0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : run_vampire %s %d THM 0.12/0.34 % Computer : n023.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1920 0.12/0.34 % WCLimit : 240 0.12/0.34 % DateTime : Wed Jul 30 02:44:19 EDT 2025 0.12/0.34 % CPUTime : 0.12/0.36 This is a THF_ problem 0.12/0.36 Running higher-order theorem proving 0.12/0.37 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.OXIin7MTFw/E---3.1_14315.p -m 16384 -t 240 0.12/0.39 % (14423)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_14315 for (2399ds/4Mi) 0.12/0.39 % (14425)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/2Mi) 0.12/0.39 % (14426)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_14315 for (2399ds/2Mi) 0.12/0.39 % (14424)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_14315 for (2399ds/27Mi) 0.12/0.39 % (14428)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/18Mi) 0.12/0.39 % (14427)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_14315 for (2399ds/275Mi) 0.12/0.39 % (14425)Instruction limit reached! 0.12/0.39 % (14425)------------------------------ 0.12/0.39 % (14425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 % (14425)Termination reason: Unknown 0.12/0.39 % (14425)Termination phase: shuffling 0.12/0.39 % (14426)Instruction limit reached! 0.12/0.39 % (14426)------------------------------ 0.12/0.39 % (14426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 0.12/0.39 % (14425)Memory used [KB]: 1023 0.12/0.39 % (14425)Time elapsed: 0.003 s 0.12/0.39 % (14425)Instructions burned: 2 (million) 0.12/0.39 % (14425)------------------------------ 0.12/0.39 % (14425)------------------------------ 0.12/0.39 % (14426)Termination reason: Unknown 0.12/0.39 % (14426)Termination phase: shuffling 0.12/0.39 0.12/0.39 % (14426)Memory used [KB]: 1023 0.12/0.39 % (14426)Time elapsed: 0.003 s 0.12/0.39 % (14426)Instructions burned: 2 (million) 0.12/0.39 % (14426)------------------------------ 0.12/0.39 % (14426)------------------------------ 0.12/0.39 % (14422)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/183Mi) 0.12/0.39 % (14423)Instruction limit reached! 0.12/0.39 % (14423)------------------------------ 0.12/0.39 % (14423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 % (14423)Termination reason: Unknown 0.12/0.39 % (14423)Termination phase: Saturation 0.12/0.39 0.12/0.39 % (14423)Memory used [KB]: 1023 0.12/0.39 % (14423)Time elapsed: 0.005 s 0.12/0.39 % (14423)Instructions burned: 5 (million) 0.12/0.39 % (14423)------------------------------ 0.12/0.39 % (14423)------------------------------ 0.12/0.40 % (14427)Refutation not found, incomplete strategy 0.12/0.40 % (14427)------------------------------ 0.12/0.40 % (14427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.40 % (14427)Termination reason: Refutation not found, incomplete strategy 0.12/0.40 0.12/0.40 0.12/0.40 % (14427)Memory used [KB]: 5628 0.12/0.40 % (14427)Time elapsed: 0.007 s 0.12/0.40 % (14427)Instructions burned: 8 (million) 0.12/0.40 % (14427)------------------------------ 0.12/0.40 % (14427)------------------------------ 0.12/0.40 % (14428)Instruction limit reached! 0.12/0.40 % (14428)------------------------------ 0.12/0.40 % (14428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.40 % (14428)Termination reason: Unknown 0.12/0.40 % (14428)Termination phase: Saturation 0.12/0.40 0.12/0.40 % (14428)Memory used [KB]: 5628 0.12/0.40 % (14428)Time elapsed: 0.011 s 0.12/0.40 % (14428)Instructions burned: 18 (million) 0.12/0.40 % (14428)------------------------------ 0.12/0.40 % (14428)------------------------------ 0.12/0.40 % (14424)Instruction limit reached! 0.12/0.40 % (14424)------------------------------ 0.12/0.40 % (14424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.40 % (14424)Termination reason: Unknown 0.12/0.40 % (14424)Termination phase: Saturation 0.12/0.40 0.12/0.40 % (14424)Memory used [KB]: 5756 0.12/0.40 % (14424)Time elapsed: 0.016 s 0.12/0.40 % (14424)Instructions burned: 28 (million) 0.12/0.40 % (14424)------------------------------ 0.12/0.40 % (14424)------------------------------ 0.12/0.41 % (14429)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_14315 for (2399ds/3Mi) 0.12/0.41 % (14430)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_14315 for (2399ds/37Mi) 0.12/0.41 % (14429)Instruction limit reached! 0.12/0.41 % (14429)------------------------------ 0.12/0.41 % (14429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.41 % (14431)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_14315 for (2399ds/15Mi) 0.12/0.41 % (14429)Termination reason: Unknown 0.12/0.41 % (14429)Termination phase: Preprocessing 3 0.12/0.41 0.12/0.41 % (14429)Memory used [KB]: 1023 0.12/0.41 % (14429)Time elapsed: 0.003 s 0.12/0.41 % (14429)Instructions burned: 3 (million) 0.12/0.41 % (14429)------------------------------ 0.12/0.41 % (14429)------------------------------ 0.22/0.41 % (14432)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_14315 for (2399ds/3Mi) 0.22/0.41 % (14432)Instruction limit reached! 0.22/0.41 % (14432)------------------------------ 0.22/0.41 % (14432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.41 % (14432)Termination reason: Unknown 0.22/0.41 % (14432)Termination phase: Property scanning 0.22/0.41 0.22/0.41 % (14432)Memory used [KB]: 1023 0.22/0.41 % (14432)Time elapsed: 0.003 s 0.22/0.41 % (14432)Instructions burned: 3 (million) 0.22/0.41 % (14432)------------------------------ 0.22/0.41 % (14432)------------------------------ 0.22/0.42 % (14433)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_14315 for (2399ds/1041Mi) 0.22/0.42 % (14431)Instruction limit reached! 0.22/0.42 % (14431)------------------------------ 0.22/0.42 % (14431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.42 % (14431)Termination reason: Unknown 0.22/0.42 % (14431)Termination phase: Saturation 0.22/0.42 0.22/0.42 % (14431)Memory used [KB]: 5756 0.22/0.42 % (14431)Time elapsed: 0.010 s 0.22/0.42 % (14431)Instructions burned: 16 (million) 0.22/0.42 % (14431)------------------------------ 0.22/0.42 % (14431)------------------------------ 0.22/0.42 % (14434)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/7Mi) 0.22/0.42 % (14434)Instruction limit reached! 0.22/0.42 % (14434)------------------------------ 0.22/0.42 % (14434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.42 % (14434)Termination reason: Unknown 0.22/0.42 % (14434)Termination phase: Saturation 0.22/0.42 0.22/0.42 % (14434)Memory used [KB]: 1023 0.22/0.42 % (14434)Time elapsed: 0.005 s 0.22/0.42 % (14434)Instructions burned: 7 (million) 0.22/0.42 % (14434)------------------------------ 0.22/0.42 % (14434)------------------------------ 0.22/0.42 % (14430)Instruction limit reached! 0.22/0.42 % (14430)------------------------------ 0.22/0.42 % (14430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.42 % (14430)Termination reason: Unknown 0.22/0.42 % (14430)Termination phase: Saturation 0.22/0.42 0.22/0.42 % (14430)Memory used [KB]: 5756 0.22/0.42 % (14430)Time elapsed: 0.019 s 0.22/0.42 % (14430)Instructions burned: 38 (million) 0.22/0.42 % (14430)------------------------------ 0.22/0.42 % (14430)------------------------------ 0.22/0.43 % (14435)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/16Mi) 0.22/0.43 % (14436)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_14315 for (2399ds/3Mi) 0.22/0.43 % (14436)Instruction limit reached! 0.22/0.43 % (14436)------------------------------ 0.22/0.43 % (14436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.43 % (14436)Termination reason: Unknown 0.22/0.43 % (14436)Termination phase: Property scanning 0.22/0.43 0.22/0.43 % (14436)Memory used [KB]: 1023 0.22/0.43 % (14436)Time elapsed: 0.003 s 0.22/0.43 % (14436)Instructions burned: 3 (million) 0.22/0.43 % (14436)------------------------------ 0.22/0.43 % (14436)------------------------------ 0.22/0.43 % (14437)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_14315 for (2399ds/3Mi) 0.22/0.43 % (14435)Instruction limit reached! 0.22/0.43 % (14435)------------------------------ 0.22/0.43 % (14435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.43 % (14435)Termination reason: Unknown 0.22/0.43 % (14435)Termination phase: Saturation 0.22/0.43 0.22/0.43 % (14435)Memory used [KB]: 5884 0.22/0.43 % (14435)Time elapsed: 0.011 s 0.22/0.43 % (14435)Instructions burned: 16 (million) 0.22/0.43 % (14435)------------------------------ 0.22/0.43 % (14435)------------------------------ 0.22/0.43 % (14437)Instruction limit reached! 0.22/0.43 % (14437)------------------------------ 0.22/0.43 % (14437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.43 % (14437)Termination reason: Unknown 0.22/0.43 % (14437)Termination phase: Property scanning 0.22/0.43 0.22/0.43 % (14437)Memory used [KB]: 1023 0.22/0.43 % (14437)Time elapsed: 0.003 s 0.22/0.43 % (14437)Instructions burned: 3 (million) 0.22/0.43 % (14437)------------------------------ 0.22/0.43 % (14437)------------------------------ 0.22/0.44 % (14439)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_14315 for (2399ds/3Mi) 0.22/0.44 % (14438)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_14315 for (2399ds/7Mi) 0.22/0.44 % (14439)Instruction limit reached! 0.22/0.44 % (14439)------------------------------ 0.22/0.44 % (14439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.44 % (14439)Termination reason: Unknown 0.22/0.44 % (14439)Termination phase: Property scanning 0.22/0.44 0.22/0.44 % (14439)Memory used [KB]: 1023 0.22/0.44 % (14439)Time elapsed: 0.003 s 0.22/0.44 % (14439)Instructions burned: 3 (million) 0.22/0.44 % (14439)------------------------------ 0.22/0.44 % (14439)------------------------------ 0.22/0.44 % (14438)Instruction limit reached! 0.22/0.44 % (14438)------------------------------ 0.22/0.44 % (14438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.44 % (14438)Termination reason: Unknown 0.22/0.44 % (14438)Termination phase: Saturation 0.22/0.44 0.22/0.44 % (14438)Memory used [KB]: 5500 0.22/0.44 % (14438)Time elapsed: 0.005 s 0.22/0.44 % (14438)Instructions burned: 7 (million) 0.22/0.44 % (14438)------------------------------ 0.22/0.44 % (14438)------------------------------ 0.22/0.45 % (14440)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/4Mi) 0.22/0.45 % (14440)Instruction limit reached! 0.22/0.45 % (14440)------------------------------ 0.22/0.45 % (14440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.45 % (14440)Termination reason: Unknown 0.22/0.45 % (14440)Termination phase: Saturation 0.22/0.45 0.22/0.45 % (14440)Memory used [KB]: 1023 0.22/0.45 % (14440)Time elapsed: 0.004 s 0.22/0.45 % (14440)Instructions burned: 5 (million) 0.22/0.45 % (14440)------------------------------ 0.22/0.45 % (14440)------------------------------ 0.22/0.45 % (14441)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_14315 for (2399ds/18Mi) 0.22/0.45 % (14442)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/710Mi) 0.22/0.46 % (14443)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/6Mi) 0.22/0.46 % (14441)Instruction limit reached! 0.22/0.46 % (14441)------------------------------ 0.22/0.46 % (14441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.46 % (14441)Termination reason: Unknown 0.22/0.46 % (14441)Termination phase: Saturation 0.22/0.46 0.22/0.46 % (14441)Memory used [KB]: 5628 0.22/0.46 % (14441)Time elapsed: 0.011 s 0.22/0.46 % (14441)Instructions burned: 18 (million) 0.22/0.46 % (14441)------------------------------ 0.22/0.46 % (14441)------------------------------ 0.22/0.46 % (14444)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_14315 for (2399ds/902Mi) 0.22/0.46 % (14443)Instruction limit reached! 0.22/0.46 % (14443)------------------------------ 0.22/0.46 % (14443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.46 % (14443)Termination reason: Unknown 0.22/0.46 % (14443)Termination phase: Saturation 0.22/0.46 0.22/0.46 % (14443)Memory used [KB]: 5500 0.22/0.46 % (14443)Time elapsed: 0.005 s 0.22/0.46 % (14443)Instructions burned: 6 (million) 0.22/0.46 % (14443)------------------------------ 0.22/0.46 % (14443)------------------------------ 0.22/0.46 % (14444)Refutation not found, incomplete strategy 0.22/0.46 % (14444)------------------------------ 0.22/0.46 % (14444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.46 % (14444)Termination reason: Refutation not found, incomplete strategy 0.22/0.46 0.22/0.46 0.22/0.46 % (14444)Memory used [KB]: 5500 0.22/0.46 % (14444)Time elapsed: 0.004 s 0.22/0.46 % (14444)Instructions burned: 5 (million) 0.22/0.46 % (14444)------------------------------ 0.22/0.46 % (14444)------------------------------ 0.22/0.47 % (14445)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_14315 for (2399ds/21Mi) 0.22/0.48 % (14445)Instruction limit reached! 0.22/0.48 % (14445)------------------------------ 0.22/0.48 % (14445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.48 % (14445)Termination reason: Unknown 0.22/0.48 % (14445)Termination phase: Saturation 0.22/0.48 0.22/0.48 % (14445)Memory used [KB]: 5628 0.22/0.48 % (14445)Time elapsed: 0.013 s 0.22/0.48 % (14445)Instructions burned: 21 (million) 0.22/0.48 % (14445)------------------------------ 0.22/0.48 % (14445)------------------------------ 0.22/0.48 % (14422)Instruction limit reached! 0.22/0.48 % (14422)------------------------------ 0.22/0.48 % (14422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.48 % (14422)Termination reason: Unknown 0.22/0.48 % (14422)Termination phase: Saturation 0.22/0.48 0.22/0.48 % (14422)Memory used [KB]: 6396 0.22/0.48 % (14422)Time elapsed: 0.088 s 0.22/0.48 % (14422)Instructions burned: 183 (million) 0.22/0.48 % (14422)------------------------------ 0.22/0.48 % (14422)------------------------------ 0.22/0.48 % (14446)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/5Mi) 0.22/0.48 % (14447)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_14315 for (2399ds/6Mi) 0.22/0.48 % (14448)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/377Mi) 0.22/0.48 % (14446)Instruction limit reached! 0.22/0.48 % (14446)------------------------------ 0.22/0.48 % (14446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.48 % (14446)Termination reason: Unknown 0.22/0.48 % (14446)Termination phase: Saturation 0.22/0.48 % (14447)Instruction limit reached! 0.22/0.48 % (14447)------------------------------ 0.22/0.48 % (14447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.48 % (14447)Termination reason: Unknown 0.22/0.48 % (14447)Termination phase: Saturation 0.22/0.48 0.22/0.48 % (14447)Memory used [KB]: 5500 0.22/0.48 % (14447)Time elapsed: 0.005 s 0.22/0.48 % (14447)Instructions burned: 6 (million) 0.22/0.48 % (14447)------------------------------ 0.22/0.48 % (14447)------------------------------ 0.22/0.48 0.22/0.48 % (14446)Memory used [KB]: 5500 0.22/0.48 % (14446)Time elapsed: 0.005 s 0.22/0.48 % (14446)Instructions burned: 6 (million) 0.22/0.48 % (14446)------------------------------ 0.22/0.48 % (14446)------------------------------ 0.22/0.49 % (14449)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_14315 for (2399ds/779Mi) 0.22/0.49 % (14450)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_14315 for (2399ds/19Mi) 0.22/0.50 % (14452)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_14315 for (2399ds/17Mi) 0.22/0.50 % (14450)Refutation not found, incomplete strategy 0.22/0.50 % (14450)------------------------------ 0.22/0.50 % (14450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.50 % (14450)Termination reason: Refutation not found, incomplete strategy 0.22/0.50 0.22/0.50 0.22/0.50 % (14450)Memory used [KB]: 5628 0.22/0.50 % (14450)Time elapsed: 0.009 s 0.22/0.50 % (14450)Instructions burned: 13 (million) 0.22/0.50 % (14450)------------------------------ 0.22/0.50 % (14450)------------------------------ 0.22/0.50 % (14451)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_14315 for (2399ds/879Mi) 0.22/0.51 % (14452)Instruction limit reached! 0.22/0.51 % (14452)------------------------------ 0.22/0.51 % (14452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.51 % (14452)Termination reason: Unknown 0.22/0.51 % (14452)Termination phase: Saturation 0.22/0.51 0.22/0.51 % (14452)Memory used [KB]: 5756 0.22/0.51 % (14452)Time elapsed: 0.033 s 0.22/0.51 % (14452)Instructions burned: 17 (million) 0.22/0.51 % (14452)------------------------------ 0.22/0.51 % (14452)------------------------------ 0.22/0.52 % (14454)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_14315 for (2398ds/30Mi) 0.22/0.53 % (14453)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_14315 for (2398ds/3Mi) 0.22/0.53 % (14453)Instruction limit reached! 0.22/0.53 % (14453)------------------------------ 0.22/0.53 % (14453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.53 % (14453)Termination reason: Unknown 0.22/0.53 % (14453)Termination phase: shuffling 0.22/0.53 0.22/0.53 % (14453)Memory used [KB]: 1023 0.22/0.53 % (14453)Time elapsed: 0.003 s 0.22/0.53 % (14453)Instructions burned: 3 (million) 0.22/0.53 % (14453)------------------------------ 0.22/0.53 % (14453)------------------------------ 0.22/0.53 % (14454)Refutation not found, incomplete strategy 0.22/0.53 % (14454)------------------------------ 0.22/0.53 % (14454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.22/0.53 % (14454)Termination reason: Refutation not found, incomplete strategy 0.22/0.53 0.22/0.53 0.22/0.53 % (14454)Memory used [KB]: 5628 0.22/0.53 % (14454)Time elapsed: 0.010 s 0.22/0.53 % (14454)Instructions burned: 17 (million) 0.22/0.53 % (14454)------------------------------ 0.22/0.53 % (14454)------------------------------ 0.22/0.55 % (14456)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on E---3.1_14315 for (2398ds/100Mi) 0.22/0.55 % (14455)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_14315 for (2398ds/127Mi) 1.65/0.60 % (14456)Instruction limit reached! 1.65/0.60 % (14456)------------------------------ 1.65/0.60 % (14456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.65/0.60 % (14456)Termination reason: Unknown 1.65/0.60 % (14456)Termination phase: Saturation 1.65/0.60 1.65/0.60 % (14456)Memory used [KB]: 6012 1.65/0.60 % (14456)Time elapsed: 0.073 s 1.65/0.60 % (14456)Instructions burned: 100 (million) 1.65/0.60 % (14456)------------------------------ 1.65/0.60 % (14456)------------------------------ 1.77/0.61 % (14455)Instruction limit reached! 1.77/0.61 % (14455)------------------------------ 1.77/0.61 % (14455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.77/0.61 % (14455)Termination reason: Unknown 1.77/0.61 % (14455)Termination phase: Saturation 1.77/0.61 1.77/0.61 % (14455)Memory used [KB]: 5884 1.77/0.61 % (14455)Time elapsed: 0.089 s 1.77/0.61 % (14455)Instructions burned: 127 (million) 1.77/0.61 % (14455)------------------------------ 1.77/0.61 % (14455)------------------------------ 1.77/0.62 % (14457)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on E---3.1_14315 for (2397ds/3Mi) 1.77/0.62 % (14457)Instruction limit reached! 1.77/0.62 % (14457)------------------------------ 1.77/0.62 % (14457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.77/0.62 % (14457)Termination reason: Unknown 1.77/0.62 % (14457)Termination phase: Function definition elimination 1.77/0.62 1.77/0.62 % (14457)Memory used [KB]: 1023 1.77/0.62 % (14457)Time elapsed: 0.004 s 1.77/0.62 % (14457)Instructions burned: 4 (million) 1.77/0.62 % (14457)------------------------------ 1.77/0.62 % (14457)------------------------------ 1.88/0.63 % (14458)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on E---3.1_14315 for (2397ds/20Mi) 1.88/0.64 % (14459)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on E---3.1_14315 for (2397ds/86Mi) 1.88/0.64 % (14458)First to succeed. 1.88/0.64 % (14458)Refutation found. Thanks to Tanya! 1.88/0.64 % SZS status Theorem for E---3.1_14315 1.88/0.64 % SZS output start Proof for E---3.1_14315 1.88/0.64 thf(func_def_0, type, in: $i > $i > $o). 1.88/0.64 thf(func_def_2, type, setadjoin: $i > $i > $i). 1.88/0.64 thf(func_def_3, type, setunion: $i > $i). 1.88/0.64 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i). 1.88/0.64 thf(func_def_7, type, iskpair: $i > $o). 1.88/0.64 thf(func_def_8, type, kpair: $i > $i > $i). 1.88/0.64 thf(func_def_10, type, singleton: $i > $o). 1.88/0.64 thf(func_def_12, type, kfst: $i > $i). 1.88/0.64 thf(func_def_15, type, ksnd: $i > $i). 1.88/0.64 thf(func_def_31, type, sK6: $i > $o). 1.88/0.64 thf(func_def_38, type, sP13: $o > $o). 1.88/0.64 thf(func_def_39, type, sP14: $o > $o). 1.88/0.64 thf(func_def_40, type, sP15: $o > $o). 1.88/0.64 thf(func_def_41, type, sP16: $i > $o). 1.88/0.64 thf(func_def_42, type, sP17: $o > $o). 1.88/0.64 thf(func_def_45, type, ph19: !>[X0: $tType]:(X0)). 1.88/0.64 thf(f137,plain,( 1.88/0.64 $false), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f136])). 1.88/0.64 thf(f136,plain,( 1.88/0.64 ($true = $false)), 1.88/0.64 inference(backward_demodulation,[status(thm)],[f104,f135])). 1.88/0.64 thf(f135,plain,( 1.88/0.64 ($false = (sP16 @ sK10))), 1.88/0.64 inference(backward_demodulation,[status(thm)],[f113,f132])). 1.88/0.64 thf(f132,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : (((setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = X1)) )), 1.88/0.64 inference(equality_resolution,[status(thm)],[f127])). 1.88/0.64 thf(f127,plain,( 1.88/0.64 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X2 @ X3) != (kpair @ X0 @ X1)) | ((setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = X3)) )), 1.88/0.64 inference(superposition,[status(thm)],[f107,f123])). 1.88/0.64 thf(f123,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : (((kpair @ (kfst @ (kpair @ X0 @ X1)) @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1)))))) = (kpair @ X0 @ X1))) )), 1.88/0.64 inference(equality_proxy_clausification,[status(thm)],[f122])). 1.88/0.64 thf(f122,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : ((((kpair @ (kfst @ (kpair @ X0 @ X1)) @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1)))))) = (kpair @ X0 @ X1)) = $true)) )), 1.88/0.64 inference(beta_eta_normalization,[status(thm)],[f121])). 1.88/0.64 thf(f121,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))) @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1)))))))) )), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f120])). 1.88/0.64 thf(f120,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))) @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))))) | ($true != $true)) )), 1.88/0.64 inference(superposition,[status(thm)],[f109,f119])). 1.88/0.64 thf(f119,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : (((in @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = $true)) )), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f118])). 1.88/0.64 thf(f118,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : (((in @ (setunion @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = $true) | ($true != $true)) )), 1.88/0.64 inference(superposition,[status(thm)],[f111,f117])). 1.88/0.64 thf(f117,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : (((singleton @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = $true)) )), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f116])). 1.88/0.64 thf(f116,plain,( 1.88/0.64 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((singleton @ (dsetconstr @ (setunion @ (kpair @ X0 @ X1)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ X0 @ X1)) @ Y0) = (kpair @ X0 @ X1))))) = $true)) )), 1.88/0.64 inference(superposition,[status(thm)],[f110,f112])). 1.88/0.64 thf(f112,plain,( 1.88/0.64 ( ! [X2 : $i,X3 : $i] : (((iskpair @ (kpair @ X2 @ X3)) = $true)) )), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f96])). 1.88/0.64 thf(f96,plain,( 1.88/0.64 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ((iskpair @ (kpair @ X2 @ X3)) = $true)) )), 1.88/0.64 inference(definition_unfolding,[status(thm)],[f80,f78])). 1.88/0.64 thf(f78,plain,( 1.88/0.64 (kpairp = $true)), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f56])). 1.88/0.64 thf(f56,plain,( 1.88/0.64 (dsetconstrER = $true) & (kpairp = $true) & (ksndsingleton = $true) & (theprop = $true) & (setukpairinjR = $true) & ((ksnd @ (kpair @ sK9 @ sK10)) != sK10)), 1.88/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f38,f55])). 1.88/0.64 thf(f55,plain,( 1.88/0.64 ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1) => ((ksnd @ (kpair @ sK9 @ sK10)) != sK10)), 1.88/0.64 introduced(definition,[],[choice_axiom])). 1.88/0.64 thf(f38,plain,( 1.88/0.64 (dsetconstrER = $true) & (kpairp = $true) & (ksndsingleton = $true) & (theprop = $true) & (setukpairinjR = $true) & ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1)), 1.88/0.64 inference(flattening,[status(thm)],[f37])). 1.88/0.64 thf(f37,plain,( 1.88/0.64 ((((? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (theprop = $true)) & (kpairp = $true)) & (dsetconstrER = $true)), 1.88/0.64 inference(ennf_transformation,[status(thm)],[f28])). 1.88/0.64 thf(f28,plain,( 1.88/0.64 ~((dsetconstrER = $true) => ((kpairp = $true) => ((theprop = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1))))))), 1.88/0.64 inference(fool_elimination,[status(thm)],[f27])). 1.88/0.64 thf(f27,plain,( 1.88/0.64 ~(dsetconstrER => (kpairp => (theprop => (setukpairinjR => (ksndsingleton => ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1))))))), 1.88/0.64 inference(rectify,[status(thm)],[f11])). 1.88/0.64 thf(f11,negated_conjecture,( 1.88/0.64 ~(dsetconstrER => (kpairp => (theprop => (setukpairinjR => (ksndsingleton => ! [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) = X3))))))), 1.88/0.64 inference(negated_conjecture,[status(cth)],[f10])). 1.88/0.64 thf(f10,conjecture,( 1.88/0.64 dsetconstrER => (kpairp => (theprop => (setukpairinjR => (ksndsingleton => ! [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) = X3)))))), 1.88/0.64 file('/export/starexec/sandbox/tmp/tmp.OXIin7MTFw/E---3.1_14315.p',ksndpairEq)). 1.88/0.64 thf(f80,plain,( 1.88/0.64 ( ! [X2 : $i,X3 : $i] : (((iskpair @ (kpair @ X2 @ X3)) = $true) | (kpairp != $true)) )), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f60])). 1.88/0.64 thf(f60,plain,( 1.88/0.64 ((kpairp = $true) | ($true != (iskpair @ (kpair @ sK11 @ sK12)))) & (! [X2 : $i,X3 : $i] : ((iskpair @ (kpair @ X2 @ X3)) = $true) | (kpairp != $true))), 1.88/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK11,sK12])],[f58,f59])). 1.88/0.64 thf(f59,plain,( 1.88/0.64 ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (kpair @ X0 @ X1))) => ($true != (iskpair @ (kpair @ sK11 @ sK12)))), 1.88/0.64 introduced(definition,[],[choice_axiom])). 1.88/0.64 thf(f58,plain,( 1.88/0.64 ((kpairp = $true) | ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (kpair @ X0 @ X1)))) & (! [X2 : $i,X3 : $i] : ((iskpair @ (kpair @ X2 @ X3)) = $true) | (kpairp != $true))), 1.88/0.64 inference(rectify,[status(thm)],[f57])). 1.88/0.64 thf(f57,plain,( 1.88/0.64 ((kpairp = $true) | ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (kpair @ X0 @ X1)))) & (! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X0 @ X1))) | (kpairp != $true))), 1.88/0.64 inference(nnf_transformation,[status(thm)],[f24])). 1.88/0.64 thf(f24,plain,( 1.88/0.64 (kpairp = $true) <=> ! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X0 @ X1)))), 1.88/0.64 inference(fool_elimination,[status(thm)],[f23])). 1.88/0.64 thf(f23,plain,( 1.88/0.64 (kpairp = ! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)))), 1.88/0.64 inference(rectify,[status(thm)],[f4])). 1.88/0.64 thf(f4,axiom,( 1.88/0.64 (kpairp = ! [X2 : $i,X3 : $i] : (iskpair @ (kpair @ X2 @ X3)))), 1.88/0.64 file('/export/starexec/sandbox/tmp/tmp.OXIin7MTFw/E---3.1_14315.p',kpairp)). 1.88/0.64 thf(f110,plain,( 1.88/0.64 ( ! [X1 : $i] : (((iskpair @ X1) != $true) | ($true = (singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1)))))) )), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f90])). 1.88/0.64 thf(f90,plain,( 1.88/0.64 ( ! [X1 : $i] : (($true = (singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1))))) | ((iskpair @ X1) != $true) | ($true != $true)) )), 1.88/0.64 inference(definition_unfolding,[status(thm)],[f68,f77])). 1.88/0.64 thf(f77,plain,( 1.88/0.64 (ksndsingleton = $true)), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f56])). 1.88/0.64 thf(f68,plain,( 1.88/0.64 ( ! [X1 : $i] : (($true = (singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1))))) | ((iskpair @ X1) != $true) | (ksndsingleton != $true)) )), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f50])). 1.88/0.64 thf(f50,plain,( 1.88/0.64 ((ksndsingleton = $true) | (((singleton @ (dsetconstr @ (setunion @ sK5) @ (^[Y0 : $i]: ((kpair @ (kfst @ sK5) @ Y0) = sK5)))) != $true) & ((iskpair @ sK5) = $true))) & (! [X1 : $i] : (($true = (singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1))))) | ((iskpair @ X1) != $true)) | (ksndsingleton != $true))), 1.88/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f48,f49])). 1.88/0.64 thf(f49,plain,( 1.88/0.64 ? [X0 : $i] : (((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) != $true) & ($true = (iskpair @ X0))) => (((singleton @ (dsetconstr @ (setunion @ sK5) @ (^[Y0 : $i]: ((kpair @ (kfst @ sK5) @ Y0) = sK5)))) != $true) & ((iskpair @ sK5) = $true))), 1.88/0.64 introduced(definition,[],[choice_axiom])). 1.88/0.64 thf(f48,plain,( 1.88/0.64 ((ksndsingleton = $true) | ? [X0 : $i] : (((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) != $true) & ($true = (iskpair @ X0)))) & (! [X1 : $i] : (($true = (singleton @ (dsetconstr @ (setunion @ X1) @ (^[Y0 : $i]: ((kpair @ (kfst @ X1) @ Y0) = X1))))) | ((iskpair @ X1) != $true)) | (ksndsingleton != $true))), 1.88/0.64 inference(rectify,[status(thm)],[f47])). 1.88/0.64 thf(f47,plain,( 1.88/0.64 ((ksndsingleton = $true) | ? [X0 : $i] : (((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) != $true) & ($true = (iskpair @ X0)))) & (! [X0 : $i] : (((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) = $true) | ($true != (iskpair @ X0))) | (ksndsingleton != $true))), 1.88/0.64 inference(nnf_transformation,[status(thm)],[f36])). 1.88/0.64 thf(f36,plain,( 1.88/0.64 (ksndsingleton = $true) <=> ! [X0 : $i] : (((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) = $true) | ($true != (iskpair @ X0)))), 1.88/0.64 inference(ennf_transformation,[status(thm)],[f20])). 1.88/0.64 thf(f20,plain,( 1.88/0.64 (ksndsingleton = $true) <=> ! [X0 : $i] : (($true = (iskpair @ X0)) => ((singleton @ (dsetconstr @ (setunion @ X0) @ (^[Y0 : $i]: ((kpair @ (kfst @ X0) @ Y0) = X0)))) = $true))), 1.88/0.64 inference(fool_elimination,[status(thm)],[f19])). 1.88/0.64 thf(f19,plain,( 1.88/0.64 (! [X0 : $i] : ((iskpair @ X0) => (singleton @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))) = ksndsingleton)), 1.88/0.64 inference(rectify,[status(thm)],[f8])). 1.88/0.64 thf(f8,axiom,( 1.88/0.64 (! [X6 : $i] : ((iskpair @ X6) => (singleton @ (dsetconstr @ (setunion @ X6) @ (^[X2 : $i] : (((kpair @ (kfst @ X6) @ X2) = X6)))))) = ksndsingleton)), 1.88/0.64 file('/export/starexec/sandbox/tmp/tmp.OXIin7MTFw/E---3.1_14315.p',ksndsingleton)). 1.88/0.64 thf(f111,plain,( 1.88/0.64 ( ! [X1 : $i] : (((singleton @ X1) != $true) | ((in @ (setunion @ X1) @ X1) = $true)) )), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f87])). 1.88/0.64 thf(f87,plain,( 1.88/0.64 ( ! [X1 : $i] : (((singleton @ X1) != $true) | ((in @ (setunion @ X1) @ X1) = $true) | ($true != $true)) )), 1.88/0.64 inference(definition_unfolding,[status(thm)],[f64,f76])). 1.88/0.64 thf(f76,plain,( 1.88/0.64 (theprop = $true)), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f56])). 1.88/0.64 thf(f64,plain,( 1.88/0.64 ( ! [X1 : $i] : (((singleton @ X1) != $true) | ((in @ (setunion @ X1) @ X1) = $true) | (theprop != $true)) )), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f46])). 1.88/0.64 thf(f46,plain,( 1.88/0.64 ((theprop = $true) | (($true = (singleton @ sK4)) & ($true != (in @ (setunion @ sK4) @ sK4)))) & (! [X1 : $i] : (((singleton @ X1) != $true) | ((in @ (setunion @ X1) @ X1) = $true)) | (theprop != $true))), 1.88/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f44,f45])). 1.88/0.64 thf(f45,plain,( 1.88/0.64 ? [X0 : $i] : (($true = (singleton @ X0)) & ($true != (in @ (setunion @ X0) @ X0))) => (($true = (singleton @ sK4)) & ($true != (in @ (setunion @ sK4) @ sK4)))), 1.88/0.64 introduced(definition,[],[choice_axiom])). 1.88/0.64 thf(f44,plain,( 1.88/0.64 ((theprop = $true) | ? [X0 : $i] : (($true = (singleton @ X0)) & ($true != (in @ (setunion @ X0) @ X0)))) & (! [X1 : $i] : (((singleton @ X1) != $true) | ((in @ (setunion @ X1) @ X1) = $true)) | (theprop != $true))), 1.88/0.64 inference(rectify,[status(thm)],[f43])). 1.88/0.64 thf(f43,plain,( 1.88/0.64 ((theprop = $true) | ? [X0 : $i] : (($true = (singleton @ X0)) & ($true != (in @ (setunion @ X0) @ X0)))) & (! [X0 : $i] : (($true != (singleton @ X0)) | ($true = (in @ (setunion @ X0) @ X0))) | (theprop != $true))), 1.88/0.64 inference(nnf_transformation,[status(thm)],[f33])). 1.88/0.64 thf(f33,plain,( 1.88/0.64 (theprop = $true) <=> ! [X0 : $i] : (($true != (singleton @ X0)) | ($true = (in @ (setunion @ X0) @ X0)))), 1.88/0.64 inference(ennf_transformation,[status(thm)],[f26])). 1.88/0.64 thf(f26,plain,( 1.88/0.64 ! [X0 : $i] : (($true = (singleton @ X0)) => ($true = (in @ (setunion @ X0) @ X0))) <=> (theprop = $true)), 1.88/0.64 inference(fool_elimination,[status(thm)],[f25])). 1.88/0.64 thf(f25,plain,( 1.88/0.64 (! [X0 : $i] : ((singleton @ X0) => (in @ (setunion @ X0) @ X0)) = theprop)), 1.88/0.64 inference(rectify,[status(thm)],[f6])). 1.88/0.64 thf(f6,axiom,( 1.88/0.64 (! [X4 : $i] : ((singleton @ X4) => (in @ (setunion @ X4) @ X4)) = theprop)), 1.88/0.64 file('/export/starexec/sandbox/tmp/tmp.OXIin7MTFw/E---3.1_14315.p',theprop)). 1.88/0.64 thf(f109,plain,( 1.88/0.64 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (((in @ X4 @ (dsetconstr @ X5 @ X3)) != $true) | ($true = (X3 @ X4))) )), 1.88/0.64 inference(beta_eta_normalization,[status(thm)],[f108])). 1.88/0.64 thf(f108,plain,( 1.88/0.64 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (X3 @ X4)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true)) )), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f93])). 1.88/0.64 thf(f93,plain,( 1.88/0.64 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true != $true) | ($true = (X3 @ X4)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true)) )), 1.88/0.64 inference(definition_unfolding,[status(thm)],[f71,f79])). 1.88/0.64 thf(f79,plain,( 1.88/0.64 (dsetconstrER = $true)), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f56])). 1.88/0.64 thf(f71,plain,( 1.88/0.64 ( ! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (X3 @ X4)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true) | (dsetconstrER != $true)) )), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f54])). 1.88/0.64 thf(f54,plain,( 1.88/0.64 ((dsetconstrER = $true) | (($true != (sK6 @ sK7)) & ((in @ sK7 @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (sK6 @ Y0)))) = $true))) & (! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (X3 @ X4)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true)) | (dsetconstrER != $true))), 1.88/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f52,f53])). 1.88/0.64 thf(f53,plain,( 1.88/0.64 ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true != (X0 @ X1)) & ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) => (($true != (sK6 @ sK7)) & ((in @ sK7 @ (dsetconstr @ sK8 @ (^[Y0 : $i]: (sK6 @ Y0)))) = $true))), 1.88/0.64 introduced(definition,[],[choice_axiom])). 1.88/0.64 thf(f52,plain,( 1.88/0.64 ((dsetconstrER = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true != (X0 @ X1)) & ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))) & (! [X3 : $i > $o,X4 : $i,X5 : $i] : (($true = (X3 @ X4)) | ((in @ X4 @ (dsetconstr @ X5 @ (^[Y0 : $i]: (X3 @ Y0)))) != $true)) | (dsetconstrER != $true))), 1.88/0.64 inference(rectify,[status(thm)],[f51])). 1.88/0.64 thf(f51,plain,( 1.88/0.64 ((dsetconstrER = $true) | ? [X0 : $i > $o,X1 : $i,X2 : $i] : (($true != (X0 @ X1)) & ($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))) & (! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (X0 @ X1)) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0)))))) | (dsetconstrER != $true))), 1.88/0.64 inference(nnf_transformation,[status(thm)],[f35])). 1.88/0.64 thf(f35,plain,( 1.88/0.64 (dsetconstrER = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (X0 @ X1)) | ($true != (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))))), 1.88/0.64 inference(ennf_transformation,[status(thm)],[f30])). 1.88/0.64 thf(f30,plain,( 1.88/0.64 (dsetconstrER = $true) <=> ! [X0 : $i > $o,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X0 @ Y0))))) => ($true = (X0 @ X1)))), 1.88/0.64 inference(fool_elimination,[status(thm)],[f29])). 1.88/0.64 thf(f29,plain,( 1.88/0.64 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X1)) = dsetconstrER)), 1.88/0.64 inference(rectify,[status(thm)],[f1])). 1.88/0.64 thf(f1,axiom,( 1.88/0.64 (! [X1 : $i > $o,X2 : $i,X0 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)), 1.88/0.64 file('/export/starexec/sandbox/tmp/tmp.OXIin7MTFw/E---3.1_14315.p',dsetconstrER)). 1.88/0.64 thf(f107,plain,( 1.88/0.64 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X0 = X3)) )), 1.88/0.64 inference(trivial_inequality_removal,[status(thm)],[f82])). 1.88/0.64 thf(f82,plain,( 1.88/0.64 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X0 = X3) | ($true != $true)) )), 1.88/0.64 inference(definition_unfolding,[status(thm)],[f63,f75])). 1.88/0.64 thf(f75,plain,( 1.88/0.64 (setukpairinjR = $true)), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f56])). 1.88/0.64 thf(f63,plain,( 1.88/0.64 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X0 = X3) | (setukpairinjR != $true)) )), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f42])). 1.88/0.64 thf(f42,plain,( 1.88/0.64 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X0 = X3)) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | (((kpair @ sK1 @ sK0) = (kpair @ sK2 @ sK3)) & (sK0 != sK3)))), 1.88/0.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f40,f41])). 1.88/0.64 thf(f41,plain,( 1.88/0.64 ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((kpair @ X5 @ X4) = (kpair @ X6 @ X7)) & (X4 != X7)) => (((kpair @ sK1 @ sK0) = (kpair @ sK2 @ sK3)) & (sK0 != sK3))), 1.88/0.64 introduced(definition,[],[choice_axiom])). 1.88/0.64 thf(f40,plain,( 1.88/0.64 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X0 = X3)) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ? [X4 : $i,X5 : $i,X6 : $i,X7 : $i] : (((kpair @ X5 @ X4) = (kpair @ X6 @ X7)) & (X4 != X7)))), 1.88/0.64 inference(rectify,[status(thm)],[f39])). 1.88/0.64 thf(f39,plain,( 1.88/0.64 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X0 = X3)) | (setukpairinjR != $true)) & ((setukpairinjR = $true) | ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) = (kpair @ X1 @ X0)) & (X0 != X3)))), 1.88/0.64 inference(nnf_transformation,[status(thm)],[f34])). 1.88/0.64 thf(f34,plain,( 1.88/0.64 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) != (kpair @ X1 @ X0)) | (X0 = X3)) <=> (setukpairinjR = $true)), 1.88/0.64 inference(ennf_transformation,[status(thm)],[f14])). 1.88/0.64 thf(f14,plain,( 1.88/0.64 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) = (kpair @ X1 @ X0)) => (X0 = X3)) <=> (setukpairinjR = $true)), 1.88/0.64 inference(fool_elimination,[status(thm)],[f13])). 1.88/0.64 thf(f13,plain,( 1.88/0.64 (! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((kpair @ X2 @ X3) = (kpair @ X1 @ X0)) => (X0 = X3)) = setukpairinjR)), 1.88/0.64 inference(rectify,[status(thm)],[f7])). 1.88/0.64 thf(f7,axiom,( 1.88/0.64 (! [X3 : $i,X2 : $i,X5 : $i,X6 : $i] : (((kpair @ X2 @ X3) = (kpair @ X5 @ X6)) => (X3 = X6)) = setukpairinjR)), 1.88/0.64 file('/export/starexec/sandbox/tmp/tmp.OXIin7MTFw/E---3.1_14315.p',setukpairinjR)). 1.88/0.64 thf(f113,plain,( 1.88/0.64 ($false = (sP16 @ (setunion @ (dsetconstr @ (setunion @ (kpair @ sK9 @ sK10)) @ (^[Y0 : $i]: ((kpair @ (kfst @ (kpair @ sK9 @ sK10)) @ Y0) = (kpair @ sK9 @ sK10)))))))), 1.88/0.64 inference(beta_eta_normalization,[status(thm)],[f103])). 1.88/0.64 thf(f103,plain,( 1.88/0.64 ((sP16 @ ((^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))) @ (kpair @ sK9 @ sK10))) = $false)), 1.88/0.64 introduced(definition,[new_symbols(naming,[sP16])],[inequality_splitting_name_introduction])). 1.88/0.64 thf(f104,plain,( 1.88/0.64 ($true = (sP16 @ sK10))), 1.88/0.64 inference(inequality_splitting,[status(thm)],[f94,f103])). 1.88/0.64 thf(f94,plain,( 1.88/0.64 (((^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))) @ (kpair @ sK9 @ sK10)) != sK10)), 1.88/0.64 inference(definition_unfolding,[status(thm)],[f74,f67])). 1.88/0.64 thf(f67,plain,( 1.88/0.64 (ksnd = (^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f22])). 1.88/0.64 thf(f22,plain,( 1.88/0.64 (ksnd = (^[Y0 : $i]: (setunion @ (dsetconstr @ (setunion @ Y0) @ (^[Y1 : $i]: ((kpair @ (kfst @ Y0) @ Y1) = Y0))))))), 1.88/0.64 inference(fool_elimination,[status(thm)],[f21])). 1.88/0.64 thf(f21,plain,( 1.88/0.64 (ksnd = (^[X0 : $i] : (setunion @ (dsetconstr @ (setunion @ X0) @ (^[X1 : $i] : (((kpair @ (kfst @ X0) @ X1) = X0)))))))), 1.88/0.64 inference(rectify,[status(thm)],[f9])). 1.88/0.64 thf(f9,axiom,( 1.88/0.64 (ksnd = (^[X6 : $i] : (setunion @ (dsetconstr @ (setunion @ X6) @ (^[X2 : $i] : (((kpair @ (kfst @ X6) @ X2) = X6)))))))), 1.88/0.64 file('/export/starexec/sandbox/tmp/tmp.OXIin7MTFw/E---3.1_14315.p',ksnd)). 1.88/0.64 thf(f74,plain,( 1.88/0.64 ((ksnd @ (kpair @ sK9 @ sK10)) != sK10)), 1.88/0.64 inference(cnf_transformation,[status(thm)],[f56])). 1.88/0.64 % SZS output end Proof for E---3.1_14315 1.88/0.64 % (14458)------------------------------ 1.88/0.64 % (14458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.88/0.64 % (14458)Termination reason: Refutation 1.88/0.64 1.88/0.64 % (14458)Memory used [KB]: 5628 1.88/0.64 % (14458)Time elapsed: 0.014 s 1.88/0.64 % (14458)Instructions burned: 18 (million) 1.88/0.64 % (14458)------------------------------ 1.88/0.64 % (14458)------------------------------ 1.88/0.64 % (14421)Success in time 0.272 s 1.88/0.64 EOF