0.02/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.11 % Command : run_vampire %s %d THM 0.10/0.31 % Computer : n021.cluster.edu 0.10/0.31 % Model : x86_64 x86_64 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.31 % Memory : 8042.1875MB 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.31 % CPULimit : 1920 0.10/0.31 % WCLimit : 240 0.10/0.31 % DateTime : Wed Jul 30 05:00:04 EDT 2025 0.16/0.31 % CPUTime : 0.16/0.32 This is a THF_ problem 0.16/0.33 Running higher-order theorem proving 0.16/0.34 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p -m 16384 -t 240 0.16/0.36 % (20220)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_20102 for (2399ds/18Mi) 0.18/0.37 % (20215)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_20102 for (2399ds/4Mi) 0.18/0.37 % (20220)Instruction limit reached! 0.18/0.37 % (20220)------------------------------ 0.18/0.37 % (20220)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.37 % (20220)Termination reason: Unknown 0.18/0.37 % (20220)Termination phase: Saturation 0.18/0.37 0.18/0.37 % (20220)Memory used [KB]: 5756 0.18/0.37 % (20220)Time elapsed: 0.011 s 0.18/0.37 % (20220)Instructions burned: 19 (million) 0.18/0.37 % (20220)------------------------------ 0.18/0.37 % (20220)------------------------------ 0.18/0.37 % (20217)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_20102 for (2399ds/2Mi) 0.18/0.37 % (20217)Instruction limit reached! 0.18/0.37 % (20217)------------------------------ 0.18/0.37 % (20217)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.37 % (20217)Termination reason: Unknown 0.18/0.37 % (20217)Termination phase: shuffling 0.18/0.37 0.18/0.37 % (20217)Memory used [KB]: 1023 0.18/0.37 % (20217)Time elapsed: 0.004 s 0.18/0.37 % (20217)Instructions burned: 2 (million) 0.18/0.37 % (20217)------------------------------ 0.18/0.37 % (20217)------------------------------ 0.18/0.37 % (20216)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_20102 for (2399ds/27Mi) 0.18/0.37 % (20218)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_20102 for (2399ds/2Mi) 0.18/0.37 % (20214)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_20102 for (2399ds/183Mi) 0.18/0.37 % (20218)Instruction limit reached! 0.18/0.37 % (20218)------------------------------ 0.18/0.37 % (20218)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.37 % (20218)Termination reason: Unknown 0.18/0.37 % (20218)Termination phase: shuffling 0.18/0.37 0.18/0.37 % (20218)Memory used [KB]: 1151 0.18/0.37 % (20218)Time elapsed: 0.004 s 0.18/0.37 % (20218)Instructions burned: 4 (million) 0.18/0.37 % (20218)------------------------------ 0.18/0.37 % (20218)------------------------------ 0.18/0.37 % (20219)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_20102 for (2399ds/275Mi) 0.18/0.38 % (20219)Refutation not found, incomplete strategy 0.18/0.38 % (20219)------------------------------ 0.18/0.38 % (20219)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.38 % (20219)Termination reason: Refutation not found, incomplete strategy 0.18/0.38 0.18/0.38 0.18/0.38 % (20219)Memory used [KB]: 5628 0.18/0.38 % (20219)Time elapsed: 0.007 s 0.18/0.38 % (20219)Instructions burned: 10 (million) 0.18/0.38 % (20219)------------------------------ 0.18/0.38 % (20219)------------------------------ 0.18/0.38 % (20221)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_20102 for (2399ds/3Mi) 0.18/0.38 % (20215)Instruction limit reached! 0.18/0.38 % (20215)------------------------------ 0.18/0.38 % (20215)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.38 % (20215)Termination reason: Unknown 0.18/0.38 % (20215)Termination phase: shuffling 0.18/0.38 0.18/0.38 % (20215)Memory used [KB]: 1151 0.18/0.38 % (20215)Time elapsed: 0.006 s 0.18/0.38 % (20215)Instructions burned: 4 (million) 0.18/0.38 % (20215)------------------------------ 0.18/0.38 % (20215)------------------------------ 0.18/0.38 % (20221)Instruction limit reached! 0.18/0.38 % (20221)------------------------------ 0.18/0.38 % (20221)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.38 % (20221)Termination reason: Unknown 0.18/0.38 % (20221)Termination phase: shuffling 0.18/0.38 0.18/0.38 % (20221)Memory used [KB]: 1151 0.18/0.38 % (20221)Time elapsed: 0.004 s 0.18/0.38 % (20221)Instructions burned: 4 (million) 0.18/0.38 % (20221)------------------------------ 0.18/0.38 % (20221)------------------------------ 0.18/0.38 % (20216)Instruction limit reached! 0.18/0.38 % (20216)------------------------------ 0.18/0.38 % (20216)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.38 % (20216)Termination reason: Unknown 0.18/0.38 % (20216)Termination phase: Saturation 0.18/0.38 0.18/0.38 % (20216)Memory used [KB]: 5756 0.18/0.38 % (20216)Time elapsed: 0.016 s 0.18/0.38 % (20216)Instructions burned: 29 (million) 0.18/0.38 % (20216)------------------------------ 0.18/0.38 % (20216)------------------------------ 0.18/0.40 % (20226)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_20102 for (2399ds/7Mi) 0.18/0.40 % (20226)Instruction limit reached! 0.18/0.40 % (20226)------------------------------ 0.18/0.40 % (20226)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.40 % (20226)Termination reason: Unknown 0.18/0.40 % (20226)Termination phase: SInE selection 0.18/0.40 0.18/0.40 % (20226)Memory used [KB]: 1151 0.18/0.40 % (20226)Time elapsed: 0.006 s 0.18/0.40 % (20226)Instructions burned: 7 (million) 0.18/0.40 % (20226)------------------------------ 0.18/0.40 % (20226)------------------------------ 0.18/0.41 % (20224)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_20102 for (2399ds/3Mi) 0.18/0.41 % (20222)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_20102 for (2399ds/37Mi) 0.18/0.41 % (20224)Instruction limit reached! 0.18/0.41 % (20224)------------------------------ 0.18/0.41 % (20224)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (20224)Termination reason: Unknown 0.18/0.41 % (20224)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (20224)Memory used [KB]: 1151 0.18/0.41 % (20224)Time elapsed: 0.005 s 0.18/0.41 % (20224)Instructions burned: 4 (million) 0.18/0.41 % (20224)------------------------------ 0.18/0.41 % (20224)------------------------------ 0.18/0.41 % (20225)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_20102 for (2399ds/1041Mi) 0.18/0.41 % (20223)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_20102 for (2399ds/15Mi) 0.18/0.41 % (20228)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_20102 for (2399ds/3Mi) 0.18/0.41 % (20228)Instruction limit reached! 0.18/0.41 % (20228)------------------------------ 0.18/0.41 % (20228)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (20228)Termination reason: Unknown 0.18/0.41 % (20228)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (20228)Memory used [KB]: 1151 0.18/0.41 % (20228)Time elapsed: 0.004 s 0.18/0.41 % (20228)Instructions burned: 4 (million) 0.18/0.41 % (20228)------------------------------ 0.18/0.41 % (20228)------------------------------ 0.18/0.42 % (20223)Instruction limit reached! 0.18/0.42 % (20223)------------------------------ 0.18/0.42 % (20223)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.42 % (20223)Termination reason: Unknown 0.18/0.42 % (20223)Termination phase: Saturation 0.18/0.42 0.18/0.42 % (20223)Memory used [KB]: 1151 0.18/0.42 % (20223)Time elapsed: 0.010 s 0.18/0.42 % (20223)Instructions burned: 15 (million) 0.18/0.42 % (20223)------------------------------ 0.18/0.42 % (20223)------------------------------ 0.18/0.42 % (20227)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_20102 for (2399ds/16Mi) 0.18/0.43 % (20227)Instruction limit reached! 0.18/0.43 % (20227)------------------------------ 0.18/0.43 % (20227)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.43 % (20227)Termination reason: Unknown 0.18/0.43 % (20227)Termination phase: Saturation 0.18/0.43 0.18/0.43 % (20227)Memory used [KB]: 5756 0.18/0.43 % (20227)Time elapsed: 0.010 s 0.18/0.43 % (20227)Instructions burned: 16 (million) 0.18/0.43 % (20227)------------------------------ 0.18/0.43 % (20227)------------------------------ 0.18/0.43 % (20230)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_20102 for (2399ds/7Mi) 0.18/0.43 % (20230)Instruction limit reached! 0.18/0.43 % (20230)------------------------------ 0.18/0.43 % (20230)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.43 % (20230)Termination reason: Unknown 0.18/0.43 % (20230)Termination phase: Property scanning 0.18/0.43 0.18/0.43 % (20230)Memory used [KB]: 1151 0.18/0.43 % (20230)Time elapsed: 0.005 s 0.18/0.43 % (20230)Instructions burned: 8 (million) 0.18/0.43 % (20230)------------------------------ 0.18/0.43 % (20230)------------------------------ 0.18/0.44 % (20222)Instruction limit reached! 0.18/0.44 % (20222)------------------------------ 0.18/0.44 % (20222)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.44 % (20222)Termination reason: Unknown 0.18/0.44 % (20222)Termination phase: Saturation 0.18/0.44 0.18/0.44 % (20222)Memory used [KB]: 5884 0.18/0.44 % (20222)Time elapsed: 0.051 s 0.18/0.44 % (20222)Instructions burned: 38 (million) 0.18/0.44 % (20222)------------------------------ 0.18/0.44 % (20222)------------------------------ 0.18/0.45 % (20233)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_20102 for (2399ds/18Mi) 0.18/0.45 % (20231)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_20102 for (2399ds/3Mi) 0.18/0.45 % (20231)Instruction limit reached! 0.18/0.45 % (20231)------------------------------ 0.18/0.45 % (20231)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.45 % (20231)Termination reason: Unknown 0.18/0.45 % (20231)Termination phase: shuffling 0.18/0.45 0.18/0.45 % (20231)Memory used [KB]: 1023 0.18/0.45 % (20231)Time elapsed: 0.004 s 0.18/0.45 % (20231)Instructions burned: 3 (million) 0.18/0.45 % (20231)------------------------------ 0.18/0.45 % (20231)------------------------------ 0.18/0.46 % (20232)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_20102 for (2399ds/4Mi) 0.18/0.46 % (20233)Instruction limit reached! 0.18/0.46 % (20233)------------------------------ 0.18/0.46 % (20233)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.46 % (20233)Termination reason: Unknown 0.18/0.46 % (20233)Termination phase: Saturation 0.18/0.46 0.18/0.46 % (20233)Memory used [KB]: 5756 0.18/0.46 % (20233)Time elapsed: 0.012 s 0.18/0.46 % (20233)Instructions burned: 18 (million) 0.18/0.46 % (20233)------------------------------ 0.18/0.46 % (20233)------------------------------ 0.18/0.46 % (20232)Instruction limit reached! 0.18/0.46 % (20232)------------------------------ 0.18/0.46 % (20232)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.46 % (20232)Termination reason: Unknown 0.18/0.46 % (20232)Termination phase: Property scanning 0.18/0.46 0.18/0.46 % (20232)Memory used [KB]: 1151 0.18/0.46 % (20232)Time elapsed: 0.005 s 0.18/0.46 % (20232)Instructions burned: 5 (million) 0.18/0.46 % (20232)------------------------------ 0.18/0.46 % (20232)------------------------------ 0.18/0.46 % (20234)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_20102 for (2399ds/710Mi) 0.18/0.46 % (20229)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_20102 for (2399ds/3Mi) 0.18/0.46 % (20229)Instruction limit reached! 0.18/0.46 % (20229)------------------------------ 0.18/0.46 % (20229)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.46 % (20229)Termination reason: Unknown 0.18/0.46 % (20229)Termination phase: shuffling 0.18/0.46 0.18/0.46 % (20229)Memory used [KB]: 1023 0.18/0.46 % (20229)Time elapsed: 0.003 s 0.18/0.46 % (20229)Instructions burned: 3 (million) 0.18/0.46 % (20229)------------------------------ 0.18/0.46 % (20229)------------------------------ 0.18/0.48 % (20238)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_20102 for (2398ds/5Mi) 0.18/0.48 % (20238)Instruction limit reached! 0.18/0.48 % (20238)------------------------------ 0.18/0.48 % (20238)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.48 % (20238)Termination reason: Unknown 0.18/0.48 % (20238)Termination phase: Property scanning 0.18/0.48 0.18/0.48 % (20238)Memory used [KB]: 1151 0.18/0.48 % (20238)Time elapsed: 0.005 s 0.18/0.48 % (20238)Instructions burned: 6 (million) 0.18/0.48 % (20238)------------------------------ 0.18/0.48 % (20238)------------------------------ 0.18/0.49 % (20236)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_20102 for (2398ds/902Mi) 0.18/0.49 % (20235)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_20102 for (2398ds/6Mi) 0.18/0.49 % (20236)Refutation not found, incomplete strategy 0.18/0.49 % (20236)------------------------------ 0.18/0.49 % (20236)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.49 % (20236)Termination reason: Refutation not found, incomplete strategy 0.18/0.49 0.18/0.49 0.18/0.49 % (20236)Memory used [KB]: 5628 0.18/0.49 % (20236)Time elapsed: 0.029 s 0.18/0.49 % (20236)Instructions burned: 11 (million) 0.18/0.49 % (20236)------------------------------ 0.18/0.49 % (20236)------------------------------ 0.18/0.49 % (20237)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_20102 for (2398ds/21Mi) 0.18/0.50 % (20235)Instruction limit reached! 0.18/0.50 % (20235)------------------------------ 0.18/0.50 % (20235)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.50 % (20235)Termination reason: Unknown 0.18/0.50 % (20235)Termination phase: Property scanning 0.18/0.50 0.18/0.50 % (20235)Memory used [KB]: 1151 0.18/0.50 % (20235)Time elapsed: 0.005 s 0.18/0.50 % (20235)Instructions burned: 6 (million) 0.18/0.50 % (20235)------------------------------ 0.18/0.50 % (20235)------------------------------ 0.18/0.50 % (20214)Instruction limit reached! 0.18/0.50 % (20214)------------------------------ 0.18/0.50 % (20214)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.50 % (20214)Termination reason: Unknown 0.18/0.50 % (20214)Termination phase: Saturation 0.18/0.50 0.18/0.50 % (20214)Memory used [KB]: 7291 0.18/0.50 % (20214)Time elapsed: 0.132 s 0.18/0.50 % (20214)Instructions burned: 183 (million) 0.18/0.50 % (20214)------------------------------ 0.18/0.50 % (20214)------------------------------ 0.18/0.50 % (20237)Instruction limit reached! 0.18/0.50 % (20237)------------------------------ 0.18/0.50 % (20237)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.50 % (20237)Termination reason: Unknown 0.18/0.50 % (20237)Termination phase: Saturation 0.18/0.50 0.18/0.50 % (20237)Memory used [KB]: 5756 0.18/0.50 % (20237)Time elapsed: 0.040 s 0.18/0.50 % (20237)Instructions burned: 21 (million) 0.18/0.50 % (20237)------------------------------ 0.18/0.50 % (20237)------------------------------ 0.18/0.51 % (20242)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_20102 for (2398ds/19Mi) 0.18/0.52 % (20240)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_20102 for (2398ds/377Mi) 0.18/0.52 % (20242)Refutation not found, incomplete strategy 0.18/0.52 % (20242)------------------------------ 0.18/0.52 % (20242)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.52 % (20242)Termination reason: Refutation not found, incomplete strategy 0.18/0.52 0.18/0.52 0.18/0.52 % (20242)Memory used [KB]: 5628 0.18/0.52 % (20242)Time elapsed: 0.008 s 0.18/0.52 % (20242)Instructions burned: 12 (million) 0.18/0.52 % (20242)------------------------------ 0.18/0.52 % (20242)------------------------------ 0.18/0.55 % (20239)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_20102 for (2398ds/6Mi) 0.18/0.55 % (20241)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_20102 for (2398ds/779Mi) 0.18/0.55 % (20239)Instruction limit reached! 0.18/0.55 % (20239)------------------------------ 0.18/0.55 % (20239)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.55 % (20239)Termination reason: Unknown 0.18/0.55 % (20239)Termination phase: Property scanning 0.18/0.55 0.18/0.55 % (20239)Memory used [KB]: 1151 0.18/0.55 % (20239)Time elapsed: 0.005 s 0.18/0.55 % (20239)Instructions burned: 6 (million) 0.18/0.55 % (20239)------------------------------ 0.18/0.55 % (20239)------------------------------ 0.95/0.56 % (20225)First to succeed. 0.95/0.56 % (20244)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_20102 for (2398ds/17Mi) 0.95/0.57 % (20243)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_20102 for (2398ds/879Mi) 1.00/0.59 % (20225)Refutation found. Thanks to Tanya! 1.00/0.59 % SZS status Theorem for E---3.1_20102 1.00/0.59 % SZS output start Proof for E---3.1_20102 1.00/0.59 thf(type_def_5, type, mu: $tType). 1.00/0.59 thf(type_def_7, type, reg: $tType). 1.00/0.59 thf(func_def_0, type, mu: $tType). 1.00/0.59 thf(func_def_1, type, meq_ind: mu > mu > $i > $o). 1.00/0.59 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_4, type, mnot: ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o). 1.00/0.59 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o). 1.00/0.59 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o). 1.00/0.59 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o). 1.00/0.59 thf(func_def_15, type, mtrue: $i > $o). 1.00/0.59 thf(func_def_16, type, mfalse: $i > $o). 1.00/0.59 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o). 1.00/0.59 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_21, type, mserial: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o). 1.00/0.59 thf(func_def_29, type, mvalid: ($i > $o) > $o). 1.00/0.59 thf(func_def_30, type, minvalid: ($i > $o) > $o). 1.00/0.59 thf(func_def_31, type, msatisfiable: ($i > $o) > $o). 1.00/0.59 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o). 1.00/0.59 thf(func_def_33, type, reg: $tType). 1.00/0.59 thf(func_def_34, type, c: reg > reg > $o). 1.00/0.59 thf(func_def_35, type, dc: reg > reg > $o). 1.00/0.59 thf(func_def_36, type, p: reg > reg > $o). 1.00/0.59 thf(func_def_37, type, eq: reg > reg > $o). 1.00/0.59 thf(func_def_38, type, o: reg > reg > $o). 1.00/0.59 thf(func_def_39, type, po: reg > reg > $o). 1.00/0.59 thf(func_def_40, type, ec: reg > reg > $o). 1.00/0.59 thf(func_def_41, type, pp: reg > reg > $o). 1.00/0.59 thf(func_def_42, type, tpp: reg > reg > $o). 1.00/0.59 thf(func_def_43, type, ntpp: reg > reg > $o). 1.00/0.59 thf(func_def_44, type, catalunya: reg). 1.00/0.59 thf(func_def_45, type, france: reg). 1.00/0.59 thf(func_def_46, type, spain: reg). 1.00/0.59 thf(func_def_47, type, paris: reg). 1.00/0.59 thf(func_def_48, type, a: $i > $i > $o). 1.00/0.59 thf(func_def_49, type, fool: $i > $i > $o). 1.00/0.59 thf(func_def_66, type, ph1: !>[X0: $tType]:(X0)). 1.00/0.59 thf(func_def_70, type, sK5: reg). 1.00/0.59 thf(func_def_71, type, sK6: reg). 1.00/0.59 thf(func_def_72, type, sK7: $i > $i > $i). 1.00/0.59 thf(func_def_73, type, sK8: reg). 1.00/0.59 thf(func_def_74, type, sK9: reg). 1.00/0.59 thf(func_def_75, type, sK10: reg). 1.00/0.59 thf(func_def_76, type, sK11: reg). 1.00/0.59 thf(func_def_77, type, sK12: reg). 1.00/0.59 thf(func_def_78, type, sK13: reg). 1.00/0.59 thf(func_def_79, type, sK14: reg). 1.00/0.59 thf(func_def_80, type, sK15: reg). 1.00/0.59 thf(func_def_81, type, sK16: reg). 1.00/0.59 thf(func_def_82, type, sK17: reg). 1.00/0.59 thf(f1603,plain,( 1.00/0.59 $false), 1.00/0.59 inference(avatar_sat_refutation,[],[f337,f409,f612,f1571,f1599])). 1.00/0.59 thf(f1599,plain,( 1.00/0.59 spl0_5 | ~spl0_2 | ~spl0_4), 1.00/0.59 inference(avatar_split_clause,[],[f1598,f405,f335,f545])). 1.00/0.59 thf(f545,plain,( 1.00/0.59 spl0_5 <=> ($false = (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))))), 1.00/0.59 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])). 1.00/0.59 thf(f335,plain,( 1.00/0.59 spl0_2 <=> ($true = ((c @ spain @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))), 1.00/0.59 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 1.00/0.59 thf(f405,plain,( 1.00/0.59 spl0_4 <=> ((((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))) = $true)), 1.00/0.59 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])). 1.00/0.59 thf(f1598,plain,( 1.00/0.59 ($false = (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))))) | (~spl0_2 | ~spl0_4)), 1.00/0.59 inference(boolean_simplification,[],[f1597])). 1.00/0.59 thf(f1597,plain,( 1.00/0.59 (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))) & $true) = $false) | (~spl0_2 | ~spl0_4)), 1.00/0.59 inference(boolean_simplification,[],[f1596])). 1.00/0.59 thf(f1596,plain,( 1.00/0.59 (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))) & (~ $false)) = $false) | (~spl0_2 | ~spl0_4)), 1.00/0.59 inference(forward_demodulation,[],[f1595,f657])). 1.00/0.59 thf(f657,plain,( 1.00/0.59 ($false = (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))) | ~spl0_2), 1.00/0.59 inference(not_proxy_clausification,[],[f621])). 1.00/0.59 thf(f621,plain,( 1.00/0.59 ($true = (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))) | ~spl0_2), 1.00/0.59 inference(binary_proxy_clausification,[],[f336])). 1.00/0.59 thf(f336,plain,( 1.00/0.59 ($true = ((c @ spain @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))) | ~spl0_2), 1.00/0.59 inference(avatar_component_clause,[],[f335])). 1.00/0.59 thf(f1595,plain,( 1.00/0.59 (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))) = $false) | (~spl0_2 | ~spl0_4)), 1.00/0.59 inference(boolean_simplification,[],[f1594])). 1.00/0.59 thf(f1594,plain,( 1.00/0.59 ((($true & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))))) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))) = $false) | (~spl0_2 | ~spl0_4)), 1.00/0.59 inference(forward_demodulation,[],[f634,f960])). 1.00/0.59 thf(f960,plain,( 1.00/0.59 ((c @ spain @ paris) = $true)), 1.00/0.59 inference(boolean_simplification,[],[f958])). 1.00/0.59 thf(f958,plain,( 1.00/0.59 (($true => (c @ spain @ paris)) = $true)), 1.00/0.59 inference(superposition,[],[f231,f920])). 1.00/0.59 thf(f920,plain,( 1.00/0.59 ($true = (c @ paris @ spain))), 1.00/0.59 inference(boolean_simplification,[],[f909])). 1.00/0.59 thf(f909,plain,( 1.00/0.59 ($true = ($true => (c @ paris @ spain)))), 1.00/0.59 inference(superposition,[],[f899,f311])). 1.00/0.59 thf(f311,plain,( 1.00/0.59 ($true = (c @ paris @ catalunya))), 1.00/0.59 inference(boolean_simplification,[],[f309])). 1.00/0.59 thf(f309,plain,( 1.00/0.59 ($true = ($true => (c @ paris @ catalunya)))), 1.00/0.59 inference(superposition,[],[f305,f292])). 1.00/0.59 thf(f292,plain,( 1.00/0.59 ((c @ paris @ sK5) = $true)), 1.00/0.59 inference(boolean_simplification,[],[f289])). 1.00/0.59 thf(f289,plain,( 1.00/0.59 (($true => (c @ paris @ sK5)) = $true)), 1.00/0.59 inference(superposition,[],[f231,f287])). 1.00/0.59 thf(f287,plain,( 1.00/0.59 ($true = (c @ sK5 @ paris))), 1.00/0.59 inference(boolean_simplification,[],[f285])). 1.00/0.59 thf(f285,plain,( 1.00/0.59 ($true = ($true => (c @ sK5 @ paris)))), 1.00/0.59 inference(superposition,[],[f282,f227])). 1.00/0.59 thf(f227,plain,( 1.00/0.59 ( ! [X1 : reg] : (((c @ X1 @ X1) = $true)) )), 1.00/0.59 inference(beta_eta_normalization,[],[f226])). 1.00/0.59 thf(f226,plain,( 1.00/0.59 ( ! [X1 : reg] : ((((^[Y0 : reg]: (c @ Y0 @ Y0)) @ X1) = $true)) )), 1.00/0.59 inference(pi_clausification,[],[f151])). 1.00/0.59 thf(f151,plain,( 1.00/0.59 ($true = (!! @ reg @ (^[Y0 : reg]: (c @ Y0 @ Y0))))), 1.00/0.59 inference(cnf_transformation,[],[f112])). 1.00/0.59 thf(f112,plain,( 1.00/0.59 ($true = (!! @ reg @ (^[Y0 : reg]: (c @ Y0 @ Y0))))), 1.00/0.59 inference(fool_elimination,[],[f111])). 1.00/0.59 thf(f111,plain,( 1.00/0.59 ! [X0 : reg] : (c @ X0 @ X0)), 1.00/0.59 inference(rectify,[],[f41])). 1.00/0.59 thf(f41,axiom,( 1.00/0.59 ! [X0 : reg] : (c @ X0 @ X0)), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',c_reflexive)). 1.00/0.59 thf(f282,plain,( 1.00/0.59 ( ! [X1 : reg] : ((((c @ X1 @ sK5) => (c @ X1 @ paris)) = $true)) )), 1.00/0.59 inference(beta_eta_normalization,[],[f281])). 1.00/0.59 thf(f281,plain,( 1.00/0.59 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ sK5) => (c @ Y0 @ paris))) @ X1))) )), 1.00/0.59 inference(pi_clausification,[],[f278])). 1.00/0.59 thf(f278,plain,( 1.00/0.59 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK5) => (c @ Y0 @ paris)))))), 1.00/0.59 inference(not_proxy_clausification,[],[f277])). 1.00/0.59 thf(f277,plain,( 1.00/0.59 ($false = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK5) => (c @ Y0 @ paris))))))), 1.00/0.59 inference(boolean_simplification,[],[f276])). 1.00/0.59 thf(f276,plain,( 1.00/0.59 (($true => (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK5) => (c @ Y0 @ paris)))))) = $false)), 1.00/0.59 inference(backward_demodulation,[],[f273,f275])). 1.00/0.59 thf(f275,plain,( 1.00/0.59 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK5) => (c @ Y0 @ catalunya)))) = $true)), 1.00/0.59 inference(binary_proxy_clausification,[],[f273])). 1.00/0.59 thf(f273,plain,( 1.00/0.59 (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK5) => (c @ Y0 @ catalunya)))) => (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK5) => (c @ Y0 @ paris)))))) = $false)), 1.00/0.59 inference(beta_eta_normalization,[],[f272])). 1.00/0.59 thf(f272,plain,( 1.00/0.59 (((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) => (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))) @ sK5) = $false)), 1.00/0.59 inference(sigma_clausification,[],[f257])). 1.00/0.59 thf(f257,plain,( 1.00/0.59 ($false = (!! @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) => (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))))), 1.00/0.59 inference(boolean_simplification,[],[f256])). 1.00/0.59 thf(f256,plain,( 1.00/0.59 (($false | (!! @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) => (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))))) = $false)), 1.00/0.59 inference(backward_demodulation,[],[f253,f255])). 1.00/0.59 thf(f255,plain,( 1.00/0.59 ((~ (a @ sK2 @ sK3)) = $false)), 1.00/0.59 inference(binary_proxy_clausification,[],[f253])). 1.00/0.59 thf(f253,plain,( 1.00/0.59 (((~ (a @ sK2 @ sK3)) | (!! @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))) => (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))))) = $false)), 1.00/0.59 inference(beta_eta_normalization,[],[f252])). 1.00/0.59 thf(f252,plain,( 1.00/0.59 (((^[Y0 : $i]: ((~ (a @ sK2 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) => (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))))))))) @ sK3) = $false)), 1.00/0.59 inference(sigma_clausification,[],[f251])). 1.00/0.59 thf(f251,plain,( 1.00/0.59 ((!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK2 @ Y0)) | (!! @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) => (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))))) = $false)), 1.00/0.59 inference(beta_eta_normalization,[],[f250])). 1.00/0.59 thf(f250,plain,( 1.00/0.59 (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) => (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))))))))))) @ sK2) = $false)), 1.00/0.59 inference(sigma_clausification,[],[f247])). 1.00/0.59 thf(f247,plain,( 1.00/0.59 ($false = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) => (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))))))))))), 1.00/0.59 inference(not_proxy_clausification,[],[f224])). 1.00/0.59 thf(f224,plain,( 1.00/0.59 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (!! @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) => (~ (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))))))))))))))), 1.00/0.59 inference(beta_eta_normalization,[],[f217])). 1.00/0.59 thf(f217,plain,( 1.00/0.59 ($true = (~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ catalunya) => (~ ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ paris))))))))))), 1.00/0.59 inference(definition_unfolding,[],[f192,f160,f178,f185,f185])). 1.00/0.59 thf(f185,plain,( 1.00/0.59 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))), 1.00/0.59 inference(cnf_transformation,[],[f65])). 1.00/0.59 thf(f65,plain,( 1.00/0.59 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))), 1.00/0.59 inference(fool_elimination,[],[f64])). 1.00/0.59 thf(f64,plain,( 1.00/0.59 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))), 1.00/0.59 inference(rectify,[],[f33])). 1.00/0.59 thf(f33,axiom,( 1.00/0.59 (p = (^[X0 : reg, X1 : reg] : (! [X11 : reg] : ((c @ X11 @ X0) => (c @ X11 @ X1)))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',p)). 1.00/0.59 thf(f178,plain,( 1.00/0.59 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))), 1.00/0.59 inference(cnf_transformation,[],[f57])). 1.00/0.59 thf(f57,plain,( 1.00/0.59 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))), 1.00/0.59 inference(fool_elimination,[],[f56])). 1.00/0.59 thf(f56,plain,( 1.00/0.59 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))))), 1.00/0.59 inference(rectify,[],[f16])). 1.00/0.59 thf(f16,axiom,( 1.00/0.59 (mbox = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',mbox)). 1.00/0.59 thf(f160,plain,( 1.00/0.59 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 1.00/0.59 inference(cnf_transformation,[],[f135])). 1.00/0.59 thf(f135,plain,( 1.00/0.59 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 1.00/0.59 inference(fool_elimination,[],[f134])). 1.00/0.59 thf(f134,plain,( 1.00/0.59 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))), 1.00/0.59 inference(rectify,[],[f28])). 1.00/0.59 thf(f28,axiom,( 1.00/0.59 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',mvalid)). 1.00/0.59 thf(f192,plain,( 1.00/0.59 ($true = (~ (mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: ((p @ Y1 @ catalunya) => (~ (p @ Y1 @ paris))))))))))), 1.00/0.59 inference(cnf_transformation,[],[f133])). 1.00/0.59 thf(f133,plain,( 1.00/0.59 ($true = (~ (mvalid @ (mbox @ a @ (^[Y0 : $i]: (!! @ reg @ (^[Y1 : reg]: ((p @ Y1 @ catalunya) => (~ (p @ Y1 @ paris))))))))))), 1.00/0.59 inference(fool_elimination,[],[f132])). 1.00/0.59 thf(f132,plain,( 1.00/0.59 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X1 : reg] : ((p @ X1 @ catalunya) => ~(p @ X1 @ paris))))))), 1.00/0.59 inference(rectify,[],[f49])). 1.00/0.59 thf(f49,negated_conjecture,( 1.00/0.59 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X11 : reg] : ((p @ X11 @ catalunya) => ~(p @ X11 @ paris))))))), 1.00/0.59 inference(negated_conjecture,[],[f48])). 1.00/0.59 thf(f48,conjecture,( 1.00/0.59 (mvalid @ (mbox @ a @ (^[X0 : $i] : (! [X11 : reg] : ((p @ X11 @ catalunya) => ~(p @ X11 @ paris))))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',con)). 1.00/0.59 thf(f305,plain,( 1.00/0.59 ( ! [X1 : reg] : ((((c @ X1 @ sK5) => (c @ X1 @ catalunya)) = $true)) )), 1.00/0.59 inference(beta_eta_normalization,[],[f304])). 1.00/0.59 thf(f304,plain,( 1.00/0.59 ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ sK5) => (c @ Y0 @ catalunya))) @ X1) = $true)) )), 1.00/0.59 inference(pi_clausification,[],[f275])). 1.00/0.59 thf(f899,plain,( 1.00/0.59 ( ! [X1 : reg] : (($true = ((c @ X1 @ catalunya) => (c @ X1 @ spain)))) )), 1.00/0.59 inference(beta_eta_normalization,[],[f896])). 1.00/0.59 thf(f896,plain,( 1.00/0.59 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X1))) )), 1.00/0.59 inference(pi_clausification,[],[f889])). 1.00/0.59 thf(f889,plain,( 1.00/0.59 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))), 1.00/0.59 inference(boolean_simplification,[],[f888])). 1.00/0.59 thf(f888,plain,( 1.00/0.59 ($true = ($true & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))), 1.00/0.59 inference(backward_demodulation,[],[f824,f887])). 1.00/0.59 thf(f887,plain,( 1.00/0.59 ($true = (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))))), 1.00/0.59 inference(binary_proxy_clausification,[],[f824])). 1.00/0.59 thf(f824,plain,( 1.00/0.59 (((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))) = $true)), 1.00/0.59 inference(binary_proxy_clausification,[],[f374])). 1.00/0.59 thf(f374,plain,( 1.00/0.59 ($true = ((?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya))))))))) & ((c @ Y0 @ spain) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))))), 1.00/0.59 inference(boolean_simplification,[],[f373])). 1.00/0.59 thf(f373,plain,( 1.00/0.59 (($false | ((?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya))))))))) & ((c @ Y0 @ spain) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))) = $true)), 1.00/0.59 inference(boolean_simplification,[],[f370])). 1.00/0.59 thf(f370,plain,( 1.00/0.59 ($true = ((~ $true) | ((?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya))))))))) & ((c @ Y0 @ spain) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))))), 1.00/0.59 inference(superposition,[],[f359,f267])). 1.00/0.59 thf(f267,plain,( 1.00/0.59 ($true = (a @ sK2 @ sK4))), 1.00/0.59 inference(not_proxy_clausification,[],[f264])). 1.00/0.59 thf(f264,plain,( 1.00/0.59 ((~ (a @ sK2 @ sK4)) = $false)), 1.00/0.59 inference(beta_eta_normalization,[],[f263])). 1.00/0.59 thf(f263,plain,( 1.00/0.59 (((^[Y0 : $i]: (~ (a @ sK2 @ Y0))) @ sK4) = $false)), 1.00/0.59 inference(sigma_clausification,[],[f259])). 1.00/0.59 thf(f259,plain,( 1.00/0.59 ((!! @ $i @ (^[Y0 : $i]: (~ (a @ sK2 @ Y0)))) = $false)), 1.00/0.59 inference(boolean_simplification,[],[f258])). 1.00/0.59 thf(f258,plain,( 1.00/0.59 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK2 @ Y0)) | $false))))), 1.00/0.59 inference(backward_demodulation,[],[f251,f257])). 1.00/0.59 thf(f359,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : ((((~ (a @ X1 @ X2)) | ((?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ catalunya) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya))))))))) & ((c @ Y0 @ spain) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))) = $true)) )), 1.00/0.59 inference(beta_eta_normalization,[],[f358])). 1.00/0.59 thf(f358,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | ((?? @ reg @ (^[Y1 : reg]: (((c @ Y1 @ catalunya) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya))))))))) & ((c @ Y1 @ spain) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))))))))) & ((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))))))) @ X2) = $true)) )), 1.00/0.59 inference(pi_clausification,[],[f353])). 1.00/0.59 thf(f353,plain,( 1.00/0.59 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | ((?? @ reg @ (^[Y1 : reg]: (((c @ Y1 @ catalunya) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya))))))))) & ((c @ Y1 @ spain) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))))))))) & ((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain))))))))))) )), 1.00/0.59 inference(beta_eta_normalization,[],[f352])). 1.00/0.59 thf(f352,plain,( 1.00/0.59 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | ((?? @ reg @ (^[Y2 : reg]: (((c @ Y2 @ catalunya) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya))))))))) & ((c @ Y2 @ spain) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))))))))))) & ((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))))))))) @ X1))) )), 1.00/0.59 inference(pi_clausification,[],[f219])). 1.00/0.59 thf(f219,plain,( 1.00/0.59 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | ((?? @ reg @ (^[Y2 : reg]: (((c @ Y2 @ catalunya) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya))))))))) & ((c @ Y2 @ spain) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))))))))))) & ((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain))))))))))))), 1.00/0.59 inference(beta_eta_normalization,[],[f215])). 1.00/0.59 thf(f215,plain,( 1.00/0.59 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2)))) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4))))) @ Y1 @ Y2))))) @ catalunya @ spain)))) = $true)), 1.00/0.59 inference(definition_unfolding,[],[f180,f160,f178,f210])). 1.00/0.59 thf(f210,plain,( 1.00/0.59 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((c @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((c @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)))))) @ Y2 @ Y1)))) & ((^[Y2 : reg]: ((^[Y3 : reg]: ((~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)) & ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3))))) @ Y0 @ Y1))))))), 1.00/0.59 inference(definition_unfolding,[],[f173,f208,f208,f209])). 1.00/0.59 thf(f209,plain,( 1.00/0.59 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ Y0)) & ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y0 @ Y1))))))), 1.00/0.59 inference(definition_unfolding,[],[f156,f185,f185])). 1.00/0.59 thf(f156,plain,( 1.00/0.59 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (p @ Y1 @ Y0)) & (p @ Y0 @ Y1))))))), 1.00/0.59 inference(cnf_transformation,[],[f88])). 1.00/0.59 thf(f88,plain,( 1.00/0.59 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (p @ Y1 @ Y0)) & (p @ Y0 @ Y1))))))), 1.00/0.59 inference(fool_elimination,[],[f87])). 1.00/0.59 thf(f87,plain,( 1.00/0.59 ((^[X0 : reg, X1 : reg] : ((p @ X0 @ X1) & ~(p @ X1 @ X0))) = pp)), 1.00/0.59 inference(rectify,[],[f38])). 1.00/0.59 thf(f38,axiom,( 1.00/0.59 ((^[X0 : reg, X1 : reg] : ((p @ X0 @ X1) & ~(p @ X1 @ X0))) = pp)), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',pp)). 1.00/0.59 thf(f208,plain,( 1.00/0.59 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ reg @ (^[Y4 : reg]: (((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y0 @ Y1)))))))), 1.00/0.59 inference(definition_unfolding,[],[f189,f206])). 1.00/0.59 thf(f206,plain,( 1.00/0.59 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1))))))))), 1.00/0.59 inference(definition_unfolding,[],[f177,f185,f185])). 1.00/0.59 thf(f177,plain,( 1.00/0.59 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))), 1.00/0.59 inference(cnf_transformation,[],[f76])). 1.00/0.59 thf(f76,plain,( 1.00/0.59 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))), 1.00/0.59 inference(fool_elimination,[],[f75])). 1.00/0.59 thf(f75,plain,( 1.00/0.59 ((^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X1) & (p @ X2 @ X0)))) = o)), 1.00/0.59 inference(rectify,[],[f35])). 1.00/0.59 thf(f35,axiom,( 1.00/0.59 ((^[X0 : reg, X1 : reg] : (? [X11 : reg] : ((p @ X11 @ X1) & (p @ X11 @ X0)))) = o)), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',o)). 1.00/0.59 thf(f189,plain,( 1.00/0.59 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))), 1.00/0.59 inference(cnf_transformation,[],[f82])). 1.00/0.59 thf(f82,plain,( 1.00/0.59 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((c @ Y0 @ Y1) & (~ (o @ Y0 @ Y1)))))))), 1.00/0.59 inference(fool_elimination,[],[f81])). 1.00/0.59 thf(f81,plain,( 1.00/0.59 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))), 1.00/0.59 inference(rectify,[],[f37])). 1.00/0.59 thf(f37,axiom,( 1.00/0.59 (ec = (^[X0 : reg, X1 : reg] : (~(o @ X0 @ X1) & (c @ X0 @ X1))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',ec)). 1.00/0.59 thf(f173,plain,( 1.00/0.59 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))) & (pp @ Y0 @ Y1))))))), 1.00/0.59 inference(cnf_transformation,[],[f114])). 1.00/0.59 thf(f114,plain,( 1.00/0.59 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))) & (pp @ Y0 @ Y1))))))), 1.00/0.59 inference(fool_elimination,[],[f113])). 1.00/0.59 thf(f113,plain,( 1.00/0.59 ((^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)))) = tpp)), 1.00/0.59 inference(rectify,[],[f39])). 1.00/0.59 thf(f39,axiom,( 1.00/0.59 ((^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ? [X11 : reg] : ((ec @ X11 @ X1) & (ec @ X11 @ X0)))) = tpp)), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',tpp)). 1.00/0.59 thf(f180,plain,( 1.00/0.59 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))))), 1.00/0.59 inference(cnf_transformation,[],[f55])). 1.00/0.59 thf(f55,plain,( 1.00/0.59 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))))), 1.00/0.59 inference(fool_elimination,[],[f54])). 1.00/0.59 thf(f54,plain,( 1.00/0.59 (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))), 1.00/0.59 inference(rectify,[],[f47])). 1.00/0.59 thf(f47,axiom,( 1.00/0.59 (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',ax1)). 1.00/0.59 thf(f231,plain,( 1.00/0.59 ( ! [X2 : reg,X1 : reg] : (($true = ((c @ X2 @ X1) => (c @ X1 @ X2)))) )), 1.00/0.59 inference(beta_eta_normalization,[],[f230])). 1.00/0.59 thf(f230,plain,( 1.00/0.59 ( ! [X2 : reg,X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ X1 @ Y0))) @ X2))) )), 1.00/0.59 inference(pi_clausification,[],[f229])). 1.00/0.59 thf(f229,plain,( 1.00/0.59 ( ! [X1 : reg] : (($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ X1 @ Y0)))))) )), 1.00/0.59 inference(beta_eta_normalization,[],[f228])). 1.00/0.59 thf(f228,plain,( 1.00/0.59 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y0 @ Y1))))) @ X1))) )), 1.00/0.59 inference(pi_clausification,[],[f167])). 1.00/0.59 thf(f167,plain,( 1.00/0.59 ($true = (!! @ reg @ (^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y0 @ Y1)))))))), 1.00/0.59 inference(cnf_transformation,[],[f125])). 1.00/0.59 thf(f125,plain,( 1.00/0.59 ($true = (!! @ reg @ (^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y0 @ Y1)))))))), 1.00/0.59 inference(fool_elimination,[],[f124])). 1.00/0.59 thf(f124,plain,( 1.00/0.59 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))), 1.00/0.59 inference(rectify,[],[f42])). 1.00/0.59 thf(f42,axiom,( 1.00/0.59 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',c_symmetric)). 1.00/0.59 thf(f634,plain,( 1.00/0.59 ((((c @ spain @ paris) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))))) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))) = $false) | (~spl0_2 | ~spl0_4)), 1.00/0.59 inference(boolean_simplification,[],[f629])). 1.00/0.59 thf(f629,plain,( 1.00/0.59 ((((c @ spain @ paris) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))))) & ($true & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))) = $false) | (~spl0_2 | ~spl0_4)), 1.00/0.59 inference(superposition,[],[f431,f626])). 1.00/0.59 thf(f626,plain,( 1.00/0.59 ($true = (c @ spain @ france)) | ~spl0_2), 1.00/0.59 inference(boolean_simplification,[],[f625])). 1.00/0.59 thf(f625,plain,( 1.00/0.59 ($true = ((c @ spain @ france) & $true)) | ~spl0_2), 1.00/0.59 inference(backward_demodulation,[],[f336,f621])). 1.00/0.59 thf(f431,plain,( 1.00/0.59 ( ! [X1 : reg] : (((((c @ X1 @ paris) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ X1)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))))) & ((c @ X1 @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ X1)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))) = $false)) ) | ~spl0_4), 1.00/0.59 inference(beta_eta_normalization,[],[f430])). 1.00/0.59 thf(f430,plain,( 1.00/0.59 ( ! [X1 : reg] : ((((^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))) @ X1) = $false)) ) | ~spl0_4), 1.00/0.59 inference(pi_clausification,[],[f423])). 1.00/0.59 thf(f423,plain,( 1.00/0.59 ((?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))) = $false) | ~spl0_4), 1.00/0.59 inference(not_proxy_clausification,[],[f418])). 1.00/0.59 thf(f418,plain,( 1.00/0.59 ($true = (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))) | ~spl0_4), 1.00/0.59 inference(boolean_simplification,[],[f417])). 1.00/0.59 thf(f417,plain,( 1.00/0.59 (($true & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))) = $true) | ~spl0_4), 1.00/0.59 inference(backward_demodulation,[],[f406,f416])). 1.00/0.59 thf(f416,plain,( 1.00/0.59 (((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) = $true) | ~spl0_4), 1.00/0.59 inference(binary_proxy_clausification,[],[f406])). 1.00/0.59 thf(f406,plain,( 1.00/0.59 ((((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))) = $true) | ~spl0_4), 1.00/0.59 inference(avatar_component_clause,[],[f405])). 1.00/0.59 thf(f1571,plain,( 1.00/0.59 ~spl0_2 | ~spl0_4 | ~spl0_5), 1.00/0.59 inference(avatar_contradiction_clause,[],[f1570])). 1.00/0.59 thf(f1570,plain,( 1.00/0.59 $false | (~spl0_2 | ~spl0_4 | ~spl0_5)), 1.00/0.59 inference(trivial_inequality_removal,[],[f1569])). 1.00/0.59 thf(f1569,plain,( 1.00/0.59 ($true = $false) | (~spl0_2 | ~spl0_4 | ~spl0_5)), 1.00/0.59 inference(boolean_simplification,[],[f1568])). 1.00/0.59 thf(f1568,plain,( 1.00/0.59 ((~ $true) = $true) | (~spl0_2 | ~spl0_4 | ~spl0_5)), 1.00/0.59 inference(backward_demodulation,[],[f1504,f1567])). 1.00/0.59 thf(f1567,plain,( 1.00/0.59 ($true = (c @ sK15 @ paris)) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(boolean_simplification,[],[f1557])). 1.00/0.59 thf(f1557,plain,( 1.00/0.59 ($true = ($true => (c @ sK15 @ paris))) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(superposition,[],[f1420,f1486])). 1.00/0.59 thf(f1486,plain,( 1.00/0.59 ((c @ sK15 @ sK12) = $true) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(binary_proxy_clausification,[],[f1476])). 1.00/0.59 thf(f1476,plain,( 1.00/0.59 ($false = ((c @ sK15 @ sK12) => (c @ sK15 @ france))) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(beta_eta_normalization,[],[f1473])). 1.00/0.59 thf(f1473,plain,( 1.00/0.59 ($false = ((^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ france))) @ sK15)) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(sigma_clausification,[],[f1127])). 1.00/0.59 thf(f1127,plain,( 1.00/0.59 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ france)))) = $false) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(boolean_simplification,[],[f1126])). 1.00/0.59 thf(f1126,plain,( 1.00/0.59 (($true & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ france))))) = $false) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(superposition,[],[f677,f956])). 1.00/0.59 thf(f956,plain,( 1.00/0.59 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ spain))))) | ~spl0_5), 1.00/0.59 inference(boolean_simplification,[],[f955])). 1.00/0.59 thf(f955,plain,( 1.00/0.59 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ spain)))) & $true)) | ~spl0_5), 1.00/0.59 inference(backward_demodulation,[],[f943,f953])). 1.00/0.59 thf(f953,plain,( 1.00/0.59 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ paris)))) = $true) | ~spl0_5), 1.00/0.59 inference(binary_proxy_clausification,[],[f943])). 1.00/0.59 thf(f943,plain,( 1.00/0.59 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ spain)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ paris)))))) | ~spl0_5), 1.00/0.59 inference(beta_eta_normalization,[],[f941])). 1.00/0.59 thf(f941,plain,( 1.00/0.59 ($true = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))) @ sK12)) | ~spl0_5), 1.00/0.59 inference(sigma_clausification,[],[f929])). 1.00/0.59 thf(f929,plain,( 1.00/0.59 ($true = (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))))))) | ~spl0_5), 1.00/0.59 inference(not_proxy_clausification,[],[f546])). 1.00/0.59 thf(f546,plain,( 1.00/0.59 ($false = (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris))))))))) | ~spl0_5), 1.00/0.59 inference(avatar_component_clause,[],[f545])). 1.00/0.59 thf(f677,plain,( 1.00/0.59 ( ! [X1 : reg] : ((((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france))))) = $false)) ) | ~spl0_2), 1.00/0.59 inference(beta_eta_normalization,[],[f675])). 1.00/0.59 thf(f675,plain,( 1.00/0.59 ( ! [X1 : reg] : ((((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))) @ X1) = $false)) ) | ~spl0_2), 1.00/0.59 inference(pi_clausification,[],[f657])). 1.00/0.59 thf(f1420,plain,( 1.00/0.59 ( ! [X1 : reg] : (($true = ((c @ X1 @ sK12) => (c @ X1 @ paris)))) ) | ~spl0_5), 1.00/0.59 inference(beta_eta_normalization,[],[f1419])). 1.00/0.59 thf(f1419,plain,( 1.00/0.59 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ sK12) => (c @ Y0 @ paris))) @ X1))) ) | ~spl0_5), 1.00/0.59 inference(pi_clausification,[],[f953])). 1.00/0.59 thf(f1504,plain,( 1.00/0.59 ((~ (c @ sK15 @ paris)) = $true) | (~spl0_2 | ~spl0_4 | ~spl0_5)), 1.00/0.59 inference(boolean_simplification,[],[f1498])). 1.00/0.59 thf(f1498,plain,( 1.00/0.59 ($true = ((c @ sK15 @ paris) => $false)) | (~spl0_2 | ~spl0_4 | ~spl0_5)), 1.00/0.59 inference(superposition,[],[f429,f1493])). 1.00/0.59 thf(f1493,plain,( 1.00/0.59 ($false = (c @ sK15 @ france)) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(boolean_simplification,[],[f1492])). 1.00/0.59 thf(f1492,plain,( 1.00/0.59 (($true => (c @ sK15 @ france)) = $false) | (~spl0_2 | ~spl0_5)), 1.00/0.59 inference(backward_demodulation,[],[f1476,f1486])). 1.00/0.59 thf(f429,plain,( 1.00/0.59 ( ! [X1 : reg] : ((((c @ X1 @ paris) => (c @ X1 @ france)) = $true)) ) | ~spl0_4), 1.00/0.59 inference(beta_eta_normalization,[],[f426])). 1.00/0.59 thf(f426,plain,( 1.00/0.59 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X1))) ) | ~spl0_4), 1.00/0.59 inference(pi_clausification,[],[f419])). 1.00/0.59 thf(f419,plain,( 1.00/0.59 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) | ~spl0_4), 1.00/0.59 inference(binary_proxy_clausification,[],[f416])). 1.00/0.59 thf(f612,plain,( 1.00/0.59 ~spl0_1), 1.00/0.59 inference(avatar_contradiction_clause,[],[f611])). 1.00/0.59 thf(f611,plain,( 1.00/0.59 $false | ~spl0_1), 1.00/0.59 inference(trivial_inequality_removal,[],[f610])). 1.00/0.59 thf(f610,plain,( 1.00/0.59 ($true = $false) | ~spl0_1), 1.00/0.59 inference(boolean_simplification,[],[f609])). 1.00/0.59 thf(f609,plain,( 1.00/0.59 ( ! [X0 : $i,X1 : $i] : ((($true | (fool @ X0 @ (sK7 @ X1 @ X0))) = $false)) ) | ~spl0_1), 1.00/0.59 inference(boolean_simplification,[],[f608])). 1.00/0.59 thf(f608,plain,( 1.00/0.59 ( ! [X0 : $i,X1 : $i] : ((((~ $false) | (fool @ X0 @ (sK7 @ X1 @ X0))) = $false)) ) | ~spl0_1), 1.00/0.59 inference(forward_demodulation,[],[f603,f559])). 1.00/0.59 thf(f559,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : (($false = (fool @ X1 @ X2))) ) | ~spl0_1), 1.00/0.59 inference(not_proxy_clausification,[],[f333])). 1.00/0.59 thf(f333,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : (($true = (~ (fool @ X1 @ X2)))) ) | ~spl0_1), 1.00/0.59 inference(avatar_component_clause,[],[f332])). 1.00/0.59 thf(f332,plain,( 1.00/0.59 spl0_1 <=> ! [X2,X1] : ($true = (~ (fool @ X1 @ X2)))), 1.00/0.59 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 1.00/0.59 thf(f603,plain,( 1.00/0.59 ( ! [X0 : $i,X1 : $i] : (($false = ((~ (fool @ X1 @ (sK7 @ X1 @ X0))) | (fool @ X0 @ (sK7 @ X1 @ X0))))) ) | ~spl0_1), 1.00/0.59 inference(beta_eta_normalization,[],[f597])). 1.00/0.59 thf(f597,plain,( 1.00/0.59 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (fool @ X0 @ Y0))) @ (sK7 @ X1 @ X0)) = $false)) ) | ~spl0_1), 1.00/0.59 inference(sigma_clausification,[],[f580])). 1.00/0.59 thf(f580,plain,( 1.00/0.59 ( ! [X0 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (fool @ X0 @ Y0)))) = $false)) ) | ~spl0_1), 1.00/0.59 inference(not_proxy_clausification,[],[f563])). 1.00/0.59 thf(f563,plain,( 1.00/0.59 ( ! [X0 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (fool @ X0 @ Y0))))))) ) | ~spl0_1), 1.00/0.59 inference(boolean_simplification,[],[f562])). 1.00/0.59 thf(f562,plain,( 1.00/0.59 ( ! [X0 : $i,X1 : $i] : ((($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (fool @ X0 @ Y0)))))) = $true)) ) | ~spl0_1), 1.00/0.59 inference(superposition,[],[f240,f559])). 1.00/0.59 thf(f240,plain,( 1.00/0.59 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((X2 @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0)))))))) )), 1.00/0.59 inference(beta_eta_normalization,[],[f239])). 1.00/0.59 thf(f239,plain,( 1.00/0.59 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))))) @ X2))) )), 1.00/0.59 inference(pi_clausification,[],[f238])). 1.00/0.59 thf(f238,plain,( 1.00/0.59 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1)))))))) = $true)) )), 1.00/0.59 inference(beta_eta_normalization,[],[f237])). 1.00/0.59 thf(f237,plain,( 1.00/0.59 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))))))) @ X1))) )), 1.00/0.59 inference(pi_clausification,[],[f222])). 1.00/0.59 thf(f222,plain,( 1.00/0.59 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2)))))))))))), 1.00/0.59 inference(beta_eta_normalization,[],[f213])). 1.00/0.59 thf(f213,plain,( 1.00/0.59 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: ((Y4 @ Y5) | (Y3 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((~ (Y1 @ Y3 @ Y4)) | (Y2 @ Y4))))))))) @ fool @ Y0) @ Y0)))))), 1.00/0.59 inference(definition_unfolding,[],[f170,f160,f182,f197,f178])). 1.00/0.59 thf(f197,plain,( 1.00/0.59 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))), 1.00/0.59 inference(definition_unfolding,[],[f174,f183,f164])). 1.00/0.59 thf(f164,plain,( 1.00/0.59 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))), 1.00/0.59 inference(cnf_transformation,[],[f63])). 1.00/0.59 thf(f63,plain,( 1.00/0.59 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))), 1.00/0.59 inference(fool_elimination,[],[f62])). 1.00/0.59 thf(f62,plain,( 1.00/0.59 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)), 1.00/0.59 inference(rectify,[],[f3])). 1.00/0.59 thf(f3,axiom,( 1.00/0.59 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',mnot)). 1.00/0.59 thf(f183,plain,( 1.00/0.59 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))), 1.00/0.59 inference(cnf_transformation,[],[f104])). 1.00/0.59 thf(f104,plain,( 1.00/0.59 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))), 1.00/0.59 inference(fool_elimination,[],[f103])). 1.00/0.59 thf(f103,plain,( 1.00/0.59 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))), 1.00/0.59 inference(rectify,[],[f4])). 1.00/0.59 thf(f4,axiom,( 1.00/0.59 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',mor)). 1.00/0.59 thf(f174,plain,( 1.00/0.59 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))), 1.00/0.59 inference(cnf_transformation,[],[f120])). 1.00/0.59 thf(f120,plain,( 1.00/0.59 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))), 1.00/0.59 inference(fool_elimination,[],[f119])). 1.00/0.59 thf(f119,plain,( 1.00/0.59 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)), 1.00/0.59 inference(rectify,[],[f6])). 1.00/0.59 thf(f6,axiom,( 1.00/0.59 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',mimplies)). 1.00/0.59 thf(f182,plain,( 1.00/0.59 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))), 1.00/0.59 inference(cnf_transformation,[],[f137])). 1.00/0.59 thf(f137,plain,( 1.00/0.59 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))), 1.00/0.59 inference(fool_elimination,[],[f136])). 1.00/0.59 thf(f136,plain,( 1.00/0.59 (mforall_prop = (^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))))), 1.00/0.59 inference(rectify,[],[f11])). 1.00/0.59 thf(f11,axiom,( 1.00/0.59 (mforall_prop = (^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',mforall_prop)). 1.00/0.59 thf(f170,plain,( 1.00/0.59 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)))))), 1.00/0.59 inference(cnf_transformation,[],[f96])). 1.00/0.59 thf(f96,plain,( 1.00/0.59 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)))))), 1.00/0.59 inference(fool_elimination,[],[f95])). 1.00/0.59 thf(f95,plain,( 1.00/0.59 (mvalid @ (mforall_prop @ (^[X0 : $i > $o] : (mimplies @ (mbox @ fool @ X0) @ X0))))), 1.00/0.59 inference(rectify,[],[f46])). 1.00/0.59 thf(f46,axiom,( 1.00/0.59 (mvalid @ (mforall_prop @ (^[X12 : $i > $o] : (mimplies @ (mbox @ fool @ X12) @ X12))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',t_axiom_for_fool)). 1.00/0.59 thf(f409,plain,( 1.00/0.59 spl0_4), 1.00/0.59 inference(avatar_split_clause,[],[f398,f405])). 1.00/0.59 thf(f398,plain,( 1.00/0.59 ((((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))) = $true)), 1.00/0.59 inference(boolean_simplification,[],[f397])). 1.00/0.59 thf(f397,plain,( 1.00/0.59 ($true = ($false | (((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))))))))), 1.00/0.59 inference(boolean_simplification,[],[f396])). 1.00/0.59 thf(f396,plain,( 1.00/0.59 ($true = ((~ $true) | (((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))))))))), 1.00/0.59 inference(superposition,[],[f391,f267])). 1.00/0.59 thf(f391,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : ((((~ (a @ X1 @ X2)) | (((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((c @ Y0 @ paris) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris))))))))) & ((c @ Y0 @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))))))) = $true)) )), 1.00/0.59 inference(beta_eta_normalization,[],[f390])). 1.00/0.59 thf(f390,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france))))) & (~ (?? @ reg @ (^[Y1 : reg]: (((c @ Y1 @ paris) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))))) & ((c @ Y1 @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))))))))))))))) @ X2))) )), 1.00/0.59 inference(pi_clausification,[],[f386])). 1.00/0.59 thf(f386,plain,( 1.00/0.59 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france))))) & (~ (?? @ reg @ (^[Y1 : reg]: (((c @ Y1 @ paris) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris))))))))) & ((c @ Y1 @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))))))))) )), 1.00/0.59 inference(beta_eta_normalization,[],[f385])). 1.00/0.59 thf(f385,plain,( 1.00/0.59 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france))))) & (~ (?? @ reg @ (^[Y2 : reg]: (((c @ Y2 @ paris) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris))))))))) & ((c @ Y2 @ france) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))))))))))))))))) @ X1))) )), 1.00/0.59 inference(pi_clausification,[],[f223])). 1.00/0.59 thf(f223,plain,( 1.00/0.59 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france))))) & (~ (?? @ reg @ (^[Y2 : reg]: (((c @ Y2 @ paris) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris))))))))) & ((c @ Y2 @ france) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france))))))))))))))))))) = $true)), 1.00/0.59 inference(beta_eta_normalization,[],[f212])). 1.00/0.59 thf(f212,plain,( 1.00/0.59 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4))))) @ Y1 @ Y2) & (~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((c @ Y4 @ Y5) & (~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)))))) @ Y3 @ Y2))))))))) @ paris @ france)))))), 1.00/0.59 inference(definition_unfolding,[],[f163,f160,f178,f211])). 1.00/0.59 thf(f211,plain,( 1.00/0.59 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: ((~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)) & ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3))))) @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((c @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((c @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)))))) @ Y2 @ Y1))))))))))), 1.00/0.59 inference(definition_unfolding,[],[f172,f209,f208,f208])). 1.00/0.59 thf(f172,plain,( 1.00/0.59 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))), 1.00/0.59 inference(cnf_transformation,[],[f74])). 1.00/0.59 thf(f74,plain,( 1.00/0.59 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))), 1.00/0.59 inference(fool_elimination,[],[f73])). 1.00/0.59 thf(f73,plain,( 1.00/0.59 ((^[X0 : reg, X1 : reg] : (~? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))) = ntpp)), 1.00/0.59 inference(rectify,[],[f40])). 1.00/0.59 thf(f40,axiom,( 1.00/0.59 ((^[X0 : reg, X1 : reg] : (~? [X11 : reg] : ((ec @ X11 @ X1) & (ec @ X11 @ X0)) & (pp @ X0 @ X1))) = ntpp)), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',ntpp)). 1.00/0.59 thf(f163,plain,( 1.00/0.59 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))))), 1.00/0.59 inference(cnf_transformation,[],[f102])). 1.00/0.59 thf(f102,plain,( 1.00/0.59 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))))), 1.00/0.59 inference(fool_elimination,[],[f101])). 1.00/0.59 thf(f101,plain,( 1.00/0.59 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))), 1.00/0.59 inference(rectify,[],[f44])). 1.00/0.59 thf(f44,axiom,( 1.00/0.59 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',ax3)). 1.00/0.59 thf(f337,plain,( 1.00/0.59 spl0_1 | spl0_2), 1.00/0.59 inference(avatar_split_clause,[],[f330,f335,f332])). 1.00/0.59 thf(f330,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : (($true = (~ (fool @ X1 @ X2))) | ($true = ((c @ spain @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france))))))))))) )), 1.00/0.59 inference(binary_proxy_clausification,[],[f323])). 1.00/0.59 thf(f323,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (fool @ X1 @ X2)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))))))) )), 1.00/0.59 inference(beta_eta_normalization,[],[f322])). 1.00/0.59 thf(f322,plain,( 1.00/0.59 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france))))))))))) @ X2) = $true)) )), 1.00/0.59 inference(pi_clausification,[],[f315])). 1.00/0.59 thf(f315,plain,( 1.00/0.59 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))))))))) )), 1.00/0.59 inference(beta_eta_normalization,[],[f314])). 1.00/0.59 thf(f314,plain,( 1.00/0.59 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france))))))))))))) @ X1))) )), 1.00/0.59 inference(pi_clausification,[],[f221])). 1.00/0.59 thf(f221,plain,( 1.00/0.59 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | ((c @ spain @ france) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))))))))))))))), 1.00/0.59 inference(beta_eta_normalization,[],[f214])). 1.00/0.59 thf(f214,plain,( 1.00/0.59 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))) @ fool @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((c @ Y1 @ Y2) & (~ ((^[Y3 : reg]: ((^[Y4 : reg]: (?? @ reg @ (^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y3) & ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4))))))) @ Y1 @ Y2)))))) @ spain @ france)))))), 1.00/0.59 inference(definition_unfolding,[],[f175,f160,f178,f208])). 1.00/0.59 thf(f175,plain,( 1.00/0.59 ($true = (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)))))), 1.00/0.59 inference(cnf_transformation,[],[f146])). 1.00/0.59 thf(f146,plain,( 1.00/0.59 ($true = (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)))))), 1.00/0.59 inference(fool_elimination,[],[f145])). 1.00/0.59 thf(f145,plain,( 1.00/0.59 (mvalid @ (mbox @ fool @ (^[X0 : $i] : (ec @ spain @ france))))), 1.00/0.59 inference(rectify,[],[f45])). 1.00/0.59 thf(f45,axiom,( 1.00/0.59 (mvalid @ (mbox @ fool @ (^[X0 : $i] : (ec @ spain @ france))))), 1.00/0.59 file('/export/starexec/sandbox/tmp/tmp.HqprRMsJGY/E---3.1_20102.p',ax2)). 1.00/0.59 % SZS output end Proof for E---3.1_20102 1.00/0.59 % (20225)------------------------------ 1.00/0.59 % (20225)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.00/0.59 % (20225)Termination reason: Refutation 1.00/0.59 1.00/0.59 % (20225)Memory used [KB]: 6780 1.00/0.59 % (20225)Time elapsed: 0.173 s 1.00/0.59 % (20225)Instructions burned: 200 (million) 1.00/0.59 % (20225)------------------------------ 1.00/0.59 % (20225)------------------------------ 1.00/0.59 % (20213)Success in time 0.234 s 1.00/0.59 EOF