0.07/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : run_vampire %s %d THM
0.13/0.34	% Computer   : n023.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 1920
0.13/0.34	% WCLimit    : 240
0.13/0.34	% DateTime   : Wed Jul 30 02:46:49 EDT 2025
0.13/0.34	% CPUTime    : 
0.13/0.36	This is a THF_ problem
0.13/0.36	Running higher-order theorem proving
0.13/0.40	Running /export/starexec/sandbox/solver/bin/vampire-hol --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --print_def_sorts on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.hzHB0bubAS/E---3.1_19791.p -m 16384 -t 240
0.25/0.43	% (20050)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_19791 for (2399ds/27Mi)
0.25/0.43	% (20049)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_19791 for (2399ds/4Mi)
0.25/0.43	% (20048)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_19791 for (2399ds/183Mi)
0.25/0.43	% (20052)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_19791 for (2399ds/2Mi)
0.25/0.43	% (20051)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_19791 for (2399ds/2Mi)
0.25/0.43	% (20053)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_19791 for (2399ds/275Mi)
0.25/0.43	% (20054)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_19791 for (2399ds/18Mi)
0.25/0.43	% (20051)Instruction limit reached!
0.25/0.43	% (20051)------------------------------
0.25/0.43	% (20051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.43	% (20051)Termination reason: Unknown
0.25/0.43	% (20051)Termination phase: shuffling
0.25/0.43	
0.25/0.43	% (20051)Memory used [KB]: 1279
0.25/0.43	% (20051)Time elapsed: 0.003 s
0.25/0.43	% (20051)Instructions burned: 2 (million)
0.25/0.43	% (20051)------------------------------
0.25/0.43	% (20051)------------------------------
0.25/0.43	% (20052)Instruction limit reached!
0.25/0.43	% (20052)------------------------------
0.25/0.43	% (20052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.43	% (20052)Termination reason: Unknown
0.25/0.43	% (20052)Termination phase: shuffling
0.25/0.43	
0.25/0.43	% (20052)Memory used [KB]: 1279
0.25/0.43	% (20052)Time elapsed: 0.003 s
0.25/0.43	% (20052)Instructions burned: 2 (million)
0.25/0.43	% (20052)------------------------------
0.25/0.43	% (20052)------------------------------
0.25/0.43	% (20049)Instruction limit reached!
0.25/0.43	% (20049)------------------------------
0.25/0.43	% (20049)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.43	% (20049)Termination reason: Unknown
0.25/0.43	% (20049)Termination phase: shuffling
0.25/0.43	
0.25/0.43	% (20049)Memory used [KB]: 1279
0.25/0.43	% (20049)Time elapsed: 0.004 s
0.25/0.43	% (20049)Instructions burned: 4 (million)
0.25/0.43	% (20049)------------------------------
0.25/0.43	% (20049)------------------------------
0.25/0.44	% (20054)Instruction limit reached!
0.25/0.44	% (20054)------------------------------
0.25/0.44	% (20054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.44	% (20054)Termination reason: Unknown
0.25/0.44	% (20054)Termination phase: Property scanning
0.25/0.44	
0.25/0.44	% (20054)Memory used [KB]: 1535
0.25/0.44	% (20054)Time elapsed: 0.013 s
0.25/0.44	% (20054)Instructions burned: 19 (million)
0.25/0.44	% (20054)------------------------------
0.25/0.44	% (20054)------------------------------
0.25/0.45	% (20050)Instruction limit reached!
0.25/0.45	% (20050)------------------------------
0.25/0.45	% (20050)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.45	% (20050)Termination reason: Unknown
0.25/0.45	% (20050)Termination phase: Property scanning
0.25/0.45	
0.25/0.45	% (20050)Memory used [KB]: 1791
0.25/0.45	% (20050)Time elapsed: 0.016 s
0.25/0.45	% (20050)Instructions burned: 27 (million)
0.25/0.45	% (20050)------------------------------
0.25/0.45	% (20050)------------------------------
0.25/0.45	% (20055)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_19791 for (2399ds/3Mi)
0.25/0.45	% (20056)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_19791 for (2399ds/37Mi)
0.25/0.45	% (20057)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_19791 for (2399ds/15Mi)
0.25/0.45	% (20055)Instruction limit reached!
0.25/0.45	% (20055)------------------------------
0.25/0.45	% (20055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.45	% (20055)Termination reason: Unknown
0.25/0.45	% (20055)Termination phase: shuffling
0.25/0.45	
0.25/0.45	% (20055)Memory used [KB]: 1279
0.25/0.45	% (20055)Time elapsed: 0.004 s
0.25/0.45	% (20055)Instructions burned: 3 (million)
0.25/0.45	% (20055)------------------------------
0.25/0.45	% (20055)------------------------------
0.25/0.46	% (20058)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_19791 for (2399ds/3Mi)
0.25/0.46	% (20057)Instruction limit reached!
0.25/0.46	% (20057)------------------------------
0.25/0.46	% (20057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.46	% (20057)Termination reason: Unknown
0.25/0.46	% (20057)Termination phase: Property scanning
0.25/0.46	
0.25/0.46	% (20057)Memory used [KB]: 1535
0.25/0.46	% (20057)Time elapsed: 0.012 s
0.25/0.46	% (20057)Instructions burned: 15 (million)
0.25/0.46	% (20057)------------------------------
0.25/0.46	% (20057)------------------------------
0.25/0.46	% (20058)Instruction limit reached!
0.25/0.46	% (20058)------------------------------
0.25/0.46	% (20058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.46	% (20058)Termination reason: Unknown
0.25/0.46	% (20058)Termination phase: shuffling
0.25/0.46	
0.25/0.46	% (20058)Memory used [KB]: 1279
0.25/0.46	% (20058)Time elapsed: 0.004 s
0.25/0.46	% (20058)Instructions burned: 3 (million)
0.25/0.46	% (20058)------------------------------
0.25/0.46	% (20058)------------------------------
0.25/0.46	% (20059)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_19791 for (2399ds/1041Mi)
0.25/0.47	% (20056)Instruction limit reached!
0.25/0.47	% (20056)------------------------------
0.25/0.47	% (20056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.47	% (20056)Termination reason: Unknown
0.25/0.47	% (20056)Termination phase: Property scanning
0.25/0.47	
0.25/0.47	% (20056)Memory used [KB]: 1791
0.25/0.47	% (20056)Time elapsed: 0.021 s
0.25/0.47	% (20056)Instructions burned: 38 (million)
0.25/0.47	% (20056)------------------------------
0.25/0.47	% (20056)------------------------------
0.25/0.47	% (20060)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_19791 for (2399ds/7Mi)
0.25/0.48	% (20060)Instruction limit reached!
0.25/0.48	% (20060)------------------------------
0.25/0.48	% (20060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.48	% (20060)Termination reason: Unknown
0.25/0.48	% (20060)Termination phase: shuffling
0.25/0.48	
0.25/0.48	% (20060)Memory used [KB]: 1407
0.25/0.48	% (20060)Time elapsed: 0.006 s
0.25/0.48	% (20060)Instructions burned: 7 (million)
0.25/0.48	% (20060)------------------------------
0.25/0.48	% (20060)------------------------------
0.25/0.48	% (20061)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_19791 for (2399ds/16Mi)
0.25/0.48	% (20062)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_19791 for (2399ds/3Mi)
0.25/0.48	% (20062)Instruction limit reached!
0.25/0.48	% (20062)------------------------------
0.25/0.48	% (20062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.48	% (20062)Termination reason: Unknown
0.25/0.48	% (20062)Termination phase: shuffling
0.25/0.48	
0.25/0.48	% (20062)Memory used [KB]: 1279
0.25/0.48	% (20062)Time elapsed: 0.004 s
0.25/0.48	% (20062)Instructions burned: 3 (million)
0.25/0.48	% (20062)------------------------------
0.25/0.48	% (20062)------------------------------
0.25/0.49	% (20063)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_19791 for (2399ds/3Mi)
0.25/0.49	% (20061)Instruction limit reached!
0.25/0.49	% (20061)------------------------------
0.25/0.49	% (20061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.49	% (20061)Termination reason: Unknown
0.25/0.49	% (20061)Termination phase: shuffling
0.25/0.49	
0.25/0.49	% (20061)Memory used [KB]: 1663
0.25/0.49	% (20061)Time elapsed: 0.011 s
0.25/0.49	% (20061)Instructions burned: 16 (million)
0.25/0.49	% (20061)------------------------------
0.25/0.49	% (20061)------------------------------
0.25/0.49	% (20063)Instruction limit reached!
0.25/0.49	% (20063)------------------------------
0.25/0.49	% (20063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.49	% (20063)Termination reason: Unknown
0.25/0.49	% (20063)Termination phase: shuffling
0.25/0.49	
0.25/0.49	% (20063)Memory used [KB]: 1279
0.25/0.49	% (20063)Time elapsed: 0.004 s
0.25/0.49	% (20063)Instructions burned: 3 (million)
0.25/0.49	% (20063)------------------------------
0.25/0.49	% (20063)------------------------------
0.25/0.49	% (20064)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_19791 for (2399ds/7Mi)
0.25/0.50	% (20064)Instruction limit reached!
0.25/0.50	% (20064)------------------------------
0.25/0.50	% (20064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.50	% (20064)Termination reason: Unknown
0.25/0.50	% (20064)Termination phase: shuffling
0.25/0.50	
0.25/0.50	% (20064)Memory used [KB]: 1407
0.25/0.50	% (20064)Time elapsed: 0.006 s
0.25/0.50	% (20064)Instructions burned: 7 (million)
0.25/0.50	% (20064)------------------------------
0.25/0.50	% (20064)------------------------------
0.25/0.50	% (20065)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_19791 for (2399ds/3Mi)
0.25/0.50	% (20065)Instruction limit reached!
0.25/0.50	% (20065)------------------------------
0.25/0.50	% (20065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.50	% (20065)Termination reason: Unknown
0.25/0.50	% (20065)Termination phase: shuffling
0.25/0.50	
0.25/0.50	% (20065)Memory used [KB]: 1279
0.25/0.50	% (20065)Time elapsed: 0.004 s
0.25/0.50	% (20065)Instructions burned: 3 (million)
0.25/0.50	% (20065)------------------------------
0.25/0.50	% (20065)------------------------------
0.25/0.51	% (20066)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_19791 for (2399ds/4Mi)
0.25/0.51	% (20067)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_19791 for (2399ds/18Mi)
0.25/0.51	% (20066)Instruction limit reached!
0.25/0.51	% (20066)------------------------------
0.25/0.51	% (20066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.51	% (20066)Termination reason: Unknown
0.25/0.51	% (20066)Termination phase: shuffling
0.25/0.51	
0.25/0.51	% (20066)Memory used [KB]: 1279
0.25/0.51	% (20066)Time elapsed: 0.004 s
0.25/0.51	% (20066)Instructions burned: 4 (million)
0.25/0.51	% (20066)------------------------------
0.25/0.51	% (20066)------------------------------
0.25/0.52	% (20068)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_19791 for (2399ds/710Mi)
0.25/0.52	% (20067)Instruction limit reached!
0.25/0.52	% (20067)------------------------------
0.25/0.52	% (20067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.52	% (20067)Termination reason: Unknown
0.25/0.52	% (20067)Termination phase: shuffling
0.25/0.52	
0.25/0.52	% (20067)Memory used [KB]: 1663
0.25/0.52	% (20067)Time elapsed: 0.012 s
0.25/0.52	% (20067)Instructions burned: 18 (million)
0.25/0.52	% (20067)------------------------------
0.25/0.52	% (20067)------------------------------
0.25/0.52	% (20069)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_19791 for (2399ds/6Mi)
0.25/0.53	% (20069)Instruction limit reached!
0.25/0.53	% (20069)------------------------------
0.25/0.53	% (20069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.53	% (20069)Termination reason: Unknown
0.25/0.53	% (20069)Termination phase: shuffling
0.25/0.53	
0.25/0.53	% (20069)Memory used [KB]: 1407
0.25/0.53	% (20069)Time elapsed: 0.005 s
0.25/0.53	% (20069)Instructions burned: 6 (million)
0.25/0.53	% (20069)------------------------------
0.25/0.53	% (20069)------------------------------
0.25/0.53	% (20048)Instruction limit reached!
0.25/0.53	% (20048)------------------------------
0.25/0.53	% (20048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.53	% (20048)Termination reason: Unknown
0.25/0.53	% (20048)Termination phase: Saturation
0.25/0.53	
0.25/0.53	% (20048)Memory used [KB]: 7419
0.25/0.53	% (20048)Time elapsed: 0.095 s
0.25/0.53	% (20048)Instructions burned: 183 (million)
0.25/0.53	% (20048)------------------------------
0.25/0.53	% (20048)------------------------------
0.25/0.53	% (20073)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_19791 for (2399ds/902Mi)
0.25/0.54	% (20076)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_19791 for (2398ds/21Mi)
0.25/0.54	% (20078)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_19791 for (2398ds/6Mi)
0.25/0.54	% (20077)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_19791 for (2398ds/5Mi)
0.25/0.55	% (20078)Instruction limit reached!
0.25/0.55	% (20078)------------------------------
0.25/0.55	% (20078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.55	% (20076)Instruction limit reached!
0.25/0.55	% (20076)------------------------------
0.25/0.55	% (20076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.55	% (20076)Termination reason: Unknown
0.25/0.55	% (20076)Termination phase: shuffling
0.25/0.55	
0.25/0.55	% (20076)Memory used [KB]: 1791
0.25/0.55	% (20076)Time elapsed: 0.012 s
0.25/0.55	% (20076)Instructions burned: 23 (million)
0.25/0.55	% (20076)------------------------------
0.25/0.55	% (20076)------------------------------
0.25/0.55	% (20078)Termination reason: Unknown
0.25/0.55	% (20078)Termination phase: shuffling
0.25/0.55	
0.25/0.55	% (20078)Memory used [KB]: 1407
0.25/0.55	% (20078)Time elapsed: 0.004 s
0.25/0.55	% (20078)Instructions burned: 6 (million)
0.25/0.55	% (20078)------------------------------
0.25/0.55	% (20078)------------------------------
0.25/0.55	% (20077)Instruction limit reached!
0.25/0.55	% (20077)------------------------------
0.25/0.55	% (20077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.55	% (20077)Termination reason: Unknown
0.25/0.55	% (20077)Termination phase: shuffling
0.25/0.55	
0.25/0.55	% (20077)Memory used [KB]: 1407
0.25/0.55	% (20077)Time elapsed: 0.005 s
0.25/0.55	% (20077)Instructions burned: 6 (million)
0.25/0.55	% (20077)------------------------------
0.25/0.55	% (20077)------------------------------
0.25/0.56	% (20080)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_19791 for (2398ds/779Mi)
0.25/0.56	% (20079)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_19791 for (2398ds/377Mi)
0.25/0.56	% (20081)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_19791 for (2398ds/19Mi)
0.25/0.57	% (20081)Instruction limit reached!
0.25/0.57	% (20081)------------------------------
0.25/0.57	% (20081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.57	% (20081)Termination reason: Unknown
0.25/0.57	% (20081)Termination phase: shuffling
0.25/0.57	
0.25/0.57	% (20081)Memory used [KB]: 1663
0.25/0.57	% (20081)Time elapsed: 0.008 s
0.25/0.57	% (20081)Instructions burned: 20 (million)
0.25/0.57	% (20081)------------------------------
0.25/0.57	% (20081)------------------------------
0.25/0.57	% (20053)Instruction limit reached!
0.25/0.57	% (20053)------------------------------
0.25/0.57	% (20053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.57	% (20053)Termination reason: Unknown
0.25/0.57	% (20053)Termination phase: Saturation
0.25/0.57	
0.25/0.57	% (20053)Memory used [KB]: 8187
0.25/0.57	% (20053)Time elapsed: 0.138 s
0.25/0.57	% (20053)Instructions burned: 277 (million)
0.25/0.57	% (20053)------------------------------
0.25/0.57	% (20053)------------------------------
0.25/0.58	% (20082)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_19791 for (2398ds/879Mi)
0.25/0.58	% (20083)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_19791 for (2398ds/17Mi)
0.25/0.58	% (20083)Instruction limit reached!
0.25/0.58	% (20083)------------------------------
0.25/0.58	% (20083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.58	% (20083)Termination reason: Unknown
0.25/0.58	% (20083)Termination phase: shuffling
0.25/0.58	
0.25/0.58	% (20083)Memory used [KB]: 1663
0.25/0.58	% (20083)Time elapsed: 0.006 s
0.25/0.58	% (20083)Instructions burned: 17 (million)
0.25/0.58	% (20083)------------------------------
0.25/0.58	% (20083)------------------------------
0.25/0.60	% (20084)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_19791 for (2398ds/3Mi)
0.25/0.60	% (20084)Instruction limit reached!
0.25/0.60	% (20084)------------------------------
0.25/0.60	% (20084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
0.25/0.60	% (20084)Termination reason: Unknown
0.25/0.60	% (20084)Termination phase: shuffling
0.25/0.60	
0.25/0.60	% (20084)Memory used [KB]: 1279
0.25/0.60	% (20084)Time elapsed: 0.003 s
0.25/0.60	% (20084)Instructions burned: 3 (million)
0.25/0.60	% (20084)------------------------------
0.25/0.60	% (20084)------------------------------
1.46/0.61	% (20085)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_19791 for (2398ds/30Mi)
1.46/0.62	% (20085)Instruction limit reached!
1.46/0.62	% (20085)------------------------------
1.46/0.62	% (20085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
1.46/0.62	% (20085)Termination reason: Unknown
1.46/0.62	% (20085)Termination phase: Property scanning
1.46/0.62	
1.46/0.62	% (20085)Memory used [KB]: 1791
1.46/0.62	% (20085)Time elapsed: 0.010 s
1.46/0.62	% (20085)Instructions burned: 30 (million)
1.46/0.62	% (20085)------------------------------
1.46/0.62	% (20085)------------------------------
1.61/0.63	% (20086)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_19791 for (2397ds/127Mi)
1.68/0.66	% (20073)First to succeed.
1.68/0.66	% (20073)Refutation found. Thanks to Tanya!
1.68/0.66	% SZS status Theorem for E---3.1_19791
1.68/0.66	% SZS output start Proof for E---3.1_19791
1.68/0.66	thf(func_def_0, type, in: $i > $i > $o).
1.68/0.66	thf(func_def_1, type, exu: ($i > $o) > $o).
1.68/0.66	thf(func_def_6, type, setadjoin: $i > $i > $i).
1.68/0.66	thf(func_def_8, type, powerset: $i > $i).
1.68/0.66	thf(func_def_10, type, setunion: $i > $i).
1.68/0.66	thf(func_def_19, type, descr: ($i > $o) > $i).
1.68/0.66	thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_26, type, prop2set: $o > $i).
1.68/0.66	thf(func_def_36, type, nonempty: $i > $o).
1.68/0.66	thf(func_def_69, type, set2prop: $i > $o).
1.68/0.66	thf(func_def_88, type, subset: $i > $i > $o).
1.68/0.66	thf(func_def_89, type, disjoint: $i > $i > $o).
1.68/0.66	thf(func_def_90, type, setsmeet: $i > $i > $o).
1.68/0.66	thf(func_def_114, type, binunion: $i > $i > $i).
1.68/0.66	thf(func_def_122, type, binintersect: $i > $i > $i).
1.68/0.66	thf(func_def_135, type, regular: $i > $o).
1.68/0.66	thf(func_def_136, type, setminus: $i > $i > $i).
1.68/0.66	thf(func_def_147, type, symdiff: $i > $i > $i).
1.68/0.66	thf(func_def_153, type, iskpair: $i > $o).
1.68/0.66	thf(func_def_158, type, kpair: $i > $i > $i).
1.68/0.66	thf(func_def_160, type, cartprod: $i > $i > $i).
1.68/0.66	thf(func_def_177, type, singleton: $i > $o).
1.68/0.66	thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
1.68/0.66	thf(func_def_184, type, atmost1p: $i > $o).
1.68/0.66	thf(func_def_185, type, atleast2p: $i > $o).
1.68/0.66	thf(func_def_186, type, atmost2p: $i > $o).
1.68/0.66	thf(func_def_187, type, upairsetp: $i > $o).
1.68/0.66	thf(func_def_191, type, kfst: $i > $i).
1.68/0.66	thf(func_def_212, type, sP1: $i > $i > $i > $o > $o).
1.68/0.66	thf(func_def_213, type, sP2: $i > $i > $o).
1.68/0.66	thf(func_def_214, type, sP3: $i > $o).
1.68/0.66	thf(func_def_215, type, sP4: $i > $i > $o).
1.68/0.66	thf(func_def_216, type, sP5: $i > $i > $o).
1.68/0.66	thf(func_def_219, type, sK8: $i > $i > $i).
1.68/0.66	thf(func_def_240, type, sK29: $i > $o).
1.68/0.66	thf(func_def_256, type, sK45: $o > $i > $i > $i).
1.68/0.66	thf(func_def_269, type, sK58: $i > $i > $i > $i).
1.68/0.66	thf(func_def_270, type, sK59: $i > $i > $i > $i).
1.68/0.66	thf(func_def_275, type, sK64: $i > $o).
1.68/0.66	thf(func_def_278, type, sK67: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_279, type, sK68: $i > $o).
1.68/0.66	thf(func_def_280, type, sK69: ($i > $o) > $i).
1.68/0.66	thf(func_def_282, type, sK71: $i > $o).
1.68/0.66	thf(func_def_283, type, sK72: ($i > $o) > $i > $i).
1.68/0.66	thf(func_def_285, type, sK74: $i > $o).
1.68/0.66	thf(func_def_287, type, sK76: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_288, type, sK77: $i > $o).
1.68/0.66	thf(func_def_305, type, sK94: ($i > $o) > $i).
1.68/0.66	thf(func_def_306, type, sK95: ($i > $o) > $i).
1.68/0.66	thf(func_def_307, type, sK96: $i > $o).
1.68/0.66	thf(func_def_309, type, sK98: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_310, type, sK99: $i > $o).
1.68/0.66	thf(func_def_313, type, sK102: $i > $i).
1.68/0.66	thf(func_def_317, type, sK106: $i > $i > $i).
1.68/0.66	thf(func_def_330, type, sK119: $i > $o).
1.68/0.66	thf(func_def_332, type, sK121: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_338, type, sK127: $i > $o).
1.68/0.66	thf(func_def_353, type, sK142: $i > $i > $i).
1.68/0.66	thf(func_def_356, type, sK145: $i > $o).
1.68/0.66	thf(func_def_359, type, sK148: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_360, type, sK149: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_371, type, sK160: $i > $i > $i).
1.68/0.66	thf(func_def_375, type, sK164: $i > $i).
1.68/0.66	thf(func_def_377, type, sK166: $i > $i).
1.68/0.66	thf(func_def_378, type, sK167: $i > $i > $i).
1.68/0.66	thf(func_def_379, type, sK168: $i > $i > $i).
1.68/0.66	thf(func_def_389, type, sK178: $i > $o).
1.68/0.66	thf(func_def_398, type, sK187: $i > $o).
1.68/0.66	thf(func_def_411, type, sK200: $i > $i > $i).
1.68/0.66	thf(func_def_423, type, sK212: $i > $o).
1.68/0.66	thf(func_def_426, type, sK215: ($i > $o) > $i > $i > $i).
1.68/0.66	thf(func_def_429, type, sK218: $i > $o).
1.68/0.66	thf(func_def_433, type, sK222: ($i > $o) > ($i > $o) > $i).
1.68/0.66	thf(func_def_434, type, sK223: ($i > $o) > ($i > $o) > $i).
1.68/0.66	thf(func_def_435, type, sK224: $i > $o).
1.68/0.66	thf(func_def_436, type, sK225: $i > $o).
1.68/0.66	thf(func_def_462, type, sK251: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_463, type, sK252: $i > $o).
1.68/0.66	thf(func_def_480, type, sK269: $i > $i).
1.68/0.66	thf(func_def_487, type, sK276: ($i > $o) > ($i > $o) > $i).
1.68/0.66	thf(func_def_488, type, sK277: ($i > $o) > ($i > $o) > $i).
1.68/0.66	thf(func_def_489, type, sK278: $i > $o).
1.68/0.66	thf(func_def_490, type, sK279: $i > $o).
1.68/0.66	thf(func_def_503, type, sK292: $i > $o).
1.68/0.66	thf(func_def_506, type, sK295: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_520, type, sK309: $i > $o).
1.68/0.66	thf(func_def_522, type, sK311: $i > $i > $i).
1.68/0.66	thf(func_def_523, type, sK312: $i > $i > $i).
1.68/0.66	thf(func_def_524, type, sK313: $i > $i > $i).
1.68/0.66	thf(func_def_525, type, sK314: $i > $i > $i).
1.68/0.66	thf(func_def_526, type, sK315: $i > $i > $i).
1.68/0.66	thf(func_def_527, type, sK316: $i > $i > $i > $i).
1.68/0.66	thf(func_def_528, type, sK317: $i > $i).
1.68/0.66	thf(func_def_529, type, sK318: $i > $i).
1.68/0.66	thf(func_def_530, type, sK319: $i > $i).
1.68/0.66	thf(func_def_531, type, sK320: $i > $i).
1.68/0.66	thf(func_def_532, type, sK321: $i > $i > $i > $i).
1.68/0.66	thf(func_def_533, type, sK322: $i > $i > $i > $i).
1.68/0.66	thf(func_def_534, type, sK323: $i > $i > $i).
1.68/0.66	thf(func_def_535, type, sK324: $i > $i > $i).
1.68/0.66	thf(func_def_536, type, sK325: $i > $i > $i).
1.68/0.66	thf(func_def_537, type, sK326: $i > $i).
1.68/0.66	thf(func_def_539, type, sK328: $i > $i).
1.68/0.66	thf(func_def_540, type, sK329: $i > $i).
1.68/0.66	thf(func_def_541, type, sK330: $i > $i > $i).
1.68/0.66	thf(func_def_544, type, sK333: $i > $i > $i).
1.68/0.66	thf(func_def_555, type, sK344: $i > $o).
1.68/0.66	thf(func_def_573, type, sK362: $i > $o).
1.68/0.66	thf(func_def_582, type, sK371: $i > $i).
1.68/0.66	thf(func_def_589, type, sK378: $i > $i > $o).
1.68/0.66	thf(func_def_590, type, sK379: $i > $i).
1.68/0.66	thf(func_def_591, type, sK380: $i > $i).
1.68/0.66	thf(func_def_592, type, sK381: ($i > $i > $o) > $i > $i).
1.68/0.66	thf(func_def_593, type, sK382: ($i > $i > $o) > $i > $i).
1.68/0.66	thf(func_def_594, type, sK383: $i > ($i > $i > $o) > $i > $i).
1.68/0.66	thf(func_def_600, type, sK389: $i > $o).
1.68/0.66	thf(func_def_610, type, sK399: $i > $o).
1.68/0.66	thf(func_def_612, type, sK401: $i > ($i > $o) > $i).
1.68/0.66	thf(func_def_613, type, sK402: ($i > $o) > $i).
1.68/0.66	thf(func_def_614, type, sK403: $i > $o).
1.68/0.66	thf(func_def_615, type, sK404: $i > $i).
1.68/0.66	thf(func_def_618, type, sK407: $i > $o).
1.68/0.66	thf(func_def_619, type, sK408: $i > $o).
1.68/0.66	thf(func_def_620, type, sK409: ($i > $o) > ($i > $o) > $i > $i > $i).
1.68/0.66	thf(func_def_621, type, sK410: ($i > $o) > ($i > $o) > $i > $i > $i).
1.68/0.66	thf(func_def_623, type, sK412: $i > $o).
1.68/0.66	thf(func_def_625, type, sK414: ($i > $o) > $i > $i).
1.68/0.66	thf(func_def_626, type, sK415: ($i > $o) > $i > $i).
1.68/0.66	thf(func_def_631, type, sK420: $i > $i > $i).
1.68/0.66	thf(func_def_642, type, sK431: $i > $o).
1.68/0.66	thf(func_def_646, type, sK435: $i > $i).
1.68/0.66	thf(func_def_649, type, sK438: ($i > $o) > $i).
1.68/0.66	thf(func_def_650, type, sK439: $i > $o).
1.68/0.66	thf(func_def_651, type, sK440: $i > $i).
1.68/0.66	thf(func_def_652, type, sK441: $i > $o).
1.68/0.66	thf(func_def_665, type, sK454: $i > $o).
1.68/0.66	thf(func_def_667, type, sK456: ($i > $o) > $i > $i).
1.68/0.66	thf(func_def_678, type, sK467: $i > $i).
1.68/0.66	thf(func_def_683, type, ph472: !>[X0: $tType]:(X0)).
1.68/0.66	thf(f3305,plain,(
1.68/0.66	  $false),
1.68/0.66	  inference(avatar_sat_refutation,[status(thm)],[f3230,f3291,f3304])).
1.68/0.66	thf(f3304,plain,(
1.68/0.66	  ~spl471_20 | ~spl471_17),
1.68/0.66	  inference(avatar_split_clause,[status(thm)],[f3303,f3183,f3253])).
1.68/0.66	thf(f3253,definition,(
1.68/0.66	  spl471_20 <=> (sK341 = sK342)),
1.68/0.66	  introduced(definition,[new_symbols(naming,[spl471_20])],[avatar_definition])).
1.68/0.66	thf(f3183,definition,(
1.68/0.66	  spl471_17 <=> (sK343 = sK342)),
1.68/0.66	  introduced(definition,[new_symbols(naming,[spl471_17])],[avatar_definition])).
1.68/0.66	thf(f3303,plain,(
1.68/0.66	  (sK341 != sK342) | ~spl471_17),
1.68/0.66	  inference(superposition,[status(thm)],[f2045,f3185])).
1.68/0.66	thf(f3185,plain,(
1.68/0.66	  (sK343 = sK342) | ~spl471_17),
1.68/0.66	  inference(avatar_component_clause,[status(thm)],[f3183])).
1.68/0.66	thf(f2045,plain,(
1.68/0.66	  (sK341 != sK343)),
1.68/0.66	  inference(cnf_transformation,[status(thm)],[f1309])).
1.68/0.66	thf(f1309,plain,(
1.68/0.66	  (prop2setE = $true) & (singletoninpowerset = $true) & (omega0Ax = $true) & (binintersectEL = $true) & (inPowerset = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (powersetE1 = $true) & (emptyI = $true) & (notinsingleton = $true) & (setunionE = $true) & (powersetAx = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (kpairp = $true) & (setminusLsub = $true) & (powersetE = $true) & (exuE1 = $true) & (setukpairinjR1 = $true) & (eqimpsubset2 = $true) & (omegaSAx = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (quantDeMorgan2 = $true) & (setukpairIR = $true) & (powerset__Cong = $true) & (foundationAx = $true) & (setminusSubset1 = $true) & (upairsetIR = $true) & (setukpairinjL1 = $true) & (setminusI = $true) & (binintersectSubset5 = $true) & (notinemptyset = $true) & (subsetE2 = $true) & (notdallE = $true) & (setminusEL = $true) & (singletonsubset = $true) & (subsetI2 = $true) & (exuE2 = $true) & (binintersectSubset4 = $true) & (setunion__Cong = $true) & (setoftrueEq = $true) & (upairset2E = $true) & (disjointsetsI1 = $true) & (setextsub = $true) & (quantDeMorgan4 = $true) & (binintersectER = $true) & (setadjoinOr = $true) & (setunionsingleton = $true) & (in__Cong = $true) & (binintersectRsub = $true) & (subsetTrans = $true) & (notdexE = $true) & (upairsetIL = $true) & (setextAx = $true) & (emptyinPowerset = $true) & (quantDeMorgan3 = $true) & (dsetconstrI = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI1 = $true) & (prop2set2propI = $true) & (exu__Cong = $true) & (exuI2 = $true) & (binunionLsub = $true) & (setadjoinSub = $true) & (setukpairinjL = $true) & (symdiffE = $true) & (singletoninpowunion = $true) & (kpairiskpair = $true) & (secondinupair = $true) & (notsubsetI = $true) & (uniqinunit = $true) & (ubforcartprodlem2 = $true) & (subsetI1 = $true) & (setminusER = $true) & (wellorderingAx = $true) & (sepInPowerset = $true) & (prop2setI = $true) & (setbeta = $true) & (eqinunit = $true) & (descrp = $true) & (binintersectSubset3 = $true) & (singletonsswitch = $true) & (setadjoinE = $true) & (setunionsingleton1 = $true) & (exuE3u = $true) & (cartprodmempair1 = $true) & (ex1I = $true) & (setminusERneg = $true) & (omega__Cong = $true) & (cartprodfstin = $true) & (omegaIndAx = $true) & (exuEu = $true) & (nonemptyI1 = $true) & (setunionsingleton2 = $true) & (binunionRsub = $true) & (powersetI1 = $true) & (exuI1 = $true) & (replAx = $true) & (setadjoinAx = $true) & (dsetconstrER = $true) & (kfstsingleton = $true) & (setext = $true) & (exuI3 = $true) & (upairsetE = $true) & (singletonsuniq = $true) & (setadjoinIL = $true) & (singletonprop = $true) & (setukpairinjL2 = $true) & (subsetemptysetimpeq = $true) & (powersetsubset = $true) & (binintersectI = $true) & (emptyE1 = $true) & (setukpairIL = $true) & ((sK341 != sK343) & ((setadjoin @ sK343 @ (setadjoin @ sK341 @ emptyset)) = (setadjoin @ sK342 @ emptyset))) & (setadjoinSub2 = $true) & (setadjoin__Cong = $true) & (emptysetE = $true) & (setunionE2 = $true) & (emptysetAx = $true) & (binintersectSubset2 = $true) & (binunionEcases = $true) & (binunionIR = $true) & (binunionIL = $true) & (emptyset__Cong = $true) & (emptyinunitempty = $true) & (subset2powerset = $true) & (powersetI = $true) & (subPowSU = $true) & (notequalI1 = $true) & (eqimpsubset1 = $true) & (cartprodpairin = $true) & (setminusILneg = $true) & (descr__Cong = $true) & (binunionE = $true) & (upairsubunion = $true) & (notequalI2 = $true) & (setminusSubset2 = $true) & (vacuousDall = $true) & (emptyInPowerset = $true) & (ex1I2 = $true) & (ubforcartprodlem3 = $true) & (setunionI = $true) & (upairinpowunion = $true) & (symdiffI2 = $true) & (subsetE = $true) & (ex1E1 = $true) & (subsetRefl = $true) & (binintersectLsub = $true) & (nonemptyI = $true) & (binintersectSubset1 = $true) & (dsetconstr__Cong = $true) & (cartprodmempair = $true) & (emptysetimpfalse = $true) & (setminusELneg = $true) & (nonemptyImpWitness = $true) & (upairset2IR = $true) & (emptysetsubset = $true) & (kfstpairEq = $true) & (setukpairinjR12 = $true) & (noeltsimpempty = $true) & (sepSubset = $true) & (bs114d = $true) & (quantDeMorgan1 = $true) & (theprop = $true) & (setminusIRneg = $true) & (ubforcartprodlem1 = $true) & (setukpairinjR11 = $true)),
1.68/0.66	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK341,sK342,sK343])],[f591,f1308])).
1.68/0.66	thf(f1308,plain,(
1.68/0.66	  ? [X0 : $i,X1 : $i,X2 : $i] : ((X0 != X2) & ((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) => ((sK341 != sK343) & ((setadjoin @ sK343 @ (setadjoin @ sK341 @ emptyset)) = (setadjoin @ sK342 @ emptyset)))),
1.68/0.66	  introduced(definition,[],[choice_axiom])).
1.68/0.66	thf(f591,plain,(
1.68/0.66	  (prop2setE = $true) & (singletoninpowerset = $true) & (omega0Ax = $true) & (binintersectEL = $true) & (inPowerset = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (powersetE1 = $true) & (emptyI = $true) & (notinsingleton = $true) & (setunionE = $true) & (powersetAx = $true) & (setadjoinIR = $true) & (exuE3e = $true) & (kpairp = $true) & (setminusLsub = $true) & (powersetE = $true) & (exuE1 = $true) & (setukpairinjR1 = $true) & (eqimpsubset2 = $true) & (omegaSAx = $true) & (setunionAx = $true) & (dsetconstrEL = $true) & (quantDeMorgan2 = $true) & (setukpairIR = $true) & (powerset__Cong = $true) & (foundationAx = $true) & (setminusSubset1 = $true) & (upairsetIR = $true) & (setukpairinjL1 = $true) & (setminusI = $true) & (binintersectSubset5 = $true) & (notinemptyset = $true) & (subsetE2 = $true) & (notdallE = $true) & (setminusEL = $true) & (singletonsubset = $true) & (subsetI2 = $true) & (exuE2 = $true) & (binintersectSubset4 = $true) & (setunion__Cong = $true) & (setoftrueEq = $true) & (upairset2E = $true) & (disjointsetsI1 = $true) & (setextsub = $true) & (quantDeMorgan4 = $true) & (binintersectER = $true) & (setadjoinOr = $true) & (setunionsingleton = $true) & (in__Cong = $true) & (binintersectRsub = $true) & (subsetTrans = $true) & (notdexE = $true) & (upairsetIL = $true) & (setextAx = $true) & (emptyinPowerset = $true) & (quantDeMorgan3 = $true) & (dsetconstrI = $true) & (symdiffIneg2 = $true) & (symdiffIneg1 = $true) & (symdiffI1 = $true) & (prop2set2propI = $true) & (exu__Cong = $true) & (exuI2 = $true) & (binunionLsub = $true) & (setadjoinSub = $true) & (setukpairinjL = $true) & (symdiffE = $true) & (singletoninpowunion = $true) & (kpairiskpair = $true) & (secondinupair = $true) & (notsubsetI = $true) & (uniqinunit = $true) & (ubforcartprodlem2 = $true) & (subsetI1 = $true) & (setminusER = $true) & (wellorderingAx = $true) & (sepInPowerset = $true) & (prop2setI = $true) & (setbeta = $true) & (eqinunit = $true) & (descrp = $true) & (binintersectSubset3 = $true) & (singletonsswitch = $true) & (setadjoinE = $true) & (setunionsingleton1 = $true) & (exuE3u = $true) & (cartprodmempair1 = $true) & (ex1I = $true) & (setminusERneg = $true) & (omega__Cong = $true) & (cartprodfstin = $true) & (omegaIndAx = $true) & (exuEu = $true) & (nonemptyI1 = $true) & (setunionsingleton2 = $true) & (binunionRsub = $true) & (powersetI1 = $true) & (exuI1 = $true) & (replAx = $true) & (setadjoinAx = $true) & (dsetconstrER = $true) & (kfstsingleton = $true) & (setext = $true) & (exuI3 = $true) & (upairsetE = $true) & (singletonsuniq = $true) & (setadjoinIL = $true) & (singletonprop = $true) & (setukpairinjL2 = $true) & (subsetemptysetimpeq = $true) & (powersetsubset = $true) & (binintersectI = $true) & (emptyE1 = $true) & (setukpairIL = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : ((X0 != X2) & ((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) & (setadjoinSub2 = $true) & (setadjoin__Cong = $true) & (emptysetE = $true) & (setunionE2 = $true) & (emptysetAx = $true) & (binintersectSubset2 = $true) & (binunionEcases = $true) & (binunionIR = $true) & (binunionIL = $true) & (emptyset__Cong = $true) & (emptyinunitempty = $true) & (subset2powerset = $true) & (powersetI = $true) & (subPowSU = $true) & (notequalI1 = $true) & (eqimpsubset1 = $true) & (cartprodpairin = $true) & (setminusILneg = $true) & (descr__Cong = $true) & (binunionE = $true) & (upairsubunion = $true) & (notequalI2 = $true) & (setminusSubset2 = $true) & (vacuousDall = $true) & (emptyInPowerset = $true) & (ex1I2 = $true) & (ubforcartprodlem3 = $true) & (setunionI = $true) & (upairinpowunion = $true) & (symdiffI2 = $true) & (subsetE = $true) & (ex1E1 = $true) & (subsetRefl = $true) & (binintersectLsub = $true) & (nonemptyI = $true) & (binintersectSubset1 = $true) & (dsetconstr__Cong = $true) & (cartprodmempair = $true) & (emptysetimpfalse = $true) & (setminusELneg = $true) & (nonemptyImpWitness = $true) & (upairset2IR = $true) & (emptysetsubset = $true) & (kfstpairEq = $true) & (setukpairinjR12 = $true) & (noeltsimpempty = $true) & (sepSubset = $true) & (bs114d = $true) & (quantDeMorgan1 = $true) & (theprop = $true) & (setminusIRneg = $true) & (ubforcartprodlem1 = $true) & (setukpairinjR11 = $true)),
1.68/0.66	  inference(flattening,[status(thm)],[f590])).
1.68/0.66	thf(f590,plain,(
1.68/0.66	  (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((X0 != X2) & ((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset)))) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
1.68/0.66	  inference(ennf_transformation,[status(thm)],[f324])).
1.68/0.66	thf(f324,plain,(
1.68/0.66	  ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => (X0 = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
1.68/0.66	  inference(fool_elimination,[status(thm)],[f323])).
1.68/0.66	thf(f323,plain,(
1.68/0.66	  ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => ! [X0 : $i,X1 : $i,X2 : $i] : (((setadjoin @ X1 @ emptyset) = (setadjoin @ X2 @ (setadjoin @ X0 @ emptyset))) => (X0 = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
1.68/0.66	  inference(rectify,[status(thm)],[f176])).
1.68/0.66	thf(f176,negated_conjecture,(
1.68/0.66	  ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => ! [X2 : $i,X8 : $i,X1 : $i] : (((setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) = (setadjoin @ X8 @ emptyset)) => (X1 = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
1.68/0.66	  inference(negated_conjecture,[status(cth)],[f175])).
1.68/0.66	thf(f175,conjecture,(
1.68/0.66	  setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => ! [X2 : $i,X8 : $i,X1 : $i] : (((setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) = (setadjoin @ X8 @ emptyset)) => (X1 = X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
1.68/0.66	  file('/export/starexec/sandbox/tmp/tmp.hzHB0bubAS/E---3.1_19791.p',upairequniteq)).
1.68/0.66	thf(f3291,plain,(
1.68/0.66	  spl471_20),
1.68/0.66	  inference(avatar_split_clause,[status(thm)],[f3290,f3253])).
1.68/0.66	thf(f3290,plain,(
1.68/0.66	  (sK341 = sK342)),
1.68/0.66	  inference(trivial_inequality_removal,[status(thm)],[f3289])).
1.68/0.66	thf(f3289,plain,(
1.68/0.66	  (sK341 = sK342) | ($true != $true)),
1.68/0.66	  inference(forward_demodulation,[status(thm)],[f3280,f2151])).
1.68/0.66	thf(f2151,plain,(
1.68/0.66	  (notinsingleton = $true)),
1.68/0.66	  inference(cnf_transformation,[status(thm)],[f1309])).
1.68/0.66	thf(f3280,plain,(
1.68/0.66	  (sK341 = sK342) | (notinsingleton != $true)),
1.68/0.66	  inference(trivial_inequality_removal,[status(thm)],[f3271])).
1.68/0.66	thf(f3271,plain,(
1.68/0.66	  (sK341 = sK342) | ($true != $true) | (notinsingleton != $true)),
1.68/0.66	  inference(superposition,[status(thm)],[f1834,f2518])).
1.68/0.66	thf(f2518,plain,(
1.68/0.66	  ($true = (in @ sK341 @ (setadjoin @ sK342 @ emptyset)))),
1.68/0.66	  inference(trivial_inequality_removal,[status(thm)],[f2517])).
1.68/0.66	thf(f2517,plain,(
1.68/0.66	  ($true = (in @ sK341 @ (setadjoin @ sK342 @ emptyset))) | ($true != $true)),
1.68/0.66	  inference(forward_demodulation,[status(thm)],[f2478,f2132])).
1.68/0.66	thf(f2132,plain,(
1.68/0.66	  (upairsetIR = $true)),
1.68/0.66	  inference(cnf_transformation,[status(thm)],[f1309])).
1.68/0.66	thf(f2478,plain,(
1.68/0.66	  (upairsetIR != $true) | ($true = (in @ sK341 @ (setadjoin @ sK342 @ emptyset)))),
1.68/0.66	  inference(superposition,[status(thm)],[f2272,f2044])).
1.68/0.66	thf(f2044,plain,(
1.68/0.66	  ((setadjoin @ sK343 @ (setadjoin @ sK341 @ emptyset)) = (setadjoin @ sK342 @ emptyset))),
1.68/0.66	  inference(cnf_transformation,[status(thm)],[f1309])).
1.68/0.66	thf(f2272,plain,(
1.68/0.66	  ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (upairsetIR != $true)) )),
1.68/0.66	  inference(cnf_transformation,[status(thm)],[f1431])).
1.68/0.66	thf(f1431,plain,(
1.68/0.66	  (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (upairsetIR != $true)) & ((upairsetIR = $true) | ($true != (in @ sK418 @ (setadjoin @ sK419 @ (setadjoin @ sK418 @ emptyset)))))),
1.68/0.66	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK418,sK419])],[f1429,f1430])).
1.68/0.66	thf(f1430,plain,(
1.68/0.66	  ? [X2 : $i,X3 : $i] : ($true != (in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))) => ($true != (in @ sK418 @ (setadjoin @ sK419 @ (setadjoin @ sK418 @ emptyset))))),
1.68/0.66	  introduced(definition,[],[choice_axiom])).
1.68/0.66	thf(f1429,plain,(
1.68/0.66	  (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (upairsetIR != $true)) & ((upairsetIR = $true) | ? [X2 : $i,X3 : $i] : ($true != (in @ X2 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))))),
1.68/0.66	  inference(rectify,[status(thm)],[f1428])).
1.68/0.66	thf(f1428,plain,(
1.68/0.66	  (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) | (upairsetIR != $true)) & ((upairsetIR = $true) | ? [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) != $true))),
1.68/0.66	  inference(nnf_transformation,[status(thm)],[f320])).
1.68/0.66	thf(f320,plain,(
1.68/0.66	  ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = $true) <=> (upairsetIR = $true)),
1.68/0.66	  inference(fool_elimination,[status(thm)],[f319])).
1.68/0.66	thf(f319,plain,(
1.68/0.66	  (! [X0 : $i,X1 : $i] : (in @ X0 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) = upairsetIR)),
1.68/0.66	  inference(rectify,[status(thm)],[f52])).
1.68/0.66	thf(f52,axiom,(
1.68/0.66	  (! [X2 : $i,X1 : $i] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) = upairsetIR)),
1.68/0.66	  file('/export/starexec/sandbox/tmp/tmp.hzHB0bubAS/E---3.1_19791.p',upairsetIR)).
1.68/0.66	thf(f1834,plain,(
1.68/0.66	  ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ emptyset))) | (X0 = X1) | (notinsingleton != $true)) )),
1.68/0.66	  inference(cnf_transformation,[status(thm)],[f1117])).
1.68/0.66	thf(f1117,plain,(
1.68/0.66	  (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ emptyset))) | (X0 = X1)) | (notinsingleton != $true)) & ((notinsingleton = $true) | (($true = (in @ sK230 @ (setadjoin @ sK231 @ emptyset))) & (sK231 != sK230)))),
1.68/0.66	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK230,sK231])],[f1115,f1116])).
1.68/0.66	thf(f1116,plain,(
1.68/0.66	  ? [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true) & (X2 != X3)) => (($true = (in @ sK230 @ (setadjoin @ sK231 @ emptyset))) & (sK231 != sK230))),
1.68/0.66	  introduced(definition,[],[choice_axiom])).
1.68/0.66	thf(f1115,plain,(
1.68/0.66	  (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ emptyset))) | (X0 = X1)) | (notinsingleton != $true)) & ((notinsingleton = $true) | ? [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true) & (X2 != X3)))),
1.68/0.66	  inference(rectify,[status(thm)],[f1114])).
1.68/0.66	thf(f1114,plain,(
1.68/0.66	  (! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ emptyset))) | (X0 = X1)) | (notinsingleton != $true)) & ((notinsingleton = $true) | ? [X0 : $i,X1 : $i] : (($true = (in @ X0 @ (setadjoin @ X1 @ emptyset))) & (X0 != X1)))),
1.68/0.66	  inference(nnf_transformation,[status(thm)],[f695])).
1.68/0.66	thf(f695,plain,(
1.68/0.66	  ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (setadjoin @ X1 @ emptyset))) | (X0 = X1)) <=> (notinsingleton = $true)),
1.68/0.66	  inference(ennf_transformation,[status(thm)],[f547])).
1.68/0.66	thf(f547,plain,(
1.68/0.66	  ! [X0 : $i,X1 : $i] : ((X0 != X1) => ($true != (in @ X0 @ (setadjoin @ X1 @ emptyset)))) <=> (notinsingleton = $true)),
1.68/0.66	  inference(flattening,[status(thm)],[f408])).
1.68/0.66	thf(f408,plain,(
1.68/0.66	  ! [X0 : $i,X1 : $i] : ((X0 != X1) => ~($true = (in @ X0 @ (setadjoin @ X1 @ emptyset)))) <=> (notinsingleton = $true)),
1.68/0.66	  inference(fool_elimination,[status(thm)],[f407])).
1.68/0.66	thf(f407,plain,(
1.68/0.66	  (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X0 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
1.68/0.66	  inference(rectify,[status(thm)],[f47])).
1.68/0.66	thf(f47,axiom,(
1.68/0.66	  (! [X2 : $i,X1 : $i] : ((X1 != X2) => ~(in @ X2 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
1.68/0.66	  file('/export/starexec/sandbox/tmp/tmp.hzHB0bubAS/E---3.1_19791.p',notinsingleton)).
1.68/0.66	thf(f3230,plain,(
1.68/0.66	  spl471_17),
1.68/0.66	  inference(avatar_split_clause,[status(thm)],[f3229,f3183])).
1.68/0.66	thf(f3229,plain,(
1.68/0.66	  (sK343 = sK342)),
1.68/0.66	  inference(trivial_inequality_removal,[status(thm)],[f3228])).
1.68/0.66	thf(f3228,plain,(
1.68/0.66	  ($true != $true) | (sK343 = sK342)),
1.68/0.66	  inference(forward_demodulation,[status(thm)],[f3212,f2151])).
1.68/0.66	thf(f3212,plain,(
1.68/0.66	  (sK343 = sK342) | (notinsingleton != $true)),
1.68/0.66	  inference(trivial_inequality_removal,[status(thm)],[f3205])).
1.68/0.66	thf(f3205,plain,(
1.68/0.66	  (sK343 = sK342) | ($true != $true) | (notinsingleton != $true)),
1.68/0.66	  inference(superposition,[status(thm)],[f1834,f2514])).
1.68/0.66	thf(f2514,plain,(
1.68/0.66	  ($true = (in @ sK343 @ (setadjoin @ sK342 @ emptyset)))),
1.68/0.66	  inference(trivial_inequality_removal,[status(thm)],[f2513])).
1.68/0.66	thf(f2513,plain,(
1.68/0.66	  ($true != $true) | ($true = (in @ sK343 @ (setadjoin @ sK342 @ emptyset)))),
1.68/0.66	  inference(forward_demodulation,[status(thm)],[f2476,f2107])).
1.68/0.66	thf(f2107,plain,(
1.68/0.66	  (upairsetIL = $true)),
1.68/0.66	  inference(cnf_transformation,[status(thm)],[f1309])).
1.68/0.66	thf(f2476,plain,(
1.68/0.66	  (upairsetIL != $true) | ($true = (in @ sK343 @ (setadjoin @ sK342 @ emptyset)))),
1.68/0.66	  inference(superposition,[status(thm)],[f1924,f2044])).
1.68/0.66	thf(f1924,plain,(
1.68/0.66	  ( ! [X2 : $i,X3 : $i] : (($true = (in @ X3 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))) | (upairsetIL != $true)) )),
1.68/0.66	  inference(cnf_transformation,[status(thm)],[f1236])).
1.68/0.66	thf(f1236,plain,(
1.68/0.66	  ((upairsetIL = $true) | ($true != (in @ sK298 @ (setadjoin @ sK298 @ (setadjoin @ sK297 @ emptyset))))) & (! [X2 : $i,X3 : $i] : ($true = (in @ X3 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))) | (upairsetIL != $true))),
1.68/0.66	  inference(skolemisation,[status(esa),new_symbols(skolem,[sK297,sK298])],[f1234,f1235])).
1.68/0.66	thf(f1235,plain,(
1.68/0.66	  ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) => ($true != (in @ sK298 @ (setadjoin @ sK298 @ (setadjoin @ sK297 @ emptyset))))),
1.68/0.66	  introduced(definition,[],[choice_axiom])).
1.68/0.66	thf(f1234,plain,(
1.68/0.66	  ((upairsetIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))) & (! [X2 : $i,X3 : $i] : ($true = (in @ X3 @ (setadjoin @ X3 @ (setadjoin @ X2 @ emptyset)))) | (upairsetIL != $true))),
1.68/0.66	  inference(rectify,[status(thm)],[f1233])).
1.68/0.66	thf(f1233,plain,(
1.68/0.66	  ((upairsetIL = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))) & (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset)))) | (upairsetIL != $true))),
1.68/0.66	  inference(nnf_transformation,[status(thm)],[f426])).
1.68/0.66	thf(f426,plain,(
1.68/0.66	  (upairsetIL = $true) <=> ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
1.68/0.66	  inference(fool_elimination,[status(thm)],[f425])).
1.68/0.66	thf(f425,plain,(
1.68/0.66	  (upairsetIL = ! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))))),
1.68/0.66	  inference(rectify,[status(thm)],[f51])).
1.68/0.66	thf(f51,axiom,(
1.68/0.66	  (upairsetIL = ! [X2 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))))),
1.68/0.66	  file('/export/starexec/sandbox/tmp/tmp.hzHB0bubAS/E---3.1_19791.p',upairsetIL)).
1.68/0.66	% SZS output end Proof for E---3.1_19791
1.68/0.66	% (20073)------------------------------
1.68/0.66	% (20073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
1.68/0.66	% (20073)Termination reason: Refutation
1.68/0.66	
1.68/0.66	% (20073)Memory used [KB]: 8571
1.68/0.66	% (20073)Time elapsed: 0.154 s
1.68/0.66	% (20073)Instructions burned: 246 (million)
1.68/0.66	% (20073)------------------------------
1.68/0.66	% (20073)------------------------------
1.68/0.66	% (20047)Success in time 0.264 s
1.68/0.66	EOF