0.06/0.15 % Problem : Vampire---4.8_10714 : TPTP v0.0.0. Released v0.0.0. 0.06/0.17 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s 0.17/0.38 % Computer : n026.cluster.edu 0.17/0.38 % Model : x86_64 x86_64 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.17/0.38 % Memory : 8042.1875MB 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64 0.17/0.38 % CPULimit : 1440 0.17/0.38 % WCLimit : 180 0.17/0.38 % DateTime : Mon Jul 3 13:18:37 EDT 2023 0.17/0.38 % CPUTime : 0.17/0.38 This is a THF_ problem 0.17/0.39 Running vampire_rel_static_ahmed-new-hol_6848 --cores 8 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.TfVhRNnzGC/Vampire---4.8_10714 -m 12000 -t 180 0.25/0.41 % (10827)ott+1010_1:1_cnfonf=lazy_gen:fe=off:kws=inv_arity:plsq=on:plsqc=1:plsqr=32,1:prag=on:sp=const_frequency:i=74:si=on:rtra=on_0 on Vampire---4 for (1799ds/74Mi) 0.25/0.41 % (10825)lrs+1002_1:1_au=on:s2a=on:s2agt=32:sgt=8:ss=axioms:i=385:si=on:rtra=on_0 on Vampire---4 for (1799ds/385Mi) 0.25/0.41 % (10826)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on Vampire---4 for (1799ds/17Mi) 0.25/0.41 % (10829)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=915:si=on:rtra=on_0 on Vampire---4 for (1799ds/915Mi) 0.25/0.41 % (10822)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on Vampire---4 for (1799ds/96Mi) 0.25/0.42 % (10823)lrs+10_1:2_cnfonf=off:hud=1:inj=on:i=36:si=on:rtra=on_0 on Vampire---4 for (1799ds/36Mi) 0.25/0.42 % (10826)Instruction limit reached! 0.25/0.42 % (10826)------------------------------ 0.25/0.42 % (10826)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.42 % (10826)Termination reason: Unknown 0.25/0.42 % (10826)Termination phase: shuffling 0.25/0.42 0.25/0.42 % (10826)Memory used [KB]: 1535 0.25/0.42 % (10826)Time elapsed: 0.009 s 0.25/0.42 % (10826)Instructions burned: 17 (million) 0.25/0.42 % (10826)------------------------------ 0.25/0.42 % (10826)------------------------------ 0.25/0.43 % (10824)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=34:si=on:rtra=on_0 on Vampire---4 for (1799ds/34Mi) 0.25/0.43 % (10828)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on Vampire---4 for (1799ds/4Mi) 0.25/0.43 % (10828)Instruction limit reached! 0.25/0.43 % (10828)------------------------------ 0.25/0.43 % (10828)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.43 % (10828)Termination reason: Unknown 0.25/0.43 % (10828)Termination phase: shuffling 0.25/0.43 0.25/0.43 % (10828)Memory used [KB]: 1279 0.25/0.43 % (10828)Time elapsed: 0.005 s 0.25/0.43 % (10828)Instructions burned: 5 (million) 0.25/0.43 % (10828)------------------------------ 0.25/0.43 % (10828)------------------------------ 0.25/0.43 % (10823)Instruction limit reached! 0.25/0.43 % (10823)------------------------------ 0.25/0.43 % (10823)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.43 % (10823)Termination reason: Unknown 0.25/0.43 % (10823)Termination phase: Property scanning 0.25/0.43 0.25/0.43 % (10823)Memory used [KB]: 1791 0.25/0.43 % (10823)Time elapsed: 0.019 s 0.25/0.43 % (10823)Instructions burned: 36 (million) 0.25/0.43 % (10823)------------------------------ 0.25/0.43 % (10823)------------------------------ 0.25/0.43 % (10830)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 Vampire---4 for (1799ds/21Mi) 0.25/0.44 % (10824)Instruction limit reached! 0.25/0.44 % (10824)------------------------------ 0.25/0.44 % (10824)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.44 % (10824)Termination reason: Unknown 0.25/0.44 % (10824)Termination phase: Property scanning 0.25/0.44 0.25/0.44 % (10824)Memory used [KB]: 1791 0.25/0.44 % (10824)Time elapsed: 0.017 s 0.25/0.44 % (10824)Instructions burned: 35 (million) 0.25/0.44 % (10824)------------------------------ 0.25/0.44 % (10824)------------------------------ 0.25/0.44 % (10830)Instruction limit reached! 0.25/0.44 % (10830)------------------------------ 0.25/0.44 % (10830)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.44 % (10830)Termination reason: Unknown 0.25/0.44 % (10830)Termination phase: shuffling 0.25/0.44 0.25/0.44 % (10830)Memory used [KB]: 1663 0.25/0.44 % (10830)Time elapsed: 0.010 s 0.25/0.44 % (10830)Instructions burned: 22 (million) 0.25/0.44 % (10830)------------------------------ 0.25/0.44 % (10830)------------------------------ 0.25/0.44 % (10827)Instruction limit reached! 0.25/0.44 % (10827)------------------------------ 0.25/0.44 % (10827)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.44 % (10827)Termination reason: Unknown 0.25/0.44 % (10827)Termination phase: Function definition elimination 0.25/0.44 0.25/0.44 % (10827)Memory used [KB]: 1918 0.25/0.44 % (10827)Time elapsed: 0.031 s 0.25/0.44 % (10827)Instructions burned: 77 (million) 0.25/0.44 % (10827)------------------------------ 0.25/0.44 % (10827)------------------------------ 0.25/0.45 % (10831)lrs-3_1:1024_cbe=off:chr=on:tnu=1:i=7:si=on:rtra=on_0 on Vampire---4 for (1799ds/7Mi) 0.25/0.45 % (10832)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on Vampire---4 for (1799ds/1021Mi) 0.25/0.45 % (10831)Instruction limit reached! 0.25/0.45 % (10831)------------------------------ 0.25/0.45 % (10831)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.45 % (10831)Termination reason: Unknown 0.25/0.45 % (10831)Termination phase: shuffling 0.25/0.45 0.25/0.45 % (10831)Memory used [KB]: 1407 0.25/0.45 % (10831)Time elapsed: 0.006 s 0.25/0.45 % (10831)Instructions burned: 8 (million) 0.25/0.45 % (10831)------------------------------ 0.25/0.45 % (10831)------------------------------ 0.25/0.45 % (10834)lrs-1010_1:50_au=on:awrs=converge:awrsf=430:bet=on:cbe=off:cha=on:nm=20:sac=on:i=9:si=on:rtra=on_0 on Vampire---4 for (1799ds/9Mi) 0.25/0.45 % (10833)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on Vampire---4 for (1799ds/71Mi) 0.25/0.45 % (10835)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=1044:si=on:rtra=on_0 on Vampire---4 for (1799ds/1044Mi) 0.25/0.46 % (10834)Instruction limit reached! 0.25/0.46 % (10834)------------------------------ 0.25/0.46 % (10834)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.46 % (10834)Termination reason: Unknown 0.25/0.46 % (10834)Termination phase: shuffling 0.25/0.46 0.25/0.46 % (10834)Memory used [KB]: 1407 0.25/0.46 % (10834)Time elapsed: 0.005 s 0.25/0.46 % (10834)Instructions burned: 9 (million) 0.25/0.46 % (10834)------------------------------ 0.25/0.46 % (10834)------------------------------ 0.25/0.46 % (10822)Instruction limit reached! 0.25/0.46 % (10822)------------------------------ 0.25/0.46 % (10822)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.46 % (10822)Termination reason: Unknown 0.25/0.46 % (10822)Termination phase: Saturation 0.25/0.46 0.25/0.46 % (10822)Memory used [KB]: 6524 0.25/0.46 % (10822)Time elapsed: 0.046 s 0.25/0.46 % (10822)Instructions burned: 96 (million) 0.25/0.46 % (10822)------------------------------ 0.25/0.46 % (10822)------------------------------ 0.25/0.46 % (10836)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=128:si=on:rtra=on_0 on Vampire---4 for (1799ds/128Mi) 0.25/0.47 % (10837)lrs+21_1:1_cond=on:e2e=on:i=61:si=on:rtra=on_0 on Vampire---4 for (1799ds/61Mi) 0.25/0.47 % (10838)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=14:si=on:rtra=on_0 on Vampire---4 for (1799ds/14Mi) 0.25/0.48 % (10835)Refutation not found, incomplete strategy 0.25/0.48 % (10835)------------------------------ 0.25/0.48 % (10835)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.48 % (10835)Termination reason: Refutation not found, incomplete strategy 0.25/0.48 0.25/0.48 0.25/0.48 % (10835)Memory used [KB]: 6268 0.25/0.48 % (10835)Time elapsed: 0.024 s 0.25/0.48 % (10835)Instructions burned: 56 (million) 0.25/0.48 % (10835)------------------------------ 0.25/0.48 % (10835)------------------------------ 0.25/0.48 % (10833)Instruction limit reached! 0.25/0.48 % (10833)------------------------------ 0.25/0.48 % (10833)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.48 % (10833)Termination reason: Unknown 0.25/0.48 % (10833)Termination phase: Function definition elimination 0.25/0.48 0.25/0.48 % (10833)Memory used [KB]: 1791 0.25/0.48 % (10833)Time elapsed: 0.030 s 0.25/0.48 % (10833)Instructions burned: 72 (million) 0.25/0.48 % (10833)------------------------------ 0.25/0.48 % (10833)------------------------------ 0.25/0.48 % (10838)Instruction limit reached! 0.25/0.48 % (10838)------------------------------ 0.25/0.48 % (10838)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.48 % (10838)Termination reason: Unknown 0.25/0.48 % (10838)Termination phase: shuffling 0.25/0.48 0.25/0.48 % (10838)Memory used [KB]: 1535 0.25/0.48 % (10838)Time elapsed: 0.011 s 0.25/0.48 % (10838)Instructions burned: 14 (million) 0.25/0.48 % (10838)------------------------------ 0.25/0.48 % (10838)------------------------------ 0.25/0.49 % (10840)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 Vampire---4 for (1799ds/1041Mi) 0.25/0.49 % (10839)lrs+2_5:1_cnfonf=lazy_not_be_gen:hud=10:inj=on:ntd=on:tnu=1:i=2:si=on:rtra=on_0 on Vampire---4 for (1799ds/2Mi) 0.25/0.49 % (10839)Instruction limit reached! 0.25/0.49 % (10839)------------------------------ 0.25/0.49 % (10839)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.49 % (10839)Termination reason: Unknown 0.25/0.49 % (10839)Termination phase: shuffling 0.25/0.49 0.25/0.49 % (10839)Memory used [KB]: 1279 0.25/0.49 % (10839)Time elapsed: 0.003 s 0.25/0.49 % (10839)Instructions burned: 2 (million) 0.25/0.49 % (10839)------------------------------ 0.25/0.49 % (10839)------------------------------ 0.25/0.49 % (10837)Instruction limit reached! 0.25/0.49 % (10837)------------------------------ 0.25/0.49 % (10837)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.49 % (10837)Termination reason: Unknown 0.25/0.49 % (10837)Termination phase: Property scanning 0.25/0.49 0.25/0.49 % (10837)Memory used [KB]: 2942 0.25/0.49 % (10837)Time elapsed: 0.027 s 0.25/0.49 % (10837)Instructions burned: 61 (million) 0.25/0.49 % (10837)------------------------------ 0.25/0.49 % (10837)------------------------------ 0.25/0.50 % (10841)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on Vampire---4 for (1799ds/11Mi) 0.25/0.50 % (10829)Refutation not found, incomplete strategy 0.25/0.50 % (10829)------------------------------ 0.25/0.50 % (10829)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.50 % (10829)Termination reason: Refutation not found, incomplete strategy 0.25/0.50 0.25/0.50 0.25/0.50 % (10829)Memory used [KB]: 8443 0.25/0.50 % (10829)Time elapsed: 0.089 s 0.25/0.50 % (10829)Instructions burned: 188 (million) 0.25/0.50 % (10829)------------------------------ 0.25/0.50 % (10829)------------------------------ 0.25/0.50 % (10841)Instruction limit reached! 0.25/0.50 % (10841)------------------------------ 0.25/0.50 % (10841)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.50 % (10841)Termination reason: Unknown 0.25/0.50 % (10841)Termination phase: shuffling 0.25/0.50 0.25/0.50 % (10841)Memory used [KB]: 1407 0.25/0.50 % (10841)Time elapsed: 0.007 s 0.25/0.50 % (10841)Instructions burned: 12 (million) 0.25/0.50 % (10841)------------------------------ 0.25/0.50 % (10841)------------------------------ 0.25/0.51 % (10843)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=26:si=on:rtra=on_0 on Vampire---4 for (1799ds/26Mi) 0.25/0.51 % (10844)lrs+1002_1:4_au=on:av=off:bsr=on:cbe=off:nm=2:i=56:si=on:rtra=on_0 on Vampire---4 for (1798ds/56Mi) 0.25/0.51 % (10836)Instruction limit reached! 0.25/0.51 % (10836)------------------------------ 0.25/0.51 % (10836)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.51 % (10836)Termination reason: Unknown 0.25/0.51 % (10836)Termination phase: Saturation 0.25/0.51 0.25/0.51 % (10836)Memory used [KB]: 6652 0.25/0.51 % (10836)Time elapsed: 0.052 s 0.25/0.51 % (10836)Instructions burned: 129 (million) 0.25/0.51 % (10836)------------------------------ 0.25/0.51 % (10836)------------------------------ 0.25/0.52 % (10845)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on Vampire---4 for (1798ds/275Mi) 0.25/0.52 % (10843)Instruction limit reached! 0.25/0.52 % (10843)------------------------------ 0.25/0.52 % (10843)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.52 % (10843)Termination reason: Unknown 0.25/0.52 % (10843)Termination phase: Property scanning 0.25/0.52 0.25/0.52 % (10843)Memory used [KB]: 1791 0.25/0.52 % (10843)Time elapsed: 0.013 s 0.25/0.52 % (10843)Instructions burned: 27 (million) 0.25/0.52 % (10843)------------------------------ 0.25/0.52 % (10843)------------------------------ 0.25/0.52 % (10846)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1798ds/3Mi) 0.25/0.52 % (10842)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on Vampire---4 for (1799ds/140Mi) 0.25/0.52 % (10846)Instruction limit reached! 0.25/0.52 % (10846)------------------------------ 0.25/0.52 % (10846)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.52 % (10846)Termination reason: Unknown 0.25/0.52 % (10846)Termination phase: shuffling 0.25/0.52 0.25/0.52 % (10846)Memory used [KB]: 1279 0.25/0.52 % (10846)Time elapsed: 0.002 s 0.25/0.52 % (10846)Instructions burned: 3 (million) 0.25/0.52 % (10846)------------------------------ 0.25/0.52 % (10846)------------------------------ 0.25/0.53 % (10844)Instruction limit reached! 0.25/0.53 % (10844)------------------------------ 0.25/0.53 % (10844)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.53 % (10844)Termination reason: Unknown 0.25/0.53 % (10844)Termination phase: Property scanning 0.25/0.53 0.25/0.53 % (10844)Memory used [KB]: 1791 0.25/0.53 % (10844)Time elapsed: 0.017 s 0.25/0.53 % (10844)Instructions burned: 58 (million) 0.25/0.53 % (10844)------------------------------ 0.25/0.53 % (10844)------------------------------ 0.25/0.53 % (10847)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 Vampire---4 for (1798ds/19Mi) 0.25/0.53 % (10848)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on Vampire---4 for (1798ds/44Mi) 0.25/0.53 % (10845)Refutation not found, incomplete strategy 0.25/0.53 % (10845)------------------------------ 0.25/0.53 % (10845)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.53 % (10845)Termination reason: Refutation not found, incomplete strategy 0.25/0.53 0.25/0.53 0.25/0.53 % (10845)Memory used [KB]: 6268 0.25/0.53 % (10845)Time elapsed: 0.019 s 0.25/0.53 % (10845)Instructions burned: 37 (million) 0.25/0.53 % (10845)------------------------------ 0.25/0.53 % (10845)------------------------------ 0.25/0.54 % (10849)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=191:si=on:rtra=on_0 on Vampire---4 for (1798ds/191Mi) 0.25/0.54 % (10847)Instruction limit reached! 0.25/0.54 % (10847)------------------------------ 0.25/0.54 % (10847)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.54 % (10847)Termination reason: Unknown 0.25/0.54 % (10847)Termination phase: shuffling 0.25/0.54 0.25/0.54 % (10847)Memory used [KB]: 1663 0.25/0.54 % (10847)Time elapsed: 0.009 s 0.25/0.54 % (10847)Instructions burned: 20 (million) 0.25/0.54 % (10847)------------------------------ 0.25/0.54 % (10847)------------------------------ 0.25/0.54 % (10848)Instruction limit reached! 0.25/0.54 % (10848)------------------------------ 0.25/0.54 % (10848)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.54 % (10848)Termination reason: Unknown 0.25/0.54 % (10848)Termination phase: Property scanning 0.25/0.54 0.25/0.54 % (10848)Memory used [KB]: 1791 0.25/0.54 % (10848)Time elapsed: 0.013 s 0.25/0.54 % (10848)Instructions burned: 44 (million) 0.25/0.54 % (10848)------------------------------ 0.25/0.54 % (10848)------------------------------ 0.25/0.55 % (10850)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on Vampire---4 for (1798ds/62Mi) 0.25/0.55 % (10842)Refutation not found, incomplete strategy 0.25/0.55 % (10842)------------------------------ 0.25/0.55 % (10842)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.55 % (10842)Termination reason: Refutation not found, incomplete strategy 0.25/0.55 0.25/0.55 0.25/0.55 % (10842)Memory used [KB]: 6268 0.25/0.55 % (10842)Time elapsed: 0.057 s 0.25/0.55 % (10842)Instructions burned: 51 (million) 0.25/0.55 % (10842)------------------------------ 0.25/0.55 % (10842)------------------------------ 0.25/0.55 % (10851)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=105:si=on:rtra=on_0 on Vampire---4 for (1798ds/105Mi) 0.25/0.55 % (10852)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on Vampire---4 for (1798ds/3Mi) 0.25/0.55 % (10852)Instruction limit reached! 0.25/0.55 % (10852)------------------------------ 0.25/0.55 % (10852)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.55 % (10852)Termination reason: Unknown 0.25/0.55 % (10852)Termination phase: shuffling 0.25/0.55 0.25/0.55 % (10852)Memory used [KB]: 1279 0.25/0.55 % (10852)Time elapsed: 0.002 s 0.25/0.55 % (10852)Instructions burned: 3 (million) 0.25/0.55 % (10852)------------------------------ 0.25/0.55 % (10852)------------------------------ 0.25/0.56 % (10854)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 Vampire---4 for (1798ds/3Mi) 0.25/0.56 % (10854)Instruction limit reached! 0.25/0.56 % (10854)------------------------------ 0.25/0.56 % (10854)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.56 % (10854)Termination reason: Unknown 0.25/0.56 % (10854)Termination phase: shuffling 0.25/0.56 0.25/0.56 % (10854)Memory used [KB]: 1279 0.25/0.56 % (10854)Time elapsed: 0.003 s 0.25/0.56 % (10854)Instructions burned: 6 (million) 0.25/0.56 % (10854)------------------------------ 0.25/0.56 % (10854)------------------------------ 0.25/0.57 % (10853)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=238:si=on:rtra=on_0 on Vampire---4 for (1798ds/238Mi) 0.25/0.57 % (10855)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 Vampire---4 for (1798ds/4Mi) 0.25/0.57 % (10850)Instruction limit reached! 0.25/0.57 % (10850)------------------------------ 0.25/0.57 % (10850)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.57 % (10850)Termination reason: Unknown 0.25/0.57 % (10850)Termination phase: Property scanning 0.25/0.57 0.25/0.57 % (10850)Memory used [KB]: 1791 0.25/0.57 % (10850)Time elapsed: 0.028 s 0.25/0.57 % (10850)Instructions burned: 64 (million) 0.25/0.57 % (10850)------------------------------ 0.25/0.57 % (10850)------------------------------ 0.25/0.57 % (10855)Instruction limit reached! 0.25/0.57 % (10855)------------------------------ 0.25/0.57 % (10855)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.57 % (10855)Termination reason: Unknown 0.25/0.57 % (10855)Termination phase: shuffling 0.25/0.57 0.25/0.57 % (10855)Memory used [KB]: 1279 0.25/0.57 % (10855)Time elapsed: 0.003 s 0.25/0.57 % (10855)Instructions burned: 6 (million) 0.25/0.57 % (10855)------------------------------ 0.25/0.57 % (10855)------------------------------ 0.25/0.58 % (10825)Instruction limit reached! 0.25/0.58 % (10825)------------------------------ 0.25/0.58 % (10825)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.58 % (10825)Termination reason: Unknown 0.25/0.58 % (10825)Termination phase: Saturation 0.25/0.58 0.25/0.58 % (10825)Memory used [KB]: 7291 0.25/0.58 % (10825)Time elapsed: 0.170 s 0.25/0.58 % (10825)Instructions burned: 386 (million) 0.25/0.58 % (10825)------------------------------ 0.25/0.58 % (10825)------------------------------ 0.25/0.58 % (10856)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on Vampire---4 for (1798ds/149Mi) 0.25/0.59 % (10857)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on Vampire---4 for (1798ds/150Mi) 0.25/0.59 % (10851)Instruction limit reached! 0.25/0.59 % (10851)------------------------------ 0.25/0.59 % (10851)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.59 % (10851)Termination reason: Unknown 0.25/0.59 % (10851)Termination phase: Saturation 0.25/0.59 0.25/0.59 % (10851)Memory used [KB]: 6652 0.25/0.59 % (10851)Time elapsed: 0.045 s 0.25/0.59 % (10851)Instructions burned: 106 (million) 0.25/0.59 % (10851)------------------------------ 0.25/0.59 % (10851)------------------------------ 0.25/0.59 % (10849)Instruction limit reached! 0.25/0.59 % (10849)------------------------------ 0.25/0.59 % (10849)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 0.25/0.59 % (10849)Termination reason: Unknown 0.25/0.59 % (10849)Termination phase: Saturation 0.25/0.59 0.25/0.59 % (10849)Memory used [KB]: 7164 0.25/0.59 % (10849)Time elapsed: 0.060 s 0.25/0.59 % (10849)Instructions burned: 191 (million) 0.25/0.59 % (10849)------------------------------ 0.25/0.59 % (10849)------------------------------ 1.62/0.61 % (10859)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on Vampire---4 for (1798ds/39Mi) 1.62/0.61 % (10858)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=199:si=on:rtra=on_0 on Vampire---4 for (1798ds/199Mi) 1.62/0.61 % (10860)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=721:si=on:rtra=on_0 on Vampire---4 for (1798ds/721Mi) 1.62/0.61 % (10840)First to succeed. 1.69/0.62 % (10860)Refutation not found, incomplete strategy 1.69/0.62 % (10860)------------------------------ 1.69/0.62 % (10860)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.62 % (10860)Termination reason: Refutation not found, incomplete strategy 1.69/0.62 1.69/0.62 1.69/0.62 % (10860)Memory used [KB]: 6140 1.69/0.62 % (10860)Time elapsed: 0.013 s 1.69/0.62 % (10860)Instructions burned: 26 (million) 1.69/0.62 % (10860)------------------------------ 1.69/0.62 % (10860)------------------------------ 1.69/0.62 % (10859)Instruction limit reached! 1.69/0.62 % (10859)------------------------------ 1.69/0.62 % (10859)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.69/0.62 % (10859)Termination reason: Unknown 1.69/0.62 % (10859)Termination phase: Property scanning 1.69/0.62 1.69/0.62 % (10859)Memory used [KB]: 1791 1.69/0.62 % (10859)Time elapsed: 0.019 s 1.69/0.62 % (10859)Instructions burned: 39 (million) 1.69/0.62 % (10859)------------------------------ 1.69/0.62 % (10859)------------------------------ 1.74/0.63 % (10861)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=3:si=on:rtra=on_0 on Vampire---4 for (1797ds/3Mi) 1.74/0.63 % (10861)Instruction limit reached! 1.74/0.63 % (10861)------------------------------ 1.74/0.63 % (10861)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.74/0.63 % (10861)Termination reason: Unknown 1.74/0.63 % (10861)Termination phase: shuffling 1.74/0.63 1.74/0.63 % (10861)Memory used [KB]: 1279 1.74/0.63 % (10861)Time elapsed: 0.003 s 1.74/0.63 % (10861)Instructions burned: 4 (million) 1.74/0.63 % (10861)------------------------------ 1.74/0.63 % (10861)------------------------------ 1.74/0.63 % (10840)Refutation found. Thanks to Tanya! 1.74/0.63 % SZS status Theorem for Vampire---4 1.74/0.63 % SZS output start Proof for Vampire---4 1.74/0.63 thf(type_def_5, type, term: $tType). 1.74/0.63 thf(type_def_7, type, subst: $tType). 1.74/0.63 thf(func_def_0, type, term: $tType). 1.74/0.63 thf(func_def_1, type, subst: $tType). 1.74/0.63 thf(func_def_2, type, one: term). 1.74/0.63 thf(func_def_3, type, ap: term > term > term). 1.74/0.63 thf(func_def_4, type, lam: term > term). 1.74/0.63 thf(func_def_5, type, sub: term > subst > term). 1.74/0.63 thf(func_def_6, type, id: subst). 1.74/0.63 thf(func_def_7, type, sh: subst). 1.74/0.63 thf(func_def_8, type, push: term > subst > subst). 1.74/0.63 thf(func_def_9, type, comp: subst > subst > subst). 1.74/0.63 thf(func_def_10, type, var: term > $o). 1.74/0.63 thf(func_def_18, type, hoasap: subst > term > subst > term > term). 1.74/0.63 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term). 1.74/0.63 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o). 1.74/0.63 thf(func_def_107, type, hoasvar: subst > term > subst > $o). 1.74/0.63 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o). 1.74/0.63 thf(func_def_142, type, ph1: !>[X0: $tType]:(X0)). 1.74/0.63 thf(func_def_143, type, sK2: subst > term > subst > $o). 1.74/0.63 thf(func_def_144, type, sK3: term). 1.74/0.63 thf(func_def_145, type, sK4: (subst > term > subst > $o) > subst > term > term). 1.74/0.63 thf(func_def_146, type, sK5: term). 1.74/0.63 thf(func_def_147, type, sK6: subst). 1.74/0.63 thf(func_def_148, type, sK7: subst). 1.74/0.63 thf(func_def_149, type, sK8: (subst > term > term) > term). 1.74/0.63 thf(func_def_150, type, sK9: (subst > term > term) > subst). 1.74/0.63 thf(func_def_151, type, sK10: (subst > term > term) > subst). 1.74/0.63 thf(func_def_152, type, sK11: (subst > term > term) > term). 1.74/0.63 thf(f1140,plain,( 1.74/0.63 $false), 1.74/0.63 inference(avatar_sat_refutation,[],[f771,f1067,f1139])). 1.74/0.63 thf(f1139,plain,( 1.74/0.63 ~spl0_1), 1.74/0.63 inference(avatar_contradiction_clause,[],[f1138])). 1.74/0.63 thf(f1138,plain,( 1.74/0.63 $false | ~spl0_1), 1.74/0.63 inference(trivial_inequality_removal,[],[f1137])). 1.74/0.63 thf(f1137,plain,( 1.74/0.63 ($false = $true) | ~spl0_1), 1.74/0.63 inference(boolean_simplification,[],[f1136])). 1.74/0.63 thf(f1136,plain,( 1.74/0.63 ((~ $true) = $true) | ~spl0_1), 1.74/0.63 inference(forward_demodulation,[],[f1130,f584])). 1.74/0.63 thf(f584,plain,( 1.74/0.63 ((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ sK3 @ (push @ Y0 @ id)) @ id)))) = $true)), 1.74/0.63 inference(binary_proxy_clausification,[],[f580])). 1.74/0.63 thf(f580,plain,( 1.74/0.63 ($false = ((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ sK3 @ (push @ Y0 @ id)) @ id)))) => (sK2 @ id @ (lam @ sK3) @ id)))), 1.74/0.63 inference(beta_eta_normalization,[],[f579])). 1.74/0.63 thf(f579,plain,( 1.74/0.63 ($false = ((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ Y0) @ id))) @ sK3))), 1.74/0.63 inference(sigma_clausification,[],[f576])). 1.74/0.63 thf(f576,plain,( 1.74/0.63 ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ Y0) @ id)))) = $false)), 1.74/0.63 inference(boolean_simplification,[],[f575])). 1.74/0.63 thf(f575,plain,( 1.74/0.63 ($false = ($true => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ Y0) @ id))))))), 1.74/0.63 inference(backward_demodulation,[],[f570,f574])). 1.74/0.63 thf(f574,plain,( 1.74/0.63 ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y1) @ Y2) = (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK2 @ id @ (lam @ (Y0 @ sh @ one)) @ id))))) = $true)), 1.74/0.63 inference(binary_proxy_clausification,[],[f570])). 1.74/0.63 thf(f570,plain,( 1.74/0.63 (((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y1) @ Y2) = (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK2 @ id @ (lam @ (Y0 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ Y0) @ id))))) = $false)), 1.74/0.63 inference(boolean_simplification,[],[f569])). 1.74/0.63 thf(f569,plain,( 1.74/0.63 (($true => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y1) @ Y2) = (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK2 @ id @ (lam @ (Y0 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ Y0) @ id)))))) = $false)), 1.74/0.63 inference(backward_demodulation,[],[f564,f568])). 1.74/0.63 thf(f568,plain,( 1.74/0.63 ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK2 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2) @ Y3) => (sK2 @ Y1 @ Y0 @ (comp @ Y2 @ Y3))))))))))) = $true)), 1.74/0.63 inference(binary_proxy_clausification,[],[f564])). 1.74/0.63 thf(f564,plain,( 1.74/0.63 ($false = ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK2 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2) @ Y3) => (sK2 @ Y1 @ Y0 @ (comp @ Y2 @ Y3))))))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y1) @ Y2) = (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK2 @ id @ (lam @ (Y0 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ Y0) @ id)))))))), 1.74/0.63 inference(boolean_simplification,[],[f563])). 1.74/0.63 thf(f563,plain,( 1.74/0.63 ($false = ($true => ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK2 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2) @ Y3) => (sK2 @ Y1 @ Y0 @ (comp @ Y2 @ Y3))))))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y1) @ Y2) = (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK2 @ id @ (lam @ (Y0 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ Y0) @ id))))))))), 1.74/0.63 inference(backward_demodulation,[],[f560,f562])). 1.74/0.63 thf(f562,plain,( 1.74/0.63 ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sK2 @ Y3 @ Y2 @ (comp @ Y0 @ Y1)) => (sK2 @ (comp @ Y3 @ Y0) @ (sub @ Y2 @ Y0) @ Y1)))))))))) = $true)), 1.74/0.63 inference(binary_proxy_clausification,[],[f560])). 1.74/0.63 thf(f560,plain,( 1.74/0.63 ($false = ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sK2 @ Y3 @ Y2 @ (comp @ Y0 @ Y1)) => (sK2 @ (comp @ Y3 @ Y0) @ (sub @ Y2 @ Y0) @ Y1)))))))))) => ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sK2 @ (comp @ Y1 @ Y2) @ (sub @ Y0 @ Y2) @ Y3) => (sK2 @ Y1 @ Y0 @ (comp @ Y2 @ Y3))))))))))) => ((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y1) @ Y2) = (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK2 @ id @ (lam @ (Y0 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ Y0) @ id))))))))), 1.74/0.63 inference(beta_eta_normalization,[],[f559])). 1.74/0.63 thf(f559,plain,( 1.74/0.63 ($false = ((^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))) @ sK2))), 1.74/0.63 inference(sigma_clausification,[],[f550])). 1.74/0.63 thf(f550,plain,( 1.74/0.63 ($false = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))), 1.74/0.63 inference(binary_proxy_clausification,[],[f536])). 1.74/0.63 thf(f536,plain,( 1.74/0.63 ($false = ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))) => (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))))))), 1.74/0.63 inference(binary_proxy_clausification,[],[f535])). 1.74/0.63 thf(f535,plain,( 1.74/0.63 (((id = (push @ one @ sh)) => ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))) => (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))) = $false)), 1.74/0.63 inference(boolean_simplification,[],[f534])). 1.74/0.63 thf(f534,plain,( 1.74/0.63 ($false = ($true => ((id = (push @ one @ sh)) => ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))) => (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))))))))), 1.74/0.63 inference(backward_demodulation,[],[f529,f533])). 1.74/0.63 thf(f533,plain,( 1.74/0.63 ((!! @ term @ (^[Y0 : term]: ((sub @ Y0 @ id) = Y0))) = $true)), 1.74/0.63 inference(binary_proxy_clausification,[],[f529])). 1.74/0.63 thf(f529,plain,( 1.74/0.63 ($false = ((!! @ term @ (^[Y0 : term]: ((sub @ Y0 @ id) = Y0))) => ((id = (push @ one @ sh)) => ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))) => (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))))))))), 1.74/0.63 inference(not_proxy_clausification,[],[f528])). 1.74/0.63 thf(f528,plain,( 1.74/0.63 ((~ ((!! @ term @ (^[Y0 : term]: ((sub @ Y0 @ id) = Y0))) => ((id = (push @ one @ sh)) => ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))) => (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))))) = $true)), 1.74/0.63 inference(beta_eta_normalization,[],[f527])). 1.74/0.63 thf(f527,plain,( 1.74/0.63 ($true = (~ ((!! @ term @ (^[Y0 : term]: ((sub @ Y0 @ id) = Y0))) => ((id = (push @ one @ sh)) => ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))) => (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))))))), 1.74/0.63 inference(definition_unfolding,[],[f388,f504])). 1.74/0.63 thf(f504,plain,( 1.74/0.63 (hoasinduction_lem3_lthm = ((!! @ term @ (^[Y0 : term]: ((sub @ Y0 @ id) = Y0))) => ((id = (push @ one @ sh)) => ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))) => (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id)))))))))))))), 1.74/0.63 inference(definition_unfolding,[],[f382,f355,f341,f479,f470])). 1.74/0.63 thf(f470,plain,( 1.74/0.63 (hoasinduction_lem3 = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))), 1.74/0.63 inference(definition_unfolding,[],[f445,f441])). 1.74/0.63 thf(f441,plain,( 1.74/0.63 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (lam @ (Y1 @ sh @ one))))))), 1.74/0.63 inference(cnf_transformation,[],[f237])). 1.74/0.63 thf(f237,plain,( 1.74/0.63 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (lam @ (Y1 @ sh @ one))))))), 1.74/0.63 inference(fool_elimination,[],[f236])). 1.74/0.63 thf(f236,plain,( 1.74/0.63 ((^[X0 : subst, X1 : subst > term > term] : (lam @ (X1 @ sh @ one))) = hoaslam)), 1.74/0.63 inference(rectify,[],[f56])). 1.74/0.63 thf(f56,axiom,( 1.74/0.63 ((^[X2 : subst, X10 : subst > term > term] : (lam @ (X10 @ sh @ one))) = hoaslam)), 1.74/0.63 file('/export/starexec/sandbox/tmp/tmp.TfVhRNnzGC/Vampire---4.8_10714',hoaslam)). 1.74/0.63 thf(f445,plain,( 1.74/0.63 (hoasinduction_lem3 = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))), 1.74/0.63 inference(cnf_transformation,[],[f214])). 1.74/0.63 thf(f214,plain,( 1.74/0.63 (hoasinduction_lem3 = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ Y4 @ Y3 @ (comp @ Y1 @ Y2)) => (Y0 @ (comp @ Y4 @ Y1) @ (sub @ Y3 @ Y1) @ Y2)))))))))) => ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((Y0 @ (comp @ Y2 @ Y3) @ (sub @ Y1 @ Y3) @ Y4) => (Y0 @ Y2 @ Y1 @ (comp @ Y3 @ Y4))))))))))) => ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y2) @ Y3) = (Y1 @ (comp @ Y4 @ Y3) @ (sub @ Y2 @ Y3))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ Y1) @ id))))))))))), 1.74/0.63 inference(fool_elimination,[],[f213])). 1.74/0.63 thf(f213,plain,( 1.74/0.63 (! [X0 : subst > term > subst > $o] : (! [X1 : subst,X2 : term,X3 : subst,X4 : subst] : ((X0 @ X1 @ X2 @ (comp @ X4 @ X3)) => (X0 @ (comp @ X1 @ X4) @ (sub @ X2 @ X4) @ X3)) => (! [X5 : subst,X6 : subst,X7 : subst,X8 : term] : ((X0 @ (comp @ X7 @ X6) @ (sub @ X8 @ X6) @ X5) => (X0 @ X7 @ X8 @ (comp @ X6 @ X5))) => (! [X9 : subst > term > term] : (! [X10 : subst,X11 : subst,X12 : term] : ((sub @ (X9 @ X10 @ X12) @ X11) = (X9 @ (comp @ X10 @ X11) @ (sub @ X12 @ X11))) => (! [X13 : term] : ((X0 @ id @ X13 @ id) => (X0 @ id @ (X9 @ id @ X13) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X14 : subst, X15 : term] : (X9 @ X14 @ X15))) @ id))) => ! [X16 : term] : (! [X17 : term] : ((X0 @ id @ X17 @ id) => (X0 @ id @ (sub @ X16 @ (push @ X17 @ id)) @ id)) => (X0 @ id @ (lam @ X16) @ id))))) = hoasinduction_lem3)), 1.74/0.63 inference(rectify,[],[f99])). 1.74/0.63 thf(f99,axiom,( 1.74/0.63 (! [X5 : subst > term > subst > $o] : (! [X2 : subst,X0 : term,X3 : subst,X4 : subst] : ((X5 @ X2 @ X0 @ (comp @ X4 @ X3)) => (X5 @ (comp @ X2 @ X4) @ (sub @ X0 @ X4) @ X3)) => (! [X3 : subst,X4 : subst,X2 : subst,X0 : term] : ((X5 @ (comp @ X2 @ X4) @ (sub @ X0 @ X4) @ X3) => (X5 @ X2 @ X0 @ (comp @ X4 @ X3))) => (! [X10 : subst > term > term] : (! [X2 : subst,X3 : subst,X0 : term] : ((sub @ (X10 @ X2 @ X0) @ X3) = (X10 @ (comp @ X2 @ X3) @ (sub @ X0 @ X3))) => (! [X0 : term] : ((X5 @ id @ X0 @ id) => (X5 @ id @ (X10 @ id @ X0) @ id)) => (X5 @ id @ (hoaslam @ id @ (^[X2 : subst, X0 : term] : (X10 @ X2 @ X0))) @ id))) => ! [X0 : term] : (! [X1 : term] : ((X5 @ id @ X1 @ id) => (X5 @ id @ (sub @ X0 @ (push @ X1 @ id)) @ id)) => (X5 @ id @ (lam @ X0) @ id))))) = hoasinduction_lem3)), 1.74/0.63 file('/export/starexec/sandbox/tmp/tmp.TfVhRNnzGC/Vampire---4.8_10714',hoasinduction_lem3)). 1.74/0.63 thf(f479,plain,( 1.74/0.63 (hoasinduction_lem3aa = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ ((^[Y2 : subst]: ((^[Y3 : subst > term > term]: (lam @ (Y3 @ sh @ one))))) @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))))), 1.74/0.63 inference(definition_unfolding,[],[f390,f441])). 1.74/0.63 thf(f390,plain,( 1.74/0.63 (hoasinduction_lem3aa = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))))), 1.74/0.63 inference(cnf_transformation,[],[f120])). 1.74/0.63 thf(f120,plain,( 1.74/0.63 (hoasinduction_lem3aa = (!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (hoaslam @ id @ (^[Y2 : subst]: ((^[Y3 : term]: (Y1 @ Y2 @ Y3))))) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))))), 1.74/0.63 inference(fool_elimination,[],[f119])). 1.74/0.63 thf(f119,plain,( 1.74/0.63 (hoasinduction_lem3aa = ! [X0 : subst > term > subst > $o] : (! [X1 : subst > term > term] : (! [X2 : subst,X3 : term,X4 : subst] : ((sub @ (X1 @ X2 @ X3) @ X4) = (X1 @ (comp @ X2 @ X4) @ (sub @ X3 @ X4))) => (! [X5 : term] : ((X0 @ id @ X5 @ id) => (X0 @ id @ (X1 @ id @ X5) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X6 : subst, X7 : term] : (X1 @ X6 @ X7))) @ id))) => ! [X8 : term] : (! [X9 : term] : ((X0 @ id @ X9 @ id) => (X0 @ id @ (sub @ X8 @ (push @ X9 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X8 @ (push @ one @ sh))) @ id))))), 1.74/0.63 inference(rectify,[],[f96])). 1.74/0.63 thf(f96,axiom,( 1.74/0.63 (hoasinduction_lem3aa = ! [X5 : subst > term > subst > $o] : (! [X10 : subst > term > term] : (! [X2 : subst,X0 : term,X3 : subst] : ((sub @ (X10 @ X2 @ X0) @ X3) = (X10 @ (comp @ X2 @ X3) @ (sub @ X0 @ X3))) => (! [X0 : term] : ((X5 @ id @ X0 @ id) => (X5 @ id @ (X10 @ id @ X0) @ id)) => (X5 @ id @ (hoaslam @ id @ (^[X2 : subst, X0 : term] : (X10 @ X2 @ X0))) @ id))) => ! [X0 : term] : (! [X1 : term] : ((X5 @ id @ X1 @ id) => (X5 @ id @ (sub @ X0 @ (push @ X1 @ id)) @ id)) => (X5 @ id @ (lam @ (sub @ X0 @ (push @ one @ sh))) @ id))))), 1.74/0.63 file('/export/starexec/sandbox/tmp/tmp.TfVhRNnzGC/Vampire---4.8_10714',hoasinduction_lem3aa)). 1.74/0.63 thf(f341,plain,( 1.74/0.63 (axvarshift = (id = (push @ one @ sh)))), 1.74/0.63 inference(cnf_transformation,[],[f246])). 1.74/0.63 thf(f246,plain,( 1.74/0.63 (axvarshift = (id = (push @ one @ sh)))), 1.74/0.63 inference(fool_elimination,[],[f11])). 1.74/0.63 thf(f11,axiom,( 1.74/0.63 (axvarshift = (id = (push @ one @ sh)))), 1.74/0.63 file('/export/starexec/sandbox/tmp/tmp.TfVhRNnzGC/Vampire---4.8_10714',axvarshift)). 1.74/0.63 thf(f355,plain,( 1.74/0.63 (axvarid = (!! @ term @ (^[Y0 : term]: ((sub @ Y0 @ id) = Y0))))), 1.74/0.63 inference(cnf_transformation,[],[f311])). 1.74/0.63 thf(f311,plain,( 1.74/0.63 (axvarid = (!! @ term @ (^[Y0 : term]: ((sub @ Y0 @ id) = Y0))))), 1.74/0.63 inference(fool_elimination,[],[f3])). 1.74/0.63 thf(f3,axiom,( 1.74/0.63 (axvarid = ! [X0 : term] : ((sub @ X0 @ id) = X0))), 1.74/0.63 file('/export/starexec/sandbox/tmp/tmp.TfVhRNnzGC/Vampire---4.8_10714',axvarid)). 1.74/0.63 thf(f382,plain,( 1.74/0.63 (hoasinduction_lem3_lthm = (axvarid => (axvarshift => (hoasinduction_lem3aa => hoasinduction_lem3))))), 1.74/0.63 inference(cnf_transformation,[],[f306])). 1.74/0.63 thf(f306,plain,( 1.74/0.63 (hoasinduction_lem3_lthm = (axvarid => (axvarshift => (hoasinduction_lem3aa => hoasinduction_lem3))))), 1.74/0.63 inference(fool_elimination,[],[f305])). 1.74/0.63 thf(f305,plain,( 1.74/0.63 (axvarid => (axvarshift => (hoasinduction_lem3aa => hoasinduction_lem3)) = hoasinduction_lem3_lthm)), 1.74/0.63 inference(rectify,[],[f101])). 1.74/0.63 thf(f101,axiom,( 1.74/0.63 (axvarid => (axvarshift => (hoasinduction_lem3aa => hoasinduction_lem3)) = hoasinduction_lem3_lthm)), 1.74/0.63 file('/export/starexec/sandbox/tmp/tmp.TfVhRNnzGC/Vampire---4.8_10714',hoasinduction_lem3_lthm)). 1.74/0.63 thf(f388,plain,( 1.74/0.63 ((~ hoasinduction_lem3_lthm) = $true)), 1.74/0.63 inference(cnf_transformation,[],[f226])). 1.74/0.63 thf(f226,plain,( 1.74/0.63 ((~ hoasinduction_lem3_lthm) = $true)), 1.74/0.63 inference(fool_elimination,[],[f225])). 1.74/0.63 thf(f225,plain,( 1.74/0.63 ~hoasinduction_lem3_lthm), 1.74/0.63 inference(rectify,[],[f115])). 1.74/0.63 thf(f115,negated_conjecture,( 1.74/0.63 ~hoasinduction_lem3_lthm), 1.74/0.63 inference(negated_conjecture,[],[f114])). 1.74/0.63 thf(f114,conjecture,( 1.74/0.63 hoasinduction_lem3_lthm), 1.74/0.63 file('/export/starexec/sandbox/tmp/tmp.TfVhRNnzGC/Vampire---4.8_10714',thm)). 1.74/0.63 thf(f1130,plain,( 1.74/0.63 ((~ (!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ sK3 @ (push @ Y0 @ id)) @ id))))) = $true) | ~spl0_1), 1.74/0.63 inference(boolean_simplification,[],[f1127])). 1.74/0.63 thf(f1127,plain,( 1.74/0.63 (((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ sK3 @ (push @ Y0 @ id)) @ id)))) => $false) = $true) | ~spl0_1), 1.74/0.63 inference(superposition,[],[f1121,f583])). 1.74/0.63 thf(f583,plain,( 1.74/0.63 ((sK2 @ id @ (lam @ sK3) @ id) = $false)), 1.74/0.63 inference(binary_proxy_clausification,[],[f580])). 1.74/0.63 thf(f1121,plain,( 1.74/0.63 ( ! [X1 : term] : ((((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ X1 @ (push @ Y0 @ id)) @ id)))) => (sK2 @ id @ (lam @ X1) @ id)) = $true)) ) | ~spl0_1), 1.74/0.63 inference(forward_demodulation,[],[f1120,f547])). 1.74/0.63 thf(f547,plain,( 1.74/0.63 ( ! [X1 : term] : (((sub @ X1 @ id) = X1)) )), 1.74/0.63 inference(equality_proxy_clausification,[],[f546])). 1.74/0.63 thf(f546,plain,( 1.74/0.63 ( ! [X1 : term] : ((((sub @ X1 @ id) = X1) = $true)) )), 1.74/0.63 inference(beta_eta_normalization,[],[f545])). 1.74/0.63 thf(f545,plain,( 1.74/0.63 ( ! [X1 : term] : (($true = ((^[Y0 : term]: ((sub @ Y0 @ id) = Y0)) @ X1))) )), 1.74/0.63 inference(pi_clausification,[],[f533])). 1.74/0.63 thf(f1120,plain,( 1.74/0.63 ( ! [X1 : term] : ((((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ X1 @ (push @ Y0 @ id)) @ id)))) => (sK2 @ id @ (lam @ (sub @ X1 @ id)) @ id)) = $true)) ) | ~spl0_1), 1.74/0.63 inference(forward_demodulation,[],[f1118,f542])). 1.74/0.63 thf(f542,plain,( 1.74/0.63 (id = (push @ one @ sh))), 1.74/0.63 inference(equality_proxy_clausification,[],[f537])). 1.74/0.63 thf(f537,plain,( 1.74/0.63 ((id = (push @ one @ sh)) = $true)), 1.74/0.63 inference(binary_proxy_clausification,[],[f535])). 1.74/0.63 thf(f1118,plain,( 1.74/0.63 ( ! [X1 : term] : (($true = ((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ X1 @ (push @ Y0 @ id)) @ id)))) => (sK2 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id)))) ) | ~spl0_1), 1.74/0.63 inference(beta_eta_normalization,[],[f1116])). 1.74/0.63 thf(f1116,plain,( 1.74/0.63 ( ! [X1 : term] : ((((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))) @ X1) = $true)) ) | ~spl0_1), 1.74/0.63 inference(pi_clausification,[],[f767])). 1.74/0.63 thf(f767,plain,( 1.74/0.63 ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))) = $true) | ~spl0_1), 1.74/0.63 inference(avatar_component_clause,[],[f766])). 1.74/0.63 thf(f766,plain,( 1.74/0.63 spl0_1 <=> ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))) = $true)), 1.74/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 1.74/0.63 thf(f1067,plain,( 1.74/0.63 ~spl0_2), 1.74/0.63 inference(avatar_contradiction_clause,[],[f1066])). 1.74/0.63 thf(f1066,plain,( 1.74/0.63 $false | ~spl0_2), 1.74/0.63 inference(trivial_inequality_removal,[],[f1058])). 1.74/0.63 thf(f1058,plain,( 1.74/0.63 ($false = $true) | ~spl0_2), 1.74/0.63 inference(superposition,[],[f1056,f777])). 1.74/0.63 thf(f777,plain,( 1.74/0.63 ((!! @ subst @ (^[Y0 : subst]: ((sub @ (sK4 @ sK2 @ Y0 @ sK5) @ sK6) = (sK4 @ sK2 @ (comp @ Y0 @ sK6) @ (sub @ sK5 @ sK6))))) = $false) | ~spl0_2), 1.74/0.63 inference(beta_eta_normalization,[],[f776])). 1.74/0.63 thf(f776,plain,( 1.74/0.63 ($false = ((^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK4 @ sK2 @ Y1 @ sK5) @ Y0) = (sK4 @ sK2 @ (comp @ Y1 @ Y0) @ (sub @ sK5 @ Y0)))))) @ sK6)) | ~spl0_2), 1.74/0.63 inference(sigma_clausification,[],[f774])). 1.74/0.63 thf(f774,plain,( 1.74/0.63 ((!! @ subst @ (^[Y0 : subst]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK4 @ sK2 @ Y1 @ sK5) @ Y0) = (sK4 @ sK2 @ (comp @ Y1 @ Y0) @ (sub @ sK5 @ Y0))))))) = $false) | ~spl0_2), 1.74/0.63 inference(beta_eta_normalization,[],[f772])). 1.74/0.63 thf(f772,plain,( 1.74/0.63 ($false = ((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ sK2 @ Y2 @ Y0) @ Y1) = (sK4 @ sK2 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1)))))))) @ sK5)) | ~spl0_2), 1.74/0.63 inference(sigma_clausification,[],[f770])). 1.74/0.63 thf(f770,plain,( 1.74/0.63 ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ sK2 @ Y2 @ Y0) @ Y1) = (sK4 @ sK2 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1)))))))))) | ~spl0_2), 1.74/0.63 inference(avatar_component_clause,[],[f769])). 1.74/0.63 thf(f769,plain,( 1.74/0.63 spl0_2 <=> ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ sK2 @ Y2 @ Y0) @ Y1) = (sK4 @ sK2 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1))))))))))), 1.74/0.63 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 1.74/0.63 thf(f1056,plain,( 1.74/0.63 ( ! [X0 : term,X1 : subst] : (((!! @ subst @ (^[Y0 : subst]: ((sub @ (sK4 @ sK2 @ Y0 @ X0) @ X1) = (sK4 @ sK2 @ (comp @ Y0 @ X1) @ (sub @ X0 @ X1))))) = $true)) )), 1.74/0.63 inference(trivial_inequality_removal,[],[f1055])). 1.74/0.63 thf(f1055,plain,( 1.74/0.63 ( ! [X0 : term,X1 : subst] : (($false = $true) | ((!! @ subst @ (^[Y0 : subst]: ((sub @ (sK4 @ sK2 @ Y0 @ X0) @ X1) = (sK4 @ sK2 @ (comp @ Y0 @ X1) @ (sub @ X0 @ X1))))) = $true)) )), 1.74/0.63 inference(boolean_simplification,[],[f1054])). 1.74/0.63 thf(f1054,plain,( 1.74/0.63 ( ! [X0 : term,X1 : subst] : (((!! @ subst @ (^[Y0 : subst]: ((sub @ (sK4 @ sK2 @ Y0 @ X0) @ X1) = (sK4 @ sK2 @ (comp @ Y0 @ X1) @ (sub @ X0 @ X1))))) = $true) | ((~ $true) = $true)) )), 1.74/0.63 inference(forward_demodulation,[],[f1053,f584])). 1.74/0.63 thf(f1053,plain,( 1.74/0.63 ( ! [X0 : term,X1 : subst] : (((~ (!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ sK3 @ (push @ Y0 @ id)) @ id))))) = $true) | ((!! @ subst @ (^[Y0 : subst]: ((sub @ (sK4 @ sK2 @ Y0 @ X0) @ X1) = (sK4 @ sK2 @ (comp @ Y0 @ X1) @ (sub @ X0 @ X1))))) = $true)) )), 1.74/0.63 inference(boolean_simplification,[],[f1050])). 1.74/0.63 thf(f1050,plain,( 1.74/0.63 ( ! [X0 : term,X1 : subst] : ((((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (sub @ sK3 @ (push @ Y0 @ id)) @ id)))) => $false) = $true) | ((!! @ subst @ (^[Y0 : subst]: ((sub @ (sK4 @ sK2 @ Y0 @ X0) @ X1) = (sK4 @ sK2 @ (comp @ Y0 @ X1) @ (sub @ X0 @ X1))))) = $true)) )), 1.74/0.63 inference(superposition,[],[f999,f583])). 1.74/0.63 thf(f999,plain,( 1.74/0.63 ( ! [X2 : term,X3 : subst,X1 : subst > term > subst > $o,X4 : term] : ((((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id)))) => (X1 @ id @ (lam @ X2) @ id)) = $true) | ((!! @ subst @ (^[Y0 : subst]: ((sub @ (sK4 @ X1 @ Y0 @ X4) @ X3) = (sK4 @ X1 @ (comp @ Y0 @ X3) @ (sub @ X4 @ X3))))) = $true)) )), 1.74/0.63 inference(beta_eta_normalization,[],[f998])). 1.74/0.63 thf(f998,plain,( 1.74/0.63 ( ! [X2 : term,X3 : subst,X1 : subst > term > subst > $o,X4 : term] : ((((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id)))) => (X1 @ id @ (lam @ X2) @ id)) = $true) | (((^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK4 @ X1 @ Y1 @ Y0) @ X3) = (sK4 @ X1 @ (comp @ Y1 @ X3) @ (sub @ Y0 @ X3)))))) @ X4) = $true)) )), 1.74/0.63 inference(pi_clausification,[],[f976])). 1.74/0.63 thf(f976,plain,( 1.74/0.63 ( ! [X2 : term,X3 : subst,X1 : subst > term > subst > $o] : (((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: ((sub @ (sK4 @ X1 @ Y1 @ Y0) @ X3) = (sK4 @ X1 @ (comp @ Y1 @ X3) @ (sub @ Y0 @ X3))))))) = $true) | (((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id)))) => (X1 @ id @ (lam @ X2) @ id)) = $true)) )), 1.74/0.63 inference(beta_eta_normalization,[],[f973])). 1.74/0.63 thf(f973,plain,( 1.74/0.63 ( ! [X2 : term,X3 : subst,X1 : subst > term > subst > $o] : (($true = ((^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ X1 @ Y2 @ Y1) @ Y0) = (sK4 @ X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0)))))))) @ X3)) | (((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id)))) => (X1 @ id @ (lam @ X2) @ id)) = $true)) )), 1.74/0.63 inference(pi_clausification,[],[f925])). 1.74/0.63 thf(f925,plain,( 1.74/0.63 ( ! [X2 : term,X1 : subst > term > subst > $o] : (($true = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ X1 @ Y2 @ Y1) @ Y0) = (sK4 @ X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0)))))))))) | (((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id)))) => (X1 @ id @ (lam @ X2) @ id)) = $true)) )), 1.74/0.63 inference(forward_demodulation,[],[f924,f547])). 1.74/0.63 thf(f924,plain,( 1.74/0.63 ( ! [X2 : term,X1 : subst > term > subst > $o] : ((((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id)))) => (X1 @ id @ (lam @ (sub @ X2 @ id)) @ id)) = $true) | ($true = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ X1 @ Y2 @ Y1) @ Y0) = (sK4 @ X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0))))))))))) )), 1.74/0.63 inference(forward_demodulation,[],[f922,f542])). 1.74/0.63 thf(f922,plain,( 1.74/0.63 ( ! [X2 : term,X1 : subst > term > subst > $o] : ((((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sub @ X2 @ (push @ Y0 @ id)) @ id)))) => (X1 @ id @ (lam @ (sub @ X2 @ (push @ one @ sh))) @ id)) = $true) | ($true = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ X1 @ Y2 @ Y1) @ Y0) = (sK4 @ X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0))))))))))) )), 1.74/0.63 inference(beta_eta_normalization,[],[f920])). 1.74/0.63 thf(f920,plain,( 1.74/0.63 ( ! [X2 : term,X1 : subst > term > subst > $o] : (($true = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ X1 @ Y2 @ Y1) @ Y0) = (sK4 @ X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0)))))))))) | (((^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))) @ X2) = $true)) )), 1.74/0.63 inference(pi_clausification,[],[f637])). 1.74/0.63 thf(f637,plain,( 1.74/0.63 ( ! [X1 : subst > term > subst > $o] : (($true = (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))))) | ($true = (!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ X1 @ Y2 @ Y1) @ Y0) = (sK4 @ X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0))))))))))) )), 1.74/0.63 inference(binary_proxy_clausification,[],[f618])). 1.74/0.63 thf(f618,plain,( 1.74/0.63 ( ! [X1 : subst > term > subst > $o] : ((((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ X1 @ Y2 @ Y1) @ Y0) = (sK4 @ X1 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0))))))))) => ((!! @ term @ (^[Y0 : term]: ((X1 @ id @ Y0 @ id) => (X1 @ id @ (sK4 @ X1 @ id @ Y0) @ id)))) => (X1 @ id @ (lam @ (sK4 @ X1 @ sh @ one)) @ id))) = $false) | ($true = (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))))) )), 1.74/0.63 inference(beta_eta_normalization,[],[f615])). 1.74/0.63 thf(f615,plain,( 1.74/0.63 ( ! [X1 : subst > term > subst > $o] : (($true = (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))))) | (((^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1))))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (Y0 @ id @ Y1) @ id)))) => (X1 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))) @ (sK4 @ X1)) = $false)) )), 1.74/0.63 inference(sigma_clausification,[],[f558])). 1.74/0.63 thf(f558,plain,( 1.74/0.63 ( ! [X1 : subst > term > subst > $o] : (($false = (!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1))))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (Y0 @ id @ Y1) @ id)))) => (X1 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))) | ($true = (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))))) )), 1.74/0.63 inference(binary_proxy_clausification,[],[f557])). 1.74/0.63 thf(f557,plain,( 1.74/0.63 ( ! [X1 : subst > term > subst > $o] : ((((!! @ (subst > term > term) @ (^[Y0 : subst > term > term]: ((!! @ subst @ (^[Y1 : subst]: (!! @ term @ (^[Y2 : term]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y2) @ Y1) = (Y0 @ (comp @ Y3 @ Y1) @ (sub @ Y2 @ Y1))))))))) => ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (Y0 @ id @ Y1) @ id)))) => (X1 @ id @ (lam @ (Y0 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((X1 @ id @ Y1 @ id) => (X1 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (X1 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id))))) = $true)) )), 1.74/0.63 inference(beta_eta_normalization,[],[f556])). 1.74/0.63 thf(f556,plain,( 1.74/0.63 ( ! [X1 : subst > term > subst > $o] : ((((^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id)))))) @ X1) = $true)) )), 1.74/0.63 inference(pi_clausification,[],[f551])). 1.74/0.63 thf(f551,plain,( 1.74/0.63 ((!! @ (subst > term > subst > $o) @ (^[Y0 : subst > term > subst > $o]: ((!! @ (subst > term > term) @ (^[Y1 : subst > term > term]: ((!! @ subst @ (^[Y2 : subst]: (!! @ term @ (^[Y3 : term]: (!! @ subst @ (^[Y4 : subst]: ((sub @ (Y1 @ Y4 @ Y3) @ Y2) = (Y1 @ (comp @ Y4 @ Y2) @ (sub @ Y3 @ Y2))))))))) => ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (Y1 @ id @ Y2) @ id)))) => (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ id))))) => (!! @ term @ (^[Y1 : term]: ((!! @ term @ (^[Y2 : term]: ((Y0 @ id @ Y2 @ id) => (Y0 @ id @ (sub @ Y1 @ (push @ Y2 @ id)) @ id)))) => (Y0 @ id @ (lam @ (sub @ Y1 @ (push @ one @ sh))) @ id))))))) = $true)), 1.74/0.63 inference(binary_proxy_clausification,[],[f536])). 1.74/0.63 thf(f771,plain,( 1.74/0.63 spl0_1 | spl0_2), 1.74/0.63 inference(avatar_split_clause,[],[f764,f769,f766])). 1.74/0.63 thf(f764,plain,( 1.74/0.63 ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ sK2 @ Y2 @ Y0) @ Y1) = (sK4 @ sK2 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1)))))))))) | ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))) = $true)), 1.74/0.63 inference(trivial_inequality_removal,[],[f763])). 1.74/0.63 thf(f763,plain,( 1.74/0.63 ($false = $true) | ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))) = $true) | ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ sK2 @ Y2 @ Y0) @ Y1) = (sK4 @ sK2 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1))))))))))), 1.74/0.63 inference(boolean_simplification,[],[f761])). 1.74/0.63 thf(f761,plain,( 1.74/0.63 (((!! @ subst @ (^[Y0 : subst]: (!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ sK2 @ Y2 @ Y1) @ Y0) = (sK4 @ sK2 @ (comp @ Y2 @ Y0) @ (sub @ Y1 @ Y0))))))))) => $true) = $false) | ((!! @ term @ (^[Y0 : term]: ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))) => (sK2 @ id @ (lam @ (sub @ Y0 @ (push @ one @ sh))) @ id)))) = $true) | ($false = (!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (sK4 @ sK2 @ Y2 @ Y0) @ Y1) = (sK4 @ sK2 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1))))))))))), 1.74/0.63 inference(superposition,[],[f618,f610])). 1.74/0.63 thf(f610,plain,( 1.74/0.63 ( ! [X1 : subst > term > term] : ((((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (X1 @ id @ Y0) @ id)))) => (sK2 @ id @ (lam @ (X1 @ sh @ one)) @ id)) = $true) | ((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y2 @ Y0) @ Y1) = (X1 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1))))))))) = $false)) )), 1.74/0.63 inference(binary_proxy_clausification,[],[f609])). 1.74/0.63 thf(f609,plain,( 1.74/0.63 ( ! [X1 : subst > term > term] : ((((!! @ term @ (^[Y0 : term]: (!! @ subst @ (^[Y1 : subst]: (!! @ subst @ (^[Y2 : subst]: ((sub @ (X1 @ Y2 @ Y0) @ Y1) = (X1 @ (comp @ Y2 @ Y1) @ (sub @ Y0 @ Y1))))))))) => ((!! @ term @ (^[Y0 : term]: ((sK2 @ id @ Y0 @ id) => (sK2 @ id @ (X1 @ id @ Y0) @ id)))) => (sK2 @ id @ (lam @ (X1 @ sh @ one)) @ id))) = $true)) )), 1.74/0.63 inference(beta_eta_normalization,[],[f608])). 1.74/0.63 thf(f608,plain,( 1.74/0.63 ( ! [X1 : subst > term > term] : ((((^[Y0 : subst > term > term]: ((!! @ term @ (^[Y1 : term]: (!! @ subst @ (^[Y2 : subst]: (!! @ subst @ (^[Y3 : subst]: ((sub @ (Y0 @ Y3 @ Y1) @ Y2) = (Y0 @ (comp @ Y3 @ Y2) @ (sub @ Y1 @ Y2))))))))) => ((!! @ term @ (^[Y1 : term]: ((sK2 @ id @ Y1 @ id) => (sK2 @ id @ (Y0 @ id @ Y1) @ id)))) => (sK2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))) @ X1) = $true)) )), 1.74/0.63 inference(pi_clausification,[],[f574])). 1.74/0.63 % SZS output end Proof for Vampire---4 1.74/0.63 % (10840)------------------------------ 1.74/0.63 % (10840)Version: Vampire 4.7 (commit 934bd2fae on 2023-06-16 16:02:25 +0100) 1.74/0.63 % (10840)Termination reason: Refutation 1.74/0.63 1.74/0.63 % (10840)Memory used [KB]: 7291 1.74/0.63 % (10840)Time elapsed: 0.137 s 1.74/0.63 % (10840)Instructions burned: 251 (million) 1.74/0.63 % (10840)------------------------------ 1.74/0.63 % (10840)------------------------------ 1.74/0.63 % (10821)Success in time 0.224 s 1.74/0.63 % Vampire---4.8 exiting 1.74/0.63 EOF