0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.10/0.12 % Command : run_vampire %s %d THM 0.12/0.33 % Computer : n005.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 1920 0.12/0.33 % WCLimit : 240 0.12/0.33 % DateTime : Wed Jul 30 02:03:34 EDT 2025 0.12/0.33 % CPUTime : 0.12/0.35 This is a THF_ problem 0.12/0.35 Running higher-order theorem proving 0.12/0.36 Running /export/starexec/sandbox/solver/bin/vampire-hol --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --print_def_sorts on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p -m 16384 -t 240 0.12/0.39 % (16548)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/183Mi) 0.12/0.39 % (16550)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_16441 for (2399ds/27Mi) 0.12/0.39 % (16549)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_16441 for (2399ds/4Mi) 0.12/0.39 % (16551)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/2Mi) 0.12/0.39 % (16552)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_16441 for (2399ds/2Mi) 0.12/0.39 % (16553)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_16441 for (2399ds/275Mi) 0.12/0.39 % (16554)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/18Mi) 0.12/0.39 % (16551)Instruction limit reached! 0.12/0.39 % (16551)------------------------------ 0.12/0.39 % (16551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 % (16551)Termination reason: Unknown 0.12/0.39 % (16551)Termination phase: shuffling 0.12/0.39 0.12/0.39 % (16551)Memory used [KB]: 1023 0.12/0.39 % (16551)Time elapsed: 0.004 s 0.12/0.39 % (16551)Instructions burned: 3 (million) 0.12/0.39 % (16551)------------------------------ 0.12/0.39 % (16551)------------------------------ 0.12/0.39 % (16552)Instruction limit reached! 0.12/0.39 % (16552)------------------------------ 0.12/0.39 % (16552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 % (16552)Termination reason: Unknown 0.12/0.39 % (16552)Termination phase: shuffling 0.12/0.39 0.12/0.39 % (16552)Memory used [KB]: 1023 0.12/0.39 % (16552)Time elapsed: 0.004 s 0.12/0.39 % (16552)Instructions burned: 3 (million) 0.12/0.39 % (16552)------------------------------ 0.12/0.39 % (16552)------------------------------ 0.12/0.39 % (16549)Instruction limit reached! 0.12/0.39 % (16549)------------------------------ 0.12/0.39 % (16549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.39 % (16549)Termination reason: Unknown 0.12/0.39 % (16549)Termination phase: shuffling 0.12/0.39 0.12/0.39 % (16549)Memory used [KB]: 1151 0.12/0.39 % (16549)Time elapsed: 0.005 s 0.12/0.39 % (16549)Instructions burned: 5 (million) 0.12/0.39 % (16549)------------------------------ 0.12/0.39 % (16549)------------------------------ 0.12/0.40 % (16553)Refutation not found, incomplete strategy 0.12/0.40 % (16553)------------------------------ 0.12/0.40 % (16553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.40 % (16553)Termination reason: Refutation not found, incomplete strategy 0.12/0.40 0.12/0.40 0.12/0.40 % (16553)Memory used [KB]: 5628 0.12/0.40 % (16553)Time elapsed: 0.010 s 0.12/0.40 % (16553)Instructions burned: 14 (million) 0.12/0.40 % (16553)------------------------------ 0.12/0.40 % (16553)------------------------------ 0.12/0.40 % (16554)Instruction limit reached! 0.12/0.40 % (16554)------------------------------ 0.12/0.40 % (16554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.40 % (16554)Termination reason: Unknown 0.12/0.40 % (16554)Termination phase: Saturation 0.12/0.40 0.12/0.40 % (16554)Memory used [KB]: 5628 0.12/0.40 % (16554)Time elapsed: 0.012 s 0.12/0.40 % (16554)Instructions burned: 18 (million) 0.12/0.40 % (16554)------------------------------ 0.12/0.40 % (16554)------------------------------ 0.12/0.40 % (16550)Instruction limit reached! 0.12/0.40 % (16550)------------------------------ 0.12/0.40 % (16550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.12/0.40 % (16550)Termination reason: Unknown 0.12/0.40 % (16550)Termination phase: Saturation 0.12/0.40 0.12/0.40 % (16550)Memory used [KB]: 5756 0.12/0.40 % (16550)Time elapsed: 0.017 s 0.12/0.40 % (16550)Instructions burned: 28 (million) 0.12/0.40 % (16550)------------------------------ 0.12/0.40 % (16550)------------------------------ 0.21/0.41 % (16555)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_16441 for (2399ds/3Mi) 0.21/0.41 % (16556)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_16441 for (2399ds/37Mi) 0.21/0.41 % (16557)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_16441 for (2399ds/15Mi) 0.21/0.41 % (16555)Instruction limit reached! 0.21/0.41 % (16555)------------------------------ 0.21/0.41 % (16555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.41 % (16555)Termination reason: Unknown 0.21/0.41 % (16555)Termination phase: shuffling 0.21/0.41 0.21/0.41 % (16555)Memory used [KB]: 1023 0.21/0.41 % (16555)Time elapsed: 0.004 s 0.21/0.41 % (16555)Instructions burned: 4 (million) 0.21/0.41 % (16555)------------------------------ 0.21/0.41 % (16555)------------------------------ 0.21/0.42 % (16558)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_16441 for (2399ds/3Mi) 0.21/0.42 % (16559)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_16441 for (2399ds/1041Mi) 0.21/0.42 % (16557)Instruction limit reached! 0.21/0.42 % (16557)------------------------------ 0.21/0.42 % (16557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.42 % (16557)Termination reason: Unknown 0.21/0.42 % (16557)Termination phase: Saturation 0.21/0.42 0.21/0.42 % (16557)Memory used [KB]: 1151 0.21/0.42 % (16557)Time elapsed: 0.010 s 0.21/0.42 % (16557)Instructions burned: 16 (million) 0.21/0.42 % (16557)------------------------------ 0.21/0.42 % (16557)------------------------------ 0.21/0.42 % (16558)Instruction limit reached! 0.21/0.42 % (16558)------------------------------ 0.21/0.42 % (16558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.42 % (16558)Termination reason: Unknown 0.21/0.42 % (16558)Termination phase: shuffling 0.21/0.42 0.21/0.42 % (16558)Memory used [KB]: 1023 0.21/0.42 % (16558)Time elapsed: 0.004 s 0.21/0.42 % (16558)Instructions burned: 4 (million) 0.21/0.42 % (16558)------------------------------ 0.21/0.42 % (16558)------------------------------ 0.21/0.42 % (16560)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/7Mi) 0.21/0.43 % (16560)Instruction limit reached! 0.21/0.43 % (16560)------------------------------ 0.21/0.43 % (16560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.43 % (16560)Termination reason: Unknown 0.21/0.43 % (16560)Termination phase: SInE selection 0.21/0.43 0.21/0.43 % (16560)Memory used [KB]: 1151 0.21/0.43 % (16560)Time elapsed: 0.006 s 0.21/0.43 % (16560)Instructions burned: 8 (million) 0.21/0.43 % (16560)------------------------------ 0.21/0.43 % (16560)------------------------------ 0.21/0.43 % (16561)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/16Mi) 0.21/0.43 % (16556)Instruction limit reached! 0.21/0.43 % (16556)------------------------------ 0.21/0.43 % (16556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.43 % (16556)Termination reason: Unknown 0.21/0.43 % (16556)Termination phase: Saturation 0.21/0.43 0.21/0.43 % (16556)Memory used [KB]: 5756 0.21/0.43 % (16556)Time elapsed: 0.022 s 0.21/0.43 % (16556)Instructions burned: 37 (million) 0.21/0.43 % (16556)------------------------------ 0.21/0.43 % (16556)------------------------------ 0.21/0.43 % (16562)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_16441 for (2399ds/3Mi) 0.21/0.44 % (16563)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_16441 for (2399ds/3Mi) 0.21/0.44 % (16562)Instruction limit reached! 0.21/0.44 % (16562)------------------------------ 0.21/0.44 % (16562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.44 % (16562)Termination reason: Unknown 0.21/0.44 % (16562)Termination phase: shuffling 0.21/0.44 0.21/0.44 % (16562)Memory used [KB]: 1023 0.21/0.44 % (16562)Time elapsed: 0.004 s 0.21/0.44 % (16562)Instructions burned: 4 (million) 0.21/0.44 % (16562)------------------------------ 0.21/0.44 % (16562)------------------------------ 0.21/0.44 % (16561)Instruction limit reached! 0.21/0.44 % (16561)------------------------------ 0.21/0.44 % (16561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.44 % (16561)Termination reason: Unknown 0.21/0.44 % (16561)Termination phase: Saturation 0.21/0.44 0.21/0.44 % (16561)Memory used [KB]: 5628 0.21/0.44 % (16561)Time elapsed: 0.011 s 0.21/0.44 % (16561)Instructions burned: 17 (million) 0.21/0.44 % (16561)------------------------------ 0.21/0.44 % (16561)------------------------------ 0.21/0.44 % (16563)Instruction limit reached! 0.21/0.44 % (16563)------------------------------ 0.21/0.44 % (16563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.44 % (16563)Termination reason: Unknown 0.21/0.44 % (16563)Termination phase: shuffling 0.21/0.44 0.21/0.44 % (16563)Memory used [KB]: 1023 0.21/0.44 % (16563)Time elapsed: 0.004 s 0.21/0.44 % (16563)Instructions burned: 4 (million) 0.21/0.44 % (16563)------------------------------ 0.21/0.44 % (16563)------------------------------ 0.21/0.44 % (16564)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_16441 for (2399ds/7Mi) 0.21/0.45 % (16565)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_16441 for (2399ds/3Mi) 0.21/0.45 % (16564)Instruction limit reached! 0.21/0.45 % (16564)------------------------------ 0.21/0.45 % (16564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.45 % (16564)Termination reason: Unknown 0.21/0.45 % (16564)Termination phase: Property scanning 0.21/0.45 0.21/0.45 % (16564)Memory used [KB]: 1151 0.21/0.45 % (16564)Time elapsed: 0.006 s 0.21/0.45 % (16564)Instructions burned: 8 (million) 0.21/0.45 % (16564)------------------------------ 0.21/0.45 % (16564)------------------------------ 0.21/0.45 % (16565)Instruction limit reached! 0.21/0.45 % (16565)------------------------------ 0.21/0.45 % (16565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.45 % (16565)Termination reason: Unknown 0.21/0.45 % (16565)Termination phase: shuffling 0.21/0.45 0.21/0.45 % (16565)Memory used [KB]: 1151 0.21/0.45 % (16565)Time elapsed: 0.004 s 0.21/0.45 % (16565)Instructions burned: 4 (million) 0.21/0.45 % (16565)------------------------------ 0.21/0.45 % (16565)------------------------------ 0.21/0.45 % (16566)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/4Mi) 0.21/0.45 % (16567)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_16441 for (2399ds/18Mi) 0.21/0.45 % (16568)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/710Mi) 0.21/0.46 % (16566)Instruction limit reached! 0.21/0.46 % (16566)------------------------------ 0.21/0.46 % (16566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.46 % (16566)Termination reason: Unknown 0.21/0.46 % (16566)Termination phase: shuffling 0.21/0.46 0.21/0.46 % (16566)Memory used [KB]: 1023 0.21/0.46 % (16566)Time elapsed: 0.004 s 0.21/0.46 % (16566)Instructions burned: 4 (million) 0.21/0.46 % (16566)------------------------------ 0.21/0.46 % (16566)------------------------------ 0.21/0.46 % (16569)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/6Mi) 0.21/0.47 % (16570)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_16441 for (2399ds/902Mi) 0.21/0.47 % (16567)Instruction limit reached! 0.21/0.47 % (16567)------------------------------ 0.21/0.47 % (16567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.47 % (16567)Termination reason: Unknown 0.21/0.47 % (16567)Termination phase: Saturation 0.21/0.47 0.21/0.47 % (16567)Memory used [KB]: 5756 0.21/0.47 % (16567)Time elapsed: 0.013 s 0.21/0.47 % (16567)Instructions burned: 18 (million) 0.21/0.47 % (16567)------------------------------ 0.21/0.47 % (16567)------------------------------ 0.21/0.47 % (16569)Instruction limit reached! 0.21/0.47 % (16569)------------------------------ 0.21/0.47 % (16569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.47 % (16569)Termination reason: Unknown 0.21/0.47 % (16569)Termination phase: Property scanning 0.21/0.47 0.21/0.47 % (16569)Memory used [KB]: 1151 0.21/0.47 % (16569)Time elapsed: 0.005 s 0.21/0.47 % (16569)Instructions burned: 6 (million) 0.21/0.47 % (16569)------------------------------ 0.21/0.47 % (16569)------------------------------ 0.21/0.47 % (16570)Refutation not found, incomplete strategy 0.21/0.47 % (16570)------------------------------ 0.21/0.47 % (16570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.47 % (16570)Termination reason: Refutation not found, incomplete strategy 0.21/0.47 0.21/0.47 0.21/0.47 % (16570)Memory used [KB]: 5628 0.21/0.47 % (16570)Time elapsed: 0.008 s 0.21/0.47 % (16570)Instructions burned: 12 (million) 0.21/0.47 % (16570)------------------------------ 0.21/0.47 % (16570)------------------------------ 0.21/0.47 % (16571)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_16441 for (2399ds/21Mi) 0.21/0.48 % (16568)Refutation not found, incomplete strategy 0.21/0.48 % (16568)------------------------------ 0.21/0.48 % (16568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.48 % (16568)Termination reason: Refutation not found, incomplete strategy 0.21/0.48 0.21/0.48 0.21/0.48 % (16568)Memory used [KB]: 5884 0.21/0.48 % (16568)Time elapsed: 0.023 s 0.21/0.48 % (16568)Instructions burned: 40 (million) 0.21/0.48 % (16568)------------------------------ 0.21/0.48 % (16568)------------------------------ 0.21/0.48 % (16572)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/5Mi) 0.21/0.48 % (16573)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_16441 for (2399ds/6Mi) 0.21/0.48 % (16574)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_16441 for (2399ds/377Mi) 0.21/0.48 % (16573)Instruction limit reached! 0.21/0.48 % (16573)------------------------------ 0.21/0.48 % (16573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.48 % (16573)Termination reason: Unknown 0.21/0.48 % (16573)Termination phase: Property scanning 0.21/0.48 0.21/0.48 % (16573)Memory used [KB]: 1151 0.21/0.48 % (16573)Time elapsed: 0.004 s 0.21/0.48 % (16573)Instructions burned: 7 (million) 0.21/0.48 % (16573)------------------------------ 0.21/0.48 % (16573)------------------------------ 0.21/0.48 % (16572)Instruction limit reached! 0.21/0.48 % (16572)------------------------------ 0.21/0.48 % (16572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.48 % (16572)Termination reason: Unknown 0.21/0.48 % (16572)Termination phase: Property scanning 0.21/0.48 0.21/0.48 % (16572)Memory used [KB]: 1151 0.21/0.48 % (16572)Time elapsed: 0.004 s 0.21/0.48 % (16572)Instructions burned: 7 (million) 0.21/0.48 % (16572)------------------------------ 0.21/0.48 % (16572)------------------------------ 0.21/0.48 % (16571)Instruction limit reached! 0.21/0.48 % (16571)------------------------------ 0.21/0.48 % (16571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.48 % (16571)Termination reason: Unknown 0.21/0.48 % (16571)Termination phase: Saturation 0.21/0.48 0.21/0.48 % (16571)Memory used [KB]: 5756 0.21/0.48 % (16571)Time elapsed: 0.013 s 0.21/0.48 % (16571)Instructions burned: 21 (million) 0.21/0.48 % (16571)------------------------------ 0.21/0.48 % (16571)------------------------------ 0.21/0.49 % (16575)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_16441 for (2399ds/779Mi) 0.21/0.49 % (16548)Instruction limit reached! 0.21/0.49 % (16548)------------------------------ 0.21/0.49 % (16548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.49 % (16548)Termination reason: Unknown 0.21/0.49 % (16548)Termination phase: Saturation 0.21/0.49 0.21/0.49 % (16548)Memory used [KB]: 7036 0.21/0.49 % (16548)Time elapsed: 0.103 s 0.21/0.49 % (16548)Instructions burned: 184 (million) 0.21/0.49 % (16548)------------------------------ 0.21/0.49 % (16548)------------------------------ 0.21/0.49 % (16576)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_16441 for (2398ds/19Mi) 0.21/0.50 % (16577)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_16441 for (2398ds/879Mi) 0.21/0.50 % (16576)Refutation not found, incomplete strategy 0.21/0.50 % (16576)------------------------------ 0.21/0.50 % (16576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.50 % (16576)Termination reason: Refutation not found, incomplete strategy 0.21/0.50 0.21/0.50 0.21/0.50 % (16576)Memory used [KB]: 5756 0.21/0.50 % (16576)Time elapsed: 0.006 s 0.21/0.50 % (16576)Instructions burned: 16 (million) 0.21/0.50 % (16576)------------------------------ 0.21/0.50 % (16576)------------------------------ 0.21/0.50 % (16579)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/3Mi) 0.21/0.50 % (16579)Instruction limit reached! 0.21/0.50 % (16579)------------------------------ 0.21/0.50 % (16579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.50 % (16579)Termination reason: Unknown 0.21/0.50 % (16579)Termination phase: shuffling 0.21/0.50 0.21/0.50 % (16579)Memory used [KB]: 1023 0.21/0.50 % (16579)Time elapsed: 0.002 s 0.21/0.50 % (16579)Instructions burned: 3 (million) 0.21/0.50 % (16579)------------------------------ 0.21/0.50 % (16579)------------------------------ 0.21/0.50 % (16578)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/17Mi) 0.21/0.51 % (16580)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/30Mi) 0.21/0.51 % (16578)Instruction limit reached! 0.21/0.51 % (16578)------------------------------ 0.21/0.51 % (16578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.51 % (16578)Termination reason: Unknown 0.21/0.51 % (16578)Termination phase: Saturation 0.21/0.51 0.21/0.51 % (16578)Memory used [KB]: 5628 0.21/0.51 % (16578)Time elapsed: 0.011 s 0.21/0.51 % (16578)Instructions burned: 18 (million) 0.21/0.51 % (16578)------------------------------ 0.21/0.51 % (16578)------------------------------ 0.21/0.51 % (16581)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/127Mi) 0.21/0.52 % (16580)Instruction limit reached! 0.21/0.52 % (16580)------------------------------ 0.21/0.52 % (16580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.52 % (16580)Termination reason: Unknown 0.21/0.52 % (16580)Termination phase: Saturation 0.21/0.52 0.21/0.52 % (16580)Memory used [KB]: 5756 0.21/0.52 % (16580)Time elapsed: 0.011 s 0.21/0.52 % (16580)Instructions burned: 30 (million) 0.21/0.52 % (16580)------------------------------ 0.21/0.52 % (16580)------------------------------ 0.21/0.53 % (16582)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/100Mi) 0.21/0.53 % (16583)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/3Mi) 0.21/0.53 % (16583)Instruction limit reached! 0.21/0.53 % (16583)------------------------------ 0.21/0.53 % (16583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.53 % (16583)Termination reason: Unknown 0.21/0.53 % (16583)Termination phase: shuffling 0.21/0.53 0.21/0.53 % (16583)Memory used [KB]: 1151 0.21/0.53 % (16583)Time elapsed: 0.003 s 0.21/0.53 % (16583)Instructions burned: 4 (million) 0.21/0.53 % (16583)------------------------------ 0.21/0.53 % (16583)------------------------------ 0.21/0.54 % (16584)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/20Mi) 0.21/0.55 % (16584)Instruction limit reached! 0.21/0.55 % (16584)------------------------------ 0.21/0.55 % (16584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.55 % (16584)Termination reason: Unknown 0.21/0.55 % (16584)Termination phase: Saturation 0.21/0.55 0.21/0.55 % (16584)Memory used [KB]: 5756 0.21/0.55 % (16584)Time elapsed: 0.008 s 0.21/0.55 % (16584)Instructions burned: 20 (million) 0.21/0.55 % (16584)------------------------------ 0.21/0.55 % (16584)------------------------------ 0.21/0.56 % (16581)Instruction limit reached! 0.21/0.56 % (16581)------------------------------ 0.21/0.56 % (16581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.56 % (16581)Termination reason: Unknown 0.21/0.56 % (16581)Termination phase: Saturation 0.21/0.56 0.21/0.56 % (16581)Memory used [KB]: 6396 0.21/0.56 % (16581)Time elapsed: 0.044 s 0.21/0.56 % (16581)Instructions burned: 129 (million) 0.21/0.56 % (16581)------------------------------ 0.21/0.56 % (16581)------------------------------ 0.21/0.56 % (16585)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/86Mi) 0.21/0.56 % (16582)Instruction limit reached! 0.21/0.56 % (16582)------------------------------ 0.21/0.56 % (16582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.56 % (16582)Termination reason: Unknown 0.21/0.56 % (16582)Termination phase: Saturation 0.21/0.56 0.21/0.56 % (16582)Memory used [KB]: 6012 0.21/0.56 % (16582)Time elapsed: 0.036 s 0.21/0.56 % (16582)Instructions burned: 100 (million) 0.21/0.56 % (16582)------------------------------ 0.21/0.56 % (16582)------------------------------ 0.21/0.57 % (16586)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/107Mi) 0.21/0.57 % (16587)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on E---3.1_16441 for (2398ds/39Mi) 0.21/0.58 % (16587)Instruction limit reached! 0.21/0.58 % (16587)------------------------------ 0.21/0.58 % (16587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.58 % (16587)Termination reason: Unknown 0.21/0.58 % (16587)Termination phase: Saturation 0.21/0.58 0.21/0.58 % (16587)Memory used [KB]: 6012 0.21/0.58 % (16587)Time elapsed: 0.014 s 0.21/0.58 % (16587)Instructions burned: 41 (million) 0.21/0.58 % (16587)------------------------------ 0.21/0.58 % (16587)------------------------------ 0.21/0.59 % (16585)Instruction limit reached! 0.21/0.59 % (16585)------------------------------ 0.21/0.59 % (16585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 0.21/0.59 % (16585)Termination reason: Unknown 0.21/0.59 % (16585)Termination phase: Saturation 0.21/0.59 0.21/0.59 % (16585)Memory used [KB]: 6268 0.21/0.59 % (16585)Time elapsed: 0.030 s 0.21/0.59 % (16585)Instructions burned: 88 (million) 0.21/0.59 % (16585)------------------------------ 0.21/0.59 % (16585)------------------------------ 0.21/0.59 % (16588)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on E---3.1_16441 for (2397ds/448Mi) 0.21/0.60 % (16559)First to succeed. 1.73/0.60 % (16586)Instruction limit reached! 1.73/0.60 % (16586)------------------------------ 1.73/0.60 % (16586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.73/0.60 % (16586)Termination reason: Unknown 1.73/0.60 % (16586)Termination phase: Saturation 1.73/0.60 1.73/0.60 % (16586)Memory used [KB]: 6140 1.73/0.60 % (16586)Time elapsed: 0.037 s 1.73/0.60 % (16586)Instructions burned: 108 (million) 1.73/0.60 % (16586)------------------------------ 1.73/0.60 % (16586)------------------------------ 1.73/0.60 % (16559)Refutation found. Thanks to Tanya! 1.73/0.60 % SZS status Theorem for E---3.1_16441 1.73/0.60 % SZS output start Proof for E---3.1_16441 1.73/0.60 thf(type_def_5, type, mu: $tType). 1.73/0.60 thf(type_def_7, type, reg: $tType). 1.73/0.60 thf(func_def_0, type, mu: $tType). 1.73/0.60 thf(func_def_1, type, meq_ind: mu > mu > $i > $o). 1.73/0.60 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_4, type, mnot: ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o). 1.73/0.60 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o). 1.73/0.60 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o). 1.73/0.60 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o). 1.73/0.60 thf(func_def_15, type, mtrue: $i > $o). 1.73/0.60 thf(func_def_16, type, mfalse: $i > $o). 1.73/0.60 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o). 1.73/0.60 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_21, type, mserial: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o). 1.73/0.60 thf(func_def_29, type, mvalid: ($i > $o) > $o). 1.73/0.60 thf(func_def_30, type, minvalid: ($i > $o) > $o). 1.73/0.60 thf(func_def_31, type, msatisfiable: ($i > $o) > $o). 1.73/0.60 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o). 1.73/0.60 thf(func_def_33, type, reg: $tType). 1.73/0.60 thf(func_def_34, type, c: reg > reg > $o). 1.73/0.60 thf(func_def_35, type, dc: reg > reg > $o). 1.73/0.60 thf(func_def_36, type, p: reg > reg > $o). 1.73/0.60 thf(func_def_37, type, eq: reg > reg > $o). 1.73/0.60 thf(func_def_38, type, o: reg > reg > $o). 1.73/0.60 thf(func_def_39, type, po: reg > reg > $o). 1.73/0.60 thf(func_def_40, type, ec: reg > reg > $o). 1.73/0.60 thf(func_def_41, type, pp: reg > reg > $o). 1.73/0.60 thf(func_def_42, type, tpp: reg > reg > $o). 1.73/0.60 thf(func_def_43, type, ntpp: reg > reg > $o). 1.73/0.60 thf(func_def_44, type, catalunya: reg). 1.73/0.60 thf(func_def_45, type, france: reg). 1.73/0.60 thf(func_def_46, type, spain: reg). 1.73/0.60 thf(func_def_47, type, paris: reg). 1.73/0.60 thf(func_def_48, type, a: $i > $i > $o). 1.73/0.60 thf(func_def_49, type, fool: $i > $i > $o). 1.73/0.60 thf(func_def_66, type, ph1: !>[X0: $tType]:(X0)). 1.73/0.60 thf(func_def_70, type, sK5: reg). 1.73/0.60 thf(func_def_71, type, sK6: reg). 1.73/0.60 thf(func_def_72, type, sK7: reg). 1.73/0.60 thf(func_def_73, type, sK8: reg). 1.73/0.60 thf(func_def_74, type, sK9: reg). 1.73/0.60 thf(func_def_75, type, sK10: reg). 1.73/0.60 thf(func_def_76, type, sK11: reg). 1.73/0.60 thf(func_def_77, type, sK12: reg). 1.73/0.60 thf(func_def_78, type, sK13: reg). 1.73/0.60 thf(func_def_79, type, sK14: reg). 1.73/0.60 thf(func_def_80, type, sK15: reg). 1.73/0.60 thf(func_def_81, type, sK16: reg). 1.73/0.60 thf(func_def_82, type, sK17: reg). 1.73/0.60 thf(func_def_83, type, sK18: reg). 1.73/0.60 thf(func_def_84, type, sK19: reg). 1.73/0.60 thf(func_def_85, type, sK20: $i > $i > $i). 1.73/0.60 thf(func_def_86, type, sK21: reg). 1.73/0.60 thf(func_def_87, type, sK22: reg). 1.73/0.60 thf(func_def_88, type, sK23: $i > ($i > $o) > $i). 1.73/0.60 thf(func_def_89, type, sK24: reg). 1.73/0.60 thf(func_def_90, type, sK25: reg). 1.73/0.60 thf(f3453,plain,( 1.73/0.60 $false), 1.73/0.60 inference(avatar_sat_refutation,[status(thm)],[f263,f642,f1069,f1835,f3108,f3452])). 1.73/0.60 thf(f3452,plain,( 1.73/0.60 ~spl0_2 | ~spl0_5 | ~spl0_15), 1.73/0.60 inference(avatar_contradiction_clause,[status(thm)],[f3451])). 1.73/0.60 thf(f3451,plain,( 1.73/0.60 $false | (~spl0_2 | ~spl0_5 | ~spl0_15)), 1.73/0.60 inference(trivial_inequality_removal,[status(thm)],[f3450])). 1.73/0.60 thf(f3450,plain,( 1.73/0.60 ($false = $true) | (~spl0_2 | ~spl0_5 | ~spl0_15)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f3449])). 1.73/0.60 thf(f3449,plain,( 1.73/0.60 ((~ $true) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_15)), 1.73/0.60 inference(forward_demodulation,[status(thm)],[f3445,f3391])). 1.73/0.60 thf(f3391,plain,( 1.73/0.60 ((c @ sK12 @ paris) = $true) | (~spl0_5 | ~spl0_15)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f3383])). 1.73/0.60 thf(f3383,plain,( 1.73/0.60 (($true => (c @ sK12 @ paris)) = $true) | (~spl0_5 | ~spl0_15)), 1.73/0.60 inference(superposition,[status(thm)],[f3205,f3375])). 1.73/0.60 thf(f3375,plain,( 1.73/0.60 ((c @ sK12 @ sK9) = $true) | ~spl0_15), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f1062])). 1.73/0.60 thf(f1062,plain,( 1.73/0.60 ((~ (c @ sK12 @ sK9)) = $false) | ~spl0_15), 1.73/0.60 inference(avatar_component_clause,[status(thm)],[f1061])). 1.73/0.60 thf(f1061,definition,( 1.73/0.60 spl0_15 <=> ((~ (c @ sK12 @ sK9)) = $false)), 1.73/0.60 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])). 1.73/0.60 thf(f3205,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((c @ X1 @ sK9) => (c @ X1 @ paris)) = $true)) ) | ~spl0_5), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f3204])). 1.73/0.60 thf(f3204,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ paris))) @ X1) = $true)) ) | ~spl0_5), 1.73/0.60 inference(pi_clausification,[status(thm)],[f3179])). 1.73/0.60 thf(f3179,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ paris)))) = $true) | ~spl0_5), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f3178])). 1.73/0.60 thf(f3178,plain,( 1.73/0.60 (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ paris)))) & $true) = $true) | ~spl0_5), 1.73/0.60 inference(backward_demodulation,[status(thm)],[f3152,f3176])). 1.73/0.60 thf(f3176,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ spain)))) = $true) | ~spl0_5), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f3152])). 1.73/0.60 thf(f3152,plain,( 1.73/0.60 (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ spain))))) = $true) | ~spl0_5), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f3149])). 1.73/0.60 thf(f3149,plain,( 1.73/0.60 ($true = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))) @ sK9)) | ~spl0_5), 1.73/0.60 inference(sigma_clausification,[status(thm)],[f3131])). 1.73/0.60 thf(f3131,plain,( 1.73/0.60 ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))) = $true) | ~spl0_5), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f638])). 1.73/0.60 thf(f638,plain,( 1.73/0.60 ($false = (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))))) | ~spl0_5), 1.73/0.60 inference(avatar_component_clause,[status(thm)],[f637])). 1.73/0.60 thf(f637,definition,( 1.73/0.60 spl0_5 <=> ($false = (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))))), 1.73/0.60 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])). 1.73/0.60 thf(f3445,plain,( 1.73/0.60 ((~ (c @ sK12 @ paris)) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_15)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f3438])). 1.73/0.60 thf(f3438,plain,( 1.73/0.60 (((c @ sK12 @ paris) => $false) = $true) | (~spl0_2 | ~spl0_5 | ~spl0_15)), 1.73/0.60 inference(superposition,[status(thm)],[f923,f3435])). 1.73/0.60 thf(f3435,plain,( 1.73/0.60 ($false = (c @ sK12 @ france)) | (~spl0_2 | ~spl0_5 | ~spl0_15)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f3434])). 1.73/0.60 thf(f3434,plain,( 1.73/0.60 (($true => (c @ sK12 @ france)) = $false) | (~spl0_2 | ~spl0_5 | ~spl0_15)), 1.73/0.60 inference(forward_demodulation,[status(thm)],[f3432,f3375])). 1.73/0.60 thf(f3432,plain,( 1.73/0.60 ($false = ((c @ sK12 @ sK9) => (c @ sK12 @ france))) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f3430])). 1.73/0.60 thf(f3430,plain,( 1.73/0.60 ($false = ((^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ france))) @ sK12)) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(sigma_clausification,[status(thm)],[f3288])). 1.73/0.60 thf(f3288,plain,( 1.73/0.60 ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ france))))) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f3287])). 1.73/0.60 thf(f3287,plain,( 1.73/0.60 ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ france)))) & $true)) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(superposition,[status(thm)],[f1922,f3176])). 1.73/0.60 thf(f1922,plain,( 1.73/0.60 ( ! [X1 : reg] : (($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain))))))) ) | ~spl0_2), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f1920])). 1.73/0.60 thf(f1920,plain,( 1.73/0.60 ( ! [X1 : reg] : (($false = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))) @ X1))) ) | ~spl0_2), 1.73/0.60 inference(pi_clausification,[status(thm)],[f1896])). 1.73/0.60 thf(f1896,plain,( 1.73/0.60 ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))) = $false) | ~spl0_2), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f1853])). 1.73/0.60 thf(f1853,plain,( 1.73/0.60 ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) = $true) | ~spl0_2), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f262])). 1.73/0.60 thf(f262,plain,( 1.73/0.60 (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ france)) = $true) | ~spl0_2), 1.73/0.60 inference(avatar_component_clause,[status(thm)],[f261])). 1.73/0.60 thf(f261,definition,( 1.73/0.60 spl0_2 <=> (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ france)) = $true)), 1.73/0.60 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])). 1.73/0.60 thf(f923,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((c @ X1 @ paris) => (c @ X1 @ france)) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f921])). 1.73/0.60 thf(f921,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X1) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f470])). 1.73/0.60 thf(f470,plain,( 1.73/0.60 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))))), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f392])). 1.73/0.60 thf(f392,plain,( 1.73/0.60 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))))), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f349])). 1.73/0.60 thf(f349,plain,( 1.73/0.60 ((((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris))))))) = $true)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f348])). 1.73/0.60 thf(f348,plain,( 1.73/0.60 (($false | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))))) = $true)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f344])). 1.73/0.60 thf(f344,plain,( 1.73/0.60 ($true = ((~ $true) | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))))))), 1.73/0.60 inference(superposition,[status(thm)],[f338,f301])). 1.73/0.60 thf(f301,plain,( 1.73/0.60 ((a @ sK2 @ sK3) = $true)), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f300])). 1.73/0.60 thf(f300,plain,( 1.73/0.60 ((~ (a @ sK2 @ sK3)) = $false)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f297])). 1.73/0.60 thf(f297,plain,( 1.73/0.60 ($false = ((~ (a @ sK2 @ sK3)) | $false))), 1.73/0.60 inference(backward_demodulation,[status(thm)],[f294,f295])). 1.73/0.60 thf(f295,plain,( 1.73/0.60 ((?? @ reg @ (^[Y0 : reg]: ((~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ Y0)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0))))))))))) = $false)), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f294])). 1.73/0.60 thf(f294,plain,( 1.73/0.60 ($false = ((~ (a @ sK2 @ sK3)) | (?? @ reg @ (^[Y0 : reg]: ((~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ Y0)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))))))))), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f293])). 1.73/0.60 thf(f293,plain,( 1.73/0.60 ($false = ((^[Y0 : $i]: ((~ (a @ sK2 @ Y0)) | (?? @ reg @ (^[Y1 : reg]: ((~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ Y1)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1))))))))))))) @ sK3))), 1.73/0.60 inference(sigma_clausification,[status(thm)],[f292])). 1.73/0.60 thf(f292,plain,( 1.73/0.60 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (a @ sK2 @ Y0)) | (?? @ reg @ (^[Y1 : reg]: ((~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ Y1)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))) & (~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))))))))))), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f291])). 1.73/0.60 thf(f291,plain,( 1.73/0.60 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (?? @ reg @ (^[Y2 : reg]: ((~ ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ spain) => (c @ Y3 @ Y2)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))))))))))) @ sK2))), 1.73/0.60 inference(sigma_clausification,[status(thm)],[f288])). 1.73/0.60 thf(f288,plain,( 1.73/0.60 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (?? @ reg @ (^[Y2 : reg]: ((~ ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ spain) => (c @ Y3 @ Y2)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))))))))))) = $false)), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f221])). 1.73/0.60 thf(f221,plain,( 1.73/0.60 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (?? @ reg @ (^[Y2 : reg]: ((~ ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ spain) => (c @ Y3 @ Y2)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))) & (~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2))))))))))))))))) = $true)), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f216])). 1.73/0.60 thf(f216,plain,( 1.73/0.60 ((~ ((^[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]: (((^[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))))) @ Y1 @ spain)) & (~ ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ 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))))))) @ Y4 @ Y2))))))) @ Y1 @ paris))))))))) = $true)), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f165,f166,f176,f205,f206])). 1.73/0.60 thf(f206,plain,( 1.73/0.60 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y0))))))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f186,f154,f154])). 1.73/0.60 thf(f154,plain,( 1.73/0.60 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f143])). 1.73/0.60 thf(f143,plain,( 1.73/0.60 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f142])). 1.73/0.60 thf(f142,plain,( 1.73/0.60 (p = (^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))))), 1.73/0.60 inference(rectify,[status(thm)],[f33])). 1.73/0.60 thf(f33,axiom,( 1.73/0.60 (p = (^[X0 : reg, X1 : reg] : (! [X11 : reg] : ((c @ X11 @ X0) => (c @ X11 @ X1)))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',p)). 1.73/0.60 thf(f186,plain,( 1.73/0.60 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y1) & (p @ Y2 @ Y0))))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f59])). 1.73/0.60 thf(f59,plain,( 1.73/0.60 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y1) & (p @ Y2 @ Y0))))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f58])). 1.73/0.60 thf(f58,plain,( 1.73/0.60 (o = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((p @ X2 @ X0) & (p @ X2 @ X1)))))), 1.73/0.60 inference(rectify,[status(thm)],[f35])). 1.73/0.60 thf(f35,axiom,( 1.73/0.60 (o = (^[X0 : reg, X1 : reg] : (? [X11 : reg] : ((p @ X11 @ X0) & (p @ X11 @ X1)))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',o)). 1.73/0.60 thf(f205,plain,( 1.73/0.60 (eq = (^[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))))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f178,f154,f154])). 1.73/0.60 thf(f178,plain,( 1.73/0.60 (eq = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y1 @ Y0) & (p @ Y0 @ Y1))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f104])). 1.73/0.60 thf(f104,plain,( 1.73/0.60 (eq = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y1 @ Y0) & (p @ Y0 @ Y1))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f103])). 1.73/0.60 thf(f103,plain,( 1.73/0.60 (eq = (^[X0 : reg, X1 : reg] : ((p @ X0 @ X1) & (p @ X1 @ X0))))), 1.73/0.60 inference(rectify,[status(thm)],[f34])). 1.73/0.60 thf(f34,axiom,( 1.73/0.60 (eq = (^[X0 : reg, X1 : reg] : ((p @ X0 @ X1) & (p @ X1 @ X0))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',eq)). 1.73/0.60 thf(f176,plain,( 1.73/0.60 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f106])). 1.73/0.60 thf(f106,plain,( 1.73/0.60 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (Y0 @ Y2 @ Y3)) | (Y1 @ Y3))))))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f105])). 1.73/0.60 thf(f105,plain,( 1.73/0.60 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3 : $i] : ((X1 @ X3) | ~(X0 @ X2 @ X3)))) = mbox)), 1.73/0.60 inference(rectify,[status(thm)],[f16])). 1.73/0.60 thf(f16,axiom,( 1.73/0.60 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7 : $i] : ((X3 @ X7) | ~(X6 @ X2 @ X7)))) = mbox)), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',mbox)). 1.73/0.60 thf(f166,plain,( 1.73/0.60 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f141])). 1.73/0.60 thf(f141,plain,( 1.73/0.60 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f140])). 1.73/0.60 thf(f140,plain,( 1.73/0.60 (mvalid = (^[X0 : $i > $o] : (! [X1 : $i] : (X0 @ X1))))), 1.73/0.60 inference(rectify,[status(thm)],[f28])). 1.73/0.60 thf(f28,axiom,( 1.73/0.60 (mvalid = (^[X3 : $i > $o] : (! [X2 : $i] : (X3 @ X2))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',mvalid)). 1.73/0.60 thf(f165,plain,( 1.73/0.60 ((~ (mvalid @ (mbox @ a @ (^[Y0 : $i]: (?? @ reg @ (^[Y1 : reg]: ((~ (eq @ Y1 @ spain)) & (~ (o @ Y1 @ paris))))))))) = $true)), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f111])). 1.73/0.60 thf(f111,plain,( 1.73/0.60 ((~ (mvalid @ (mbox @ a @ (^[Y0 : $i]: (?? @ reg @ (^[Y1 : reg]: ((~ (eq @ Y1 @ spain)) & (~ (o @ Y1 @ paris))))))))) = $true)), 1.73/0.60 inference(fool_elimination,[status(thm)],[f110])). 1.73/0.60 thf(f110,plain,( 1.73/0.60 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (? [X1 : reg] : (~(o @ X1 @ paris) & ~(eq @ X1 @ spain))))))), 1.73/0.60 inference(rectify,[status(thm)],[f47])). 1.73/0.60 thf(f47,negated_conjecture,( 1.73/0.60 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (? [X11 : reg] : (~(o @ X11 @ paris) & ~(eq @ X11 @ spain))))))), 1.73/0.60 inference(negated_conjecture,[status(cth)],[f46])). 1.73/0.60 thf(f46,conjecture,( 1.73/0.60 (mvalid @ (mbox @ a @ (^[X0 : $i] : (? [X11 : reg] : (~(o @ X11 @ paris) & ~(eq @ X11 @ spain))))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',con)). 1.73/0.60 thf(f338,plain,( 1.73/0.60 ( ! [X2 : $i,X1 : $i] : ((((~ (a @ X1 @ X2)) | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris)))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))))) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f337])). 1.73/0.60 thf(f337,plain,( 1.73/0.60 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris)))))) & (~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ paris))))))))) @ X2))) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f332])). 1.73/0.60 thf(f332,plain,( 1.73/0.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris)))))) & (~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ france)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ paris)))))))))) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f331])). 1.73/0.60 thf(f331,plain,( 1.73/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris)))))) & (~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ france)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ paris))))))))))) @ X1) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f219])). 1.73/0.60 thf(f219,plain,( 1.73/0.60 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris)))))) & (~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ france)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ paris)))))))))))))), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f212])). 1.73/0.60 thf(f212,plain,( 1.73/0.60 (((^[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))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y2) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y1))))))))) @ paris @ france)))) = $true)), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f150,f166,f176,f211])). 1.73/0.60 thf(f211,plain,( 1.73/0.60 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y1) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y0))))))))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f151,f209,f208,f208])). 1.73/0.60 thf(f208,plain,( 1.73/0.60 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ ((^[Y2 : reg]: ((^[Y3 : reg]: (?? @ 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))))))) @ Y4 @ Y2))))))) @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f169,f206])). 1.73/0.60 thf(f169,plain,( 1.73/0.60 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f61])). 1.73/0.60 thf(f61,plain,( 1.73/0.60 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f60])). 1.73/0.60 thf(f60,plain,( 1.73/0.60 ((^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))) = ec)), 1.73/0.60 inference(rectify,[status(thm)],[f37])). 1.73/0.60 thf(f37,axiom,( 1.73/0.60 ((^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))) = ec)), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',ec)). 1.73/0.60 thf(f209,plain,( 1.73/0.60 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y0 @ Y1) & (~ ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ Y0)))))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f184,f154,f154])). 1.73/0.60 thf(f184,plain,( 1.73/0.60 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f94])). 1.73/0.60 thf(f94,plain,( 1.73/0.60 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (~ (p @ Y1 @ Y0)))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f93])). 1.73/0.60 thf(f93,plain,( 1.73/0.60 ((^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))) = pp)), 1.73/0.60 inference(rectify,[status(thm)],[f38])). 1.73/0.60 thf(f38,axiom,( 1.73/0.60 ((^[X0 : reg, X1 : reg] : (~(p @ X1 @ X0) & (p @ X0 @ X1))) = pp)), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',pp)). 1.73/0.60 thf(f151,plain,( 1.73/0.60 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y1) & (ec @ Y2 @ Y0))))))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f146])). 1.73/0.60 thf(f146,plain,( 1.73/0.60 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y1) & (ec @ Y2 @ Y0))))))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f145])). 1.73/0.60 thf(f145,plain,( 1.73/0.60 ((^[X0 : reg, X1 : reg] : (~? [X2 : reg] : ((ec @ X2 @ X0) & (ec @ X2 @ X1)) & (pp @ X0 @ X1))) = ntpp)), 1.73/0.60 inference(rectify,[status(thm)],[f40])). 1.73/0.60 thf(f40,axiom,( 1.73/0.60 ((^[X0 : reg, X1 : reg] : (~? [X11 : reg] : ((ec @ X11 @ X0) & (ec @ X11 @ X1)) & (pp @ X0 @ X1))) = ntpp)), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',ntpp)). 1.73/0.60 thf(f150,plain,( 1.73/0.60 ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))) = $true)), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f100])). 1.73/0.60 thf(f100,plain,( 1.73/0.60 ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))) = $true)), 1.73/0.60 inference(fool_elimination,[status(thm)],[f99])). 1.73/0.60 thf(f99,plain,( 1.73/0.60 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))), 1.73/0.60 inference(rectify,[status(thm)],[f49])). 1.73/0.60 thf(f49,axiom,( 1.73/0.60 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',ax3)). 1.73/0.60 thf(f3108,plain,( 1.73/0.60 ~spl0_6), 1.73/0.60 inference(avatar_contradiction_clause,[status(thm)],[f3107])). 1.73/0.60 thf(f3107,plain,( 1.73/0.60 $false | ~spl0_6), 1.73/0.60 inference(trivial_inequality_removal,[status(thm)],[f3106])). 1.73/0.60 thf(f3106,plain,( 1.73/0.60 ($false = $true) | ~spl0_6), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f3105])). 1.73/0.60 thf(f3105,plain,( 1.73/0.60 ((~ $true) = $true) | ~spl0_6), 1.73/0.60 inference(forward_demodulation,[status(thm)],[f3092,f1631])). 1.73/0.60 thf(f1631,plain,( 1.73/0.60 ((c @ paris @ sK18) = $true)), 1.73/0.60 inference(trivial_inequality_removal,[status(thm)],[f1621])). 1.73/0.60 thf(f1621,plain,( 1.73/0.60 ($false = $true) | ((c @ paris @ sK18) = $true)), 1.73/0.60 inference(superposition,[status(thm)],[f232,f1607])). 1.73/0.60 thf(f1607,plain,( 1.73/0.60 ((c @ sK18 @ paris) = $true)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f1602])). 1.73/0.60 thf(f1602,plain,( 1.73/0.60 (($true => (c @ sK18 @ paris)) = $true)), 1.73/0.60 inference(superposition,[status(thm)],[f1583,f227])). 1.73/0.60 thf(f227,plain,( 1.73/0.60 ( ! [X1 : reg] : (((c @ X1 @ X1) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f226])). 1.73/0.60 thf(f226,plain,( 1.73/0.60 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: (c @ Y0 @ Y0)) @ X1))) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f159])). 1.73/0.60 thf(f159,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: (c @ Y0 @ Y0))) = $true)), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f67])). 1.73/0.60 thf(f67,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: (c @ Y0 @ Y0))) = $true)), 1.73/0.60 inference(fool_elimination,[status(thm)],[f66])). 1.73/0.60 thf(f66,plain,( 1.73/0.60 ! [X0 : reg] : (c @ X0 @ X0)), 1.73/0.60 inference(rectify,[status(thm)],[f41])). 1.73/0.60 thf(f41,axiom,( 1.73/0.60 ! [X0 : reg] : (c @ X0 @ X0)), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',c_reflexive)). 1.73/0.60 thf(f1583,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((c @ X1 @ sK18) => (c @ X1 @ paris)) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f1582])). 1.73/0.60 thf(f1582,plain,( 1.73/0.60 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ sK18) => (c @ Y0 @ paris))) @ X1))) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f1573])). 1.73/0.60 thf(f1573,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK18) => (c @ Y0 @ paris)))) = $true)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f1572])). 1.73/0.60 thf(f1572,plain,( 1.73/0.60 (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK18) => (c @ Y0 @ paris)))) & $true) = $true)), 1.73/0.60 inference(backward_demodulation,[status(thm)],[f1548,f1570])). 1.73/0.60 thf(f1570,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK18) => (c @ Y0 @ catalunya)))) = $true)), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f1548])). 1.73/0.60 thf(f1548,plain,( 1.73/0.60 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK18) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK18) => (c @ Y0 @ catalunya))))))), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f1543])). 1.73/0.60 thf(f1543,plain,( 1.73/0.60 ($true = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))))) @ sK18))), 1.73/0.60 inference(sigma_clausification,[status(thm)],[f1529])). 1.73/0.60 thf(f1529,plain,( 1.73/0.60 ($true = (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f361])). 1.73/0.60 thf(f361,plain,( 1.73/0.60 ($false = (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya)))))))))), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f360])). 1.73/0.60 thf(f360,plain,( 1.73/0.60 ($false = ($true & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))))), 1.73/0.60 inference(forward_demodulation,[status(thm)],[f357,f342])). 1.73/0.60 thf(f342,plain,( 1.73/0.60 ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) = $true)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f341])). 1.73/0.60 thf(f341,plain,( 1.73/0.60 (($true & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) = $true)), 1.73/0.60 inference(backward_demodulation,[status(thm)],[f334,f340])). 1.73/0.60 thf(f340,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) = $true)), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f334])). 1.73/0.60 thf(f334,plain,( 1.73/0.60 (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) = $true)), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f326])). 1.73/0.60 thf(f326,plain,( 1.73/0.60 ((((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain)))))) = $true)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f325])). 1.73/0.60 thf(f325,plain,( 1.73/0.60 (($false | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain))))))) = $true)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f321])). 1.73/0.60 thf(f321,plain,( 1.73/0.60 (((~ $true) | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain))))))) = $true)), 1.73/0.60 inference(superposition,[status(thm)],[f319,f301])). 1.73/0.60 thf(f319,plain,( 1.73/0.60 ( ! [X2 : $i,X1 : $i] : ((((~ (a @ X1 @ X2)) | (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) & (~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))))) & (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ spain))))))) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f318])). 1.73/0.60 thf(f318,plain,( 1.73/0.60 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya)))))) & (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ catalunya)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain)))))))) @ X2) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f316])). 1.73/0.60 thf(f316,plain,( 1.73/0.60 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (a @ X1 @ Y0)) | (((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))) & (~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya)))))) & (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ catalunya)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))))))) & (c @ Y1 @ spain))))))))) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f315])). 1.73/0.60 thf(f315,plain,( 1.73/0.60 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya)))))) & (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ catalunya)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ spain)))))))))) @ X1))) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f224])). 1.73/0.60 thf(f224,plain,( 1.73/0.60 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (a @ Y0 @ Y1)) | (((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))) & (~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya)))))) & (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ catalunya)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))))))) & (c @ Y2 @ spain))))))))))) = $true)), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f214])). 1.73/0.60 thf(f214,plain,( 1.73/0.60 ($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))))))) @ Y3 @ Y4) & (~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)))))) @ Y1 @ Y2) & (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y1) & ((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y2)))))))) @ catalunya @ spain)))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f158,f166,f176,f210])). 1.73/0.60 thf(f210,plain,( 1.73/0.60 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3) & (~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)))))) @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y1)))))))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f181,f209,f208,f208])). 1.73/0.60 thf(f181,plain,( 1.73/0.60 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f84])). 1.73/0.60 thf(f84,plain,( 1.73/0.60 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f83])). 1.73/0.60 thf(f83,plain,( 1.73/0.60 (tpp = (^[X0 : reg, X1 : reg] : (? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))), 1.73/0.60 inference(rectify,[status(thm)],[f39])). 1.73/0.60 thf(f39,axiom,( 1.73/0.60 (tpp = (^[X0 : reg, X1 : reg] : (? [X11 : reg] : ((ec @ X11 @ X1) & (ec @ X11 @ X0)) & (pp @ X0 @ X1))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',tpp)). 1.73/0.60 thf(f158,plain,( 1.73/0.60 ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))) = $true)), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f102])). 1.73/0.60 thf(f102,plain,( 1.73/0.60 ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))) = $true)), 1.73/0.60 inference(fool_elimination,[status(thm)],[f101])). 1.73/0.60 thf(f101,plain,( 1.73/0.60 (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))), 1.73/0.60 inference(rectify,[status(thm)],[f43])). 1.73/0.60 thf(f43,axiom,( 1.73/0.60 (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',ax1)). 1.73/0.60 thf(f357,plain,( 1.73/0.60 ($false = ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))))), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f356])). 1.73/0.60 thf(f356,plain,( 1.73/0.60 (((~ ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya)))) & $true)) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ catalunya))))))))) = $false)), 1.73/0.60 inference(superposition,[status(thm)],[f314,f340])). 1.73/0.60 thf(f314,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((~ ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ X1)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain)))))) & (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ X1))))))))) = $false)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f313])). 1.73/0.60 thf(f313,plain,( 1.73/0.60 ( ! [X1 : reg] : (($false = ((^[Y0 : reg]: ((~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ Y0)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))) & (~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))))) @ X1))) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f295])). 1.73/0.60 thf(f232,plain,( 1.73/0.60 ( ! [X2 : reg,X1 : reg] : (((c @ X2 @ X1) = $false) | ((c @ X1 @ X2) = $true)) )), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f231])). 1.73/0.60 thf(f231,plain,( 1.73/0.60 ( ! [X2 : reg,X1 : reg] : ((((c @ X2 @ X1) => (c @ X1 @ X2)) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f230])). 1.73/0.60 thf(f230,plain,( 1.73/0.60 ( ! [X2 : reg,X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ X1 @ Y0))) @ X2) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f229])). 1.73/0.60 thf(f229,plain,( 1.73/0.60 ( ! [X1 : reg] : (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ X1 @ Y0)))) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f228])). 1.73/0.60 thf(f228,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y0 @ Y1))))) @ X1) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f194])). 1.73/0.60 thf(f194,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y0 @ Y1)))))) = $true)), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f80])). 1.73/0.60 thf(f80,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y0 @ Y1)))))) = $true)), 1.73/0.60 inference(fool_elimination,[status(thm)],[f79])). 1.73/0.60 thf(f79,plain,( 1.73/0.60 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))), 1.73/0.60 inference(rectify,[status(thm)],[f42])). 1.73/0.60 thf(f42,axiom,( 1.73/0.60 ! [X0 : reg,X1 : reg] : ((c @ X0 @ X1) => (c @ X1 @ X0))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',c_symmetric)). 1.73/0.60 thf(f3092,plain,( 1.73/0.60 ($true = (~ (c @ paris @ sK18))) | ~spl0_6), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f3067])). 1.73/0.60 thf(f3067,plain,( 1.73/0.60 ($true = ((c @ paris @ sK18) => $false)) | ~spl0_6), 1.73/0.60 inference(superposition,[status(thm)],[f3046,f1216])). 1.73/0.60 thf(f1216,plain,( 1.73/0.60 ((c @ paris @ catalunya) = $false) | ~spl0_6), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f1091])). 1.73/0.60 thf(f1091,plain,( 1.73/0.60 ((~ (c @ paris @ catalunya)) = $true) | ~spl0_6), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f1088])). 1.73/0.60 thf(f1088,plain,( 1.73/0.60 (((c @ paris @ catalunya) => $false) = $true) | ~spl0_6), 1.73/0.60 inference(superposition,[status(thm)],[f358,f1083])). 1.73/0.60 thf(f1083,plain,( 1.73/0.60 ($false = (c @ paris @ spain)) | ~spl0_6), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f1079])). 1.73/0.60 thf(f1079,plain,( 1.73/0.60 ((~ (c @ paris @ spain)) = $true) | ~spl0_6), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f1076])). 1.73/0.60 thf(f1076,plain,( 1.73/0.60 (((c @ paris @ spain) => $false) = $true) | ~spl0_6), 1.73/0.60 inference(superposition,[status(thm)],[f231,f641])). 1.73/0.60 thf(f641,plain,( 1.73/0.60 ($false = (c @ spain @ paris)) | ~spl0_6), 1.73/0.60 inference(avatar_component_clause,[status(thm)],[f640])). 1.73/0.60 thf(f640,definition,( 1.73/0.60 spl0_6 <=> ($false = (c @ spain @ paris))), 1.73/0.60 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])). 1.73/0.60 thf(f358,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((c @ X1 @ catalunya) => (c @ X1 @ spain)) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f354])). 1.73/0.60 thf(f354,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))) @ X1) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f340])). 1.73/0.60 thf(f3046,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((c @ X1 @ sK18) => (c @ X1 @ catalunya)) = $true)) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f3043])). 1.73/0.60 thf(f3043,plain,( 1.73/0.60 ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ sK18) => (c @ Y0 @ catalunya))) @ X1) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f1570])). 1.73/0.60 thf(f1835,plain,( 1.73/0.60 ~spl0_1), 1.73/0.60 inference(avatar_contradiction_clause,[status(thm)],[f1834])). 1.73/0.60 thf(f1834,plain,( 1.73/0.60 $false | ~spl0_1), 1.73/0.60 inference(trivial_inequality_removal,[status(thm)],[f1833])). 1.73/0.60 thf(f1833,plain,( 1.73/0.60 ($false = $true) | ~spl0_1), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f1832])). 1.73/0.60 thf(f1832,plain,( 1.73/0.60 ( ! [X0 : $i,X1 : $i] : (($false = ($true | (fool @ X0 @ (sK20 @ X1 @ X0))))) ) | ~spl0_1), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f1831])). 1.73/0.60 thf(f1831,plain,( 1.73/0.60 ( ! [X0 : $i,X1 : $i] : ((((~ $false) | (fool @ X0 @ (sK20 @ X1 @ X0))) = $false)) ) | ~spl0_1), 1.73/0.60 inference(forward_demodulation,[status(thm)],[f1823,f1781])). 1.73/0.60 thf(f1781,plain,( 1.73/0.60 ( ! [X2 : $i,X1 : $i] : (((fool @ X1 @ X2) = $false)) ) | ~spl0_1), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f259])). 1.73/0.60 thf(f259,plain,( 1.73/0.60 ( ! [X2 : $i,X1 : $i] : (($true = (~ (fool @ X1 @ X2)))) ) | ~spl0_1), 1.73/0.60 inference(avatar_component_clause,[status(thm)],[f258])). 1.73/0.60 thf(f258,definition,( 1.73/0.60 spl0_1 <=> ! [X2 : $i,X1 : $i] : ($true = (~ (fool @ X1 @ X2)))), 1.73/0.60 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])). 1.73/0.60 thf(f1823,plain,( 1.73/0.60 ( ! [X0 : $i,X1 : $i] : (($false = ((~ (fool @ X1 @ (sK20 @ X1 @ X0))) | (fool @ X0 @ (sK20 @ X1 @ X0))))) ) | ~spl0_1), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f1818])). 1.73/0.60 thf(f1818,plain,( 1.73/0.60 ( ! [X0 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (fool @ X0 @ Y0))) @ (sK20 @ X1 @ X0)) = $false)) ) | ~spl0_1), 1.73/0.60 inference(sigma_clausification,[status(thm)],[f1801])). 1.73/0.60 thf(f1801,plain,( 1.73/0.60 ( ! [X0 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (fool @ X0 @ Y0)))) = $false)) ) | ~spl0_1), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f1785])). 1.73/0.60 thf(f1785,plain,( 1.73/0.60 ( ! [X0 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (fool @ X0 @ Y0))))))) ) | ~spl0_1), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f1784])). 1.73/0.60 thf(f1784,plain,( 1.73/0.60 ( ! [X0 : $i,X1 : $i] : ((($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (fool @ X0 @ Y0)))))) = $true)) ) | ~spl0_1), 1.73/0.60 inference(superposition,[status(thm)],[f240,f1781])). 1.73/0.60 thf(f240,plain,( 1.73/0.60 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((X2 @ X1) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | (X2 @ Y0)))))))) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f239])). 1.73/0.60 thf(f239,plain,( 1.73/0.60 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1))))))) @ X2) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f238])). 1.73/0.60 thf(f238,plain,( 1.73/0.60 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((Y0 @ X1) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ X1 @ Y1)) | (Y0 @ Y1)))))))))) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f237])). 1.73/0.60 thf(f237,plain,( 1.73/0.60 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2))))))))) @ X1) = $true)) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f220])). 1.73/0.60 thf(f220,plain,( 1.73/0.60 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((Y1 @ Y0) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (fool @ Y0 @ Y2)) | (Y1 @ Y2)))))))))) = $true)), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f215])). 1.73/0.60 thf(f215,plain,( 1.73/0.60 ($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)))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f163,f166,f175,f197,f176])). 1.73/0.60 thf(f197,plain,( 1.73/0.60 (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)))))), 1.73/0.60 inference(definition_unfolding,[status(thm)],[f167,f190,f174])). 1.73/0.60 thf(f174,plain,( 1.73/0.60 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f92])). 1.73/0.60 thf(f92,plain,( 1.73/0.60 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f91])). 1.73/0.60 thf(f91,plain,( 1.73/0.60 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)), 1.73/0.60 inference(rectify,[status(thm)],[f3])). 1.73/0.60 thf(f3,axiom,( 1.73/0.60 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',mnot)). 1.73/0.60 thf(f190,plain,( 1.73/0.60 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f86])). 1.73/0.60 thf(f86,plain,( 1.73/0.60 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f85])). 1.73/0.60 thf(f85,plain,( 1.73/0.60 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))), 1.73/0.60 inference(rectify,[status(thm)],[f4])). 1.73/0.60 thf(f4,axiom,( 1.73/0.60 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',mor)). 1.73/0.60 thf(f167,plain,( 1.73/0.60 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f139])). 1.73/0.60 thf(f139,plain,( 1.73/0.60 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f138])). 1.73/0.60 thf(f138,plain,( 1.73/0.60 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))), 1.73/0.60 inference(rectify,[status(thm)],[f6])). 1.73/0.60 thf(f6,axiom,( 1.73/0.60 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',mimplies)). 1.73/0.60 thf(f175,plain,( 1.73/0.60 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f108])). 1.73/0.60 thf(f108,plain,( 1.73/0.60 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f107])). 1.73/0.60 thf(f107,plain,( 1.73/0.60 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)), 1.73/0.60 inference(rectify,[status(thm)],[f11])). 1.73/0.60 thf(f11,axiom,( 1.73/0.60 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',mforall_prop)). 1.73/0.60 thf(f163,plain,( 1.73/0.60 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)))))), 1.73/0.60 inference(cnf_transformation,[status(thm)],[f72])). 1.73/0.60 thf(f72,plain,( 1.73/0.60 ($true = (mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)))))), 1.73/0.60 inference(fool_elimination,[status(thm)],[f71])). 1.73/0.60 thf(f71,plain,( 1.73/0.60 (mvalid @ (mforall_prop @ (^[X0 : $i > $o] : (mimplies @ (mbox @ fool @ X0) @ X0))))), 1.73/0.60 inference(rectify,[status(thm)],[f44])). 1.73/0.60 thf(f44,axiom,( 1.73/0.60 (mvalid @ (mforall_prop @ (^[X12 : $i > $o] : (mimplies @ (mbox @ fool @ X12) @ X12))))), 1.73/0.60 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',t_axiom_for_fool)). 1.73/0.60 thf(f1069,plain,( 1.73/0.60 spl0_15 | ~spl0_2 | ~spl0_5), 1.73/0.60 inference(avatar_split_clause,[status(thm)],[f1068,f637,f261,f1061])). 1.73/0.60 thf(f1068,plain,( 1.73/0.60 ((~ (c @ sK12 @ sK9)) = $false) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f1067])). 1.73/0.60 thf(f1067,plain,( 1.73/0.60 ($false = ((c @ sK12 @ sK9) => $false)) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(backward_demodulation,[status(thm)],[f1031,f1053])). 1.73/0.60 thf(f1053,plain,( 1.73/0.60 ($false = (c @ sK12 @ france)) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f1031])). 1.73/0.60 thf(f1031,plain,( 1.73/0.60 ($false = ((c @ sK12 @ sK9) => (c @ sK12 @ france))) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f1028])). 1.73/0.60 thf(f1028,plain,( 1.73/0.60 ($false = ((^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ france))) @ sK12)) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(sigma_clausification,[status(thm)],[f699])). 1.73/0.60 thf(f699,plain,( 1.73/0.60 ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ france))))) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f694])). 1.73/0.60 thf(f694,plain,( 1.73/0.60 ($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ france)))) & $true)) | (~spl0_2 | ~spl0_5)), 1.73/0.60 inference(superposition,[status(thm)],[f286,f686])). 1.73/0.60 thf(f686,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ spain)))) = $true) | ~spl0_5), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f685])). 1.73/0.60 thf(f685,plain,( 1.73/0.60 (($true & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ spain))))) = $true) | ~spl0_5), 1.73/0.60 inference(backward_demodulation,[status(thm)],[f672,f684])). 1.73/0.60 thf(f684,plain,( 1.73/0.60 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ paris)))) = $true) | ~spl0_5), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f672])). 1.73/0.60 thf(f672,plain,( 1.73/0.60 (((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ sK9) => (c @ Y0 @ spain))))) = $true) | ~spl0_5), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f669])). 1.73/0.60 thf(f669,plain,( 1.73/0.60 ($true = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))) @ sK9)) | ~spl0_5), 1.73/0.60 inference(sigma_clausification,[status(thm)],[f653])). 1.73/0.60 thf(f653,plain,( 1.73/0.60 ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))) = $true) | ~spl0_5), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f638])). 1.73/0.60 thf(f286,plain,( 1.73/0.60 ( ! [X1 : reg] : (($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain))))))) ) | ~spl0_2), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f285])). 1.73/0.60 thf(f285,plain,( 1.73/0.60 ( ! [X1 : reg] : (($false = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))) @ X1))) ) | ~spl0_2), 1.73/0.60 inference(pi_clausification,[status(thm)],[f278])). 1.73/0.60 thf(f278,plain,( 1.73/0.60 ((?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))) = $false) | ~spl0_2), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f273])). 1.73/0.60 thf(f273,plain,( 1.73/0.60 ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) = $true) | ~spl0_2), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f272])). 1.73/0.60 thf(f272,plain,( 1.73/0.60 (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & $true) = $true) | ~spl0_2), 1.73/0.60 inference(backward_demodulation,[status(thm)],[f262,f270])). 1.73/0.60 thf(f270,plain,( 1.73/0.60 ((c @ spain @ france) = $true) | ~spl0_2), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f262])). 1.73/0.60 thf(f642,plain,( 1.73/0.60 spl0_5 | spl0_6 | ~spl0_2), 1.73/0.60 inference(avatar_split_clause,[status(thm)],[f631,f261,f640,f637])). 1.73/0.60 thf(f631,plain,( 1.73/0.60 ($false = (~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain))))))))) | ($false = (c @ spain @ paris)) | ~spl0_2), 1.73/0.60 inference(binary_proxy_clausification,[status(thm)],[f427])). 1.73/0.60 thf(f427,plain,( 1.73/0.60 ($false = ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ paris))) | ~spl0_2), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f426])). 1.73/0.60 thf(f426,plain,( 1.73/0.60 (($true & ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ paris))) = $false) | ~spl0_2), 1.73/0.60 inference(forward_demodulation,[status(thm)],[f421,f270])). 1.73/0.60 thf(f421,plain,( 1.73/0.60 (((c @ spain @ france) & ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ paris))) = $false) | ~spl0_2), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f420])). 1.73/0.60 thf(f420,plain,( 1.73/0.60 ((($true & (c @ spain @ france)) & ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ paris))) = $false) | ~spl0_2), 1.73/0.60 inference(boolean_simplification,[status(thm)],[f418])). 1.73/0.60 thf(f418,plain,( 1.73/0.60 ((((~ $false) & (c @ spain @ france)) & ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ paris))) = $false) | ~spl0_2), 1.73/0.60 inference(superposition,[status(thm)],[f409,f278])). 1.73/0.60 thf(f409,plain,( 1.73/0.60 ( ! [X1 : reg] : (($false = (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ X1)))))))) & (c @ X1 @ france)) & ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ X1)))))))) & (c @ X1 @ paris))))) )), 1.73/0.60 inference(beta_eta_normalization,[status(thm)],[f408])). 1.73/0.60 thf(f408,plain,( 1.73/0.60 ( ! [X1 : reg] : (($false = ((^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))) @ X1))) )), 1.73/0.60 inference(pi_clausification,[status(thm)],[f399])). 1.73/0.60 thf(f399,plain,( 1.73/0.60 ($false = (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris))))))), 1.73/0.60 inference(not_proxy_clausification,[status(thm)],[f394])). 1.73/0.60 thf(f394,plain,( 1.73/0.60 ((~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris)))))) = $true)), 1.73/0.61 inference(boolean_simplification,[status(thm)],[f393])). 1.73/0.61 thf(f393,plain,( 1.73/0.61 (($true & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ france)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))))))) & (c @ Y0 @ paris))))))) = $true)), 1.73/0.61 inference(backward_demodulation,[status(thm)],[f349,f392])). 1.73/0.61 thf(f263,plain,( 1.73/0.61 spl0_1 | spl0_2), 1.73/0.61 inference(avatar_split_clause,[status(thm)],[f256,f261,f258])). 1.73/0.61 thf(f256,plain,( 1.73/0.61 ( ! [X2 : $i,X1 : $i] : ((((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ france)) = $true) | ($true = (~ (fool @ X1 @ X2)))) )), 1.73/0.61 inference(binary_proxy_clausification,[status(thm)],[f255])). 1.73/0.61 thf(f255,plain,( 1.73/0.61 ( ! [X2 : $i,X1 : $i] : ((((~ (fool @ X1 @ X2)) | ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))))))) & (c @ spain @ france))) = $true)) )), 1.73/0.61 inference(beta_eta_normalization,[status(thm)],[f254])). 1.73/0.61 thf(f254,plain,( 1.73/0.61 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) & (c @ spain @ france)))) @ X2) = $true)) )), 1.73/0.61 inference(pi_clausification,[status(thm)],[f253])). 1.73/0.61 thf(f253,plain,( 1.73/0.61 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (fool @ X1 @ Y0)) | ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) & (c @ spain @ france))))) = $true)) )), 1.73/0.61 inference(beta_eta_normalization,[status(thm)],[f252])). 1.73/0.61 thf(f252,plain,( 1.73/0.61 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))))) & (c @ spain @ france)))))) @ X1) = $true)) )), 1.73/0.61 inference(pi_clausification,[status(thm)],[f223])). 1.73/0.61 thf(f223,plain,( 1.73/0.61 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ (fool @ Y0 @ Y1)) | ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))))) & (c @ spain @ france))))))) = $true)), 1.73/0.61 inference(beta_eta_normalization,[status(thm)],[f213])). 1.73/0.61 thf(f213,plain,( 1.73/0.61 (((^[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]: ((~ ((^[Y3 : reg]: ((^[Y4 : reg]: (?? @ reg @ (^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4) & ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y3))))))) @ Y1 @ Y2)) & (c @ Y1 @ Y2))))) @ spain @ france)))) = $true)), 1.73/0.61 inference(definition_unfolding,[status(thm)],[f153,f166,f176,f208])). 1.73/0.61 thf(f153,plain,( 1.73/0.61 ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)))) = $true)), 1.73/0.61 inference(cnf_transformation,[status(thm)],[f117])). 1.73/0.61 thf(f117,plain,( 1.73/0.61 ((mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)))) = $true)), 1.73/0.61 inference(fool_elimination,[status(thm)],[f116])). 1.73/0.61 thf(f116,plain,( 1.73/0.61 (mvalid @ (mbox @ fool @ (^[X0 : $i] : (ec @ spain @ france))))), 1.73/0.61 inference(rectify,[status(thm)],[f45])). 1.73/0.61 thf(f45,axiom,( 1.73/0.61 (mvalid @ (mbox @ fool @ (^[X0 : $i] : (ec @ spain @ france))))), 1.73/0.61 file('/export/starexec/sandbox/tmp/tmp.PVWJ0J60R9/E---3.1_16441.p',ax2)). 1.73/0.61 % SZS output end Proof for E---3.1_16441 1.73/0.61 % (16559)------------------------------ 1.73/0.61 % (16559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100) 1.73/0.61 % (16559)Termination reason: Refutation 1.73/0.61 1.73/0.61 % (16559)Memory used [KB]: 7164 1.73/0.61 % (16559)Time elapsed: 0.188 s 1.73/0.61 % (16559)Instructions burned: 435 (million) 1.73/0.61 % (16559)------------------------------ 1.73/0.61 % (16559)------------------------------ 1.73/0.61 % (16547)Success in time 0.236 s 1.73/0.61 EOF