)Termination phase: Saturation 711.73/101.42 711.73/101.42 % (31904)Memory used [KB]: 36204 711.73/101.42 % (31904)Time elapsed: 12.752 s 711.73/101.42 % (31904)Instructions burned: 50861 (million) 711.73/101.42 % (31904)------------------------------ 711.73/101.42 % (31904)------------------------------ 711.73/101.43 % (31913)lrs+10_1:1_ins=2:sd=1:ss=axioms:st=3.0:i=173649:si=on:rtra=on_0 on E---3.1_30784 for (1390ds/173649Mi) 738.85/105.32 % (31912)Instruction limit reached! 738.85/105.32 % (31912)------------------------------ 738.85/105.32 % (31912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 738.85/105.32 % (31912)Termination reason: Unknown 738.85/105.32 % (31912)Termination phase: Saturation 738.85/105.32 738.85/105.32 % (31912)Memory used [KB]: 61790 738.85/105.32 % (31912)Time elapsed: 4.119 s 738.85/105.32 % (31912)Instructions burned: 15814 (million) 738.85/105.32 % (31912)------------------------------ 738.85/105.32 % (31912)------------------------------ 738.85/105.34 % (31914)lrs+1002_8:1_au=on:cs=on:e2e=on:nm=10:s2a=on:i=35602:si=on:rtra=on_0 on E---3.1_30784 for (1351ds/35602Mi) 803.42/114.50 % (31906)Instruction limit reached! 803.42/114.50 % (31906)------------------------------ 803.42/114.50 % (31906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 803.42/114.50 % (31906)Termination reason: Unknown 803.42/114.50 % (31906)Termination phase: Saturation 803.42/114.50 803.42/114.50 % (31906)Memory used [KB]: 84433 803.42/114.50 % (31906)Time elapsed: 23.797 s 803.42/114.50 % (31906)Instructions burned: 77527 (million) 803.42/114.50 % (31906)------------------------------ 803.42/114.50 % (31906)------------------------------ 803.42/114.52 % (31916)dis+1002_16:1_au=on:nwc=5.0:i=37202:si=on:rtra=on_0 on E---3.1_30784 for (1259ds/37202Mi) 812.88/115.88 % (31914)Instruction limit reached! 812.88/115.88 % (31914)------------------------------ 812.88/115.88 % (31914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 812.88/115.88 % (31914)Termination reason: Unknown 812.88/115.88 % (31914)Termination phase: Saturation 812.88/115.88 812.88/115.88 % (31914)Memory used [KB]: 71512 812.88/115.88 % (31914)Time elapsed: 10.540 s 812.88/115.88 % (31914)Instructions burned: 35602 (million) 812.88/115.88 % (31914)------------------------------ 812.88/115.88 % (31914)------------------------------ 812.88/115.90 % (31917)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=16361:si=on:rtra=on_0 on E---3.1_30784 for (1245ds/16361Mi) 849.14/121.01 % (31917)Instruction limit reached! 849.14/121.01 % (31917)------------------------------ 849.14/121.01 % (31917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 849.14/121.01 % (31917)Termination reason: Unknown 849.14/121.01 % (31917)Termination phase: Saturation 849.14/121.01 849.14/121.01 % (31917)Memory used [KB]: 28912 849.14/121.01 % (31917)Time elapsed: 5.136 s 849.14/121.01 % (31917)Instructions burned: 16361 (million) 849.14/121.01 % (31917)------------------------------ 849.14/121.01 % (31917)------------------------------ 849.14/121.02 % (31918)lrs+1010_1:3_au=on:bd=off:c=on:cbe=off:fsr=off:ins=1:ss=axioms:st=1.5:i=15670:si=on:rtra=on_0 on E---3.1_30784 for (1194ds/15670Mi) 858.35/122.39 % (31899)Instruction limit reached! 858.35/122.39 % (31899)------------------------------ 858.35/122.39 % (31899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 858.35/122.39 % (31899)Termination reason: Unknown 858.35/122.39 % (31899)Termination phase: Saturation 858.35/122.39 858.35/122.39 % (31899)Memory used [KB]: 85712 858.35/122.39 % (31899)Time elapsed: 38.748 s 858.35/122.39 % (31899)Instructions burned: 129286 (million) 858.35/122.39 % (31899)------------------------------ 858.35/122.39 % (31899)------------------------------ 858.35/122.40 % (31919)dis+1010_1:1_bd=off:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=137969:si=on:rtra=on_0 on E---3.1_30784 for (1180ds/137969Mi) 883.60/126.00 % (31918)Instruction limit reached! 883.60/126.00 % (31918)------------------------------ 883.60/126.00 % (31918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 883.60/126.00 % (31918)Termination reason: Unknown 883.60/126.00 % (31918)Termination phase: Saturation 883.60/126.00 883.60/126.00 % (31918)Memory used [KB]: 16630 883.60/126.00 % (31918)Time elapsed: 5.004 s 883.60/126.00 % (31918)Instructions burned: 15672 (million) 883.60/126.00 % (31918)------------------------------ 883.60/126.00 % (31918)------------------------------ 883.60/126.01 % (31920)lrs+1004_1:24_i=198698:si=on:rtra=on_0 on E---3.1_30784 for (1144ds/198698Mi) 884.84/126.14 % (31916)Instruction limit reached! 884.84/126.14 % (31916)------------------------------ 884.84/126.14 % (31916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 884.84/126.14 % (31916)Termination reason: Unknown 884.84/126.14 % (31916)Termination phase: Saturation 884.84/126.14 884.84/126.14 % (31916)Memory used [KB]: 38890 884.84/126.14 % (31916)Time elapsed: 11.624 s 884.84/126.14 % (31916)Instructions burned: 37204 (million) 884.84/126.14 % (31916)------------------------------ 884.84/126.14 % (31916)------------------------------ 884.84/126.15 % (31921)dis+1010_1:64_bet=on:cond=fast:e2e=on:fe=off:hud=5:nm=0:ntd=on:nwc=7.0:piset=and:prag=on:rawr=on:sgt=40:ss=included:uhcvi=on:i=42318:si=on:rtra=on_0 on E---3.1_30784 for (1143ds/42318Mi) 887.18/126.59 % (31905)Instruction limit reached! 887.18/126.59 % (31905)------------------------------ 887.18/126.59 % (31905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 887.18/126.59 % (31905)Termination reason: Unknown 887.18/126.59 % (31905)Termination phase: Saturation 887.18/126.59 887.18/126.59 % (31905)Memory used [KB]: 55393 887.18/126.59 % (31905)Time elapsed: 36.219 s 887.18/126.59 % (31905)Instructions burned: 120493 (million) 887.18/126.59 % (31905)------------------------------ 887.18/126.59 % (31905)------------------------------ 888.34/126.60 % (31922)dis+1002_1:1_av=off:prag=on:sd=1:sos=on:sp=occurrence:ss=axioms:i=33524:si=on:rtra=on_0 on E---3.1_30784 for (1138ds/33524Mi) 896.01/127.74 % (31911)Instruction limit reached! 896.01/127.74 % (31911)------------------------------ 896.01/127.74 % (31911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 896.01/127.74 % (31911)Termination reason: Unknown 896.01/127.74 % (31911)Termination phase: Saturation 896.01/127.74 896.01/127.74 % (31911)Memory used [KB]: 84305 896.01/127.74 % (31911)Time elapsed: 27.310 s 896.01/127.74 % (31911)Instructions burned: 84974 (million) 896.01/127.74 % (31911)------------------------------ 896.01/127.74 % (31911)------------------------------ 896.01/127.76 % (31923)dis+10_3366879:524288_awrs=decay:bd=preordered:cbe=off:e2e=on:kws=arity_squared:nwc=3.0:piset=pi_sigma:sac=on:sd=1:sgt=64:sp=const_max:ss=axioms:tgt=full:i=29485:si=on:rtra=on_0 on E---3.1_30784 for (1126ds/29485Mi) 959.54/136.80 % (31923)Instruction limit reached! 959.54/136.80 % (31923)------------------------------ 959.54/136.80 % (31923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 959.54/136.80 % (31923)Termination reason: Unknown 959.54/136.80 % (31923)Termination phase: Saturation 959.54/136.80 959.54/136.80 % (31923)Memory used [KB]: 47078 959.54/136.80 % (31923)Time elapsed: 9.048 s 959.54/136.80 % (31923)Instructions burned: 29487 (million) 959.54/136.80 % (31923)------------------------------ 959.54/136.80 % (31923)------------------------------ 959.87/136.82 % (31924)dis+1002_1:1_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:nm=0:i=20308:si=on:rtra=on_0 on E---3.1_30784 for (1036ds/20308Mi) 959.87/136.83 % (31922)Instruction limit reached! 959.87/136.83 % (31922)------------------------------ 959.87/136.83 % (31922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 959.87/136.83 % (31922)Termination reason: Unknown 959.87/136.83 % (31922)Termination phase: Saturation 959.87/136.83 959.87/136.83 % (31922)Memory used [KB]: 28272 959.87/136.83 % (31922)Time elapsed: 10.225 s 959.87/136.83 % (31922)Instructions burned: 33526 (million) 959.87/136.83 % (31922)------------------------------ 959.87/136.83 % (31922)------------------------------ 959.87/136.84 % (31925)lrs-1_1:1_au=on:cbe=off:ntd=on:i=22706:si=on:rtra=on_0 on E---3.1_30784 for (1036ds/22706Mi) 976.49/139.20 % (31921)Instruction limit reached! 976.49/139.20 % (31921)------------------------------ 976.49/139.20 % (31921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 976.49/139.20 % (31921)Termination reason: Unknown 976.49/139.20 % (31921)Termination phase: Saturation 976.49/139.20 976.49/139.20 % (31921)Memory used [KB]: 70617 976.49/139.20 % (31921)Time elapsed: 13.071 s 976.49/139.20 % (31921)Instructions burned: 42320 (million) 976.49/139.20 % (31921)------------------------------ 976.49/139.20 % (31921)------------------------------ 976.71/139.22 % (31926)dis+1010_1:1_anc=all_dependent:au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:fde=none:ins=2:nwc=10.0:piset=or:i=99377:si=on:rtra=on_0 on E---3.1_30784 for (1012ds/99377Mi) 995.89/141.96 % (31924)Instruction limit reached! 995.89/141.96 % (31924)------------------------------ 995.89/141.96 % (31924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 995.89/141.96 % (31924)Termination reason: Unknown 995.89/141.96 % (31924)Termination phase: Saturation 995.89/141.96 995.89/141.96 % (31924)Memory used [KB]: 14072 995.89/141.96 % (31924)Time elapsed: 5.146 s 995.89/141.96 % (31924)Instructions burned: 20309 (million) 995.89/141.96 % (31924)------------------------------ 995.89/141.96 % (31924)------------------------------ 995.89/141.97 % (31927)ott+1010_1:4_cnfonf=lazy_simp:fe=off:hud=5:piset=or:prag=on:i=112304:si=on:rtra=on_0 on E---3.1_30784 for (984ds/112304Mi) 1008.52/143.80 % (31925)Instruction limit reached! 1008.52/143.80 % (31925)------------------------------ 1008.52/143.80 % (31925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1008.52/143.80 % (31925)Termination reason: Unknown 1008.52/143.80 % (31925)Termination phase: Saturation 1008.52/143.80 1008.52/143.80 % (31925)Memory used [KB]: 23283 1008.52/143.80 % (31925)Time elapsed: 6.962 s 1008.52/143.80 % (31925)Instructions burned: 22707 (million) 1008.52/143.80 % (31925)------------------------------ 1008.52/143.80 % (31925)------------------------------ 1008.52/143.81 % (31928)lrs+1010_1:1_chr=on:ntd=on:i=32514:si=on:rtra=on_0 on E---3.1_30784 for (966ds/32514Mi) 1046.54/149.23 % (31910)Refutation not found, non-redundant clauses discarded% (31910)------------------------------ 1046.54/149.23 % (31910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1046.54/149.23 % (31910)Termination reason: Refutation not found, non-redundant clauses discarded 1046.54/149.23 1046.54/149.23 % (31910)Memory used [KB]: 22899 1046.54/149.23 % (31910)Time elapsed: 48.900 s 1046.54/149.23 % (31910)Instructions burned: 168675 (million) 1046.54/149.23 % (31910)------------------------------ 1046.54/149.23 % (31910)------------------------------ 1046.54/149.24 % (31929)lrs+10_1:5_av=off:awrs=converge:awrsf=200:kws=precedence:i=31508:si=on:rtra=on_0 on E---3.1_30784 for (912ds/31508Mi) 1078.15/153.73 % (31928)Instruction limit reached! 1078.15/153.73 % (31928)------------------------------ 1078.15/153.73 % (31928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1078.15/153.73 % (31928)Termination reason: Unknown 1078.15/153.73 % (31928)Termination phase: Saturation 1078.15/153.73 1078.15/153.73 % (31928)Memory used [KB]: 24946 1078.15/153.73 % (31928)Time elapsed: 9.922 s 1078.15/153.73 % (31928)Instructions burned: 32516 (million) 1078.15/153.73 % (31928)------------------------------ 1078.15/153.73 % (31928)------------------------------ 1078.15/153.74 % (31930)ott+10_1:1_au=on:av=off:sd=1:ss=axioms:st=2.0:i=29617:si=on:rtra=on_0 on E---3.1_30784 for (867ds/29617Mi) 1083.47/154.46 % (31913)Instruction limit reached! 1083.47/154.46 % (31913)------------------------------ 1083.47/154.46 % (31913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1083.47/154.46 % (31913)Termination reason: Unknown 1083.47/154.46 % (31913)Termination phase: Saturation 1083.47/154.46 1083.47/154.46 % (31913)Memory used [KB]: 83410 1083.47/154.46 % (31913)Time elapsed: 53.038 s 1083.47/154.46 % (31913)Instructions burned: 173649 (million) 1083.47/154.46 % (31913)------------------------------ 1083.47/154.46 % (31913)------------------------------ 1083.47/154.48 % (31931)lrs-1010_8:1_au=on:c=on:ins=1:i=70437:si=on:rtra=on_0 on E---3.1_30784 for (859ds/70437Mi) 1112.24/158.58 % (31929)Instruction limit reached! 1112.24/158.58 % (31929)------------------------------ 1112.24/158.58 % (31929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1112.24/158.58 % (31929)Termination reason: Unknown 1112.24/158.58 % (31929)Termination phase: Saturation 1112.24/158.58 1112.24/158.58 % (31929)Memory used [KB]: 14456 1112.24/158.58 % (31929)Time elapsed: 9.347 s 1112.24/158.58 % (31929)Instructions burned: 31509 (million) 1112.24/158.58 % (31929)------------------------------ 1112.24/158.58 % (31929)------------------------------ 1112.52/158.60 % (31933)dis+1010_4:1_atotf=0.3:erd=off:sd=2:sgt=8:ss=axioms:i=33157:si=on:rtra=on_0 on E---3.1_30784 for (818ds/33157Mi) 1122.87/160.08 % (31926)Instruction limit reached! 1122.87/160.08 % (31926)------------------------------ 1122.87/160.08 % (31926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1122.87/160.08 % (31926)Termination reason: Unknown 1122.87/160.08 % (31926)Termination phase: Saturation 1122.87/160.08 1122.87/160.08 % (31926)Memory used [KB]: 19573 1122.87/160.08 % (31926)Time elapsed: 20.861 s 1122.87/160.08 % (31926)Instructions burned: 99378 (million) 1122.87/160.08 % (31926)------------------------------ 1122.87/160.08 % (31926)------------------------------ 1122.95/160.09 % (31934)lrs+1010_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=axiom:hud=10:prag=on:ss=axioms:i=37349:si=on:rtra=on_0 on E---3.1_30784 for (803ds/37349Mi) 1140.58/162.64 % (31930)Instruction limit reached! 1140.58/162.64 % (31930)------------------------------ 1140.58/162.64 % (31930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1140.58/162.64 % (31930)Termination reason: Unknown 1140.58/162.64 % (31930)Termination phase: Saturation 1140.58/162.64 1140.58/162.64 % (31930)Memory used [KB]: 18166 1140.58/162.64 % (31930)Time elapsed: 8.897 s 1140.58/162.64 % (31930)Instructions burned: 29618 (million) 1140.58/162.64 % (31930)------------------------------ 1140.58/162.64 % (31930)------------------------------ 1140.58/162.65 % (31935)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=98380:si=on:rtra=on_0 on E---3.1_30784 for (778ds/98380Mi) 1143.36/163.05 % (31919)Instruction limit reached! 1143.36/163.05 % (31919)------------------------------ 1143.36/163.05 % (31919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1143.36/163.05 % (31919)Termination reason: Unknown 1143.36/163.05 % (31919)Termination phase: Saturation 1143.36/163.05 1143.36/163.05 % (31919)Memory used [KB]: 36587 1143.36/163.05 % (31919)Time elapsed: 40.665 s 1143.36/163.05 % (31919)Instructions burned: 137970 (million) 1143.36/163.05 % (31919)------------------------------ 1143.36/163.05 % (31919)------------------------------ 1143.36/163.06 % (31936)ott+10_1:10_avsq=on:bd=off:cnfonf=lazy_gen:sd=2:sgt=16:sos=on:ss=axioms:i=56001:si=on:rtra=on_0 on E---3.1_30784 for (774ds/56001Mi) 1182.64/168.62 % (31933)Instruction limit reached! 1182.64/168.62 % (31933)------------------------------ 1182.64/168.62 % (31933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1182.64/168.62 % (31933)Termination reason: Unknown 1182.64/168.62 % (31933)Termination phase: Saturation 1182.64/168.62 1182.64/168.62 % (31933)Memory used [KB]: 37227 1182.64/168.62 % (31933)Time elapsed: 10.051 s 1182.64/168.62 % (31933)Instructions burned: 33157 (million) 1182.64/168.62 % (31933)------------------------------ 1182.64/168.62 % (31933)------------------------------ 1182.64/168.64 % (31937)lrs+1010_1:1_au=on:bd=off:e2e=on:fde=unused:nm=4:s2a=on:sos=all:sp=const_frequency:i=141566:si=on:rtra=on_0 on E---3.1_30784 for (718ds/141566Mi) 1192.38/170.01 % (31934)Instruction limit reached! 1192.38/170.01 % (31934)------------------------------ 1192.38/170.01 % (31934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1192.38/170.01 % (31934)Termination reason: Unknown 1192.38/170.01 % (31934)Termination phase: Saturation 1192.38/170.01 1192.38/170.01 % (31934)Memory used [KB]: 14839 1192.38/170.01 % (31934)Time elapsed: 9.946 s 1192.38/170.01 % (31934)Instructions burned: 37349 (million) 1192.38/170.01 % (31934)------------------------------ 1192.38/170.01 % (31934)------------------------------ 1192.38/170.02 % (31938)lrs+1010_1:1_e2e=on:plsq=on:i=63430:si=on:rtra=on_0 on E---3.1_30784 for (704ds/63430Mi) 1204.12/171.68 % (31927)Instruction limit reached! 1204.12/171.68 % (31927)------------------------------ 1204.12/171.68 % (31927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1204.12/171.68 % (31927)Termination reason: Unknown 1204.12/171.68 % (31927)Termination phase: Saturation 1204.12/171.68 1204.12/171.68 % (31927)Memory used [KB]: 27121 1204.12/171.68 % (31927)Time elapsed: 29.708 s 1204.12/171.68 % (31927)Instructions burned: 112304 (million) 1204.12/171.68 % (31927)------------------------------ 1204.12/171.68 % (31927)------------------------------ 1204.12/171.69 % (31939)dis+1010_1:1_av=off:fe=off:sd=2:slsq=on:slsqr=1,16:ss=axioms:st=5.0:i=82580:si=on:rtra=on_0 on E---3.1_30784 for (687ds/82580Mi) 1235.34/176.17 % (31931)Instruction limit reached! 1235.34/176.17 % (31931)------------------------------ 1235.34/176.17 % (31931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1235.34/176.17 % (31931)Termination reason: Unknown 1235.34/176.17 % (31931)Termination phase: Saturation 1235.34/176.17 1235.34/176.17 % (31931)Memory used [KB]: 51427 1235.34/176.17 % (31931)Time elapsed: 21.696 s 1235.34/176.17 % (31931)Instructions burned: 70439 (million) 1235.34/176.17 % (31931)------------------------------ 1235.34/176.17 % (31931)------------------------------ 1235.34/176.19 % (31940)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=220001:si=on:rtra=on_0 on E---3.1_30784 for (642ds/220001Mi) 1245.58/177.61 % (31936)Instruction limit reached! 1245.58/177.61 % (31936)------------------------------ 1245.58/177.61 % (31936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1245.58/177.61 % (31936)Termination reason: Unknown 1245.58/177.61 % (31936)Termination phase: Saturation 1245.58/177.61 1245.58/177.61 % (31936)Memory used [KB]: 17014 1245.58/177.61 % (31936)Time elapsed: 14.557 s 1245.58/177.61 % (31936)Instructions burned: 56002 (million) 1245.58/177.61 % (31936)------------------------------ 1245.58/177.61 % (31936)------------------------------ 1245.58/177.62 % (31941)lrs+2_1:1_cnfonf=off:e2e=on:nm=4:ntd=on:s2a=on:i=97391:si=on:rtra=on_0 on E---3.1_30784 for (628ds/97391Mi) 1270.17/181.15 % (31920)Refutation not found, non-redundant clauses discarded% (31920)------------------------------ 1270.17/181.15 % (31920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1270.17/181.15 % (31920)Termination reason: Refutation not found, non-redundant clauses discarded 1270.17/181.15 1270.17/181.15 % (31920)Memory used [KB]: 24050 1270.17/181.15 % (31920)Time elapsed: 55.157 s 1270.17/181.15 % (31920)Instructions burned: 198540 (million) 1270.17/181.15 % (31920)------------------------------ 1270.17/181.15 % (31920)------------------------------ 1270.17/181.16 % (31942)lrs+1002_1:1_fe=axiom:nwc=5.0:prag=on:sos=on:ss=axioms:i=73072:si=on:rtra=on_0 on E---3.1_30784 for (592ds/73072Mi) 1338.15/190.79 % (31938)Instruction limit reached! 1338.15/190.79 % (31938)------------------------------ 1338.15/190.79 % (31938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1338.15/190.79 % (31938)Termination reason: Unknown 1338.15/190.79 % (31938)Termination phase: Saturation 1338.15/190.79 1338.15/190.79 % (31938)Memory used [KB]: 74455 1338.15/190.79 % (31938)Time elapsed: 20.768 s 1338.15/190.79 % (31938)Instructions burned: 63433 (million) 1338.15/190.79 % (31938)------------------------------ 1338.15/190.79 % (31938)------------------------------ 1338.28/190.80 % (31943)lrs+1010_1:1_anc=all_dependent:cnfonf=conj_eager:cond=fast:fe=axiom:nm=16:s2a=on:s2at=4.0:sd=2:ss=axioms:st=3.0:i=96745:si=on:rtra=on_0 on E---3.1_30784 for (496ds/96745Mi) 1350.69/192.60 % (31935)Instruction limit reached! 1350.69/192.60 % (31935)------------------------------ 1350.69/192.60 % (31935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1350.69/192.60 % (31935)Termination reason: Unknown 1350.69/192.60 % (31935)Termination phase: Saturation 1350.69/192.60 1350.69/192.60 % (31935)Memory used [KB]: 53090 1350.69/192.60 % (31935)Time elapsed: 29.957 s 1350.69/192.60 % (31935)Instructions burned: 98381 (million) 1350.69/192.60 % (31935)------------------------------ 1350.69/192.60 % (31935)------------------------------ 1350.86/192.61 % (31944)lrs+1002_1:1_au=on:e2e=on:nm=10:sos=all:sp=reverse_arity:i=88102:si=on:rtra=on_0 on E---3.1_30784 for (478ds/88102Mi) 1378.37/196.57 % (31939)Instruction limit reached! 1378.37/196.57 % (31939)------------------------------ 1378.37/196.57 % (31939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1378.37/196.57 % (31939)Termination reason: Unknown 1378.37/196.57 % (31939)Termination phase: Saturation 1378.37/196.57 1378.37/196.57 % (31939)Memory used [KB]: 55777 1378.37/196.57 % (31939)Time elapsed: 24.878 s 1378.37/196.57 % (31939)Instructions burned: 82580 (million) 1378.37/196.57 % (31939)------------------------------ 1378.37/196.57 % (31939)------------------------------ 1378.37/196.59 % (31945)lrs+1010_1:4_cnfonf=lazy_not_be_gen:fe=off:hud=10:i=171919:si=on:rtra=on_0 on E---3.1_30784 for (438ds/171919Mi) 1423.88/203.10 % (31942)Instruction limit reached! 1423.88/203.10 % (31942)------------------------------ 1423.88/203.10 % (31942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1423.88/203.10 % (31942)Termination reason: Unknown 1423.88/203.10 % (31942)Termination phase: Saturation 1423.88/203.10 1423.88/203.10 % (31942)Memory used [KB]: 37099 1423.88/203.10 % (31942)Time elapsed: 21.945 s 1423.88/203.10 % (31942)Instructions burned: 73073 (million) 1423.88/203.10 % (31942)------------------------------ 1423.88/203.10 % (31942)------------------------------ 1423.88/203.12 % (31947)ott+1666_1:1_hfaw=0:hfsq=on:hfsql=off:hfsqr=1,16:hud=15:slsq=on:slsqr=1,2:tnu=2:i=3602:si=on:rtra=on_0 on E---3.1_30784 for (373ds/3602Mi) 1431.93/204.20 % (31947)Instruction limit reached! 1431.93/204.20 % (31947)------------------------------ 1431.93/204.20 % (31947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1431.93/204.20 % (31947)Termination reason: Unknown 1431.93/204.20 % (31947)Termination phase: Saturation 1431.93/204.20 1431.93/204.20 % (31947)Memory used [KB]: 14839 1431.93/204.20 % (31947)Time elapsed: 1.087 s 1431.93/204.20 % (31947)Instructions burned: 3605 (million) 1431.93/204.20 % (31947)------------------------------ 1431.93/204.20 % (31947)------------------------------ 1431.93/204.21 % (31948)lrs+10_1:1_cnfonf=off:sd=1:ss=axioms:st=3.0:i=13159:si=on:rtra=on_0 on E---3.1_30784 for (362ds/13159Mi) 1457.16/207.80 % (31948)Instruction limit reached! 1457.16/207.80 % (31948)------------------------------ 1457.16/207.80 % (31948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1457.16/207.80 % (31948)Termination reason: Unknown 1457.16/207.80 % (31948)Termination phase: Saturation 1457.16/207.80 1457.16/207.80 % (31948)Memory used [KB]: 10874 1457.16/207.80 % (31948)Time elapsed: 3.585 s 1457.16/207.80 % (31948)Instructions burned: 13160 (million) 1457.16/207.80 % (31948)------------------------------ 1457.16/207.80 % (31948)------------------------------ 1457.40/207.81 % (31949)ott+2_1:1_au=on:hfsq=on:hfsqc=5:hfsql=off:nwc=5.0:sd=3:ss=axioms:st=5.0:i=15187:si=on:rtra=on_0 on E---3.1_30784 for (326ds/15187Mi) 1461.79/208.45 % (31941)Instruction limit reached! 1461.79/208.45 % (31941)------------------------------ 1461.79/208.45 % (31941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1461.79/208.45 % (31941)Termination reason: Unknown 1461.79/208.45 % (31941)Termination phase: Saturation 1461.79/208.45 1461.79/208.45 % (31941)Memory used [KB]: 85968 1461.79/208.45 % (31941)Time elapsed: 30.822 s 1461.79/208.45 % (31941)Instructions burned: 97392 (million) 1461.79/208.45 % (31941)------------------------------ 1461.79/208.45 % (31941)------------------------------ 1461.79/208.46 % (31950)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=28134:si=on:rtra=on_0 on E---3.1_30784 for (319ds/28134Mi) 1489.62/212.44 % (31949)Instruction limit reached! 1489.62/212.44 % (31949)------------------------------ 1489.62/212.44 % (31949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1489.62/212.44 % (31949)Termination reason: Unknown 1489.62/212.44 % (31949)Termination phase: Saturation 1489.62/212.44 1489.62/212.44 % (31949)Memory used [KB]: 20084 1489.62/212.44 % (31949)Time elapsed: 4.631 s 1489.62/212.44 % (31949)Instructions burned: 15188 (million) 1489.62/212.44 % (31949)------------------------------ 1489.62/212.44 % (31949)------------------------------ 1489.62/212.45 % (31951)dis+1010_1:64_bet=on:cond=fast:e2e=on:fe=off:hud=5:nm=0:ntd=on:nwc=7.0:piset=and:prag=on:rawr=on:sgt=40:ss=included:uhcvi=on:i=42318:si=on:rtra=on_0 on E---3.1_30784 for (280ds/42318Mi) 1491.78/212.71 % (31950)Refutation not found, incomplete strategy 1491.78/212.71 % (31950)------------------------------ 1491.78/212.71 % (31950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1491.78/212.71 % (31950)Termination reason: Refutation not found, incomplete strategy 1491.78/212.71 1491.78/212.71 1491.78/212.71 % (31950)Memory used [KB]: 11129 1491.78/212.71 % (31950)Time elapsed: 4.252 s 1491.78/212.71 % (31950)Instructions burned: 15710 (million) 1491.78/212.71 % (31950)------------------------------ 1491.78/212.71 % (31950)------------------------------ 1491.78/212.73 % (31952)dis+1002_16:1_au=on:nwc=5.0:i=37202:si=on:rtra=on_0 on E---3.1_30784 for (277ds/37202Mi) 1496.04/213.37 % (31937)Instruction limit reached! 1496.04/213.37 % (31937)------------------------------ 1496.04/213.37 % (31937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1496.04/213.37 % (31937)Termination reason: Unknown 1496.04/213.37 % (31937)Termination phase: Saturation 1496.04/213.37 1496.04/213.37 % (31937)Memory used [KB]: 92493 1496.04/213.37 % (31937)Time elapsed: 44.722 s 1496.04/213.37 % (31937)Instructions burned: 141567 (million) 1496.04/213.37 % (31937)------------------------------ 1496.04/213.37 % (31937)------------------------------ 1496.04/213.38 % (31953)ott+10_1:1_au=on:av=off:sd=1:ss=axioms:st=2.0:i=36665:si=on:rtra=on_0 on E---3.1_30784 for (270ds/36665Mi) 1540.77/219.78 % (31944)Instruction limit reached! 1540.77/219.78 % (31944)------------------------------ 1540.77/219.78 % (31944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1540.77/219.78 % (31944)Termination reason: Unknown 1540.77/219.78 % (31944)Termination phase: Saturation 1540.77/219.78 1540.77/219.78 % (31944)Memory used [KB]: 58719 1540.77/219.78 % (31944)Time elapsed: 27.177 s 1540.77/219.78 % (31944)Instructions burned: 88103 (million) 1540.77/219.78 % (31944)------------------------------ 1540.77/219.78 % (31944)------------------------------ 1540.77/219.80 % (31954)dis+1010_1:1_anc=all_dependent:au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:fde=none:ins=2:nwc=10.0:piset=or:i=99377:si=on:rtra=on_0 on E---3.1_30784 for (206ds/99377Mi) 1548.40/220.79 % (31943)Instruction limit reached! 1548.40/220.79 % (31943)------------------------------ 1548.40/220.79 % (31943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1548.40/220.79 % (31943)Termination reason: Unknown 1548.40/220.79 % (31943)Termination phase: Saturation 1548.40/220.79 1548.40/220.79 % (31943)Memory used [KB]: 53986 1548.40/220.79 % (31943)Time elapsed: 29.989 s 1548.40/220.79 % (31943)Instructions burned: 96748 (million) 1548.40/220.79 % (31943)------------------------------ 1548.40/220.79 % (31943)------------------------------ 1548.49/220.81 % (31955)dis-1666_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:i=50861:si=on:rtra=on_0 on E---3.1_30784 for (196ds/50861Mi) 1569.61/223.86 % (31953)Instruction limit reached! 1569.61/223.86 % (31953)------------------------------ 1569.61/223.86 % (31953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1569.61/223.86 % (31953)Termination reason: Unknown 1569.61/223.86 % (31953)Termination phase: Saturation 1569.61/223.86 1569.61/223.86 % (31953)Memory used [KB]: 21620 1569.61/223.86 % (31953)Time elapsed: 10.479 s 1569.61/223.86 % (31953)Instructions burned: 36666 (million) 1569.61/223.86 % (31953)------------------------------ 1569.61/223.86 % (31953)------------------------------ 1569.61/223.87 % (31956)ott+1010_1:4_cnfonf=lazy_simp:fe=off:hud=5:piset=or:prag=on:i=112304:si=on:rtra=on_0 on E---3.1_30784 for (165ds/112304Mi) 1572.31/224.20 % (31952)Instruction limit reached! 1572.31/224.20 % (31952)------------------------------ 1572.31/224.20 % (31952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1572.31/224.20 % (31952)Termination reason: Unknown 1572.31/224.20 % (31952)Termination phase: Saturation 1572.31/224.20 1572.31/224.20 % (31952)Memory used [KB]: 37355 1572.31/224.20 % (31952)Time elapsed: 11.475 s 1572.31/224.20 % (31952)Instructions burned: 37204 (million) 1572.31/224.20 % (31952)------------------------------ 1572.31/224.20 % (31952)------------------------------ 1572.31/224.21 % (31957)lrs+1002_1:1_fe=axiom:nwc=5.0:prag=on:sos=on:ss=axioms:i=73072:si=on:rtra=on_0 on E---3.1_30784 for (162ds/73072Mi) 1580.10/225.40 % (31951)Instruction limit reached! 1580.10/225.40 % (31951)------------------------------ 1580.10/225.40 % (31951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1580.10/225.40 % (31951)Termination reason: Unknown 1580.10/225.40 % (31951)Termination phase: Saturation 1580.10/225.40 1580.10/225.40 % (31951)Memory used [KB]: 74455 1580.10/225.40 % (31951)Time elapsed: 12.948 s 1580.10/225.40 % (31951)Instructions burned: 42320 (million) 1580.10/225.40 % (31951)------------------------------ 1580.10/225.40 % (31951)------------------------------ 1580.70/225.41 % (31958)lrs+1010_1:1_e2e=on:plsq=on:i=90575:si=on:rtra=on_0 on E---3.1_30784 for (150ds/90575Mi) 1636.90/233.47 % (31955)Instruction limit reached! 1636.90/233.47 % (31955)------------------------------ 1636.90/233.47 % (31955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1636.90/233.47 % (31955)Termination reason: Unknown 1636.90/233.47 % (31955)Termination phase: Saturation 1636.90/233.47 1636.90/233.47 % (31955)Memory used [KB]: 32238 1636.90/233.47 % (31955)Time elapsed: 12.664 s 1636.90/233.47 % (31955)Instructions burned: 50862 (million) 1636.90/233.47 % (31955)------------------------------ 1636.90/233.47 % (31955)------------------------------ 1636.90/233.48 % (31959)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=77965:si=on:rtra=on_0 on E---3.1_30784 for (69ds/77965Mi) 1647.31/234.97 % (31954)First to succeed. 1648.62/235.11 % (31954)Refutation found. Thanks to Tanya! 1648.62/235.11 % SZS status Theorem for E---3.1_30784 1648.62/235.11 % SZS output start Proof for E---3.1_30784 1648.62/235.11 thf(func_def_0, type, in: $i > $i > $o). 1648.62/235.11 thf(func_def_1, type, exu: ($i > $o) > $o). 1648.62/235.11 thf(func_def_6, type, setadjoin: $i > $i > $i). 1648.62/235.11 thf(func_def_8, type, powerset: $i > $i). 1648.62/235.11 thf(func_def_10, type, setunion: $i > $i). 1648.62/235.11 thf(func_def_19, type, descr: ($i > $o) > $i). 1648.62/235.11 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i). 1648.62/235.11 thf(func_def_26, type, prop2set: $o > $i). 1648.62/235.11 thf(func_def_36, type, nonempty: $i > $o). 1648.62/235.11 thf(func_def_69, type, set2prop: $i > $o). 1648.62/235.11 thf(func_def_88, type, subset: $i > $i > $o). 1648.62/235.11 thf(func_def_89, type, disjoint: $i > $i > $o). 1648.62/235.11 thf(func_def_90, type, setsmeet: $i > $i > $o). 1648.62/235.11 thf(func_def_114, type, binunion: $i > $i > $i). 1648.62/235.11 thf(func_def_122, type, binintersect: $i > $i > $i). 1648.62/235.11 thf(func_def_135, type, regular: $i > $o). 1648.62/235.11 thf(func_def_136, type, setminus: $i > $i > $i). 1648.62/235.11 thf(func_def_147, type, symdiff: $i > $i > $i). 1648.62/235.11 thf(func_def_153, type, iskpair: $i > $o). 1648.62/235.11 thf(func_def_158, type, kpair: $i > $i > $i). 1648.62/235.11 thf(func_def_160, type, cartprod: $i > $i > $i). 1648.62/235.11 thf(func_def_177, type, singleton: $i > $o). 1648.62/235.11 thf(func_def_179, type, ex1: $i > ($i > $o) > $o). 1648.62/235.11 thf(func_def_184, type, atmost1p: $i > $o). 1648.62/235.11 thf(func_def_185, type, atleast2p: $i > $o). 1648.62/235.11 thf(func_def_186, type, atmost2p: $i > $o). 1648.62/235.11 thf(func_def_187, type, upairsetp: $i > $o). 1648.62/235.11 thf(func_def_191, type, kfst: $i > $i). 1648.62/235.11 thf(func_def_203, type, ksnd: $i > $i). 1648.62/235.11 thf(func_def_213, type, breln: $i > $i > $i > $o). 1648.62/235.11 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i). 1648.62/235.11 thf(func_def_222, type, func: $i > $i > $i > $o). 1648.62/235.11 thf(func_def_223, type, funcSet: $i > $i > $i). 1648.62/235.11 thf(func_def_226, type, ap: $i > $i > $i > $i > $i). 1648.62/235.11 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i). 1648.62/235.11 thf(func_def_259, type, if: $i > $o > $i > $i > $i). 1648.62/235.11 thf(func_def_323, type, breln1: $i > $i > $o). 1648.62/235.11 thf(func_def_325, type, breln1Set: $i > $i). 1648.62/235.11 thf(func_def_327, type, transitive: $i > $i > $o). 1648.62/235.11 thf(func_def_328, type, antisymmetric: $i > $i > $o). 1648.62/235.11 thf(func_def_329, type, reflexive: $i > $i > $o). 1648.62/235.11 thf(func_def_330, type, refltransitive: $i > $i > $o). 1648.62/235.11 thf(func_def_331, type, refllinearorder: $i > $i > $o). 1648.62/235.11 thf(func_def_332, type, reflwellordering: $i > $i > $o). 1648.62/235.11 thf(func_def_355, type, ph1: !>[X0: $tType]:(X0)). 1648.62/235.11 thf(func_def_365, type, sK11: ($i > $o) > $i). 1648.62/235.11 thf(func_def_367, type, sK13: $i > $i). 1648.62/235.11 thf(func_def_375, type, sK21: $i > $i > $o). 1648.62/235.11 thf(func_def_376, type, sK22: $i > $i > $i). 1648.62/235.11 thf(func_def_377, type, sK23: ($i > $o) > $i > $i). 1648.62/235.11 thf(func_def_378, type, sK24: $i > $i > $i). 1648.62/235.11 thf(func_def_393, type, sK39: ($i > $o) > $i > $i). 1648.62/235.11 thf(func_def_399, type, sK45: $i > $o > $i). 1648.62/235.11 thf(func_def_400, type, sK46: $o > $i > $i > $i). 1648.62/235.11 thf(func_def_401, type, sK47: ($i > $o) > $i > $i). 1648.62/235.11 thf(func_def_402, type, sK48: $i > $o). 1648.62/235.11 thf(func_def_403, type, sK49: ($i > $o) > $i). 1648.62/235.11 thf(func_def_404, type, sK50: ($i > $o) > $i). 1648.62/235.11 thf(func_def_405, type, sK51: $i > ($i > $o) > $i). 1648.62/235.11 thf(func_def_412, type, sK58: $i > ($i > $i) > $i > $i). 1648.62/235.11 thf(func_def_413, type, sK59: $i > $i). 1648.62/235.11 thf(func_def_421, type, sK67: $i > $i). 1648.62/235.11 thf(func_def_425, type, sK71: $i > $i > ($i > $o) > $i). 1648.62/235.11 thf(func_def_426, type, sK72: $i > $i > $i > $i). 1648.62/235.11 thf(func_def_427, type, sK73: ($i > $o) > ($i > $o) > $i). 1648.62/235.11 thf(func_def_428, type, sK74: ($i > $o) > ($i > $o) > $i). 1648.62/235.11 thf(func_def_438, type, sK84: ($i > $o) > $i > $i). 1648.62/235.11 thf(func_def_439, type, sK85: ($i > $o) > $i > $i > $i). 1648.62/235.11 thf(func_def_442, type, sK88: $i > $i > $i > $i > $i). 1648.62/235.11 thf(func_def_444, type, sK90: $i > $i > ($i > $o) > $i > $i). 1648.62/235.11 thf(func_def_445, type, sK91: $i > $i > $i > $i > $i). 1648.62/235.11 thf(func_def_448, type, sK94: ($i > $o) > $i > ($i > $o) > $i). 1648.62/235.11 thf(func_def_449, type, sK95: ($i > $o) > ($i > $o) > $i > $i > $i). 1648.62/235.11 thf(func_def_450, type, sK96: $i > ($i > $i > $o) > $i > $i). 1648.62/235.11 thf(func_def_451, type, sK97: $i > $i > $o). 1648.62/235.11 thf(f99751,plain,( 1648.62/235.11 $false), 1648.62/235.11 inference(avatar_sat_refutation,[status(thm)],[f3486,f6181,f7964,f66791,f66821,f66852,f66872,f66928,f98668,f98844,f99613,f99748])). 1648.62/235.11 thf(f99748,plain,( 1648.62/235.11 ~spl0_8493), 1648.62/235.11 inference(avatar_contradiction_clause,[status(thm)],[f99747])). 1648.62/235.11 thf(f99747,plain,( 1648.62/235.11 $false | ~spl0_8493), 1648.62/235.11 inference(trivial_inequality_removal,[status(thm)],[f99743])). 1648.62/235.11 thf(f99743,plain,( 1648.62/235.11 ($true = $false) | ~spl0_8493), 1648.62/235.11 inference(backward_demodulation,[status(thm)],[f8307,f99611])). 1648.62/235.11 thf(f99611,plain,( 1648.62/235.11 ((breln1 @ sK3 @ sK2) = $false) | ~spl0_8493), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f99609])). 1648.62/235.11 thf(f99609,definition,( 1648.62/235.11 spl0_8493 <=> ((breln1 @ sK3 @ sK2) = $false)), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_8493])],[avatar_definition])). 1648.62/235.11 thf(f8307,plain,( 1648.62/235.11 ((breln1 @ sK3 @ sK2) = $true)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f8305])). 1648.62/235.11 thf(f8305,plain,( 1648.62/235.11 (((breln1 @ sK3 @ sK2) => (!! @ $i @ (^[Y0 : $i]: ((breln1 @ sK3 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => ((in @ (kpair @ Y1 @ Y2) @ sK2) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK2 @ Y0)))))) = $false)), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f8304])). 1648.62/235.11 thf(f8304,plain,( 1648.62/235.11 (((^[Y0 : $i]: ((breln1 @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ sK2) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ sK2 @ Y1))))))) @ sK3) = $false)), 1648.62/235.11 inference(sigma_clausification,[status(thm)],[f8303])). 1648.62/235.11 thf(f8303,plain,( 1648.62/235.11 ((!! @ $i @ (^[Y0 : $i]: ((breln1 @ Y0 @ sK2) => (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ (kpair @ Y2 @ Y3) @ sK2) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ sK2 @ Y1)))))))) = $false)), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f8302])). 1648.62/235.11 thf(f8302,plain,( 1648.62/235.11 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))) @ sK2) = $false)), 1648.62/235.11 inference(sigma_clausification,[status(thm)],[f6150])). 1648.62/235.11 thf(f6150,plain,( 1648.62/235.11 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6148])). 1648.62/235.11 thf(f6148,plain,( 1648.62/235.11 ((breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6146])). 1648.62/235.11 thf(f6146,plain,( 1648.62/235.11 ((setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6144])). 1648.62/235.11 thf(f6144,plain,( 1648.62/235.11 ((choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6142])). 1648.62/235.11 thf(f6142,plain,( 1648.62/235.11 ((breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6140])). 1648.62/235.11 thf(f6140,plain,( 1648.62/235.11 ((breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6138])). 1648.62/235.11 thf(f6138,plain,( 1648.62/235.11 ((woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6136])). 1648.62/235.11 thf(f6136,plain,( 1648.62/235.11 ((woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6134])). 1648.62/235.11 thf(f6134,plain,( 1648.62/235.11 ($false = (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6131])). 1648.62/235.11 thf(f6131,plain,( 1648.62/235.11 ((woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6128])). 1648.62/235.11 thf(f6128,plain,( 1648.62/235.11 ((woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6126])). 1648.62/235.11 thf(f6126,plain,( 1648.62/235.11 ((woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6124])). 1648.62/235.11 thf(f6124,plain,( 1648.62/235.11 ((woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6122])). 1648.62/235.11 thf(f6122,plain,( 1648.62/235.11 ((woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6119])). 1648.62/235.11 thf(f6119,plain,( 1648.62/235.11 ($false = (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6117])). 1648.62/235.11 thf(f6117,plain,( 1648.62/235.11 ((woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6115])). 1648.62/235.11 thf(f6115,plain,( 1648.62/235.11 ((demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6113])). 1648.62/235.11 thf(f6113,plain,( 1648.62/235.11 ((demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6110])). 1648.62/235.11 thf(f6110,plain,( 1648.62/235.11 ((demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6108])). 1648.62/235.11 thf(f6108,plain,( 1648.62/235.11 ((demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6106])). 1648.62/235.11 thf(f6106,plain,( 1648.62/235.11 ((demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6103])). 1648.62/235.11 thf(f6103,plain,( 1648.62/235.11 ((demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6101])). 1648.62/235.11 thf(f6101,plain,( 1648.62/235.11 ($false = (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6099])). 1648.62/235.11 thf(f6099,plain,( 1648.62/235.11 ((demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6097])). 1648.62/235.11 thf(f6097,plain,( 1648.62/235.11 ((complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6095])). 1648.62/235.11 thf(f6095,plain,( 1648.62/235.11 ($false = (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6092])). 1648.62/235.11 thf(f6092,plain,( 1648.62/235.11 ($false = (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6090])). 1648.62/235.11 thf(f6090,plain,( 1648.62/235.11 ((binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6088])). 1648.62/235.11 thf(f6088,plain,( 1648.62/235.11 ($false = (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6085])). 1648.62/235.11 thf(f6085,plain,( 1648.62/235.11 ($false = (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6083])). 1648.62/235.11 thf(f6083,plain,( 1648.62/235.11 ((intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6081])). 1648.62/235.11 thf(f6081,plain,( 1648.62/235.11 ((inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6079])). 1648.62/235.11 thf(f6079,plain,( 1648.62/235.11 ((inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6077])). 1648.62/235.11 thf(f6077,plain,( 1648.62/235.11 ((inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6074])). 1648.62/235.11 thf(f6074,plain,( 1648.62/235.11 ((binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6071])). 1648.62/235.11 thf(f6071,plain,( 1648.62/235.11 ((binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6069])). 1648.62/235.11 thf(f6069,plain,( 1648.62/235.11 ((complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6067])). 1648.62/235.11 thf(f6067,plain,( 1648.62/235.11 ((contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6064])). 1648.62/235.11 thf(f6064,plain,( 1648.62/235.11 ($false = (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6062])). 1648.62/235.11 thf(f6062,plain,( 1648.62/235.11 ((complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6060])). 1648.62/235.11 thf(f6060,plain,( 1648.62/235.11 ((complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6058])). 1648.62/235.11 thf(f6058,plain,( 1648.62/235.11 ((complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6056])). 1648.62/235.11 thf(f6056,plain,( 1648.62/235.11 ((doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6053])). 1648.62/235.11 thf(f6053,plain,( 1648.62/235.11 ($false = (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6051])). 1648.62/235.11 thf(f6051,plain,( 1648.62/235.11 ((doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6049])). 1648.62/235.11 thf(f6049,plain,( 1648.62/235.11 ((doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6047])). 1648.62/235.11 thf(f6047,plain,( 1648.62/235.11 ((doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6044])). 1648.62/235.11 thf(f6044,plain,( 1648.62/235.11 ((contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6041])). 1648.62/235.11 thf(f6041,plain,( 1648.62/235.11 ($false = (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6038])). 1648.62/235.11 thf(f6038,plain,( 1648.62/235.11 ((contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6036])). 1648.62/235.11 thf(f6036,plain,( 1648.62/235.11 ((contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6034])). 1648.62/235.11 thf(f6034,plain,( 1648.62/235.11 ((binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6032])). 1648.62/235.11 thf(f6032,plain,( 1648.62/235.11 ((binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6029])). 1648.62/235.11 thf(f6029,plain,( 1648.62/235.11 ((complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6027])). 1648.62/235.11 thf(f6027,plain,( 1648.62/235.11 ((complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6025])). 1648.62/235.11 thf(f6025,plain,( 1648.62/235.11 ((powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6022])). 1648.62/235.11 thf(f6022,plain,( 1648.62/235.11 ((powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6019])). 1648.62/235.11 thf(f6019,plain,( 1648.62/235.11 ((subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6016])). 1648.62/235.11 thf(f6016,plain,( 1648.62/235.11 ((setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6013])). 1648.62/235.11 thf(f6013,plain,( 1648.62/235.11 ((complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6011])). 1648.62/235.11 thf(f6011,plain,( 1648.62/235.11 ((setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6008])). 1648.62/235.11 thf(f6008,plain,( 1648.62/235.11 ((powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6006])). 1648.62/235.11 thf(f6006,plain,( 1648.62/235.11 ($false = (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6004])). 1648.62/235.11 thf(f6004,plain,( 1648.62/235.11 ((binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6002])). 1648.62/235.11 thf(f6002,plain,( 1648.62/235.11 ((iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f6000])). 1648.62/235.11 thf(f6000,plain,( 1648.62/235.11 ($false = (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5998])). 1648.62/235.11 thf(f5998,plain,( 1648.62/235.11 ((iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5995])). 1648.62/235.11 thf(f5995,plain,( 1648.62/235.11 ((theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5993])). 1648.62/235.11 thf(f5993,plain,( 1648.62/235.11 ((ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5991])). 1648.62/235.11 thf(f5991,plain,( 1648.62/235.11 ($false = (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5989])). 1648.62/235.11 thf(f5989,plain,( 1648.62/235.11 ((iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5986])). 1648.62/235.11 thf(f5986,plain,( 1648.62/235.11 ($false = (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5984])). 1648.62/235.11 thf(f5984,plain,( 1648.62/235.11 ((iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5981])). 1648.62/235.11 thf(f5981,plain,( 1648.62/235.11 ((iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5979])). 1648.62/235.11 thf(f5979,plain,( 1648.62/235.11 ($false = (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5976])). 1648.62/235.11 thf(f5976,plain,( 1648.62/235.11 ((beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5974])). 1648.62/235.11 thf(f5974,plain,( 1648.62/235.11 ($false = (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5972])). 1648.62/235.11 thf(f5972,plain,( 1648.62/235.11 ((eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5970])). 1648.62/235.11 thf(f5970,plain,( 1648.62/235.11 ((beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5967])). 1648.62/235.11 thf(f5967,plain,( 1648.62/235.11 ((ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5965])). 1648.62/235.11 thf(f5965,plain,( 1648.62/235.11 ((ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5963])). 1648.62/235.11 thf(f5963,plain,( 1648.62/235.11 ((funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5960])). 1648.62/235.11 thf(f5960,plain,( 1648.62/235.11 ($false = (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5958])). 1648.62/235.11 thf(f5958,plain,( 1648.62/235.11 ($false = (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5956])). 1648.62/235.11 thf(f5956,plain,( 1648.62/235.11 ($false = (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5954])). 1648.62/235.11 thf(f5954,plain,( 1648.62/235.11 ((funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5952])). 1648.62/235.11 thf(f5952,plain,( 1648.62/235.11 ((funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5950])). 1648.62/235.11 thf(f5950,plain,( 1648.62/235.11 ($false = (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5947])). 1648.62/235.11 thf(f5947,plain,( 1648.62/235.11 ($false = (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5944])). 1648.62/235.11 thf(f5944,plain,( 1648.62/235.11 ((funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5941])). 1648.62/235.11 thf(f5941,plain,( 1648.62/235.11 ((ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5938])). 1648.62/235.11 thf(f5938,plain,( 1648.62/235.11 ((brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5936])). 1648.62/235.11 thf(f5936,plain,( 1648.62/235.11 ($false = (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5933])). 1648.62/235.11 thf(f5933,plain,( 1648.62/235.11 ((lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5931])). 1648.62/235.11 thf(f5931,plain,( 1648.62/235.11 ((lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5929])). 1648.62/235.11 thf(f5929,plain,( 1648.62/235.11 ((lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5926])). 1648.62/235.11 thf(f5926,plain,( 1648.62/235.11 ((funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5924])). 1648.62/235.11 thf(f5924,plain,( 1648.62/235.11 ($false = (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5921])). 1648.62/235.11 thf(f5921,plain,( 1648.62/235.11 ((infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5919])). 1648.62/235.11 thf(f5919,plain,( 1648.62/235.11 ((app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5916])). 1648.62/235.11 thf(f5916,plain,( 1648.62/235.11 ((apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5914])). 1648.62/235.11 thf(f5914,plain,( 1648.62/235.11 ((funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5911])). 1648.62/235.11 thf(f5911,plain,( 1648.62/235.11 ((dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5909])). 1648.62/235.11 thf(f5909,plain,( 1648.62/235.11 ((dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5906])). 1648.62/235.11 thf(f5906,plain,( 1648.62/235.11 ((dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5903])). 1648.62/235.11 thf(f5903,plain,( 1648.62/235.11 ((dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5900])). 1648.62/235.11 thf(f5900,plain,( 1648.62/235.11 ((setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5898])). 1648.62/235.11 thf(f5898,plain,( 1648.62/235.11 ((dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5896])). 1648.62/235.11 thf(f5896,plain,( 1648.62/235.11 ((dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5893])). 1648.62/235.11 thf(f5893,plain,( 1648.62/235.11 ((cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5891])). 1648.62/235.11 thf(f5891,plain,( 1648.62/235.11 ((cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5888])). 1648.62/235.11 thf(f5888,plain,( 1648.62/235.11 ($false = (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5886])). 1648.62/235.11 thf(f5886,plain,( 1648.62/235.11 ((cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5883])). 1648.62/235.11 thf(f5883,plain,( 1648.62/235.11 ((cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5881])). 1648.62/235.11 thf(f5881,plain,( 1648.62/235.11 ((cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5878])). 1648.62/235.11 thf(f5878,plain,( 1648.62/235.11 ((cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5876])). 1648.62/235.11 thf(f5876,plain,( 1648.62/235.11 ((kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5874])). 1648.62/235.11 thf(f5874,plain,( 1648.62/235.11 ((ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5872])). 1648.62/235.11 thf(f5872,plain,( 1648.62/235.11 ($false = (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5869])). 1648.62/235.11 thf(f5869,plain,( 1648.62/235.11 ($false = (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5867])). 1648.62/235.11 thf(f5867,plain,( 1648.62/235.11 ((setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5865])). 1648.62/235.11 thf(f5865,plain,( 1648.62/235.11 ($false = (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5862])). 1648.62/235.11 thf(f5862,plain,( 1648.62/235.11 ((setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5860])). 1648.62/235.11 thf(f5860,plain,( 1648.62/235.11 ((setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5858])). 1648.62/235.11 thf(f5858,plain,( 1648.62/235.11 ($false = (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5856])). 1648.62/235.11 thf(f5856,plain,( 1648.62/235.11 ((setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5853])). 1648.62/235.11 thf(f5853,plain,( 1648.62/235.11 ((setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5850])). 1648.62/235.11 thf(f5850,plain,( 1648.62/235.11 ($false = (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5848])). 1648.62/235.11 thf(f5848,plain,( 1648.62/235.11 ((kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5845])). 1648.62/235.11 thf(f5845,plain,( 1648.62/235.11 ($false = (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5842])). 1648.62/235.11 thf(f5842,plain,( 1648.62/235.11 ((kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5839])). 1648.62/235.11 thf(f5839,plain,( 1648.62/235.11 ((setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5837])). 1648.62/235.11 thf(f5837,plain,( 1648.62/235.11 ((singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5835])). 1648.62/235.11 thf(f5835,plain,( 1648.62/235.11 ((ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5833])). 1648.62/235.11 thf(f5833,plain,( 1648.62/235.11 ((ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5831])). 1648.62/235.11 thf(f5831,plain,( 1648.62/235.11 ((ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5829])). 1648.62/235.11 thf(f5829,plain,( 1648.62/235.11 ((singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5827])). 1648.62/235.11 thf(f5827,plain,( 1648.62/235.11 ((setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5825])). 1648.62/235.11 thf(f5825,plain,( 1648.62/235.11 ((setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5823])). 1648.62/235.11 thf(f5823,plain,( 1648.62/235.11 ((setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5821])). 1648.62/235.11 thf(f5821,plain,( 1648.62/235.11 ((setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5818])). 1648.62/235.11 thf(f5818,plain,( 1648.62/235.11 ((cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5816])). 1648.62/235.11 thf(f5816,plain,( 1648.62/235.11 ((cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5813])). 1648.62/235.11 thf(f5813,plain,( 1648.62/235.11 ((cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5811])). 1648.62/235.11 thf(f5811,plain,( 1648.62/235.11 ((ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5809])). 1648.62/235.11 thf(f5809,plain,( 1648.62/235.11 ($false = (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5806])). 1648.62/235.11 thf(f5806,plain,( 1648.62/235.11 ($false = (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5803])). 1648.62/235.11 thf(f5803,plain,( 1648.62/235.11 ((upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5801])). 1648.62/235.11 thf(f5801,plain,( 1648.62/235.11 ((upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5798])). 1648.62/235.11 thf(f5798,plain,( 1648.62/235.11 ((upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5795])). 1648.62/235.11 thf(f5795,plain,( 1648.62/235.11 ((singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5793])). 1648.62/235.11 thf(f5793,plain,( 1648.62/235.11 ((singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5791])). 1648.62/235.11 thf(f5791,plain,( 1648.62/235.11 ($false = (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5789])). 1648.62/235.11 thf(f5789,plain,( 1648.62/235.11 ($false = (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5787])). 1648.62/235.11 thf(f5787,plain,( 1648.62/235.11 ((kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5785])). 1648.62/235.11 thf(f5785,plain,( 1648.62/235.11 ((setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5783])). 1648.62/235.11 thf(f5783,plain,( 1648.62/235.11 ((setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5781])). 1648.62/235.11 thf(f5781,plain,( 1648.62/235.11 ((secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5779])). 1648.62/235.11 thf(f5779,plain,( 1648.62/235.11 ((symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5777])). 1648.62/235.11 thf(f5777,plain,( 1648.62/235.11 ((symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5774])). 1648.62/235.11 thf(f5774,plain,( 1648.62/235.11 ((symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5771])). 1648.62/235.11 thf(f5771,plain,( 1648.62/235.11 ((symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5769])). 1648.62/235.11 thf(f5769,plain,( 1648.62/235.11 ($false = (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5767])). 1648.62/235.11 thf(f5767,plain,( 1648.62/235.11 ((setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5764])). 1648.62/235.11 thf(f5764,plain,( 1648.62/235.11 ((setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5761])). 1648.62/235.11 thf(f5761,plain,( 1648.62/235.11 ((setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5758])). 1648.62/235.11 thf(f5758,plain,( 1648.62/235.11 ((setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5756])). 1648.62/235.11 thf(f5756,plain,( 1648.62/235.11 ((setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5754])). 1648.62/235.11 thf(f5754,plain,( 1648.62/235.11 ((setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5752])). 1648.62/235.11 thf(f5752,plain,( 1648.62/235.11 ((setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5749])). 1648.62/235.11 thf(f5749,plain,( 1648.62/235.11 ((setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5746])). 1648.62/235.11 thf(f5746,plain,( 1648.62/235.11 ((setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5744])). 1648.62/235.11 thf(f5744,plain,( 1648.62/235.11 ($false = (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5742])). 1648.62/235.11 thf(f5742,plain,( 1648.62/235.11 ((bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5740])). 1648.62/235.11 thf(f5740,plain,( 1648.62/235.11 ((binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5737])). 1648.62/235.11 thf(f5737,plain,( 1648.62/235.11 ((binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5735])). 1648.62/235.11 thf(f5735,plain,( 1648.62/235.11 ((binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5732])). 1648.62/235.11 thf(f5732,plain,( 1648.62/235.11 ((disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5730])). 1648.62/235.11 thf(f5730,plain,( 1648.62/235.11 ((binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5728])). 1648.62/235.11 thf(f5728,plain,( 1648.62/235.11 ($false = (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5725])). 1648.62/235.11 thf(f5725,plain,( 1648.62/235.11 ($false = (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5723])). 1648.62/235.11 thf(f5723,plain,( 1648.62/235.11 ((binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5721])). 1648.62/235.11 thf(f5721,plain,( 1648.62/235.11 ((binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5719])). 1648.62/235.11 thf(f5719,plain,( 1648.62/235.11 ((binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5717])). 1648.62/235.11 thf(f5717,plain,( 1648.62/235.11 ($false = (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5715])). 1648.62/235.11 thf(f5715,plain,( 1648.62/235.11 ($false = (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5713])). 1648.62/235.11 thf(f5713,plain,( 1648.62/235.11 ($false = (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5711])). 1648.62/235.11 thf(f5711,plain,( 1648.62/235.11 ((binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5709])). 1648.62/235.11 thf(f5709,plain,( 1648.62/235.11 ((binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5707])). 1648.62/235.11 thf(f5707,plain,( 1648.62/235.11 ((binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5705])). 1648.62/235.11 thf(f5705,plain,( 1648.62/235.11 ((upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5703])). 1648.62/235.11 thf(f5703,plain,( 1648.62/235.11 ((binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5701])). 1648.62/235.11 thf(f5701,plain,( 1648.62/235.11 ((sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5699])). 1648.62/235.11 thf(f5699,plain,( 1648.62/235.11 ((sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5697])). 1648.62/235.11 thf(f5697,plain,( 1648.62/235.11 ($false = (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5694])). 1648.62/235.11 thf(f5694,plain,( 1648.62/235.11 ($false = (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5691])). 1648.62/235.11 thf(f5691,plain,( 1648.62/235.11 ((powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5689])). 1648.62/235.11 thf(f5689,plain,( 1648.62/235.11 ((powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5686])). 1648.62/235.11 thf(f5686,plain,( 1648.62/235.11 ((subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5684])). 1648.62/235.11 thf(f5684,plain,( 1648.62/235.11 ((setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5682])). 1648.62/235.11 thf(f5682,plain,( 1648.62/235.11 ($false = (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5680])). 1648.62/235.11 thf(f5680,plain,( 1648.62/235.11 ((setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5678])). 1648.62/235.11 thf(f5678,plain,( 1648.62/235.11 ((setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5675])). 1648.62/235.11 thf(f5675,plain,( 1648.62/235.11 ($false = (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5673])). 1648.62/235.11 thf(f5673,plain,( 1648.62/235.11 ($false = (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5670])). 1648.62/235.11 thf(f5670,plain,( 1648.62/235.11 ($false = (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5668])). 1648.62/235.11 thf(f5668,plain,( 1648.62/235.11 ((notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5666])). 1648.62/235.11 thf(f5666,plain,( 1648.62/235.11 ((notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5663])). 1648.62/235.11 thf(f5663,plain,( 1648.62/235.11 ((subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5660])). 1648.62/235.11 thf(f5660,plain,( 1648.62/235.11 ($false = (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5657])). 1648.62/235.11 thf(f5657,plain,( 1648.62/235.11 ($false = (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5655])). 1648.62/235.11 thf(f5655,plain,( 1648.62/235.11 ((subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5652])). 1648.62/235.11 thf(f5652,plain,( 1648.62/235.11 ((eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5650])). 1648.62/235.11 thf(f5650,plain,( 1648.62/235.11 ((eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5648])). 1648.62/235.11 thf(f5648,plain,( 1648.62/235.11 ((subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5646])). 1648.62/235.11 thf(f5646,plain,( 1648.62/235.11 ((dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5643])). 1648.62/235.11 thf(f5643,plain,( 1648.62/235.11 ($false = (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5641])). 1648.62/235.11 thf(f5641,plain,( 1648.62/235.11 ((exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5639])). 1648.62/235.11 thf(f5639,plain,( 1648.62/235.11 ($false = (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5637])). 1648.62/235.11 thf(f5637,plain,( 1648.62/235.11 ($false = (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5635])). 1648.62/235.11 thf(f5635,plain,( 1648.62/235.11 ((powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5633])). 1648.62/235.11 thf(f5633,plain,( 1648.62/235.11 ($false = (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5631])). 1648.62/235.11 thf(f5631,plain,( 1648.62/235.11 ($false = (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5629])). 1648.62/235.11 thf(f5629,plain,( 1648.62/235.11 ($false = (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5627])). 1648.62/235.11 thf(f5627,plain,( 1648.62/235.11 ((exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5625])). 1648.62/235.11 thf(f5625,plain,( 1648.62/235.11 ($false = (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5622])). 1648.62/235.11 thf(f5622,plain,( 1648.62/235.11 ((inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5620])). 1648.62/235.11 thf(f5620,plain,( 1648.62/235.11 ((exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5617])). 1648.62/235.11 thf(f5617,plain,( 1648.62/235.11 ((exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5615])). 1648.62/235.11 thf(f5615,plain,( 1648.62/235.11 ((exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5613])). 1648.62/235.11 thf(f5613,plain,( 1648.62/235.11 ($false = (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5611])). 1648.62/235.11 thf(f5611,plain,( 1648.62/235.11 ((notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5608])). 1648.62/235.11 thf(f5608,plain,( 1648.62/235.11 ($false = (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5606])). 1648.62/235.11 thf(f5606,plain,( 1648.62/235.11 ((prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5603])). 1648.62/235.11 thf(f5603,plain,( 1648.62/235.11 ((quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5601])). 1648.62/235.11 thf(f5601,plain,( 1648.62/235.11 ($false = (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5598])). 1648.62/235.11 thf(f5598,plain,( 1648.62/235.11 ((quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5596])). 1648.62/235.11 thf(f5596,plain,( 1648.62/235.11 ((quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5594])). 1648.62/235.11 thf(f5594,plain,( 1648.62/235.11 ((vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5592])). 1648.62/235.11 thf(f5592,plain,( 1648.62/235.11 ((emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5590])). 1648.62/235.11 thf(f5590,plain,( 1648.62/235.11 ((upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5588])). 1648.62/235.11 thf(f5588,plain,( 1648.62/235.11 ((upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5586])). 1648.62/235.11 thf(f5586,plain,( 1648.62/235.11 ($false = (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5583])). 1648.62/235.11 thf(f5583,plain,( 1648.62/235.11 ((singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5580])). 1648.62/235.11 thf(f5580,plain,( 1648.62/235.11 ((eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5577])). 1648.62/235.11 thf(f5577,plain,( 1648.62/235.11 ((notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5575])). 1648.62/235.11 thf(f5575,plain,( 1648.62/235.11 ((uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5572])). 1648.62/235.11 thf(f5572,plain,( 1648.62/235.11 ((nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5569])). 1648.62/235.11 thf(f5569,plain,( 1648.62/235.11 ((exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5567])). 1648.62/235.11 thf(f5567,plain,( 1648.62/235.11 ($false = (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5565])). 1648.62/235.11 thf(f5565,plain,( 1648.62/235.11 ($false = (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5562])). 1648.62/235.11 thf(f5562,plain,( 1648.62/235.11 ((setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5560])). 1648.62/235.11 thf(f5560,plain,( 1648.62/235.11 ((powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5558])). 1648.62/235.11 thf(f5558,plain,( 1648.62/235.11 ((emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5556])). 1648.62/235.11 thf(f5556,plain,( 1648.62/235.11 ($false = (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5554])). 1648.62/235.11 thf(f5554,plain,( 1648.62/235.11 ($false = (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5552])). 1648.62/235.11 thf(f5552,plain,( 1648.62/235.11 ((setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5550])). 1648.62/235.11 thf(f5550,plain,( 1648.62/235.11 ((setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5548])). 1648.62/235.11 thf(f5548,plain,( 1648.62/235.11 ((setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5546])). 1648.62/235.11 thf(f5546,plain,( 1648.62/235.11 ((setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5544])). 1648.62/235.11 thf(f5544,plain,( 1648.62/235.11 ((emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5542])). 1648.62/235.11 thf(f5542,plain,( 1648.62/235.11 ($false = (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5540])). 1648.62/235.11 thf(f5540,plain,( 1648.62/235.11 ((nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5537])). 1648.62/235.11 thf(f5537,plain,( 1648.62/235.11 ((nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5535])). 1648.62/235.11 thf(f5535,plain,( 1648.62/235.11 ($false = (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5532])). 1648.62/235.11 thf(f5532,plain,( 1648.62/235.11 ((setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5530])). 1648.62/235.11 thf(f5530,plain,( 1648.62/235.11 ((noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5528])). 1648.62/235.11 thf(f5528,plain,( 1648.62/235.11 ((emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5526])). 1648.62/235.11 thf(f5526,plain,( 1648.62/235.11 ((setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5524])). 1648.62/235.11 thf(f5524,plain,( 1648.62/235.11 ((exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5521])). 1648.62/235.11 thf(f5521,plain,( 1648.62/235.11 ((notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5519])). 1648.62/235.11 thf(f5519,plain,( 1648.62/235.11 ((emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5516])). 1648.62/235.11 thf(f5516,plain,( 1648.62/235.11 ((emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5513])). 1648.62/235.11 thf(f5513,plain,( 1648.62/235.11 ($false = (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5511])). 1648.62/235.11 thf(f5511,plain,( 1648.62/235.11 ((exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5508])). 1648.62/235.11 thf(f5508,plain,( 1648.62/235.11 ($false = (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5505])). 1648.62/235.11 thf(f5505,plain,( 1648.62/235.11 ((dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5503])). 1648.62/235.11 thf(f5503,plain,( 1648.62/235.11 ((dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5500])). 1648.62/235.11 thf(f5500,plain,( 1648.62/235.11 ((descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5498])). 1648.62/235.11 thf(f5498,plain,( 1648.62/235.11 ($false = (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5496])). 1648.62/235.11 thf(f5496,plain,( 1648.62/235.11 ((foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5494])). 1648.62/235.11 thf(f5494,plain,( 1648.62/235.11 ((replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5491])). 1648.62/235.11 thf(f5491,plain,( 1648.62/235.11 ((omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5489])). 1648.62/235.11 thf(f5489,plain,( 1648.62/235.11 ($false = (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5487])). 1648.62/235.11 thf(f5487,plain,( 1648.62/235.11 ((omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5484])). 1648.62/235.11 thf(f5484,plain,( 1648.62/235.11 ($false = (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5482])). 1648.62/235.11 thf(f5482,plain,( 1648.62/235.11 ((powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5480])). 1648.62/235.11 thf(f5480,plain,( 1648.62/235.11 ($false = (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5477])). 1648.62/235.11 thf(f5477,plain,( 1648.62/235.11 ((emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5476])). 1648.62/235.11 thf(f5476,plain,( 1648.62/235.11 ($false = (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(not_proxy_clausification,[status(thm)],[f971])). 1648.62/235.11 thf(f971,plain,( 1648.62/235.11 ($true = (~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(cnf_transformation,[status(thm)],[f330])). 1648.62/235.11 thf(f330,plain,( 1648.62/235.11 ($true = (~ (setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln1 @ Y1 @ Y0) => (!! @ $i @ (^[Y2 : $i]: ((breln1 @ Y1 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ (kpair @ Y3 @ Y4) @ Y0) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ Y0 @ Y2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(fool_elimination,[status(thm)],[f329])). 1648.62/235.11 thf(f329,plain,( 1648.62/235.11 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => ! [X0 : $i,X1 : $i] : ((breln1 @ X0 @ X1) => ! [X2 : $i] : ((breln1 @ X0 @ X2) => (! [X3 : $i] : ((in @ X3 @ X0) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ X1) => (in @ (kpair @ X3 @ X4) @ X2)))) => (subset @ X1 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(rectify,[status(thm)],[f295])). 1648.62/235.11 thf(f295,negated_conjecture,( 1648.62/235.11 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ X13) => (in @ (kpair @ X1 @ X2) @ X15)))) => (subset @ X13 @ X15)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 inference(negated_conjecture,[status(cth)],[f294])). 1648.62/235.11 thf(f294,conjecture,( 1648.62/235.11 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => (woz13rule4 => (woz1_1 => (woz1_2 => (woz1_3 => (woz1_4 => (woz1_5 => (breln1all2 => (breln1SetBreln1 => (choice2fnsingleton => (setOfPairsIsBReln1 => (breln1all1 => ! [X3 : $i,X13 : $i] : ((breln1 @ X3 @ X13) => ! [X15 : $i] : ((breln1 @ X3 @ X15) => (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X3) => ((in @ (kpair @ X1 @ X2) @ X13) => (in @ (kpair @ X1 @ X2) @ X15)))) => (subset @ X13 @ X15))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 1648.62/235.11 file('/export/starexec/sandbox2/tmp/tmp.3DV3eBGPqy/E---3.1_30784.p',subbreln1)). 1648.62/235.11 thf(f99613,plain,( 1648.62/235.11 spl0_8493 | ~spl0_5497), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f99605,f66908,f99609])). 1648.62/235.11 thf(f66908,definition,( 1648.62/235.11 spl0_5497 <=> ((breln @ sK3 @ sK3 @ sK2) = $false)), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_5497])],[avatar_definition])). 1648.62/235.11 thf(f99605,plain,( 1648.62/235.11 ((breln1 @ sK3 @ sK2) = $false) | ~spl0_5497), 1648.62/235.11 inference(trivial_inequality_removal,[status(thm)],[f99604])). 1648.62/235.11 thf(f99604,plain,( 1648.62/235.11 ((breln1 @ sK3 @ sK2) = $false) | ($true = $false) | ~spl0_5497), 1648.62/235.11 inference(superposition,[status(thm)],[f8327,f66910])). 1648.62/235.11 thf(f66910,plain,( 1648.62/235.11 ((breln @ sK3 @ sK3 @ sK2) = $false) | ~spl0_5497), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f66908])). 1648.62/235.11 thf(f8327,plain,( 1648.62/235.11 ( ! [X2 : $i,X1 : $i] : (($true = (breln @ X1 @ X1 @ X2)) | ((breln1 @ X1 @ X2) = $false)) )), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f8326])). 1648.62/235.11 thf(f8326,plain,( 1648.62/235.11 ( ! [X2 : $i,X1 : $i] : (((breln @ X1 @ X1 @ X2) = (breln1 @ X1 @ X2))) )), 1648.62/235.11 inference(argument_congruence,[status(thm)],[f7684])). 1648.62/235.11 thf(f7684,plain,( 1648.62/235.11 ( ! [X1 : $i] : (((breln1 @ X1) = (breln @ X1 @ X1))) )), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f7683])). 1648.62/235.11 thf(f7683,plain,( 1648.62/235.11 ( ! [X1 : $i] : (((breln1 @ X1) = ((^[Y0 : $i]: (breln @ Y0 @ Y0)) @ X1))) )), 1648.62/235.11 inference(argument_congruence,[status(thm)],[f1178])). 1648.62/235.11 thf(f1178,plain,( 1648.62/235.11 (breln1 = (^[Y0 : $i]: (breln @ Y0 @ Y0)))), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f1127])). 1648.62/235.11 thf(f1127,plain,( 1648.62/235.11 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))), 1648.62/235.11 inference(cnf_transformation,[status(thm)],[f668])). 1648.62/235.11 thf(f668,plain,( 1648.62/235.11 (breln1 = (^[Y0 : $i]: ((^[Y1 : $i]: (breln @ Y0 @ Y0 @ Y1)))))), 1648.62/235.11 inference(fool_elimination,[status(thm)],[f667])). 1648.62/235.11 thf(f667,plain,( 1648.62/235.11 ((^[X0 : $i, X1 : $i] : (breln @ X0 @ X0 @ X1)) = breln1)), 1648.62/235.11 inference(rectify,[status(thm)],[f288])). 1648.62/235.11 thf(f288,axiom,( 1648.62/235.11 ((^[X3 : $i, X13 : $i] : (breln @ X3 @ X3 @ X13)) = breln1)), 1648.62/235.11 file('/export/starexec/sandbox2/tmp/tmp.3DV3eBGPqy/E---3.1_30784.p',breln1)). 1648.62/235.11 thf(f98844,plain,( 1648.62/235.11 ~spl0_8390), 1648.62/235.11 inference(avatar_contradiction_clause,[status(thm)],[f98843])). 1648.62/235.11 thf(f98843,plain,( 1648.62/235.11 $false | ~spl0_8390), 1648.62/235.11 inference(trivial_inequality_removal,[status(thm)],[f98838])). 1648.62/235.11 thf(f98838,plain,( 1648.62/235.11 ($true = $false) | ~spl0_8390), 1648.62/235.11 inference(backward_demodulation,[status(thm)],[f8323,f98666])). 1648.62/235.11 thf(f98666,plain,( 1648.62/235.11 ((breln1 @ sK3 @ sK4) = $false) | ~spl0_8390), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f98664])). 1648.62/235.11 thf(f98664,definition,( 1648.62/235.11 spl0_8390 <=> ((breln1 @ sK3 @ sK4) = $false)), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_8390])],[avatar_definition])). 1648.62/235.11 thf(f8323,plain,( 1648.62/235.11 ((breln1 @ sK3 @ sK4) = $true)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f8321])). 1648.62/235.11 thf(f8321,plain,( 1648.62/235.11 (((breln1 @ sK3 @ sK4) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK4)))))))) => (subset @ sK2 @ sK4))) = $false)), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f8320])). 1648.62/235.11 thf(f8320,plain,( 1648.62/235.11 (((^[Y0 : $i]: ((breln1 @ sK3 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => ((in @ (kpair @ Y1 @ Y2) @ sK2) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK2 @ Y0)))) @ sK4) = $false)), 1648.62/235.11 inference(sigma_clausification,[status(thm)],[f8306])). 1648.62/235.11 thf(f8306,plain,( 1648.62/235.11 ($false = (!! @ $i @ (^[Y0 : $i]: ((breln1 @ sK3 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ sK3) => ((in @ (kpair @ Y1 @ Y2) @ sK2) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ sK2 @ Y0))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f8305])). 1648.62/235.11 thf(f98668,plain,( 1648.62/235.11 spl0_8390 | ~spl0_5498), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f98660,f66912,f98664])). 1648.62/235.11 thf(f66912,definition,( 1648.62/235.11 spl0_5498 <=> ($false = (breln @ sK3 @ sK3 @ sK4))), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_5498])],[avatar_definition])). 1648.62/235.11 thf(f98660,plain,( 1648.62/235.11 ((breln1 @ sK3 @ sK4) = $false) | ~spl0_5498), 1648.62/235.11 inference(trivial_inequality_removal,[status(thm)],[f98659])). 1648.62/235.11 thf(f98659,plain,( 1648.62/235.11 ((breln1 @ sK3 @ sK4) = $false) | ($true = $false) | ~spl0_5498), 1648.62/235.11 inference(superposition,[status(thm)],[f8327,f66914])). 1648.62/235.11 thf(f66914,plain,( 1648.62/235.11 ($false = (breln @ sK3 @ sK3 @ sK4)) | ~spl0_5498), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f66912])). 1648.62/235.11 thf(f66928,plain,( 1648.62/235.11 spl0_5498 | spl0_5497 | ~spl0_5496), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f66927,f66870,f66908,f66912])). 1648.62/235.11 thf(f66870,definition,( 1648.62/235.11 spl0_5496 <=> ! [X2 : $i,X4 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X4)))))))) = $false) | ($true = (subset @ X1 @ X4)) | ($false = (breln @ X3 @ X2 @ X4)) | ((breln @ X3 @ X2 @ X1) = $false))), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_5496])],[avatar_definition])). 1648.62/235.11 thf(f66927,plain,( 1648.62/235.11 ((breln @ sK3 @ sK3 @ sK2) = $false) | ($false = (breln @ sK3 @ sK3 @ sK4)) | ~spl0_5496), 1648.62/235.11 inference(trivial_inequality_removal,[status(thm)],[f66926])). 1648.62/235.11 thf(f66926,plain,( 1648.62/235.11 ($false = (breln @ sK3 @ sK3 @ sK4)) | ($true = $false) | ((breln @ sK3 @ sK3 @ sK2) = $false) | ~spl0_5496), 1648.62/235.11 inference(forward_demodulation,[status(thm)],[f66901,f8324])). 1648.62/235.11 thf(f8324,plain,( 1648.62/235.11 ((subset @ sK2 @ sK4) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f8322])). 1648.62/235.11 thf(f8322,plain,( 1648.62/235.11 (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK4)))))))) => (subset @ sK2 @ sK4)) = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f8321])). 1648.62/235.11 thf(f66901,plain,( 1648.62/235.11 ($false = (breln @ sK3 @ sK3 @ sK4)) | ($true = (subset @ sK2 @ sK4)) | ((breln @ sK3 @ sK3 @ sK2) = $false) | ~spl0_5496), 1648.62/235.11 inference(trivial_inequality_removal,[status(thm)],[f66900])). 1648.62/235.11 thf(f66900,plain,( 1648.62/235.11 ($true = (subset @ sK2 @ sK4)) | ((breln @ sK3 @ sK3 @ sK2) = $false) | ($true = $false) | ($false = (breln @ sK3 @ sK3 @ sK4)) | ~spl0_5496), 1648.62/235.11 inference(superposition,[status(thm)],[f8325,f66871])). 1648.62/235.11 thf(f66871,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X4)))))))) = $false) | ($false = (breln @ X3 @ X2 @ X4)) | ($true = (subset @ X1 @ X4)) | ((breln @ X3 @ X2 @ X1) = $false)) ) | ~spl0_5496), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f66870])). 1648.62/235.11 thf(f8325,plain,( 1648.62/235.11 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ sK3) => ((in @ (kpair @ Y0 @ Y1) @ sK2) => (in @ (kpair @ Y0 @ Y1) @ sK4)))))))))), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f8322])). 1648.62/235.11 thf(f66872,plain,( 1648.62/235.11 spl0_5496 | ~spl0_5495), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f66868,f66850,f66870])). 1648.62/235.11 thf(f66850,definition,( 1648.62/235.11 spl0_5495 <=> ! [X2 : $i,X1 : $i,X3 : $i] : (((breln @ X3 @ X2 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((breln @ X3 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0)))))))), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_5495])],[avatar_definition])). 1648.62/235.11 thf(f66868,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X4)))))))) = $false) | ($true = (subset @ X1 @ X4)) | ($false = (breln @ X3 @ X2 @ X4)) | ((breln @ X3 @ X2 @ X1) = $false)) ) | ~spl0_5495), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f66867])). 1648.62/235.11 thf(f66867,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((breln @ X3 @ X2 @ X1) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X4)))))))) => (subset @ X1 @ X4))) | ($false = (breln @ X3 @ X2 @ X4))) ) | ~spl0_5495), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f66866])). 1648.62/235.11 thf(f66866,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((breln @ X3 @ X2 @ X1) = $false) | (((breln @ X3 @ X2 @ X4) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X3) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ (kpair @ Y0 @ Y1) @ X1) => (in @ (kpair @ Y0 @ Y1) @ X4)))))))) => (subset @ X1 @ X4))) = $true)) ) | ~spl0_5495), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f66865])). 1648.62/235.11 thf(f66865,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (((breln @ X3 @ X2 @ X1) = $false) | ($true = ((^[Y0 : $i]: ((breln @ X3 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0)))) @ X4))) ) | ~spl0_5495), 1648.62/235.11 inference(pi_clausification,[status(thm)],[f66851])). 1648.62/235.11 thf(f66851,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((breln @ X3 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0)))))) | ((breln @ X3 @ X2 @ X1) = $false)) ) | ~spl0_5495), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f66850])). 1648.62/235.11 thf(f66852,plain,( 1648.62/235.11 spl0_5495 | ~spl0_5494), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f66848,f66819,f66850])). 1648.62/235.11 thf(f66819,definition,( 1648.62/235.11 spl0_5494 <=> ! [X2 : $i,X1 : $i] : ($true = (!! @ $i @ (^[Y0 : $i]: ((breln @ Y0 @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln @ Y0 @ X2 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ X1 @ Y1)))))))))), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_5494])],[avatar_definition])). 1648.62/235.11 thf(f66848,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((breln @ X3 @ X2 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((breln @ X3 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0))))))) ) | ~spl0_5494), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f66847])). 1648.62/235.11 thf(f66847,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((breln @ X3 @ X2 @ X1) => (!! @ $i @ (^[Y0 : $i]: ((breln @ X3 @ X2 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X3) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ (kpair @ Y1 @ Y2) @ X1) => (in @ (kpair @ Y1 @ Y2) @ Y0)))))))) => (subset @ X1 @ Y0)))))))) ) | ~spl0_5494), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f66846])). 1648.62/235.11 thf(f66846,plain,( 1648.62/235.11 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((breln @ Y0 @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln @ Y0 @ X2 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ X1 @ Y1))))))) @ X3))) ) | ~spl0_5494), 1648.62/235.11 inference(pi_clausification,[status(thm)],[f66820])). 1648.62/235.11 thf(f66820,plain,( 1648.62/235.11 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((breln @ Y0 @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln @ Y0 @ X2 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ X1 @ Y1)))))))))) ) | ~spl0_5494), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f66819])). 1648.62/235.11 thf(f66821,plain,( 1648.62/235.11 spl0_5494 | ~spl0_5493), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f66817,f66789,f66819])). 1648.62/235.11 thf(f66789,definition,( 1648.62/235.11 spl0_5493 <=> ! [X1 : $i] : ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln @ Y1 @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ X1 @ Y2)))))))))))), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_5493])],[avatar_definition])). 1648.62/235.11 thf(f66817,plain,( 1648.62/235.11 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((breln @ Y0 @ X2 @ X1) => (!! @ $i @ (^[Y1 : $i]: ((breln @ Y0 @ X2 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ X2) => ((in @ (kpair @ Y2 @ Y3) @ X1) => (in @ (kpair @ Y2 @ Y3) @ Y1)))))))) => (subset @ X1 @ Y1)))))))))) ) | ~spl0_5493), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f66816])). 1648.62/235.11 thf(f66816,plain,( 1648.62/235.11 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln @ Y1 @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ X1 @ Y2))))))))) @ X2))) ) | ~spl0_5493), 1648.62/235.11 inference(pi_clausification,[status(thm)],[f66790])). 1648.62/235.11 thf(f66790,plain,( 1648.62/235.11 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln @ Y1 @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ X1 @ Y2)))))))))))) ) | ~spl0_5493), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f66789])). 1648.62/235.11 thf(f66791,plain,( 1648.62/235.11 spl0_5493 | ~spl0_450), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f66787,f3483,f66789])). 1648.62/235.11 thf(f3483,definition,( 1648.62/235.11 spl0_450 <=> ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3)))))))))))))), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_450])],[avatar_definition])). 1648.62/235.11 thf(f66787,plain,( 1648.62/235.11 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((breln @ Y1 @ Y0 @ X1) => (!! @ $i @ (^[Y2 : $i]: ((breln @ Y1 @ Y0 @ Y2) => ((!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y0) => ((in @ (kpair @ Y3 @ Y4) @ X1) => (in @ (kpair @ Y3 @ Y4) @ Y2)))))))) => (subset @ X1 @ Y2)))))))))))) ) | ~spl0_450), 1648.62/235.11 inference(beta_eta_normalization,[status(thm)],[f66786])). 1648.62/235.11 thf(f66786,plain,( 1648.62/235.11 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))) @ X1))) ) | ~spl0_450), 1648.62/235.11 inference(pi_clausification,[status(thm)],[f3485])). 1648.62/235.11 thf(f3485,plain,( 1648.62/235.11 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))))) | ~spl0_450), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f3483])). 1648.62/235.11 thf(f7964,plain,( 1648.62/235.11 ~spl0_449 | ~spl0_451), 1648.62/235.11 inference(avatar_contradiction_clause,[status(thm)],[f7963])). 1648.62/235.11 thf(f7963,plain,( 1648.62/235.11 $false | (~spl0_449 | ~spl0_451)), 1648.62/235.11 inference(trivial_inequality_removal,[status(thm)],[f7962])). 1648.62/235.11 thf(f7962,plain,( 1648.62/235.11 ($true = $false) | (~spl0_449 | ~spl0_451)), 1648.62/235.11 inference(forward_demodulation,[status(thm)],[f3490,f3481])). 1648.62/235.11 thf(f3481,plain,( 1648.62/235.11 (subbreln = $false) | ~spl0_449), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f3479])). 1648.62/235.11 thf(f3479,definition,( 1648.62/235.11 spl0_449 <=> (subbreln = $false)), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_449])],[avatar_definition])). 1648.62/235.11 thf(f3490,plain,( 1648.62/235.11 (subbreln = $true) | ~spl0_451), 1648.62/235.11 inference(avatar_component_clause,[status(thm)],[f3488])). 1648.62/235.11 thf(f3488,definition,( 1648.62/235.11 spl0_451 <=> (subbreln = $true)), 1648.62/235.11 introduced(definition,[new_symbols(naming,[spl0_451])],[avatar_definition])). 1648.62/235.11 thf(f6181,plain,( 1648.62/235.11 spl0_451), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f5959,f3488])). 1648.62/235.11 thf(f5959,plain,( 1648.62/235.11 (subbreln = $true)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f5956])). 1648.62/235.11 thf(f3486,plain,( 1648.62/235.11 spl0_449 | spl0_450), 1648.62/235.11 inference(avatar_split_clause,[status(thm)],[f3477,f3483,f3479])). 1648.62/235.11 thf(f3477,plain,( 1648.62/235.11 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3))))))))))))) | (subbreln = $false)), 1648.62/235.11 inference(binary_proxy_clausification,[status(thm)],[f941])). 1648.62/235.11 thf(f941,plain,( 1648.62/235.11 (subbreln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3)))))))))))))), 1648.62/235.11 inference(cnf_transformation,[status(thm)],[f469])). 1648.62/235.11 thf(f469,plain,( 1648.62/235.11 (subbreln = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((breln @ Y2 @ Y1 @ Y0) => (!! @ $i @ (^[Y3 : $i]: ((breln @ Y2 @ Y1 @ Y3) => ((!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y2) => (!! @ $i @ (^[Y5 : $i]: ((in @ Y5 @ Y1) => ((in @ (kpair @ Y4 @ Y5) @ Y0) => (in @ (kpair @ Y4 @ Y5) @ Y3)))))))) => (subset @ Y0 @ Y3)))))))))))))), 1648.62/235.11 inference(fool_elimination,[status(thm)],[f468])). 1648.62/235.11 thf(f468,plain,( 1648.62/235.11 (! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X2 @ X3)))) = subbreln)), 1648.62/235.11 inference(rectify,[status(thm)],[f209])). 1648.62/235.11 thf(f209,axiom,( 1648.62/235.11 (! [X3 : $i,X4 : $i,X13 : $i] : ((breln @ X3 @ X4 @ X13) => ! [X15 : $i] : ((breln @ X3 @ X4 @ X15) => (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X13) => (in @ (kpair @ X1 @ X2) @ X15)))) => (subset @ X13 @ X15)))) = subbreln)), 1648.62/235.11 file('/export/starexec/sandbox2/tmp/tmp.3DV3eBGPqy/E---3.1_30784.p',subbreln)). 1648.62/235.11 % SZS output end Proof for E---3.1_30784 1648.62/235.11 % (31954)------------------------------ 1648.62/235.11 % (31954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1648.62/235.11 % (31954)Termination reason: Refutation 1648.62/235.11 1648.62/235.11 % (31954)Memory used [KB]: 81619 1648.62/235.11 % (31954)Time elapsed: 15.297 s 1648.62/235.11 % (31954)Instructions burned: 49996 (million) 1648.62/235.11 % (31954)------------------------------ 1648.62/235.11 % (31954)------------------------------ 1648.62/235.11 % (30971)Success in time 234.655 s 1648.62/235.11 EOF