0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : run_vampire %s %d THM 0.13/0.33 % Computer : n025.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 1920 0.13/0.33 % WCLimit : 240 0.13/0.33 % DateTime : Wed Jul 30 02:01:34 EDT 2025 0.13/0.34 % CPUTime : 0.13/0.35 This is a THF_ problem 0.13/0.36 Running higher-order theorem proving 0.13/0.36 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.BflOgU1pvt/E---3.1_20224.p -m 16384 -t 240 0.13/0.38 % (20333)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_20224 for (2399ds/27Mi) 0.13/0.38 % (20331)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/183Mi) 0.13/0.38 % (20334)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/2Mi) 0.13/0.38 % (20335)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_20224 for (2399ds/2Mi) 0.13/0.38 % (20332)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_20224 for (2399ds/4Mi) 0.13/0.38 % (20337)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/18Mi) 0.13/0.38 % (20336)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_20224 for (2399ds/275Mi) 0.13/0.39 % (20334)Instruction limit reached! 0.13/0.39 % (20334)------------------------------ 0.13/0.39 % (20334)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.13/0.39 % (20334)Termination reason: Unknown 0.13/0.39 % (20334)Termination phase: Preprocessing 3 0.13/0.39 0.13/0.39 % (20334)Memory used [KB]: 1023 0.13/0.39 % (20334)Time elapsed: 0.004 s 0.13/0.39 % (20334)Instructions burned: 2 (million) 0.13/0.39 % (20334)------------------------------ 0.13/0.39 % (20334)------------------------------ 0.13/0.39 % (20335)Instruction limit reached! 0.13/0.39 % (20335)------------------------------ 0.13/0.39 % (20335)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.13/0.39 % (20335)Termination reason: Unknown 0.13/0.39 % (20335)Termination phase: Property scanning 0.13/0.39 0.13/0.39 % (20335)Memory used [KB]: 1023 0.13/0.39 % (20335)Time elapsed: 0.004 s 0.13/0.39 % (20335)Instructions burned: 3 (million) 0.13/0.39 % (20335)------------------------------ 0.13/0.39 % (20335)------------------------------ 0.13/0.39 % (20332)Instruction limit reached! 0.13/0.39 % (20332)------------------------------ 0.13/0.39 % (20332)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.13/0.39 % (20332)Termination reason: Unknown 0.13/0.39 % (20332)Termination phase: Property scanning 0.13/0.39 0.13/0.39 % (20332)Memory used [KB]: 1023 0.13/0.39 % (20332)Time elapsed: 0.005 s 0.13/0.39 % (20332)Instructions burned: 4 (million) 0.13/0.39 % (20332)------------------------------ 0.13/0.39 % (20332)------------------------------ 0.22/0.40 % (20337)Instruction limit reached! 0.22/0.40 % (20337)------------------------------ 0.22/0.40 % (20337)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.40 % (20337)Termination reason: Unknown 0.22/0.40 % (20337)Termination phase: Saturation 0.22/0.40 0.22/0.40 % (20337)Memory used [KB]: 5628 0.22/0.40 % (20337)Time elapsed: 0.014 s 0.22/0.40 % (20337)Instructions burned: 19 (million) 0.22/0.40 % (20337)------------------------------ 0.22/0.40 % (20337)------------------------------ 0.22/0.40 % (20333)Instruction limit reached! 0.22/0.40 % (20333)------------------------------ 0.22/0.40 % (20333)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.40 % (20333)Termination reason: Unknown 0.22/0.40 % (20333)Termination phase: Saturation 0.22/0.40 0.22/0.40 % (20333)Memory used [KB]: 5628 0.22/0.40 % (20333)Time elapsed: 0.018 s 0.22/0.40 % (20333)Instructions burned: 27 (million) 0.22/0.40 % (20333)------------------------------ 0.22/0.40 % (20333)------------------------------ 0.22/0.40 % (20338)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_20224 for (2399ds/3Mi) 0.22/0.40 % (20339)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_20224 for (2399ds/37Mi) 0.22/0.40 % (20340)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_20224 for (2399ds/15Mi) 0.22/0.40 % (20338)Instruction limit reached! 0.22/0.40 % (20338)------------------------------ 0.22/0.40 % (20338)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.40 % (20338)Termination reason: Unknown 0.22/0.40 % (20338)Termination phase: Preprocessing 3 0.22/0.40 0.22/0.40 % (20338)Memory used [KB]: 1023 0.22/0.40 % (20338)Time elapsed: 0.004 s 0.22/0.40 % (20338)Instructions burned: 3 (million) 0.22/0.40 % (20338)------------------------------ 0.22/0.40 % (20338)------------------------------ 0.22/0.41 % (20341)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_20224 for (2399ds/3Mi) 0.22/0.41 % (20340)Instruction limit reached! 0.22/0.41 % (20340)------------------------------ 0.22/0.41 % (20340)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.41 % (20340)Termination reason: Unknown 0.22/0.41 % (20340)Termination phase: Saturation 0.22/0.41 0.22/0.41 % (20340)Memory used [KB]: 5628 0.22/0.41 % (20340)Time elapsed: 0.013 s 0.22/0.41 % (20340)Instructions burned: 16 (million) 0.22/0.41 % (20340)------------------------------ 0.22/0.41 % (20340)------------------------------ 0.22/0.41 % (20341)Instruction limit reached! 0.22/0.41 % (20341)------------------------------ 0.22/0.41 % (20341)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.41 % (20341)Termination reason: Unknown 0.22/0.41 % (20341)Termination phase: Preprocessing 3 0.22/0.41 0.22/0.41 % (20341)Memory used [KB]: 1023 0.22/0.41 % (20341)Time elapsed: 0.004 s 0.22/0.41 % (20341)Instructions burned: 3 (million) 0.22/0.41 % (20341)------------------------------ 0.22/0.41 % (20341)------------------------------ 0.22/0.42 % (20342)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_20224 for (2399ds/1041Mi) 0.22/0.42 % (20343)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/7Mi) 0.22/0.42 % (20343)Instruction limit reached! 0.22/0.42 % (20343)------------------------------ 0.22/0.42 % (20343)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.42 % (20343)Termination reason: Unknown 0.22/0.42 % (20343)Termination phase: Saturation 0.22/0.42 0.22/0.42 % (20343)Memory used [KB]: 1023 0.22/0.42 % (20343)Time elapsed: 0.006 s 0.22/0.42 % (20343)Instructions burned: 7 (million) 0.22/0.42 % (20343)------------------------------ 0.22/0.42 % (20343)------------------------------ 0.22/0.42 % (20339)Instruction limit reached! 0.22/0.42 % (20339)------------------------------ 0.22/0.42 % (20339)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.42 % (20339)Termination reason: Unknown 0.22/0.42 % (20339)Termination phase: Saturation 0.22/0.42 0.22/0.42 % (20339)Memory used [KB]: 5628 0.22/0.42 % (20339)Time elapsed: 0.024 s 0.22/0.42 % (20339)Instructions burned: 38 (million) 0.22/0.42 % (20339)------------------------------ 0.22/0.42 % (20339)------------------------------ 0.22/0.43 % (20344)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/16Mi) 0.22/0.43 % (20345)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_20224 for (2399ds/3Mi) 0.22/0.43 % (20345)Instruction limit reached! 0.22/0.43 % (20345)------------------------------ 0.22/0.43 % (20345)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.43 % (20345)Termination reason: Unknown 0.22/0.43 % (20345)Termination phase: Preprocessing 3 0.22/0.43 0.22/0.43 % (20345)Memory used [KB]: 1023 0.22/0.43 % (20345)Time elapsed: 0.004 s 0.22/0.43 % (20345)Instructions burned: 3 (million) 0.22/0.43 % (20345)------------------------------ 0.22/0.43 % (20345)------------------------------ 0.22/0.44 % (20344)Instruction limit reached! 0.22/0.44 % (20344)------------------------------ 0.22/0.44 % (20344)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.44 % (20344)Termination reason: Unknown 0.22/0.44 % (20344)Termination phase: Saturation 0.22/0.44 0.22/0.44 % (20344)Memory used [KB]: 5628 0.22/0.44 % (20344)Time elapsed: 0.011 s 0.22/0.44 % (20344)Instructions burned: 16 (million) 0.22/0.44 % (20344)------------------------------ 0.22/0.44 % (20344)------------------------------ 0.22/0.44 % (20346)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_20224 for (2399ds/3Mi) 0.22/0.44 % (20347)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_20224 for (2399ds/7Mi) 0.22/0.44 % (20346)Instruction limit reached! 0.22/0.44 % (20346)------------------------------ 0.22/0.44 % (20346)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.44 % (20346)Termination reason: Unknown 0.22/0.44 % (20346)Termination phase: Preprocessing 3 0.22/0.44 0.22/0.44 % (20346)Memory used [KB]: 1023 0.22/0.44 % (20346)Time elapsed: 0.004 s 0.22/0.44 % (20346)Instructions burned: 3 (million) 0.22/0.44 % (20346)------------------------------ 0.22/0.44 % (20346)------------------------------ 0.22/0.44 % (20347)Instruction limit reached! 0.22/0.44 % (20347)------------------------------ 0.22/0.44 % (20347)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.44 % (20347)Termination reason: Unknown 0.22/0.44 % (20347)Termination phase: Saturation 0.22/0.44 0.22/0.44 % (20347)Memory used [KB]: 5500 0.22/0.44 % (20347)Time elapsed: 0.006 s 0.22/0.44 % (20347)Instructions burned: 7 (million) 0.22/0.44 % (20347)------------------------------ 0.22/0.44 % (20347)------------------------------ 0.22/0.45 % (20348)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_20224 for (2399ds/3Mi) 0.22/0.45 % (20348)Instruction limit reached! 0.22/0.45 % (20348)------------------------------ 0.22/0.45 % (20348)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.45 % (20348)Termination reason: Unknown 0.22/0.45 % (20348)Termination phase: Property scanning 0.22/0.45 0.22/0.45 % (20348)Memory used [KB]: 1023 0.22/0.45 % (20348)Time elapsed: 0.004 s 0.22/0.45 % (20348)Instructions burned: 4 (million) 0.22/0.45 % (20348)------------------------------ 0.22/0.45 % (20348)------------------------------ 0.22/0.45 % (20349)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/4Mi) 0.22/0.46 % (20350)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_20224 for (2399ds/18Mi) 0.22/0.46 % (20349)Instruction limit reached! 0.22/0.46 % (20349)------------------------------ 0.22/0.46 % (20349)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.46 % (20349)Termination reason: Unknown 0.22/0.46 % (20349)Termination phase: Property scanning 0.22/0.46 0.22/0.46 % (20349)Memory used [KB]: 1023 0.22/0.46 % (20349)Time elapsed: 0.005 s 0.22/0.46 % (20349)Instructions burned: 5 (million) 0.22/0.46 % (20349)------------------------------ 0.22/0.46 % (20349)------------------------------ 0.22/0.46 % (20351)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/710Mi) 0.22/0.46 % (20352)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/6Mi) 0.22/0.47 % (20352)Instruction limit reached! 0.22/0.47 % (20352)------------------------------ 0.22/0.47 % (20352)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.47 % (20352)Termination reason: Unknown 0.22/0.47 % (20352)Termination phase: Saturation 0.22/0.47 0.22/0.47 % (20352)Memory used [KB]: 5500 0.22/0.47 % (20352)Time elapsed: 0.006 s 0.22/0.47 % (20352)Instructions burned: 7 (million) 0.22/0.47 % (20352)------------------------------ 0.22/0.47 % (20352)------------------------------ 0.22/0.47 % (20350)Instruction limit reached! 0.22/0.47 % (20350)------------------------------ 0.22/0.47 % (20350)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.47 % (20350)Termination reason: Unknown 0.22/0.47 % (20350)Termination phase: Saturation 0.22/0.47 0.22/0.47 % (20350)Memory used [KB]: 5628 0.22/0.47 % (20350)Time elapsed: 0.014 s 0.22/0.47 % (20350)Instructions burned: 19 (million) 0.22/0.47 % (20350)------------------------------ 0.22/0.47 % (20350)------------------------------ 0.22/0.47 % (20353)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_20224 for (2399ds/902Mi) 0.22/0.48 % (20354)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_20224 for (2399ds/21Mi) 0.22/0.48 % (20355)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_20224 for (2399ds/5Mi) 0.22/0.49 % (20355)Instruction limit reached! 0.22/0.49 % (20355)------------------------------ 0.22/0.49 % (20355)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.49 % (20355)Termination reason: Unknown 0.22/0.49 % (20355)Termination phase: Saturation 0.22/0.49 0.22/0.49 % (20355)Memory used [KB]: 5500 0.22/0.49 % (20355)Time elapsed: 0.005 s 0.22/0.49 % (20355)Instructions burned: 5 (million) 0.22/0.49 % (20355)------------------------------ 0.22/0.49 % (20355)------------------------------ 0.22/0.49 % (20331)Instruction limit reached! 0.22/0.49 % (20331)------------------------------ 0.22/0.49 % (20331)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.49 % (20331)Termination reason: Unknown 0.22/0.49 % (20331)Termination phase: Saturation 0.22/0.49 0.22/0.49 % (20331)Memory used [KB]: 6652 0.22/0.49 % (20331)Time elapsed: 0.108 s 0.22/0.49 % (20331)Instructions burned: 183 (million) 0.22/0.49 % (20331)------------------------------ 0.22/0.49 % (20331)------------------------------ 0.22/0.49 % (20354)Instruction limit reached! 0.22/0.49 % (20354)------------------------------ 0.22/0.49 % (20354)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.49 % (20354)Termination reason: Unknown 0.22/0.49 % (20354)Termination phase: Saturation 0.22/0.49 0.22/0.49 % (20354)Memory used [KB]: 5756 0.22/0.49 % (20354)Time elapsed: 0.012 s 0.22/0.49 % (20354)Instructions burned: 22 (million) 0.22/0.49 % (20354)------------------------------ 0.22/0.49 % (20354)------------------------------ 0.22/0.50 % (20356)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_20224 for (2398ds/6Mi) 0.22/0.50 % (20357)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_20224 for (2398ds/377Mi) 0.22/0.50 % (20356)Instruction limit reached! 0.22/0.50 % (20356)------------------------------ 0.22/0.50 % (20356)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.22/0.50 % (20356)Termination reason: Unknown 0.22/0.50 % (20356)Termination phase: Saturation 0.22/0.50 0.22/0.50 % (20356)Memory used [KB]: 5500 0.22/0.50 % (20356)Time elapsed: 0.004 s 0.22/0.50 % (20356)Instructions burned: 6 (million) 0.22/0.50 % (20356)------------------------------ 0.22/0.50 % (20356)------------------------------ 0.22/0.50 % (20358)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_20224 for (2398ds/779Mi) 0.22/0.51 % (20359)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_20224 for (2398ds/19Mi) 1.17/0.52 % (20359)Instruction limit reached! 1.17/0.52 % (20359)------------------------------ 1.17/0.52 % (20359)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.17/0.52 % (20359)Termination reason: Unknown 1.17/0.52 % (20359)Termination phase: Saturation 1.17/0.52 1.17/0.52 % (20359)Memory used [KB]: 5500 1.17/0.52 % (20359)Time elapsed: 0.008 s 1.17/0.52 % (20359)Instructions burned: 20 (million) 1.17/0.52 % (20359)------------------------------ 1.17/0.52 % (20359)------------------------------ 1.17/0.53 % (20336)Instruction limit reached! 1.17/0.53 % (20336)------------------------------ 1.17/0.53 % (20336)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.17/0.53 % (20336)Termination reason: Unknown 1.17/0.53 % (20336)Termination phase: Saturation 1.17/0.53 1.17/0.53 % (20336)Memory used [KB]: 6268 1.17/0.53 % (20336)Time elapsed: 0.144 s 1.17/0.53 % (20336)Instructions burned: 277 (million) 1.17/0.53 % (20336)------------------------------ 1.17/0.53 % (20336)------------------------------ 1.17/0.53 % (20360)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_20224 for (2398ds/879Mi) 1.31/0.54 % (20361)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_20224 for (2398ds/17Mi) 1.31/0.54 % (20361)Instruction limit reached! 1.31/0.54 % (20361)------------------------------ 1.31/0.54 % (20361)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.31/0.54 % (20361)Termination reason: Unknown 1.31/0.54 % (20361)Termination phase: Saturation 1.31/0.54 1.31/0.54 % (20361)Memory used [KB]: 5628 1.31/0.54 % (20361)Time elapsed: 0.008 s 1.31/0.54 % (20361)Instructions burned: 17 (million) 1.31/0.54 % (20361)------------------------------ 1.31/0.54 % (20361)------------------------------ 1.31/0.55 % (20362)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_20224 for (2398ds/3Mi) 1.31/0.55 % (20362)Instruction limit reached! 1.31/0.55 % (20362)------------------------------ 1.31/0.55 % (20362)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.31/0.55 % (20362)Termination reason: Unknown 1.31/0.55 % (20362)Termination phase: Property scanning 1.31/0.55 1.31/0.55 % (20362)Memory used [KB]: 1023 1.31/0.55 % (20362)Time elapsed: 0.003 s 1.31/0.55 % (20362)Instructions burned: 4 (million) 1.31/0.55 % (20362)------------------------------ 1.31/0.55 % (20362)------------------------------ 1.31/0.56 % (20363)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_20224 for (2398ds/30Mi) 1.31/0.57 % (20363)Instruction limit reached! 1.31/0.57 % (20363)------------------------------ 1.31/0.57 % (20363)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.31/0.57 % (20363)Termination reason: Unknown 1.31/0.57 % (20363)Termination phase: Saturation 1.31/0.57 1.31/0.57 % (20363)Memory used [KB]: 5756 1.31/0.57 % (20363)Time elapsed: 0.013 s 1.31/0.57 % (20363)Instructions burned: 30 (million) 1.31/0.57 % (20363)------------------------------ 1.31/0.57 % (20363)------------------------------ 1.31/0.58 % (20364)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_20224 for (2397ds/127Mi) 1.31/0.62 % (20342)First to succeed. 1.31/0.62 % (20364)Instruction limit reached! 1.31/0.62 % (20364)------------------------------ 1.31/0.62 % (20364)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.31/0.62 % (20364)Termination reason: Unknown 1.31/0.62 % (20364)Termination phase: Saturation 1.31/0.62 1.31/0.62 % (20364)Memory used [KB]: 6140 1.31/0.62 % (20364)Time elapsed: 0.045 s 1.31/0.62 % (20364)Instructions burned: 129 (million) 1.31/0.62 % (20364)------------------------------ 1.31/0.62 % (20364)------------------------------ 1.31/0.63 % (20342)Refutation found. Thanks to Tanya! 1.31/0.63 % SZS status Theorem for E---3.1_20224 1.31/0.63 % SZS output start Proof for E---3.1_20224 1.31/0.63 thf(type_def_5, type, a: $tType). 1.31/0.63 thf(func_def_0, type, a: $tType). 1.31/0.63 thf(func_def_21, type, ph1: !>[X0: $tType]:(X0)). 1.31/0.63 thf(func_def_22, type, sK2: a > a > $o). 1.31/0.63 thf(func_def_23, type, sK3: a). 1.31/0.63 thf(func_def_24, type, sK4: a). 1.31/0.63 thf(func_def_25, type, sK5: a > a > $o). 1.31/0.63 thf(func_def_26, type, sK6: a > $o). 1.31/0.63 thf(func_def_27, type, sK7: a). 1.31/0.63 thf(func_def_28, type, sK8: a). 1.31/0.63 thf(func_def_29, type, sK9: a). 1.31/0.63 thf(func_def_30, type, sK10: a). 1.31/0.63 thf(func_def_31, type, sK11: a). 1.31/0.63 thf(func_def_32, type, sK12: a). 1.31/0.63 thf(func_def_33, type, sK13: a). 1.31/0.63 thf(func_def_34, type, sK14: a). 1.31/0.63 thf(func_def_35, type, sK15: a). 1.31/0.63 thf(func_def_36, type, sK16: a). 1.31/0.63 thf(func_def_37, type, sK17: a). 1.31/0.63 thf(func_def_38, type, sK18: a). 1.31/0.63 thf(func_def_39, type, sK19: a). 1.31/0.63 thf(func_def_40, type, sK20: a). 1.31/0.63 thf(func_def_41, type, sK21: a). 1.31/0.63 thf(func_def_42, type, sK22: a). 1.31/0.63 thf(func_def_43, type, sK23: a). 1.31/0.63 thf(func_def_44, type, sK24: a). 1.31/0.63 thf(func_def_45, type, sK25: a). 1.31/0.63 thf(func_def_46, type, sK26: a). 1.31/0.63 thf(func_def_47, type, sK27: a). 1.31/0.63 thf(func_def_48, type, sK28: (a > $o) > a). 1.31/0.63 thf(func_def_49, type, sK29: a). 1.31/0.63 thf(func_def_50, type, sK30: a). 1.31/0.63 thf(func_def_51, type, sK31: a). 1.31/0.63 thf(func_def_52, type, sK32: a). 1.31/0.63 thf(func_def_53, type, sK33: a). 1.31/0.63 thf(func_def_54, type, sK34: a). 1.31/0.63 thf(func_def_55, type, sK35: a). 1.31/0.63 thf(func_def_56, type, sK36: a). 1.31/0.63 thf(func_def_57, type, sK37: a). 1.31/0.63 thf(func_def_58, type, sK38: a). 1.31/0.63 thf(func_def_59, type, sK39: a). 1.31/0.63 thf(f3317,plain,( 1.31/0.63 $false), 1.31/0.63 inference(avatar_sat_refutation,[],[f128,f369,f402,f1017,f1355,f1675,f1770,f2218,f2258,f2639,f2723,f2763,f3127,f3179,f3316])). 1.31/0.63 thf(f3316,plain,( 1.31/0.63 ~spl0_36), 1.31/0.63 inference(avatar_contradiction_clause,[],[f3315])). 1.31/0.63 thf(f3315,plain,( 1.31/0.63 $false | ~spl0_36), 1.31/0.63 inference(trivial_inequality_removal,[],[f3314])). 1.31/0.63 thf(f3314,plain,( 1.31/0.63 ($false = $true) | ~spl0_36), 1.31/0.63 inference(forward_demodulation,[],[f3313,f3201])). 1.31/0.63 thf(f3201,plain,( 1.31/0.63 ($false = (sK6 @ sK37)) | ~spl0_36), 1.31/0.63 inference(boolean_simplification,[],[f3200])). 1.31/0.63 thf(f3200,plain,( 1.31/0.63 ($false = ($true => (sK6 @ sK37))) | ~spl0_36), 1.31/0.63 inference(backward_demodulation,[],[f3192,f3199])). 1.31/0.63 thf(f3199,plain,( 1.31/0.63 (((sK6 @ sK38) & (sK5 @ sK38 @ sK37)) = $true) | ~spl0_36), 1.31/0.63 inference(binary_proxy_clausification,[],[f3192])). 1.31/0.63 thf(f3192,plain,( 1.31/0.63 ($false = (((sK6 @ sK38) & (sK5 @ sK38 @ sK37)) => (sK6 @ sK37))) | ~spl0_36), 1.31/0.63 inference(beta_eta_normalization,[],[f3191])). 1.31/0.63 thf(f3191,plain,( 1.31/0.63 ($false = ((^[Y0 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ sK37)) => (sK6 @ sK37))) @ sK38)) | ~spl0_36), 1.31/0.63 inference(sigma_clausification,[],[f3184])). 1.31/0.63 thf(f3184,plain,( 1.31/0.63 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ sK37)) => (sK6 @ sK37))))) | ~spl0_36), 1.31/0.63 inference(beta_eta_normalization,[],[f3182])). 1.31/0.63 thf(f3182,plain,( 1.31/0.63 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK5 @ Y1 @ Y0)) => (sK6 @ Y0))))) @ sK37)) | ~spl0_36), 1.31/0.63 inference(sigma_clausification,[],[f3123])). 1.31/0.63 thf(f3123,plain,( 1.31/0.63 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK5 @ Y1 @ Y0)) => (sK6 @ Y0))))))) | ~spl0_36), 1.31/0.63 inference(avatar_component_clause,[],[f3122])). 1.31/0.63 thf(f3122,plain,( 1.31/0.63 spl0_36 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK5 @ Y1 @ Y0)) => (sK6 @ Y0)))))))), 1.31/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_36])])). 1.31/0.63 thf(f3313,plain,( 1.31/0.63 ($true = (sK6 @ sK37)) | ~spl0_36), 1.31/0.63 inference(boolean_simplification,[],[f3312])). 1.31/0.63 thf(f3312,plain,( 1.31/0.63 ($true = ($true => (sK6 @ sK37))) | ~spl0_36), 1.31/0.63 inference(forward_demodulation,[],[f3311,f3294])). 1.31/0.63 thf(f3294,plain,( 1.31/0.63 ((sK6 @ sK39) = $true) | ~spl0_36), 1.31/0.63 inference(binary_proxy_clausification,[],[f3230])). 1.31/0.63 thf(f3230,plain,( 1.31/0.63 (((sK6 @ sK39) & (sK5 @ sK39 @ sK37)) = $true) | ~spl0_36), 1.31/0.63 inference(not_proxy_clausification,[],[f3218])). 1.31/0.63 thf(f3218,plain,( 1.31/0.63 ((~ ((sK6 @ sK39) & (sK5 @ sK39 @ sK37))) = $false) | ~spl0_36), 1.31/0.63 inference(beta_eta_normalization,[],[f3217])). 1.31/0.63 thf(f3217,plain,( 1.31/0.63 (((^[Y0 : a]: (~ ((sK6 @ Y0) & (sK5 @ Y0 @ sK37)))) @ sK39) = $false) | ~spl0_36), 1.31/0.63 inference(sigma_clausification,[],[f3203])). 1.31/0.63 thf(f3203,plain,( 1.31/0.63 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK6 @ Y0) & (sK5 @ Y0 @ sK37)))))) | ~spl0_36), 1.31/0.63 inference(boolean_simplification,[],[f3202])). 1.31/0.63 thf(f3202,plain,( 1.31/0.63 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ sK37)) => $false)))) | ~spl0_36), 1.31/0.63 inference(backward_demodulation,[],[f3184,f3201])). 1.31/0.63 thf(f3311,plain,( 1.31/0.63 ($true = ((sK6 @ sK39) => (sK6 @ sK37))) | ~spl0_36), 1.31/0.63 inference(boolean_simplification,[],[f3310])). 1.31/0.63 thf(f3310,plain,( 1.31/0.63 ((((sK6 @ sK39) & $true) => (sK6 @ sK37)) = $true) | ~spl0_36), 1.31/0.63 inference(boolean_simplification,[],[f3309])). 1.31/0.63 thf(f3309,plain,( 1.31/0.63 ((((sK6 @ sK39) & ($true | (sK2 @ sK39 @ sK37))) => (sK6 @ sK37)) = $true) | ~spl0_36), 1.31/0.63 inference(superposition,[],[f70,f3296])). 1.31/0.63 thf(f3296,plain,( 1.31/0.63 ($true = (sK5 @ sK39 @ sK37)) | ~spl0_36), 1.31/0.63 inference(boolean_simplification,[],[f3295])). 1.31/0.63 thf(f3295,plain,( 1.31/0.63 ($true = ($true & (sK5 @ sK39 @ sK37))) | ~spl0_36), 1.31/0.63 inference(backward_demodulation,[],[f3230,f3294])). 1.31/0.63 thf(f70,plain,( 1.31/0.63 ( ! [X2 : a,X1 : a] : (((((sK6 @ X2) & ((sK5 @ X2 @ X1) | (sK2 @ X2 @ X1))) => (sK6 @ X1)) = $true)) )), 1.31/0.63 inference(beta_eta_normalization,[],[f69])). 1.31/0.63 thf(f69,plain,( 1.31/0.63 ( ! [X2 : a,X1 : a] : (($true = ((^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ X1) | (sK2 @ Y0 @ X1))) => (sK6 @ X1))) @ X2))) )), 1.31/0.63 inference(pi_clausification,[],[f68])). 1.31/0.63 thf(f68,plain,( 1.31/0.63 ( ! [X1 : a] : (((!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & ((sK5 @ Y0 @ X1) | (sK2 @ Y0 @ X1))) => (sK6 @ X1)))) = $true)) )), 1.31/0.63 inference(beta_eta_normalization,[],[f67])). 1.31/0.63 thf(f67,plain,( 1.31/0.63 ( ! [X1 : a] : ((((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0))))) @ X1) = $true)) )), 1.31/0.63 inference(pi_clausification,[],[f38])). 1.31/0.63 thf(f38,plain,( 1.31/0.63 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0)))))) = $true)), 1.31/0.63 inference(binary_proxy_clausification,[],[f27])). 1.31/0.63 thf(f27,plain,( 1.31/0.63 ($true = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0))))))), 1.31/0.63 inference(binary_proxy_clausification,[],[f25])). 1.31/0.63 thf(f25,plain,( 1.31/0.63 ($false = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & ((sK5 @ Y1 @ Y0) | (sK2 @ Y1 @ Y0))) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0))))) => (sK6 @ sK3)))), 1.31/0.63 inference(beta_eta_normalization,[],[f24])). 1.31/0.63 thf(f24,plain,( 1.31/0.63 ($false = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK4 @ Y1) | (sK2 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK3))) @ sK6))), 1.31/0.63 inference(sigma_clausification,[],[f18])). 1.31/0.63 thf(f18,plain,( 1.31/0.63 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK4 @ Y1) | (sK2 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK3)))) = $false)), 1.31/0.63 inference(binary_proxy_clausification,[],[f17])). 1.31/0.63 thf(f17,plain,( 1.31/0.63 ($false = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK5 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK5 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK5 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (Y0 @ Y1))))) => (Y0 @ sK3)))) => (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & ((sK5 @ Y2 @ Y1) | (sK2 @ Y2 @ Y1))) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: (((sK5 @ sK4 @ Y1) | (sK2 @ sK4 @ Y1)) => (Y0 @ Y1))))) => (Y0 @ sK3))))))), 1.31/0.63 inference(beta_eta_normalization,[],[f16])). 1.31/0.63 thf(f16,plain,( 1.31/0.63 ($false = ((^[Y0 : a > a > $o]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y0 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (sK2 @ Y6 @ Y5)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ sK4 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (Y0 @ Y5 @ Y4)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((Y0 @ sK4 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) => (Y1 @ Y2))))) => (Y1 @ sK3)))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((Y0 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2))) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((Y0 @ sK4 @ Y2) | (sK2 @ sK4 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK3)))))) @ sK5))), 1.31/0.63 inference(sigma_clausification,[],[f15])). 1.31/0.63 thf(f15,plain,( 1.31/0.63 ($false = (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: ((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: ((((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y5) & (Y0 @ Y5 @ Y6)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: ((Y0 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (sK2 @ Y6 @ Y5)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y2 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) & (Y1 @ Y2)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: (((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((sK2 @ Y5 @ Y4) & (Y3 @ Y5)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ sK4 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (Y0 @ Y5 @ Y4)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((Y0 @ sK4 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) => (Y1 @ Y2))))) => (Y1 @ sK3)))) => (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & ((Y0 @ Y3 @ Y2) | (sK2 @ Y3 @ Y2))) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: (((Y0 @ sK4 @ Y2) | (sK2 @ sK4 @ Y2)) => (Y1 @ Y2))))) => (Y1 @ sK3))))))))), 1.31/0.63 inference(beta_eta_normalization,[],[f14])). 1.31/0.63 thf(f14,plain,( 1.31/0.63 ($false = ((^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y1 @ Y6 @ Y7)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((Y1 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & (sK2 @ Y7 @ Y6)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4))))) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y0 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y1 @ Y6 @ Y5)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((Y1 @ Y0 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) => (Y2 @ Y3))))) => (Y2 @ sK3)))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((Y1 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3))) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((Y1 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK3)))))))) @ sK4))), 1.31/0.63 inference(sigma_clausification,[],[f13])). 1.31/0.63 thf(f13,plain,( 1.31/0.63 ($false = (!! @ a @ (^[Y0 : a]: (!! @ (a > a > $o) @ (^[Y1 : a > a > $o]: ((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: ((((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y6) & (Y1 @ Y6 @ Y7)) => (Y5 @ Y7)))))) & (!! @ a @ (^[Y6 : a]: ((Y1 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & (sK2 @ Y7 @ Y6)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y3 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4))))) & (Y2 @ Y3)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: (((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((sK2 @ Y6 @ Y5) & (Y4 @ Y6)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((sK2 @ Y0 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3)))) | (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & (Y1 @ Y6 @ Y5)) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: ((Y1 @ Y0 @ Y5) => (Y4 @ Y5))))) => (Y4 @ Y3))))) => (Y2 @ Y3))))) => (Y2 @ sK3)))) => (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & ((Y1 @ Y4 @ Y3) | (sK2 @ Y4 @ Y3))) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: (((Y1 @ Y0 @ Y3) | (sK2 @ Y0 @ Y3)) => (Y2 @ Y3))))) => (Y2 @ sK3))))))))))), 1.31/0.63 inference(beta_eta_normalization,[],[f12])). 1.31/0.63 thf(f12,plain,( 1.31/0.63 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y2 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y2 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (sK2 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((sK2 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y1 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & (Y2 @ Y7 @ Y6)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((Y2 @ Y1 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4))))) => (Y3 @ Y4))))) => (Y3 @ Y0)))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y2 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((Y2 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0)))))))))) @ sK3))), 1.31/0.63 inference(sigma_clausification,[],[f11])). 1.31/0.63 thf(f11,plain,( 1.31/0.63 ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (!! @ (a > a > $o) @ (^[Y2 : a > a > $o]: ((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: ((((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y7) & (Y2 @ Y7 @ Y8)) => (Y6 @ Y8)))))) & (!! @ a @ (^[Y7 : a]: ((Y2 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (sK2 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((sK2 @ Y4 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) & (Y3 @ Y4)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: (((!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((sK2 @ Y7 @ Y6) & (Y5 @ Y7)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((sK2 @ Y1 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4)))) | (!! @ (a > $o) @ (^[Y5 : a > $o]: (((!! @ a @ (^[Y6 : a]: (!! @ a @ (^[Y7 : a]: (((Y5 @ Y7) & (Y2 @ Y7 @ Y6)) => (Y5 @ Y6)))))) & (!! @ a @ (^[Y6 : a]: ((Y2 @ Y1 @ Y6) => (Y5 @ Y6))))) => (Y5 @ Y4))))) => (Y3 @ Y4))))) => (Y3 @ Y0)))) => (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & ((Y2 @ Y5 @ Y4) | (sK2 @ Y5 @ Y4))) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: (((Y2 @ Y1 @ Y4) | (sK2 @ Y1 @ Y4)) => (Y3 @ Y4))))) => (Y3 @ Y0))))))))))) = $false)), 1.31/0.63 inference(beta_eta_normalization,[],[f10])). 1.31/0.63 thf(f10,plain,( 1.31/0.63 ($false = ((^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & (Y3 @ Y8 @ Y9)) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: ((Y3 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & (Y0 @ Y9 @ Y8)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6))))) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y3 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y3 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) => (Y4 @ Y5))))) => (Y4 @ Y1)))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y3 @ Y2 @ Y5) | (Y0 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1)))))))))))) @ sK2))), 1.31/0.63 inference(sigma_clausification,[],[f7])). 1.31/0.63 thf(f7,plain,( 1.31/0.63 ((!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & (Y3 @ Y8 @ Y9)) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: ((Y3 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & (Y0 @ Y9 @ Y8)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6))))) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y3 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y3 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) => (Y4 @ Y5))))) => (Y4 @ Y1)))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y3 @ Y2 @ Y5) | (Y0 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1))))))))))))) = $false)), 1.31/0.63 inference(not_proxy_clausification,[],[f6])). 1.31/0.63 thf(f6,plain,( 1.31/0.63 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & (Y3 @ Y8 @ Y9)) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: ((Y3 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & (Y0 @ Y9 @ Y8)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6))))) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y3 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y3 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) => (Y4 @ Y5))))) => (Y4 @ Y1)))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y3 @ Y2 @ Y5) | (Y0 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1)))))))))))))) = $true)), 1.31/0.63 inference(cnf_transformation,[],[f5])). 1.31/0.63 thf(f5,plain,( 1.31/0.63 ((~ (!! @ (a > a > $o) @ (^[Y0 : a > a > $o]: (!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (!! @ (a > a > $o) @ (^[Y3 : a > a > $o]: ((!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: ((((!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y8) & (Y3 @ Y8 @ Y9)) => (Y7 @ Y9)))))) & (!! @ a @ (^[Y8 : a]: ((Y3 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6)))) | (!! @ (a > $o) @ (^[Y7 : a > $o]: (((!! @ a @ (^[Y8 : a]: (!! @ a @ (^[Y9 : a]: (((Y7 @ Y9) & (Y0 @ Y9 @ Y8)) => (Y7 @ Y8)))))) & (!! @ a @ (^[Y8 : a]: ((Y0 @ Y5 @ Y8) => (Y7 @ Y8))))) => (Y7 @ Y6))))) & (Y4 @ Y5)) => (Y4 @ Y6)))))) & (!! @ a @ (^[Y5 : a]: (((!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y0 @ Y8 @ Y7) & (Y6 @ Y8)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y0 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5)))) | (!! @ (a > $o) @ (^[Y6 : a > $o]: (((!! @ a @ (^[Y7 : a]: (!! @ a @ (^[Y8 : a]: (((Y6 @ Y8) & (Y3 @ Y8 @ Y7)) => (Y6 @ Y7)))))) & (!! @ a @ (^[Y7 : a]: ((Y3 @ Y2 @ Y7) => (Y6 @ Y7))))) => (Y6 @ Y5))))) => (Y4 @ Y5))))) => (Y4 @ Y1)))) => (!! @ (a > $o) @ (^[Y4 : a > $o]: (((!! @ a @ (^[Y5 : a]: (!! @ a @ (^[Y6 : a]: (((Y4 @ Y6) & ((Y3 @ Y6 @ Y5) | (Y0 @ Y6 @ Y5))) => (Y4 @ Y5)))))) & (!! @ a @ (^[Y5 : a]: (((Y3 @ Y2 @ Y5) | (Y0 @ Y2 @ Y5)) => (Y4 @ Y5))))) => (Y4 @ Y1)))))))))))))) = $true)), 1.31/0.63 inference(fool_elimination,[],[f4])). 1.31/0.63 thf(f4,plain,( 1.31/0.63 ~! [X0 : a > a > $o,X1 : a,X2 : a,X3 : a > a > $o] : (! [X4 : a > $o] : ((! [X5 : a] : ((! [X6 : a > $o] : ((! [X7 : a] : ((X0 @ X1 @ X7) => (X6 @ X7)) & ! [X8 : a,X9 : a] : (((X0 @ X8 @ X9) & (X6 @ X8)) => (X6 @ X9))) => (X6 @ X5)) | ! [X10 : a > $o] : ((! [X11 : a] : ((X3 @ X1 @ X11) => (X10 @ X11)) & ! [X12 : a,X13 : a] : (((X10 @ X12) & (X3 @ X12 @ X13)) => (X10 @ X13))) => (X10 @ X5))) => (X4 @ X5)) & ! [X14 : a,X15 : a] : (((X4 @ X15) & (! [X16 : a > $o] : ((! [X17 : a] : ((X3 @ X15 @ X17) => (X16 @ X17)) & ! [X18 : a,X19 : a] : (((X3 @ X18 @ X19) & (X16 @ X18)) => (X16 @ X19))) => (X16 @ X14)) | ! [X20 : a > $o] : ((! [X21 : a] : ((X0 @ X15 @ X21) => (X20 @ X21)) & ! [X22 : a,X23 : a] : (((X0 @ X23 @ X22) & (X20 @ X23)) => (X20 @ X22))) => (X20 @ X14)))) => (X4 @ X14))) => (X4 @ X2)) => ! [X24 : a > $o] : ((! [X25 : a] : (((X3 @ X1 @ X25) | (X0 @ X1 @ X25)) => (X24 @ X25)) & ! [X26 : a,X27 : a] : ((((X3 @ X26 @ X27) | (X0 @ X26 @ X27)) & (X24 @ X26)) => (X24 @ X27))) => (X24 @ X2)))), 1.31/0.63 inference(rectify,[],[f2])). 1.31/0.63 thf(f2,negated_conjecture,( 1.31/0.63 ~! [X1 : a > a > $o,X2 : a,X3 : a,X0 : a > a > $o] : (! [X4 : a > $o] : ((! [X7 : a] : ((! [X8 : a > $o] : ((! [X9 : a] : ((X1 @ X2 @ X9) => (X8 @ X9)) & ! [X5 : a,X6 : a] : (((X1 @ X5 @ X6) & (X8 @ X5)) => (X8 @ X6))) => (X8 @ X7)) | ! [X8 : a > $o] : ((! [X9 : a] : ((X0 @ X2 @ X9) => (X8 @ X9)) & ! [X5 : a,X6 : a] : (((X8 @ X5) & (X0 @ X5 @ X6)) => (X8 @ X6))) => (X8 @ X7))) => (X4 @ X7)) & ! [X6 : a,X5 : a] : (((X4 @ X5) & (! [X8 : a > $o] : ((! [X7 : a] : ((X0 @ X5 @ X7) => (X8 @ X7)) & ! [X10 : a,X11 : a] : (((X0 @ X10 @ X11) & (X8 @ X10)) => (X8 @ X11))) => (X8 @ X6)) | ! [X8 : a > $o] : ((! [X7 : a] : ((X1 @ X5 @ X7) => (X8 @ X7)) & ! [X11 : a,X10 : a] : (((X1 @ X10 @ X11) & (X8 @ X10)) => (X8 @ X11))) => (X8 @ X6)))) => (X4 @ X6))) => (X4 @ X3)) => ! [X4 : a > $o] : ((! [X7 : a] : (((X0 @ X2 @ X7) | (X1 @ X2 @ X7)) => (X4 @ X7)) & ! [X5 : a,X6 : a] : ((((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) & (X4 @ X5)) => (X4 @ X6))) => (X4 @ X3)))), 1.31/0.63 inference(negated_conjecture,[],[f1])). 1.31/0.63 thf(f1,conjecture,( 1.31/0.63 ! [X1 : a > a > $o,X2 : a,X3 : a,X0 : a > a > $o] : (! [X4 : a > $o] : ((! [X7 : a] : ((! [X8 : a > $o] : ((! [X9 : a] : ((X1 @ X2 @ X9) => (X8 @ X9)) & ! [X5 : a,X6 : a] : (((X1 @ X5 @ X6) & (X8 @ X5)) => (X8 @ X6))) => (X8 @ X7)) | ! [X8 : a > $o] : ((! [X9 : a] : ((X0 @ X2 @ X9) => (X8 @ X9)) & ! [X5 : a,X6 : a] : (((X8 @ X5) & (X0 @ X5 @ X6)) => (X8 @ X6))) => (X8 @ X7))) => (X4 @ X7)) & ! [X6 : a,X5 : a] : (((X4 @ X5) & (! [X8 : a > $o] : ((! [X7 : a] : ((X0 @ X5 @ X7) => (X8 @ X7)) & ! [X10 : a,X11 : a] : (((X0 @ X10 @ X11) & (X8 @ X10)) => (X8 @ X11))) => (X8 @ X6)) | ! [X8 : a > $o] : ((! [X7 : a] : ((X1 @ X5 @ X7) => (X8 @ X7)) & ! [X11 : a,X10 : a] : (((X1 @ X10 @ X11) & (X8 @ X10)) => (X8 @ X11))) => (X8 @ X6)))) => (X4 @ X6))) => (X4 @ X3)) => ! [X4 : a > $o] : ((! [X7 : a] : (((X0 @ X2 @ X7) | (X1 @ X2 @ X7)) => (X4 @ X7)) & ! [X5 : a,X6 : a] : ((((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) & (X4 @ X5)) => (X4 @ X6))) => (X4 @ X3)))), 1.31/0.63 file('/export/starexec/sandbox/tmp/tmp.BflOgU1pvt/E---3.1_20224.p',cTHM251C_pme)). 1.31/0.63 thf(f3179,plain,( 1.31/0.63 ~spl0_37), 1.31/0.63 inference(avatar_contradiction_clause,[],[f3178])). 1.31/0.63 thf(f3178,plain,( 1.31/0.63 $false | ~spl0_37), 1.31/0.63 inference(trivial_inequality_removal,[],[f3177])). 1.31/0.63 thf(f3177,plain,( 1.31/0.63 ($false = $true) | ~spl0_37), 1.31/0.63 inference(boolean_simplification,[],[f3176])). 1.31/0.63 thf(f3176,plain,( 1.31/0.63 ($true = (~ $true)) | ~spl0_37), 1.31/0.63 inference(boolean_simplification,[],[f3175])). 1.31/0.63 thf(f3175,plain,( 1.31/0.63 ($true = (~ ($true | (sK2 @ sK4 @ sK36)))) | ~spl0_37), 1.31/0.63 inference(forward_demodulation,[],[f3173,f3157])). 1.31/0.63 thf(f3157,plain,( 1.31/0.63 ($true = (sK5 @ sK4 @ sK36)) | ~spl0_37), 1.31/0.63 inference(binary_proxy_clausification,[],[f3143])). 1.31/0.63 thf(f3143,plain,( 1.31/0.63 (((sK5 @ sK4 @ sK36) => (sK6 @ sK36)) = $false) | ~spl0_37), 1.31/0.63 inference(beta_eta_normalization,[],[f3139])). 1.31/0.63 thf(f3139,plain,( 1.31/0.63 ($false = ((^[Y0 : a]: ((sK5 @ sK4 @ Y0) => (sK6 @ Y0))) @ sK36)) | ~spl0_37), 1.31/0.63 inference(sigma_clausification,[],[f3126])). 1.31/0.63 thf(f3126,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: ((sK5 @ sK4 @ Y0) => (sK6 @ Y0))))) | ~spl0_37), 1.90/0.63 inference(avatar_component_clause,[],[f3125])). 1.90/0.63 thf(f3125,plain,( 1.90/0.63 spl0_37 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK5 @ sK4 @ Y0) => (sK6 @ Y0)))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_37])])). 1.90/0.63 thf(f3173,plain,( 1.90/0.63 ($true = (~ ((sK5 @ sK4 @ sK36) | (sK2 @ sK4 @ sK36)))) | ~spl0_37), 1.90/0.63 inference(boolean_simplification,[],[f3162])). 1.90/0.63 thf(f3162,plain,( 1.90/0.63 ((((sK5 @ sK4 @ sK36) | (sK2 @ sK4 @ sK36)) => $false) = $true) | ~spl0_37), 1.90/0.63 inference(superposition,[],[f42,f3156])). 1.90/0.63 thf(f3156,plain,( 1.90/0.63 ($false = (sK6 @ sK36)) | ~spl0_37), 1.90/0.63 inference(binary_proxy_clausification,[],[f3143])). 1.90/0.63 thf(f42,plain,( 1.90/0.63 ( ! [X1 : a] : (((((sK5 @ sK4 @ X1) | (sK2 @ sK4 @ X1)) => (sK6 @ X1)) = $true)) )), 1.90/0.63 inference(beta_eta_normalization,[],[f41])). 1.90/0.63 thf(f41,plain,( 1.90/0.63 ( ! [X1 : a] : ((((^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0))) @ X1) = $true)) )), 1.90/0.63 inference(pi_clausification,[],[f40])). 1.90/0.63 thf(f40,plain,( 1.90/0.63 ($true = (!! @ a @ (^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0)))))), 1.90/0.63 inference(boolean_simplification,[],[f39])). 1.90/0.63 thf(f39,plain,( 1.90/0.63 (($true & (!! @ a @ (^[Y0 : a]: (((sK5 @ sK4 @ Y0) | (sK2 @ sK4 @ Y0)) => (sK6 @ Y0))))) = $true)), 1.90/0.63 inference(backward_demodulation,[],[f27,f38])). 1.90/0.63 thf(f3127,plain,( 1.90/0.63 spl0_36 | spl0_37 | ~spl0_1 | ~spl0_10), 1.90/0.63 inference(avatar_split_clause,[],[f3118,f400,f123,f3125,f3122])). 1.90/0.63 thf(f123,plain,( 1.90/0.63 spl0_1 <=> ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 1.90/0.63 thf(f400,plain,( 1.90/0.63 spl0_10 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $true)), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])). 1.90/0.63 thf(f3118,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: ((sK5 @ sK4 @ Y0) => (sK6 @ Y0))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK5 @ Y1 @ Y0)) => (sK6 @ Y0))))))) | (~spl0_1 | ~spl0_10)), 1.90/0.63 inference(binary_proxy_clausification,[],[f3103])). 1.90/0.63 thf(f3103,plain,( 1.90/0.63 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK5 @ Y1 @ Y0)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK4 @ Y0) => (sK6 @ Y0)))))) | (~spl0_1 | ~spl0_10)), 1.90/0.63 inference(not_proxy_clausification,[],[f2962])). 1.90/0.63 thf(f2962,plain,( 1.90/0.63 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK5 @ Y1 @ Y0)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK4 @ Y0) => (sK6 @ Y0)))))) = $true) | (~spl0_1 | ~spl0_10)), 1.90/0.63 inference(boolean_simplification,[],[f2958])). 1.90/0.63 thf(f2958,plain,( 1.90/0.63 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK5 @ Y1 @ Y0)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK4 @ Y0) => (sK6 @ Y0))))) => $false) = $true) | (~spl0_1 | ~spl0_10)), 1.90/0.63 inference(superposition,[],[f2941,f2766])). 1.90/0.63 thf(f2766,plain,( 1.90/0.63 ((sK6 @ sK11) = $false) | (~spl0_1 | ~spl0_10)), 1.90/0.63 inference(boolean_simplification,[],[f2765])). 1.90/0.63 thf(f2765,plain,( 1.90/0.63 ($false = ($true => (sK6 @ sK11))) | (~spl0_1 | ~spl0_10)), 1.90/0.63 inference(boolean_simplification,[],[f2764])). 1.90/0.63 thf(f2764,plain,( 1.90/0.63 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | $true) => (sK6 @ sK11))) | (~spl0_1 | ~spl0_10)), 1.90/0.63 inference(backward_demodulation,[],[f2276,f401])). 1.90/0.63 thf(f401,plain,( 1.90/0.63 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $true) | ~spl0_10), 1.90/0.63 inference(avatar_component_clause,[],[f400])). 1.90/0.63 thf(f2276,plain,( 1.90/0.63 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))))) => (sK6 @ sK11))) | ~spl0_1), 1.90/0.63 inference(beta_eta_normalization,[],[f2270])). 1.90/0.63 thf(f2270,plain,( 1.90/0.63 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (sK6 @ Y0))) @ sK11) = $false) | ~spl0_1), 1.90/0.63 inference(sigma_clausification,[],[f124])). 1.90/0.63 thf(f124,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))) | ~spl0_1), 1.90/0.63 inference(avatar_component_clause,[],[f123])). 1.90/0.63 thf(f2941,plain,( 1.90/0.63 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & (sK5 @ Y1 @ Y0)) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK4 @ Y0) => (X1 @ Y0))))) => (X1 @ sK11)) = $true)) ) | ~spl0_10), 1.90/0.63 inference(beta_eta_normalization,[],[f2940])). 1.90/0.63 thf(f2940,plain,( 1.90/0.63 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))) @ X1) = $true)) ) | ~spl0_10), 1.90/0.63 inference(pi_clausification,[],[f401])). 1.90/0.63 thf(f2763,plain,( 1.90/0.63 ~spl0_34), 1.90/0.63 inference(avatar_contradiction_clause,[],[f2762])). 1.90/0.63 thf(f2762,plain,( 1.90/0.63 $false | ~spl0_34), 1.90/0.63 inference(trivial_inequality_removal,[],[f2761])). 1.90/0.63 thf(f2761,plain,( 1.90/0.63 ($false = $true) | ~spl0_34), 1.90/0.63 inference(forward_demodulation,[],[f2756,f2752])). 1.90/0.63 thf(f2752,plain,( 1.90/0.63 ($false = (sK6 @ sK32)) | ~spl0_34), 1.90/0.63 inference(binary_proxy_clausification,[],[f2739])). 1.90/0.63 thf(f2739,plain,( 1.90/0.63 ($false = ((sK2 @ sK4 @ sK32) => (sK6 @ sK32))) | ~spl0_34), 1.90/0.63 inference(beta_eta_normalization,[],[f2735])). 1.90/0.63 thf(f2735,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))) @ sK32)) | ~spl0_34), 1.90/0.63 inference(sigma_clausification,[],[f2638])). 1.90/0.63 thf(f2638,plain,( 1.90/0.63 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false) | ~spl0_34), 1.90/0.63 inference(avatar_component_clause,[],[f2637])). 1.90/0.63 thf(f2637,plain,( 1.90/0.63 spl0_34 <=> ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false)), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_34])])). 1.90/0.63 thf(f2756,plain,( 1.90/0.63 ((sK6 @ sK32) = $true) | ~spl0_34), 1.90/0.63 inference(trivial_inequality_removal,[],[f2755])). 1.90/0.63 thf(f2755,plain,( 1.90/0.63 ((sK6 @ sK32) = $true) | ($false = $true) | ~spl0_34), 1.90/0.63 inference(boolean_simplification,[],[f2754])). 1.90/0.63 thf(f2754,plain,( 1.90/0.63 ($false = ($false => (sK6 @ sK32))) | ((sK6 @ sK32) = $true) | ~spl0_34), 1.90/0.63 inference(superposition,[],[f2739,f445])). 1.90/0.63 thf(f445,plain,( 1.90/0.63 ( ! [X1 : a] : (($false = (sK2 @ sK4 @ X1)) | ((sK6 @ X1) = $true)) )), 1.90/0.63 inference(binary_proxy_clausification,[],[f43])). 1.90/0.63 thf(f43,plain,( 1.90/0.63 ( ! [X1 : a] : (($false = ((sK5 @ sK4 @ X1) | (sK2 @ sK4 @ X1))) | ((sK6 @ X1) = $true)) )), 1.90/0.63 inference(binary_proxy_clausification,[],[f42])). 1.90/0.63 thf(f2723,plain,( 1.90/0.63 ~spl0_33), 1.90/0.63 inference(avatar_contradiction_clause,[],[f2722])). 1.90/0.63 thf(f2722,plain,( 1.90/0.63 $false | ~spl0_33), 1.90/0.63 inference(trivial_inequality_removal,[],[f2721])). 1.90/0.63 thf(f2721,plain,( 1.90/0.63 ($false = $true) | ~spl0_33), 1.90/0.63 inference(forward_demodulation,[],[f2720,f2676])). 1.90/0.63 thf(f2676,plain,( 1.90/0.63 ($false = (sK6 @ sK29)) | ~spl0_33), 1.90/0.63 inference(boolean_simplification,[],[f2675])). 1.90/0.63 thf(f2675,plain,( 1.90/0.63 ($false = ($true => (sK6 @ sK29))) | ~spl0_33), 1.90/0.63 inference(backward_demodulation,[],[f2667,f2674])). 1.90/0.63 thf(f2674,plain,( 1.90/0.63 (((sK2 @ sK30 @ sK29) & (sK6 @ sK30)) = $true) | ~spl0_33), 1.90/0.63 inference(binary_proxy_clausification,[],[f2667])). 1.90/0.63 thf(f2667,plain,( 1.90/0.63 ((((sK2 @ sK30 @ sK29) & (sK6 @ sK30)) => (sK6 @ sK29)) = $false) | ~spl0_33), 1.90/0.63 inference(beta_eta_normalization,[],[f2666])). 1.90/0.63 thf(f2666,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (((sK2 @ Y0 @ sK29) & (sK6 @ Y0)) => (sK6 @ sK29))) @ sK30)) | ~spl0_33), 1.90/0.63 inference(sigma_clausification,[],[f2658])). 1.90/0.63 thf(f2658,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK29) & (sK6 @ Y0)) => (sK6 @ sK29))))) | ~spl0_33), 1.90/0.63 inference(beta_eta_normalization,[],[f2654])). 1.90/0.63 thf(f2654,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0))))) @ sK29)) | ~spl0_33), 1.90/0.63 inference(sigma_clausification,[],[f2635])). 1.90/0.63 thf(f2635,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0))))))) | ~spl0_33), 1.90/0.63 inference(avatar_component_clause,[],[f2634])). 1.90/0.63 thf(f2634,plain,( 1.90/0.63 spl0_33 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_33])])). 1.90/0.63 thf(f2720,plain,( 1.90/0.63 ($true = (sK6 @ sK29)) | ~spl0_33), 1.90/0.63 inference(boolean_simplification,[],[f2719])). 1.90/0.63 thf(f2719,plain,( 1.90/0.63 (($true => (sK6 @ sK29)) = $true) | ~spl0_33), 1.90/0.63 inference(forward_demodulation,[],[f2718,f2712])). 1.90/0.63 thf(f2712,plain,( 1.90/0.63 ((sK6 @ sK31) = $true) | ~spl0_33), 1.90/0.63 inference(binary_proxy_clausification,[],[f2709])). 1.90/0.63 thf(f2709,plain,( 1.90/0.63 ($true = ((sK2 @ sK31 @ sK29) & (sK6 @ sK31))) | ~spl0_33), 1.90/0.63 inference(not_proxy_clausification,[],[f2693])). 1.90/0.63 thf(f2693,plain,( 1.90/0.63 ((~ ((sK2 @ sK31 @ sK29) & (sK6 @ sK31))) = $false) | ~spl0_33), 1.90/0.63 inference(beta_eta_normalization,[],[f2692])). 1.90/0.63 thf(f2692,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (~ ((sK2 @ Y0 @ sK29) & (sK6 @ Y0)))) @ sK31)) | ~spl0_33), 1.90/0.63 inference(sigma_clausification,[],[f2678])). 1.90/0.63 thf(f2678,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK2 @ Y0 @ sK29) & (sK6 @ Y0)))))) | ~spl0_33), 1.90/0.63 inference(boolean_simplification,[],[f2677])). 1.90/0.63 thf(f2677,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (((sK2 @ Y0 @ sK29) & (sK6 @ Y0)) => $false)))) | ~spl0_33), 1.90/0.63 inference(backward_demodulation,[],[f2658,f2676])). 1.90/0.63 thf(f2718,plain,( 1.90/0.63 (((sK6 @ sK31) => (sK6 @ sK29)) = $true) | ~spl0_33), 1.90/0.63 inference(boolean_simplification,[],[f2717])). 1.90/0.63 thf(f2717,plain,( 1.90/0.63 ((((sK6 @ sK31) & $true) => (sK6 @ sK29)) = $true) | ~spl0_33), 1.90/0.63 inference(boolean_simplification,[],[f2716])). 1.90/0.63 thf(f2716,plain,( 1.90/0.63 ((((sK6 @ sK31) & ((sK5 @ sK31 @ sK29) | $true)) => (sK6 @ sK29)) = $true) | ~spl0_33), 1.90/0.63 inference(superposition,[],[f70,f2715])). 1.90/0.63 thf(f2715,plain,( 1.90/0.63 ($true = (sK2 @ sK31 @ sK29)) | ~spl0_33), 1.90/0.63 inference(boolean_simplification,[],[f2714])). 1.90/0.63 thf(f2714,plain,( 1.90/0.63 ($true = ((sK2 @ sK31 @ sK29) & $true)) | ~spl0_33), 1.90/0.63 inference(backward_demodulation,[],[f2709,f2712])). 1.90/0.63 thf(f2639,plain,( 1.90/0.63 spl0_33 | spl0_34 | ~spl0_1 | ~spl0_9), 1.90/0.63 inference(avatar_split_clause,[],[f2630,f397,f123,f2637,f2634])). 1.90/0.63 thf(f397,plain,( 1.90/0.63 spl0_9 <=> ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])). 1.90/0.63 thf(f2630,plain,( 1.90/0.63 ((!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))) = $false) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0))))))) | (~spl0_1 | ~spl0_9)), 1.90/0.63 inference(binary_proxy_clausification,[],[f2609])). 1.90/0.63 thf(f2609,plain,( 1.90/0.63 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))))) | (~spl0_1 | ~spl0_9)), 1.90/0.63 inference(not_proxy_clausification,[],[f2438])). 1.90/0.63 thf(f2438,plain,( 1.90/0.63 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0)))))) = $true) | (~spl0_1 | ~spl0_9)), 1.90/0.63 inference(boolean_simplification,[],[f2435])). 1.90/0.63 thf(f2435,plain,( 1.90/0.63 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (sK6 @ Y1)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (sK6 @ Y0))))) => $false)) | (~spl0_1 | ~spl0_9)), 1.90/0.63 inference(superposition,[],[f2427,f2279])). 1.90/0.63 thf(f2279,plain,( 1.90/0.63 ((sK6 @ sK11) = $false) | (~spl0_1 | ~spl0_9)), 1.90/0.63 inference(boolean_simplification,[],[f2278])). 1.90/0.63 thf(f2278,plain,( 1.90/0.63 ($false = ($true => (sK6 @ sK11))) | (~spl0_1 | ~spl0_9)), 1.90/0.63 inference(boolean_simplification,[],[f2277])). 1.90/0.63 thf(f2277,plain,( 1.90/0.63 ($false = (($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))))) => (sK6 @ sK11))) | (~spl0_1 | ~spl0_9)), 1.90/0.63 inference(forward_demodulation,[],[f2276,f398])). 1.90/0.63 thf(f398,plain,( 1.90/0.63 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))))) | ~spl0_9), 1.90/0.63 inference(avatar_component_clause,[],[f397])). 1.90/0.63 thf(f2427,plain,( 1.90/0.63 ( ! [X1 : a > $o] : (($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK2 @ Y1 @ Y0) & (X1 @ Y1)) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK4 @ Y0) => (X1 @ Y0))))) => (X1 @ sK11)))) ) | ~spl0_9), 1.90/0.63 inference(beta_eta_normalization,[],[f2426])). 1.90/0.63 thf(f2426,plain,( 1.90/0.63 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))) @ X1) = $true)) ) | ~spl0_9), 1.90/0.63 inference(pi_clausification,[],[f398])). 1.90/0.63 thf(f2258,plain,( 1.90/0.63 ~spl0_2 | ~spl0_8 | ~spl0_23), 1.90/0.63 inference(avatar_contradiction_clause,[],[f2257])). 1.90/0.63 thf(f2257,plain,( 1.90/0.63 $false | (~spl0_2 | ~spl0_8 | ~spl0_23)), 1.90/0.63 inference(trivial_inequality_removal,[],[f2256])). 1.90/0.63 thf(f2256,plain,( 1.90/0.63 ($false = $true) | (~spl0_2 | ~spl0_8 | ~spl0_23)), 1.90/0.63 inference(boolean_simplification,[],[f2255])). 1.90/0.63 thf(f2255,plain,( 1.90/0.63 ($true = (~ $true)) | (~spl0_2 | ~spl0_8 | ~spl0_23)), 1.90/0.63 inference(boolean_simplification,[],[f2254])). 1.90/0.63 thf(f2254,plain,( 1.90/0.63 ((~ ($true | (sK2 @ sK7 @ sK23))) = $true) | (~spl0_2 | ~spl0_8 | ~spl0_23)), 1.90/0.63 inference(forward_demodulation,[],[f2248,f2236])). 1.90/0.63 thf(f2236,plain,( 1.90/0.63 ((sK5 @ sK7 @ sK23) = $true) | ~spl0_23), 1.90/0.63 inference(binary_proxy_clausification,[],[f2226])). 1.90/0.63 thf(f2226,plain,( 1.90/0.63 ($false = ((sK5 @ sK7 @ sK23) => (sK6 @ sK23))) | ~spl0_23), 1.90/0.63 inference(beta_eta_normalization,[],[f2222])). 1.90/0.63 thf(f2222,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ Y0))) @ sK23)) | ~spl0_23), 1.90/0.63 inference(sigma_clausification,[],[f1351])). 1.90/0.63 thf(f1351,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ Y0))))) | ~spl0_23), 1.90/0.63 inference(avatar_component_clause,[],[f1350])). 1.90/0.63 thf(f1350,plain,( 1.90/0.63 spl0_23 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ Y0)))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_23])])). 1.90/0.63 thf(f2248,plain,( 1.90/0.63 ((~ ((sK5 @ sK7 @ sK23) | (sK2 @ sK7 @ sK23))) = $true) | (~spl0_2 | ~spl0_8 | ~spl0_23)), 1.90/0.63 inference(boolean_simplification,[],[f2244])). 1.90/0.63 thf(f2244,plain,( 1.90/0.63 ((((sK5 @ sK7 @ sK23) | (sK2 @ sK7 @ sK23)) => $false) = $true) | (~spl0_2 | ~spl0_8 | ~spl0_23)), 1.90/0.63 inference(superposition,[],[f1794,f2238])). 1.90/0.63 thf(f2238,plain,( 1.90/0.63 ((sK6 @ sK23) = $false) | ~spl0_23), 1.90/0.63 inference(boolean_simplification,[],[f2237])). 1.90/0.63 thf(f2237,plain,( 1.90/0.63 (($true => (sK6 @ sK23)) = $false) | ~spl0_23), 1.90/0.63 inference(backward_demodulation,[],[f2226,f2236])). 1.90/0.63 thf(f1794,plain,( 1.90/0.63 ( ! [X0 : a] : (((((sK5 @ sK7 @ X0) | (sK2 @ sK7 @ X0)) => (sK6 @ X0)) = $true)) ) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(boolean_simplification,[],[f1791])). 1.90/0.63 thf(f1791,plain,( 1.90/0.63 ( ! [X0 : a] : (((($true & ((sK5 @ sK7 @ X0) | (sK2 @ sK7 @ X0))) => (sK6 @ X0)) = $true)) ) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(superposition,[],[f70,f1775])). 1.90/0.63 thf(f1775,plain,( 1.90/0.63 ($true = (sK6 @ sK7)) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(binary_proxy_clausification,[],[f1773])). 1.90/0.63 thf(f1773,plain,( 1.90/0.63 ($false = ((sK6 @ sK7) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(boolean_simplification,[],[f1772])). 1.90/0.63 thf(f1772,plain,( 1.90/0.63 ($false = (($true & (sK6 @ sK7)) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(boolean_simplification,[],[f1771])). 1.90/0.63 thf(f1771,plain,( 1.90/0.63 ($false = ((($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))))) & (sK6 @ sK7)) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(backward_demodulation,[],[f414,f368])). 1.90/0.63 thf(f368,plain,( 1.90/0.63 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true) | ~spl0_8), 1.90/0.63 inference(avatar_component_clause,[],[f367])). 1.90/0.63 thf(f367,plain,( 1.90/0.63 spl0_8 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true)), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])). 1.90/0.63 thf(f414,plain,( 1.90/0.63 (((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))))) & (sK6 @ sK7)) => (sK6 @ sK8)) = $false) | ~spl0_2), 1.90/0.63 inference(beta_eta_normalization,[],[f413])). 1.90/0.63 thf(f413,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: ((((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK5 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) & (sK6 @ sK7)) => (sK6 @ Y0))) @ sK8)) | ~spl0_2), 1.90/0.63 inference(sigma_clausification,[],[f409])). 1.90/0.63 thf(f409,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: ((((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK5 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) & (sK6 @ sK7)) => (sK6 @ Y0))))) | ~spl0_2), 1.90/0.63 inference(beta_eta_normalization,[],[f407])). 1.90/0.63 thf(f407,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ sK7)) | ~spl0_2), 1.90/0.63 inference(sigma_clausification,[],[f127])). 1.90/0.63 thf(f127,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1))))))) | ~spl0_2), 1.90/0.63 inference(avatar_component_clause,[],[f126])). 1.90/0.63 thf(f126,plain,( 1.90/0.63 spl0_2 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 1.90/0.63 thf(f2218,plain,( 1.90/0.63 ~spl0_24), 1.90/0.63 inference(avatar_contradiction_clause,[],[f2217])). 1.90/0.63 thf(f2217,plain,( 1.90/0.63 $false | ~spl0_24), 1.90/0.63 inference(trivial_inequality_removal,[],[f2216])). 1.90/0.63 thf(f2216,plain,( 1.90/0.63 ($false = $true) | ~spl0_24), 1.90/0.63 inference(forward_demodulation,[],[f2215,f2097])). 1.90/0.63 thf(f2097,plain,( 1.90/0.63 ($false = (sK6 @ sK21)) | ~spl0_24), 1.90/0.63 inference(binary_proxy_clausification,[],[f2087])). 1.90/0.63 thf(f2087,plain,( 1.90/0.63 ($false = (((sK6 @ sK20) & (sK5 @ sK20 @ sK21)) => (sK6 @ sK21))) | ~spl0_24), 1.90/0.63 inference(beta_eta_normalization,[],[f2086])). 1.90/0.63 thf(f2086,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (((sK6 @ sK20) & (sK5 @ sK20 @ Y0)) => (sK6 @ Y0))) @ sK21)) | ~spl0_24), 1.90/0.63 inference(sigma_clausification,[],[f2067])). 1.90/0.63 thf(f2067,plain,( 1.90/0.63 ((!! @ a @ (^[Y0 : a]: (((sK6 @ sK20) & (sK5 @ sK20 @ Y0)) => (sK6 @ Y0)))) = $false) | ~spl0_24), 1.90/0.63 inference(beta_eta_normalization,[],[f2065])). 1.90/0.63 thf(f2065,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK6 @ Y1))))) @ sK20)) | ~spl0_24), 1.90/0.63 inference(sigma_clausification,[],[f1354])). 1.90/0.63 thf(f1354,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK6 @ Y1))))))) | ~spl0_24), 1.90/0.63 inference(avatar_component_clause,[],[f1353])). 1.90/0.63 thf(f1353,plain,( 1.90/0.63 spl0_24 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK6 @ Y1)))))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_24])])). 1.90/0.63 thf(f2215,plain,( 1.90/0.63 ((sK6 @ sK21) = $true) | ~spl0_24), 1.90/0.63 inference(boolean_simplification,[],[f2214])). 1.90/0.63 thf(f2214,plain,( 1.90/0.63 (($true => (sK6 @ sK21)) = $true) | ~spl0_24), 1.90/0.63 inference(forward_demodulation,[],[f2213,f2163])). 1.90/0.63 thf(f2163,plain,( 1.90/0.63 ((sK6 @ sK20) = $true) | ~spl0_24), 1.90/0.63 inference(binary_proxy_clausification,[],[f2098])). 1.90/0.63 thf(f2098,plain,( 1.90/0.63 (((sK6 @ sK20) & (sK5 @ sK20 @ sK21)) = $true) | ~spl0_24), 1.90/0.63 inference(binary_proxy_clausification,[],[f2087])). 1.90/0.63 thf(f2213,plain,( 1.90/0.63 ($true = ((sK6 @ sK20) => (sK6 @ sK21))) | ~spl0_24), 1.90/0.63 inference(boolean_simplification,[],[f2212])). 1.90/0.63 thf(f2212,plain,( 1.90/0.63 ($true = (((sK6 @ sK20) & $true) => (sK6 @ sK21))) | ~spl0_24), 1.90/0.63 inference(boolean_simplification,[],[f2211])). 1.90/0.63 thf(f2211,plain,( 1.90/0.63 ((((sK6 @ sK20) & ($true | (sK2 @ sK20 @ sK21))) => (sK6 @ sK21)) = $true) | ~spl0_24), 1.90/0.63 inference(superposition,[],[f70,f2165])). 1.90/0.63 thf(f2165,plain,( 1.90/0.63 ($true = (sK5 @ sK20 @ sK21)) | ~spl0_24), 1.90/0.63 inference(boolean_simplification,[],[f2164])). 1.90/0.63 thf(f2164,plain,( 1.90/0.63 (($true & (sK5 @ sK20 @ sK21)) = $true) | ~spl0_24), 1.90/0.63 inference(backward_demodulation,[],[f2098,f2163])). 1.90/0.63 thf(f1770,plain,( 1.90/0.63 ~spl0_22), 1.90/0.63 inference(avatar_contradiction_clause,[],[f1769])). 1.90/0.63 thf(f1769,plain,( 1.90/0.63 $false | ~spl0_22), 1.90/0.63 inference(trivial_inequality_removal,[],[f1768])). 1.90/0.63 thf(f1768,plain,( 1.90/0.63 ($false = $true) | ~spl0_22), 1.90/0.63 inference(forward_demodulation,[],[f1767,f1710])). 1.90/0.63 thf(f1710,plain,( 1.90/0.63 ((sK6 @ sK17) = $false) | ~spl0_22), 1.90/0.63 inference(boolean_simplification,[],[f1709])). 1.90/0.63 thf(f1709,plain,( 1.90/0.63 ($false = ($true => (sK6 @ sK17))) | ~spl0_22), 1.90/0.63 inference(backward_demodulation,[],[f1694,f1708])). 1.90/0.63 thf(f1708,plain,( 1.90/0.63 ($true = ((sK6 @ sK18) & (sK2 @ sK18 @ sK17))) | ~spl0_22), 1.90/0.63 inference(binary_proxy_clausification,[],[f1694])). 1.90/0.63 thf(f1694,plain,( 1.90/0.63 ((((sK6 @ sK18) & (sK2 @ sK18 @ sK17)) => (sK6 @ sK17)) = $false) | ~spl0_22), 1.90/0.63 inference(beta_eta_normalization,[],[f1693])). 1.90/0.63 thf(f1693,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ sK17)) => (sK6 @ sK17))) @ sK18)) | ~spl0_22), 1.90/0.63 inference(sigma_clausification,[],[f1681])). 1.90/0.63 thf(f1681,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ sK17)) => (sK6 @ sK17))))) | ~spl0_22), 1.90/0.63 inference(beta_eta_normalization,[],[f1679])). 1.90/0.63 thf(f1679,plain,( 1.90/0.63 (((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))) @ sK17) = $false) | ~spl0_22), 1.90/0.63 inference(sigma_clausification,[],[f1016])). 1.90/0.63 thf(f1016,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))) | ~spl0_22), 1.90/0.63 inference(avatar_component_clause,[],[f1015])). 1.90/0.63 thf(f1015,plain,( 1.90/0.63 spl0_22 <=> ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_22])])). 1.90/0.63 thf(f1767,plain,( 1.90/0.63 ((sK6 @ sK17) = $true) | ~spl0_22), 1.90/0.63 inference(boolean_simplification,[],[f1766])). 1.90/0.63 thf(f1766,plain,( 1.90/0.63 ($true = ($true => (sK6 @ sK17))) | ~spl0_22), 1.90/0.63 inference(forward_demodulation,[],[f1765,f1748])). 1.90/0.63 thf(f1748,plain,( 1.90/0.63 ($true = (sK6 @ sK19)) | ~spl0_22), 1.90/0.63 inference(boolean_simplification,[],[f1747])). 1.90/0.63 thf(f1747,plain,( 1.90/0.63 ($true = ((sK6 @ sK19) & $true)) | ~spl0_22), 1.90/0.63 inference(backward_demodulation,[],[f1742,f1745])). 1.90/0.63 thf(f1745,plain,( 1.90/0.63 ((sK2 @ sK19 @ sK17) = $true) | ~spl0_22), 1.90/0.63 inference(binary_proxy_clausification,[],[f1742])). 1.90/0.63 thf(f1742,plain,( 1.90/0.63 ($true = ((sK6 @ sK19) & (sK2 @ sK19 @ sK17))) | ~spl0_22), 1.90/0.63 inference(not_proxy_clausification,[],[f1729])). 1.90/0.63 thf(f1729,plain,( 1.90/0.63 ((~ ((sK6 @ sK19) & (sK2 @ sK19 @ sK17))) = $false) | ~spl0_22), 1.90/0.63 inference(beta_eta_normalization,[],[f1728])). 1.90/0.63 thf(f1728,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (~ ((sK6 @ Y0) & (sK2 @ Y0 @ sK17)))) @ sK19)) | ~spl0_22), 1.90/0.63 inference(sigma_clausification,[],[f1712])). 1.90/0.63 thf(f1712,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (~ ((sK6 @ Y0) & (sK2 @ Y0 @ sK17)))))) | ~spl0_22), 1.90/0.63 inference(boolean_simplification,[],[f1711])). 1.90/0.63 thf(f1711,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (((sK6 @ Y0) & (sK2 @ Y0 @ sK17)) => $false)))) | ~spl0_22), 1.90/0.63 inference(backward_demodulation,[],[f1681,f1710])). 1.90/0.63 thf(f1765,plain,( 1.90/0.63 (((sK6 @ sK19) => (sK6 @ sK17)) = $true) | ~spl0_22), 1.90/0.63 inference(boolean_simplification,[],[f1764])). 1.90/0.63 thf(f1764,plain,( 1.90/0.63 ((((sK6 @ sK19) & $true) => (sK6 @ sK17)) = $true) | ~spl0_22), 1.90/0.63 inference(boolean_simplification,[],[f1763])). 1.90/0.63 thf(f1763,plain,( 1.90/0.63 ($true = (((sK6 @ sK19) & ((sK5 @ sK19 @ sK17) | $true)) => (sK6 @ sK17))) | ~spl0_22), 1.90/0.63 inference(superposition,[],[f70,f1745])). 1.90/0.63 thf(f1675,plain,( 1.90/0.63 ~spl0_2 | ~spl0_7 | ~spl0_21), 1.90/0.63 inference(avatar_contradiction_clause,[],[f1674])). 1.90/0.63 thf(f1674,plain,( 1.90/0.63 $false | (~spl0_2 | ~spl0_7 | ~spl0_21)), 1.90/0.63 inference(trivial_inequality_removal,[],[f1673])). 1.90/0.63 thf(f1673,plain,( 1.90/0.63 ($false = $true) | (~spl0_2 | ~spl0_7 | ~spl0_21)), 1.90/0.63 inference(boolean_simplification,[],[f1672])). 1.90/0.63 thf(f1672,plain,( 1.90/0.63 ($true = (~ $true)) | (~spl0_2 | ~spl0_7 | ~spl0_21)), 1.90/0.63 inference(boolean_simplification,[],[f1671])). 1.90/0.63 thf(f1671,plain,( 1.90/0.63 ((~ ((sK5 @ sK7 @ sK16) | $true)) = $true) | (~spl0_2 | ~spl0_7 | ~spl0_21)), 1.90/0.63 inference(forward_demodulation,[],[f1666,f1648])). 1.90/0.63 thf(f1648,plain,( 1.90/0.63 ($true = (sK2 @ sK7 @ sK16)) | ~spl0_21), 1.90/0.63 inference(binary_proxy_clausification,[],[f1644])). 1.90/0.63 thf(f1644,plain,( 1.90/0.63 (((sK2 @ sK7 @ sK16) => (sK6 @ sK16)) = $false) | ~spl0_21), 1.90/0.63 inference(beta_eta_normalization,[],[f1642])). 1.90/0.63 thf(f1642,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))) @ sK16)) | ~spl0_21), 1.90/0.63 inference(sigma_clausification,[],[f1013])). 1.90/0.63 thf(f1013,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))) | ~spl0_21), 1.90/0.63 inference(avatar_component_clause,[],[f1012])). 1.90/0.63 thf(f1012,plain,( 1.90/0.63 spl0_21 <=> ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0)))))), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_21])])). 1.90/0.63 thf(f1666,plain,( 1.90/0.63 ($true = (~ ((sK5 @ sK7 @ sK16) | (sK2 @ sK7 @ sK16)))) | (~spl0_2 | ~spl0_7 | ~spl0_21)), 1.90/0.63 inference(boolean_simplification,[],[f1661])). 1.90/0.63 thf(f1661,plain,( 1.90/0.63 ((((sK5 @ sK7 @ sK16) | (sK2 @ sK7 @ sK16)) => $false) = $true) | (~spl0_2 | ~spl0_7 | ~spl0_21)), 1.90/0.63 inference(superposition,[],[f1381,f1647])). 1.90/0.63 thf(f1647,plain,( 1.90/0.63 ($false = (sK6 @ sK16)) | ~spl0_21), 1.90/0.63 inference(binary_proxy_clausification,[],[f1644])). 1.90/0.63 thf(f1381,plain,( 1.90/0.63 ( ! [X0 : a] : (((((sK5 @ sK7 @ X0) | (sK2 @ sK7 @ X0)) => (sK6 @ X0)) = $true)) ) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(boolean_simplification,[],[f1376])). 1.90/0.63 thf(f1376,plain,( 1.90/0.63 ( ! [X0 : a] : (((($true & ((sK5 @ sK7 @ X0) | (sK2 @ sK7 @ X0))) => (sK6 @ X0)) = $true)) ) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(superposition,[],[f70,f1360])). 1.90/0.63 thf(f1360,plain,( 1.90/0.63 ($true = (sK6 @ sK7)) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(binary_proxy_clausification,[],[f1358])). 1.90/0.63 thf(f1358,plain,( 1.90/0.63 ($false = ((sK6 @ sK7) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(boolean_simplification,[],[f1357])). 1.90/0.63 thf(f1357,plain,( 1.90/0.63 ($false = (($true & (sK6 @ sK7)) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(boolean_simplification,[],[f1356])). 1.90/0.63 thf(f1356,plain,( 1.90/0.63 (((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) | $true) & (sK6 @ sK7)) => (sK6 @ sK8)) = $false) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(backward_demodulation,[],[f414,f365])). 1.90/0.63 thf(f365,plain,( 1.90/0.63 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true) | ~spl0_7), 1.90/0.63 inference(avatar_component_clause,[],[f364])). 1.90/0.63 thf(f364,plain,( 1.90/0.63 spl0_7 <=> ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true)), 1.90/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])). 1.90/0.63 thf(f1355,plain,( 1.90/0.63 spl0_23 | spl0_24 | ~spl0_2 | ~spl0_8), 1.90/0.63 inference(avatar_split_clause,[],[f1346,f367,f126,f1353,f1350])). 1.90/0.63 thf(f1346,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK6 @ Y1))))))) | ($false = (!! @ a @ (^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ Y0))))) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(binary_proxy_clausification,[],[f1327])). 1.90/0.63 thf(f1327,plain,( 1.90/0.63 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ Y0)))))) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(not_proxy_clausification,[],[f1255])). 1.90/0.63 thf(f1255,plain,( 1.90/0.63 ((~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ Y0)))))) = $true) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(boolean_simplification,[],[f1250])). 1.90/0.63 thf(f1250,plain,( 1.90/0.63 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y0) & (sK5 @ Y0 @ Y1)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (sK6 @ Y0))))) => $false) = $true) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(superposition,[],[f1236,f1021])). 1.90/0.63 thf(f1021,plain,( 1.90/0.63 ($false = (sK6 @ sK8)) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(binary_proxy_clausification,[],[f1020])). 1.90/0.63 thf(f1020,plain,( 1.90/0.63 ($false = ((sK6 @ sK7) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(boolean_simplification,[],[f1019])). 1.90/0.63 thf(f1019,plain,( 1.90/0.63 ($false = (($true & (sK6 @ sK7)) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(boolean_simplification,[],[f1018])). 1.90/0.63 thf(f1018,plain,( 1.90/0.63 ($false = ((($true | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))))) & (sK6 @ sK7)) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_8)), 1.90/0.63 inference(backward_demodulation,[],[f414,f368])). 1.90/0.63 thf(f1236,plain,( 1.90/0.63 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y0) & (sK5 @ Y0 @ Y1)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: ((sK5 @ sK7 @ Y0) => (X1 @ Y0))))) => (X1 @ sK8)) = $true)) ) | ~spl0_8), 1.90/0.63 inference(beta_eta_normalization,[],[f1235])). 1.90/0.63 thf(f1235,plain,( 1.90/0.63 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))) @ X1))) ) | ~spl0_8), 1.90/0.63 inference(pi_clausification,[],[f368])). 1.90/0.63 thf(f1017,plain,( 1.90/0.63 spl0_21 | spl0_22 | ~spl0_2 | ~spl0_7), 1.90/0.63 inference(avatar_split_clause,[],[f1008,f364,f126,f1015,f1012])). 1.90/0.63 thf(f1008,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))) | ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0))))))) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(binary_proxy_clausification,[],[f1004])). 1.90/0.63 thf(f1004,plain,( 1.90/0.63 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0)))))) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(not_proxy_clausification,[],[f434])). 1.90/0.63 thf(f434,plain,( 1.90/0.63 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))))) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(boolean_simplification,[],[f428])). 1.90/0.63 thf(f428,plain,( 1.90/0.63 ($true = (((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((sK6 @ Y1) & (sK2 @ Y1 @ Y0)) => (sK6 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (sK6 @ Y0))))) => $false)) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(superposition,[],[f406,f418])). 1.90/0.63 thf(f418,plain,( 1.90/0.63 ($false = (sK6 @ sK8)) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(binary_proxy_clausification,[],[f417])). 1.90/0.63 thf(f417,plain,( 1.90/0.63 ($false = ((sK6 @ sK7) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(boolean_simplification,[],[f416])). 1.90/0.63 thf(f416,plain,( 1.90/0.63 ($false = (($true & (sK6 @ sK7)) => (sK6 @ sK8))) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(boolean_simplification,[],[f415])). 1.90/0.63 thf(f415,plain,( 1.90/0.63 (((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) | $true) & (sK6 @ sK7)) => (sK6 @ sK8)) = $false) | (~spl0_2 | ~spl0_7)), 1.90/0.63 inference(forward_demodulation,[],[f414,f365])). 1.90/0.63 thf(f406,plain,( 1.90/0.63 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: (((X1 @ Y1) & (sK2 @ Y1 @ Y0)) => (X1 @ Y0)))))) & (!! @ a @ (^[Y0 : a]: ((sK2 @ sK7 @ Y0) => (X1 @ Y0))))) => (X1 @ sK8)) = $true)) ) | ~spl0_7), 1.90/0.63 inference(beta_eta_normalization,[],[f405])). 1.90/0.63 thf(f405,plain,( 1.90/0.63 ( ! [X1 : a > $o] : ((((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))) @ X1) = $true)) ) | ~spl0_7), 1.90/0.63 inference(pi_clausification,[],[f365])). 1.90/0.63 thf(f402,plain,( 1.90/0.63 spl0_9 | spl0_10 | ~spl0_1), 1.90/0.63 inference(avatar_split_clause,[],[f395,f123,f400,f397])). 1.90/0.63 thf(f395,plain,( 1.90/0.63 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))))) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) = $true) | ~spl0_1), 1.90/0.63 inference(binary_proxy_clausification,[],[f378])). 1.90/0.63 thf(f378,plain,( 1.90/0.63 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))))) | ~spl0_1), 1.90/0.63 inference(binary_proxy_clausification,[],[f374])). 1.90/0.63 thf(f374,plain,( 1.90/0.63 ($false = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((sK2 @ Y2 @ Y1) & (Y0 @ Y2)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK5 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK4 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK11))))) => (sK6 @ sK11))) | ~spl0_1), 1.90/0.63 inference(beta_eta_normalization,[],[f372])). 1.90/0.63 thf(f372,plain,( 1.90/0.63 (((^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (sK6 @ Y0))) @ sK11) = $false) | ~spl0_1), 1.90/0.63 inference(sigma_clausification,[],[f124])). 1.90/0.63 thf(f369,plain,( 1.90/0.63 spl0_7 | spl0_8 | ~spl0_2), 1.90/0.63 inference(avatar_split_clause,[],[f362,f126,f367,f364])). 1.90/0.63 thf(f362,plain,( 1.90/0.63 ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) = $true) | ~spl0_2), 1.90/0.63 inference(binary_proxy_clausification,[],[f211])). 1.90/0.63 thf(f211,plain,( 1.90/0.63 ($true = ((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))))) | ~spl0_2), 1.90/0.63 inference(binary_proxy_clausification,[],[f139])). 1.90/0.63 thf(f139,plain,( 1.90/0.63 ($true = (((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))))) & (sK6 @ sK7))) | ~spl0_2), 1.90/0.63 inference(binary_proxy_clausification,[],[f137])). 1.90/0.63 thf(f137,plain,( 1.90/0.63 (((((!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y1) & (sK5 @ Y1 @ Y2)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: ((sK5 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8)))) | (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: (((Y0 @ Y2) & (sK2 @ Y2 @ Y1)) => (Y0 @ Y1)))))) & (!! @ a @ (^[Y1 : a]: ((sK2 @ sK7 @ Y1) => (Y0 @ Y1))))) => (Y0 @ sK8))))) & (sK6 @ sK7)) => (sK6 @ sK8)) = $false) | ~spl0_2), 1.90/0.63 inference(beta_eta_normalization,[],[f136])). 1.90/0.63 thf(f136,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: ((((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK5 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) & (sK6 @ sK7)) => (sK6 @ Y0))) @ sK8)) | ~spl0_2), 1.90/0.63 inference(sigma_clausification,[],[f133])). 1.90/0.63 thf(f133,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: ((((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y2) & (sK5 @ Y2 @ Y3)) => (Y1 @ Y3)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK2 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK7 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) & (sK6 @ sK7)) => (sK6 @ Y0))))) | ~spl0_2), 1.90/0.63 inference(beta_eta_normalization,[],[f131])). 1.90/0.63 thf(f131,plain,( 1.90/0.63 ($false = ((^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1))))) @ sK7)) | ~spl0_2), 1.90/0.63 inference(sigma_clausification,[],[f127])). 1.90/0.63 thf(f128,plain,( 1.90/0.63 spl0_1 | spl0_2), 1.90/0.63 inference(avatar_split_clause,[],[f119,f126,f123])). 1.90/0.63 thf(f119,plain,( 1.90/0.63 ($false = (!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1))))))) | ($false = (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))))), 1.90/0.63 inference(binary_proxy_clausification,[],[f103])). 1.90/0.63 thf(f103,plain,( 1.90/0.63 ($false = ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))))), 1.90/0.63 inference(not_proxy_clausification,[],[f36])). 1.90/0.63 thf(f36,plain,( 1.90/0.63 ($true = (~ ((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (sK6 @ Y0)))))))), 1.90/0.63 inference(boolean_simplification,[],[f35])). 1.90/0.63 thf(f35,plain,( 1.90/0.63 ((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (sK6 @ Y0)) => (sK6 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (sK6 @ Y0))))) => $false) = $true)), 1.90/0.63 inference(superposition,[],[f33,f26])). 1.90/0.63 thf(f26,plain,( 1.90/0.63 ($false = (sK6 @ sK3))), 1.90/0.63 inference(binary_proxy_clausification,[],[f25])). 1.90/0.63 thf(f33,plain,( 1.90/0.63 ( ! [X1 : a > $o] : (((((!! @ a @ (^[Y0 : a]: (!! @ a @ (^[Y1 : a]: ((((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y3) & (sK5 @ Y3 @ Y4)) => (Y2 @ Y4)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK2 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ Y0 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) & (X1 @ Y0)) => (X1 @ Y1)))))) & (!! @ a @ (^[Y0 : a]: (((!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((sK2 @ Y3 @ Y2) & (Y1 @ Y3)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK2 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0)))) | (!! @ (a > $o) @ (^[Y1 : a > $o]: (((!! @ a @ (^[Y2 : a]: (!! @ a @ (^[Y3 : a]: (((Y1 @ Y3) & (sK5 @ Y3 @ Y2)) => (Y1 @ Y2)))))) & (!! @ a @ (^[Y2 : a]: ((sK5 @ sK4 @ Y2) => (Y1 @ Y2))))) => (Y1 @ Y0))))) => (X1 @ Y0))))) => (X1 @ sK3)) = $true)) )), 1.90/0.63 inference(beta_eta_normalization,[],[f32])). 1.90/0.63 thf(f32,plain,( 1.90/0.63 ( ! [X1 : a > $o] : (($true = ((^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK5 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK5 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK5 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (Y0 @ Y1))))) => (Y0 @ sK3))) @ X1))) )), 1.90/0.63 inference(pi_clausification,[],[f19])). 1.90/0.63 thf(f19,plain,( 1.90/0.63 ($true = (!! @ (a > $o) @ (^[Y0 : a > $o]: (((!! @ a @ (^[Y1 : a]: (!! @ a @ (^[Y2 : a]: ((((!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y4) & (sK5 @ Y4 @ Y5)) => (Y3 @ Y5)))))) & (!! @ a @ (^[Y4 : a]: ((sK5 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2)))) | (!! @ (a > $o) @ (^[Y3 : a > $o]: (((!! @ a @ (^[Y4 : a]: (!! @ a @ (^[Y5 : a]: (((Y3 @ Y5) & (sK2 @ Y5 @ Y4)) => (Y3 @ Y4)))))) & (!! @ a @ (^[Y4 : a]: ((sK2 @ Y1 @ Y4) => (Y3 @ Y4))))) => (Y3 @ Y2))))) & (Y0 @ Y1)) => (Y0 @ Y2)))))) & (!! @ a @ (^[Y1 : a]: (((!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((sK2 @ Y4 @ Y3) & (Y2 @ Y4)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK2 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1)))) | (!! @ (a > $o) @ (^[Y2 : a > $o]: (((!! @ a @ (^[Y3 : a]: (!! @ a @ (^[Y4 : a]: (((Y2 @ Y4) & (sK5 @ Y4 @ Y3)) => (Y2 @ Y3)))))) & (!! @ a @ (^[Y3 : a]: ((sK5 @ sK4 @ Y3) => (Y2 @ Y3))))) => (Y2 @ Y1))))) => (Y0 @ Y1))))) => (Y0 @ sK3)))))), 1.90/0.63 inference(binary_proxy_clausification,[],[f17])). 1.90/0.63 % SZS output end Proof for E---3.1_20224 1.90/0.63 % (20342)------------------------------ 1.90/0.63 % (20342)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.90/0.63 % (20342)Termination reason: Refutation 1.90/0.63 1.90/0.63 % (20342)Memory used [KB]: 7164 1.90/0.63 % (20342)Time elapsed: 0.214 s 1.90/0.63 % (20342)Instructions burned: 447 (million) 1.90/0.63 % (20342)------------------------------ 1.90/0.63 % (20342)------------------------------ 1.90/0.63 % (20330)Success in time 0.266 s 1.90/0.63 EOF