0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : run_vampire %s %d THM 0.12/0.34 % Computer : n021.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1920 0.12/0.34 % WCLimit : 240 0.12/0.34 % DateTime : Wed Jul 30 03:45:49 EDT 2025 0.18/0.34 % CPUTime : 0.18/0.36 This is a THF_ problem 0.18/0.36 Running higher-order theorem proving 0.18/0.37 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p -m 16384 -t 240 0.18/0.39 % (12958)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/18Mi) 0.18/0.39 % (12953)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_12845 for (2399ds/4Mi) 0.18/0.39 % (12955)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/2Mi) 0.18/0.39 % (12952)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/183Mi) 0.18/0.39 % (12954)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_12845 for (2399ds/27Mi) 0.18/0.39 % (12957)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_12845 for (2399ds/275Mi) 0.18/0.39 % (12956)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_12845 for (2399ds/2Mi) 0.18/0.39 % (12955)Instruction limit reached! 0.18/0.39 % (12955)------------------------------ 0.18/0.39 % (12955)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.39 % (12956)Instruction limit reached! 0.18/0.39 % (12956)------------------------------ 0.18/0.39 % (12956)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.39 % (12956)Termination reason: Unknown 0.18/0.39 % (12956)Termination phase: shuffling 0.18/0.39 0.18/0.39 % (12956)Memory used [KB]: 1023 0.18/0.39 % (12956)Time elapsed: 0.004 s 0.18/0.39 % (12956)Instructions burned: 2 (million) 0.18/0.39 % (12956)------------------------------ 0.18/0.39 % (12956)------------------------------ 0.18/0.39 % (12955)Termination reason: Unknown 0.18/0.39 % (12955)Termination phase: shuffling 0.18/0.39 0.18/0.39 % (12955)Memory used [KB]: 1023 0.18/0.39 % (12955)Time elapsed: 0.004 s 0.18/0.39 % (12955)Instructions burned: 2 (million) 0.18/0.39 % (12955)------------------------------ 0.18/0.39 % (12955)------------------------------ 0.18/0.40 % (12953)Instruction limit reached! 0.18/0.40 % (12953)------------------------------ 0.18/0.40 % (12953)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.40 % (12953)Termination reason: Unknown 0.18/0.40 % (12953)Termination phase: shuffling 0.18/0.40 0.18/0.40 % (12953)Memory used [KB]: 1151 0.18/0.40 % (12953)Time elapsed: 0.004 s 0.18/0.40 % (12953)Instructions burned: 4 (million) 0.18/0.40 % (12953)------------------------------ 0.18/0.40 % (12953)------------------------------ 0.18/0.40 % (12957)Refutation not found, incomplete strategy 0.18/0.40 % (12957)------------------------------ 0.18/0.40 % (12957)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.40 % (12957)Termination reason: Refutation not found, incomplete strategy 0.18/0.40 0.18/0.40 0.18/0.40 % (12957)Memory used [KB]: 5628 0.18/0.40 % (12957)Time elapsed: 0.009 s 0.18/0.40 % (12957)Instructions burned: 11 (million) 0.18/0.40 % (12957)------------------------------ 0.18/0.40 % (12957)------------------------------ 0.18/0.40 % (12958)Instruction limit reached! 0.18/0.40 % (12958)------------------------------ 0.18/0.40 % (12958)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.40 % (12958)Termination reason: Unknown 0.18/0.40 % (12958)Termination phase: Saturation 0.18/0.40 0.18/0.40 % (12958)Memory used [KB]: 5628 0.18/0.40 % (12958)Time elapsed: 0.012 s 0.18/0.40 % (12958)Instructions burned: 18 (million) 0.18/0.40 % (12958)------------------------------ 0.18/0.40 % (12958)------------------------------ 0.18/0.41 % (12960)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_12845 for (2399ds/37Mi) 0.18/0.41 % (12954)Instruction limit reached! 0.18/0.41 % (12954)------------------------------ 0.18/0.41 % (12954)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (12954)Termination reason: Unknown 0.18/0.41 % (12954)Termination phase: Saturation 0.18/0.41 0.18/0.41 % (12954)Memory used [KB]: 5756 0.18/0.41 % (12954)Time elapsed: 0.017 s 0.18/0.41 % (12954)Instructions burned: 28 (million) 0.18/0.41 % (12954)------------------------------ 0.18/0.41 % (12954)------------------------------ 0.18/0.41 % (12959)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_12845 for (2399ds/3Mi) 0.18/0.41 % (12961)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_12845 for (2399ds/15Mi) 0.18/0.41 % (12959)Instruction limit reached! 0.18/0.41 % (12959)------------------------------ 0.18/0.41 % (12959)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.18/0.41 % (12959)Termination reason: Unknown 0.18/0.41 % (12959)Termination phase: shuffling 0.18/0.41 0.18/0.41 % (12959)Memory used [KB]: 1023 0.18/0.41 % (12959)Time elapsed: 0.004 s 0.18/0.41 % (12959)Instructions burned: 3 (million) 0.18/0.41 % (12959)------------------------------ 0.18/0.41 % (12959)------------------------------ 0.23/0.42 % (12962)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_12845 for (2399ds/3Mi) 0.23/0.42 % (12962)Instruction limit reached! 0.23/0.42 % (12962)------------------------------ 0.23/0.42 % (12962)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.42 % (12962)Termination reason: Unknown 0.23/0.42 % (12962)Termination phase: shuffling 0.23/0.42 0.23/0.42 % (12962)Memory used [KB]: 1023 0.23/0.42 % (12962)Time elapsed: 0.004 s 0.23/0.42 % (12962)Instructions burned: 3 (million) 0.23/0.42 % (12962)------------------------------ 0.23/0.42 % (12962)------------------------------ 0.23/0.42 % (12963)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_12845 for (2399ds/1041Mi) 0.23/0.42 % (12961)Instruction limit reached! 0.23/0.42 % (12961)------------------------------ 0.23/0.42 % (12961)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.42 % (12961)Termination reason: Unknown 0.23/0.42 % (12961)Termination phase: Saturation 0.23/0.42 0.23/0.42 % (12961)Memory used [KB]: 1151 0.23/0.42 % (12961)Time elapsed: 0.011 s 0.23/0.42 % (12961)Instructions burned: 16 (million) 0.23/0.42 % (12961)------------------------------ 0.23/0.42 % (12961)------------------------------ 0.23/0.42 % (12964)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/7Mi) 0.23/0.43 % (12960)Instruction limit reached! 0.23/0.43 % (12960)------------------------------ 0.23/0.43 % (12960)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.43 % (12960)Termination reason: Unknown 0.23/0.43 % (12960)Termination phase: Saturation 0.23/0.43 0.23/0.43 % (12960)Memory used [KB]: 6012 0.23/0.43 % (12960)Time elapsed: 0.019 s 0.23/0.43 % (12960)Instructions burned: 38 (million) 0.23/0.43 % (12960)------------------------------ 0.23/0.43 % (12960)------------------------------ 0.23/0.43 % (12964)Instruction limit reached! 0.23/0.43 % (12964)------------------------------ 0.23/0.43 % (12964)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.43 % (12965)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/16Mi) 0.23/0.43 % (12964)Termination reason: Unknown 0.23/0.43 % (12964)Termination phase: SInE selection 0.23/0.43 0.23/0.43 % (12964)Memory used [KB]: 1151 0.23/0.43 % (12964)Time elapsed: 0.006 s 0.23/0.43 % (12964)Instructions burned: 7 (million) 0.23/0.43 % (12964)------------------------------ 0.23/0.43 % (12964)------------------------------ 0.23/0.43 % (12966)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_12845 for (2399ds/3Mi) 0.23/0.44 % (12967)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_12845 for (2399ds/3Mi) 0.23/0.44 % (12966)Instruction limit reached! 0.23/0.44 % (12966)------------------------------ 0.23/0.44 % (12966)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.44 % (12966)Termination reason: Unknown 0.23/0.44 % (12966)Termination phase: shuffling 0.23/0.44 0.23/0.44 % (12966)Memory used [KB]: 1151 0.23/0.44 % (12966)Time elapsed: 0.004 s 0.23/0.44 % (12966)Instructions burned: 4 (million) 0.23/0.44 % (12966)------------------------------ 0.23/0.44 % (12966)------------------------------ 0.23/0.44 % (12965)Instruction limit reached! 0.23/0.44 % (12965)------------------------------ 0.23/0.44 % (12965)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.44 % (12965)Termination reason: Unknown 0.23/0.44 % (12965)Termination phase: Saturation 0.23/0.44 0.23/0.44 % (12965)Memory used [KB]: 5756 0.23/0.44 % (12965)Time elapsed: 0.011 s 0.23/0.44 % (12965)Instructions burned: 17 (million) 0.23/0.44 % (12965)------------------------------ 0.23/0.44 % (12965)------------------------------ 0.23/0.44 % (12967)Instruction limit reached! 0.23/0.44 % (12967)------------------------------ 0.23/0.44 % (12967)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.44 % (12967)Termination reason: Unknown 0.23/0.44 % (12967)Termination phase: shuffling 0.23/0.44 0.23/0.44 % (12967)Memory used [KB]: 1151 0.23/0.44 % (12967)Time elapsed: 0.004 s 0.23/0.44 % (12967)Instructions burned: 4 (million) 0.23/0.44 % (12967)------------------------------ 0.23/0.44 % (12967)------------------------------ 0.23/0.44 % (12968)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_12845 for (2399ds/7Mi) 0.23/0.44 % (12969)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_12845 for (2399ds/3Mi) 0.23/0.44 % (12968)Instruction limit reached! 0.23/0.44 % (12968)------------------------------ 0.23/0.44 % (12968)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.44 % (12968)Termination reason: Unknown 0.23/0.44 % (12968)Termination phase: Property scanning 0.23/0.44 0.23/0.44 % (12968)Memory used [KB]: 1151 0.23/0.44 % (12968)Time elapsed: 0.006 s 0.23/0.44 % (12968)Instructions burned: 7 (million) 0.23/0.44 % (12968)------------------------------ 0.23/0.44 % (12968)------------------------------ 0.23/0.45 % (12969)Instruction limit reached! 0.23/0.45 % (12969)------------------------------ 0.23/0.45 % (12969)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.45 % (12969)Termination reason: Unknown 0.23/0.45 % (12969)Termination phase: shuffling 0.23/0.45 0.23/0.45 % (12969)Memory used [KB]: 1151 0.23/0.45 % (12969)Time elapsed: 0.004 s 0.23/0.45 % (12969)Instructions burned: 3 (million) 0.23/0.45 % (12969)------------------------------ 0.23/0.45 % (12969)------------------------------ 0.23/0.45 % (12970)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/4Mi) 0.23/0.45 % (12971)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_12845 for (2399ds/18Mi) 0.23/0.45 % (12972)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/710Mi) 0.23/0.45 % (12970)Instruction limit reached! 0.23/0.45 % (12970)------------------------------ 0.23/0.45 % (12970)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.45 % (12970)Termination reason: Unknown 0.23/0.45 % (12970)Termination phase: shuffling 0.23/0.45 0.23/0.45 % (12970)Memory used [KB]: 1151 0.23/0.45 % (12970)Time elapsed: 0.004 s 0.23/0.45 % (12970)Instructions burned: 4 (million) 0.23/0.45 % (12970)------------------------------ 0.23/0.45 % (12970)------------------------------ 0.23/0.46 % (12973)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/6Mi) 0.23/0.46 % (12974)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_12845 for (2399ds/902Mi) 0.23/0.46 % (12971)Instruction limit reached! 0.23/0.46 % (12971)------------------------------ 0.23/0.46 % (12971)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.46 % (12971)Termination reason: Unknown 0.23/0.46 % (12971)Termination phase: Saturation 0.23/0.46 0.23/0.46 % (12971)Memory used [KB]: 5756 0.23/0.46 % (12971)Time elapsed: 0.036 s 0.23/0.46 % (12971)Instructions burned: 18 (million) 0.23/0.46 % (12971)------------------------------ 0.23/0.46 % (12971)------------------------------ 0.23/0.46 % (12972)Refutation not found, incomplete strategy 0.23/0.46 % (12972)------------------------------ 0.23/0.46 % (12972)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.46 % (12972)Termination reason: Refutation not found, incomplete strategy 0.23/0.46 0.23/0.46 % (12973)Instruction limit reached! 0.23/0.46 % (12973)------------------------------ 0.23/0.46 % (12973)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.46 % (12973)Termination reason: Unknown 0.23/0.46 % (12973)Termination phase: Property scanning 0.23/0.46 0.23/0.46 % (12973)Memory used [KB]: 1151 0.23/0.46 % (12973)Time elapsed: 0.006 s 0.23/0.46 % (12973)Instructions burned: 7 (million) 0.23/0.46 % (12973)------------------------------ 0.23/0.46 % (12973)------------------------------ 0.23/0.46 0.23/0.46 % (12972)Memory used [KB]: 5756 0.23/0.46 % (12972)Time elapsed: 0.037 s 0.23/0.46 % (12972)Instructions burned: 17 (million) 0.23/0.46 % (12972)------------------------------ 0.23/0.46 % (12972)------------------------------ 0.23/0.47 % (12974)Refutation not found, incomplete strategy 0.23/0.47 % (12974)------------------------------ 0.23/0.47 % (12974)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.47 % (12974)Termination reason: Refutation not found, incomplete strategy 0.23/0.47 0.23/0.47 0.23/0.47 % (12974)Memory used [KB]: 5628 0.23/0.47 % (12974)Time elapsed: 0.009 s 0.23/0.47 % (12974)Instructions burned: 12 (million) 0.23/0.47 % (12974)------------------------------ 0.23/0.47 % (12974)------------------------------ 0.23/0.47 % (12975)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_12845 for (2399ds/21Mi) 0.23/0.48 % (12976)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/5Mi) 0.23/0.48 % (12963)First to succeed. 0.23/0.48 % (12977)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_12845 for (2399ds/6Mi) 0.23/0.48 % (12978)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_12845 for (2399ds/377Mi) 0.23/0.48 % (12976)Instruction limit reached! 0.23/0.48 % (12976)------------------------------ 0.23/0.48 % (12976)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.48 % (12976)Termination reason: Unknown 0.23/0.48 % (12976)Termination phase: Property scanning 0.23/0.48 0.23/0.48 % (12976)Memory used [KB]: 1151 0.23/0.48 % (12976)Time elapsed: 0.005 s 0.23/0.48 % (12976)Instructions burned: 7 (million) 0.23/0.48 % (12976)------------------------------ 0.23/0.48 % (12976)------------------------------ 0.23/0.48 % (12975)Instruction limit reached! 0.23/0.48 % (12975)------------------------------ 0.23/0.48 % (12975)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.48 % (12975)Termination reason: Unknown 0.23/0.48 % (12975)Termination phase: Saturation 0.23/0.48 0.23/0.48 % (12975)Memory used [KB]: 5756 0.23/0.48 % (12975)Time elapsed: 0.014 s 0.23/0.48 % (12975)Instructions burned: 21 (million) 0.23/0.48 % (12975)------------------------------ 0.23/0.48 % (12975)------------------------------ 0.23/0.48 % (12977)Instruction limit reached! 0.23/0.48 % (12977)------------------------------ 0.23/0.48 % (12977)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.48 % (12977)Termination reason: Unknown 0.23/0.48 % (12977)Termination phase: Property scanning 0.23/0.48 0.23/0.48 % (12977)Memory used [KB]: 1151 0.23/0.48 % (12977)Time elapsed: 0.005 s 0.23/0.48 % (12977)Instructions burned: 6 (million) 0.23/0.48 % (12977)------------------------------ 0.23/0.48 % (12977)------------------------------ 0.23/0.49 % (12979)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_12845 for (2399ds/779Mi) 0.23/0.49 % (12963)Refutation found. Thanks to Tanya! 0.23/0.49 % SZS status Theorem for E---3.1_12845 0.23/0.49 % SZS output start Proof for E---3.1_12845 0.23/0.49 thf(type_def_5, type, mu: $tType). 0.23/0.49 thf(type_def_7, type, reg: $tType). 0.23/0.49 thf(func_def_0, type, mu: $tType). 0.23/0.49 thf(func_def_1, type, meq_ind: mu > mu > $i > $o). 0.23/0.49 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_4, type, mnot: ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o). 0.23/0.49 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o). 0.23/0.49 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o). 0.23/0.49 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o). 0.23/0.49 thf(func_def_15, type, mtrue: $i > $o). 0.23/0.49 thf(func_def_16, type, mfalse: $i > $o). 0.23/0.49 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o). 0.23/0.49 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_21, type, mserial: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o). 0.23/0.49 thf(func_def_29, type, mvalid: ($i > $o) > $o). 0.23/0.49 thf(func_def_30, type, minvalid: ($i > $o) > $o). 0.23/0.49 thf(func_def_31, type, msatisfiable: ($i > $o) > $o). 0.23/0.49 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o). 0.23/0.49 thf(func_def_33, type, reg: $tType). 0.23/0.49 thf(func_def_34, type, c: reg > reg > $o). 0.23/0.49 thf(func_def_35, type, dc: reg > reg > $o). 0.23/0.49 thf(func_def_36, type, p: reg > reg > $o). 0.23/0.49 thf(func_def_37, type, eq: reg > reg > $o). 0.23/0.49 thf(func_def_38, type, o: reg > reg > $o). 0.23/0.49 thf(func_def_39, type, po: reg > reg > $o). 0.23/0.49 thf(func_def_40, type, ec: reg > reg > $o). 0.23/0.49 thf(func_def_41, type, pp: reg > reg > $o). 0.23/0.49 thf(func_def_42, type, tpp: reg > reg > $o). 0.23/0.49 thf(func_def_43, type, ntpp: reg > reg > $o). 0.23/0.49 thf(func_def_44, type, catalunya: reg). 0.23/0.49 thf(func_def_45, type, france: reg). 0.23/0.49 thf(func_def_46, type, spain: reg). 0.23/0.49 thf(func_def_47, type, paris: reg). 0.23/0.49 thf(func_def_48, type, a: $i > $i > $o). 0.23/0.49 thf(func_def_49, type, fool: $i > $i > $o). 0.23/0.49 thf(func_def_66, type, ph1: !>[X0: $tType]:(X0)). 0.23/0.49 thf(func_def_70, type, sK5: $i > $i > $i). 0.23/0.49 thf(func_def_71, type, sK6: reg). 0.23/0.49 thf(func_def_72, type, sK7: reg). 0.23/0.49 thf(func_def_73, type, sK8: reg). 0.23/0.49 thf(f732,plain,( 0.23/0.49 $false), 0.23/0.49 inference(avatar_sat_refutation,[],[f325,f362,f402,f731])). 0.23/0.49 thf(f731,plain,( 0.23/0.49 ~spl0_1 | ~spl0_3), 0.23/0.49 inference(avatar_contradiction_clause,[],[f730])). 0.23/0.49 thf(f730,plain,( 0.23/0.49 $false | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(trivial_inequality_removal,[],[f729])). 0.23/0.49 thf(f729,plain,( 0.23/0.49 ($false = $true) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(forward_demodulation,[],[f711,f477])). 0.23/0.49 thf(f477,plain,( 0.23/0.49 ($false = (c @ sK6 @ france)) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(binary_proxy_clausification,[],[f467])). 0.23/0.49 thf(f467,plain,( 0.23/0.49 ($false = ((c @ sK6 @ catalunya) => (c @ sK6 @ france))) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(beta_eta_normalization,[],[f465])). 0.23/0.49 thf(f465,plain,( 0.23/0.49 ($false = ((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ france))) @ sK6)) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(sigma_clausification,[],[f418])). 0.23/0.49 thf(f418,plain,( 0.23/0.49 ($false = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ france))))) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(boolean_simplification,[],[f416])). 0.23/0.49 thf(f416,plain,( 0.23/0.49 (($true & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ france))))) = $false) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(superposition,[],[f381,f414])). 0.23/0.49 thf(f414,plain,( 0.23/0.49 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))) = $true) | ~spl0_3), 0.23/0.49 inference(boolean_simplification,[],[f413])). 0.23/0.49 thf(f413,plain,( 0.23/0.49 ($true = ($true & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) | ~spl0_3), 0.23/0.49 inference(backward_demodulation,[],[f410,f412])). 0.23/0.49 thf(f412,plain,( 0.23/0.49 ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) = $true) | ~spl0_3), 0.23/0.49 inference(binary_proxy_clausification,[],[f410])). 0.23/0.49 thf(f410,plain,( 0.23/0.49 (((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))) = $true) | ~spl0_3), 0.23/0.49 inference(boolean_simplification,[],[f409])). 0.23/0.49 thf(f409,plain,( 0.23/0.49 ($true = ($true & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain))))))) | ~spl0_3), 0.23/0.49 inference(backward_demodulation,[],[f396,f408])). 0.23/0.49 thf(f408,plain,( 0.23/0.49 ($true = (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) & (c @ Y0 @ spain)))))) | ~spl0_3), 0.23/0.49 inference(binary_proxy_clausification,[],[f396])). 0.23/0.49 thf(f396,plain,( 0.23/0.49 (((?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) & (c @ Y0 @ spain))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) = $true) | ~spl0_3), 0.23/0.49 inference(avatar_component_clause,[],[f395])). 0.23/0.49 thf(f395,plain,( 0.23/0.49 spl0_3 <=> (((?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) & (c @ Y0 @ spain))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) = $true)), 0.23/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])). 0.23/0.49 thf(f381,plain,( 0.23/0.49 ( ! [X1 : reg] : (($false = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ spain)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ X1) => (c @ Y0 @ france))))))) ) | ~spl0_1), 0.23/0.49 inference(beta_eta_normalization,[],[f380])). 0.23/0.49 thf(f380,plain,( 0.23/0.49 ( ! [X1 : reg] : (($false = ((^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))) @ X1))) ) | ~spl0_1), 0.23/0.49 inference(pi_clausification,[],[f373])). 0.23/0.49 thf(f373,plain,( 0.23/0.49 ($false = (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))) | ~spl0_1), 0.23/0.49 inference(not_proxy_clausification,[],[f372])). 0.23/0.49 thf(f372,plain,( 0.23/0.49 ((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))) = $true) | ~spl0_1), 0.23/0.49 inference(boolean_simplification,[],[f371])). 0.23/0.49 thf(f371,plain,( 0.23/0.49 (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))) & $true) = $true) | ~spl0_1), 0.23/0.49 inference(backward_demodulation,[],[f321,f369])). 0.23/0.49 thf(f369,plain,( 0.23/0.49 ((c @ spain @ france) = $true) | ~spl0_1), 0.23/0.49 inference(binary_proxy_clausification,[],[f321])). 0.23/0.49 thf(f321,plain,( 0.23/0.49 (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))) & (c @ spain @ france)) = $true) | ~spl0_1), 0.23/0.49 inference(avatar_component_clause,[],[f320])). 0.23/0.49 thf(f320,plain,( 0.23/0.49 spl0_1 <=> (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))) & (c @ spain @ france)) = $true)), 0.23/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 0.23/0.49 thf(f711,plain,( 0.23/0.49 ($true = (c @ sK6 @ france)) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(boolean_simplification,[],[f706])). 0.23/0.49 thf(f706,plain,( 0.23/0.49 (($true => (c @ sK6 @ france)) = $true) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(superposition,[],[f695,f497])). 0.23/0.49 thf(f497,plain,( 0.23/0.49 ((c @ sK6 @ paris) = $true) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(boolean_simplification,[],[f491])). 0.23/0.49 thf(f491,plain,( 0.23/0.49 (($true => (c @ sK6 @ paris)) = $true) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(superposition,[],[f304,f478])). 0.23/0.49 thf(f478,plain,( 0.23/0.49 ((c @ sK6 @ catalunya) = $true) | (~spl0_1 | ~spl0_3)), 0.23/0.49 inference(binary_proxy_clausification,[],[f467])). 0.23/0.49 thf(f304,plain,( 0.23/0.49 ( ! [X1 : reg] : (($true = ((c @ X1 @ catalunya) => (c @ X1 @ paris)))) )), 0.23/0.49 inference(beta_eta_normalization,[],[f303])). 0.23/0.49 thf(f303,plain,( 0.23/0.49 ( ! [X1 : reg] : (($true = ((^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris))) @ X1))) )), 0.23/0.49 inference(pi_clausification,[],[f276])). 0.23/0.49 thf(f276,plain,( 0.23/0.49 ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))) = $true)), 0.23/0.49 inference(binary_proxy_clausification,[],[f272])). 0.23/0.49 thf(f272,plain,( 0.23/0.49 ($true = ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya))))))), 0.23/0.49 inference(not_proxy_clausification,[],[f257])). 0.23/0.49 thf(f257,plain,( 0.23/0.49 ($false = (~ ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya)))))))), 0.23/0.49 inference(boolean_simplification,[],[f256])). 0.23/0.49 thf(f256,plain,( 0.23/0.49 (((~ ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya)))))) | $false) = $false)), 0.23/0.49 inference(backward_demodulation,[],[f253,f254])). 0.23/0.49 thf(f254,plain,( 0.23/0.49 ($false = (~ (a @ sK2 @ sK3)))), 0.23/0.49 inference(binary_proxy_clausification,[],[f253])). 0.23/0.49 thf(f253,plain,( 0.23/0.49 ($false = ((~ ((!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ paris)))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ catalunya)))))) | (~ (a @ sK2 @ sK3))))), 0.23/0.49 inference(beta_eta_normalization,[],[f252])). 0.23/0.49 thf(f252,plain,( 0.23/0.49 ($false = ((^[Y0 : $i]: ((~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ catalunya)))))) | (~ (a @ sK2 @ Y0)))) @ sK3))), 0.23/0.49 inference(sigma_clausification,[],[f251])). 0.23/0.49 thf(f251,plain,( 0.23/0.49 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ paris)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ catalunya)))))) | (~ (a @ sK2 @ Y0))))))), 0.23/0.49 inference(beta_eta_normalization,[],[f250])). 0.23/0.49 thf(f250,plain,( 0.23/0.49 ($false = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ catalunya)))))) | (~ (a @ Y0 @ Y1)))))) @ sK2))), 0.23/0.49 inference(sigma_clausification,[],[f247])). 0.23/0.49 thf(f247,plain,( 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ catalunya)))))) | (~ (a @ Y0 @ Y1))))))) = $false)), 0.23/0.49 inference(not_proxy_clausification,[],[f220])). 0.23/0.49 thf(f220,plain,( 0.23/0.49 ((~ (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((~ ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ paris)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ catalunya)))))) | (~ (a @ Y0 @ Y1)))))))) = $true)), 0.23/0.49 inference(beta_eta_normalization,[],[f216])). 0.23/0.49 thf(f216,plain,( 0.23/0.49 ($true = (~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))) @ a @ (^[Y0 : $i]: (~ ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y1 @ Y2) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1))))) @ catalunya @ paris)))))))), 0.23/0.49 inference(definition_unfolding,[],[f181,f180,f152,f205])). 0.23/0.49 thf(f205,plain,( 0.23/0.49 (eq = (^[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))))))), 0.23/0.49 inference(definition_unfolding,[],[f149,f184,f184])). 0.23/0.49 thf(f184,plain,( 0.23/0.49 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))), 0.23/0.49 inference(cnf_transformation,[],[f113])). 0.23/0.49 thf(f113,plain,( 0.23/0.49 (p = (^[Y0 : reg]: ((^[Y1 : reg]: (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y0) => (c @ Y2 @ Y1))))))))), 0.23/0.49 inference(fool_elimination,[],[f112])). 0.23/0.49 thf(f112,plain,( 0.23/0.49 ((^[X0 : reg, X1 : reg] : (! [X2 : reg] : ((c @ X2 @ X0) => (c @ X2 @ X1)))) = p)), 0.23/0.49 inference(rectify,[],[f33])). 0.23/0.49 thf(f33,axiom,( 0.23/0.49 ((^[X0 : reg, X1 : reg] : (! [X11 : reg] : ((c @ X11 @ X0) => (c @ X11 @ X1)))) = p)), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',p)). 0.23/0.49 thf(f149,plain,( 0.23/0.49 (eq = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (p @ Y1 @ Y0))))))), 0.23/0.49 inference(cnf_transformation,[],[f65])). 0.23/0.49 thf(f65,plain,( 0.23/0.49 (eq = (^[Y0 : reg]: ((^[Y1 : reg]: ((p @ Y0 @ Y1) & (p @ Y1 @ Y0))))))), 0.23/0.49 inference(fool_elimination,[],[f64])). 0.23/0.49 thf(f64,plain,( 0.23/0.49 ((^[X0 : reg, X1 : reg] : ((p @ X1 @ X0) & (p @ X0 @ X1))) = eq)), 0.23/0.49 inference(rectify,[],[f34])). 0.23/0.49 thf(f34,axiom,( 0.23/0.49 ((^[X0 : reg, X1 : reg] : ((p @ X1 @ X0) & (p @ X0 @ X1))) = eq)), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',eq)). 0.23/0.49 thf(f152,plain,( 0.23/0.49 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))), 0.23/0.49 inference(cnf_transformation,[],[f91])). 0.23/0.49 thf(f91,plain,( 0.23/0.49 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))), 0.23/0.49 inference(fool_elimination,[],[f90])). 0.23/0.49 thf(f90,plain,( 0.23/0.49 ((^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))) = mbox)), 0.23/0.49 inference(rectify,[],[f16])). 0.23/0.49 thf(f16,axiom,( 0.23/0.49 ((^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))) = mbox)), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',mbox)). 0.23/0.49 thf(f180,plain,( 0.23/0.49 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 0.23/0.49 inference(cnf_transformation,[],[f118])). 0.23/0.49 thf(f118,plain,( 0.23/0.49 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))), 0.23/0.49 inference(fool_elimination,[],[f117])). 0.23/0.49 thf(f117,plain,( 0.23/0.49 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))), 0.23/0.49 inference(rectify,[],[f28])). 0.23/0.49 thf(f28,axiom,( 0.23/0.49 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',mvalid)). 0.23/0.49 thf(f181,plain,( 0.23/0.49 ((~ (mvalid @ (mbox @ a @ (^[Y0 : $i]: (~ (eq @ catalunya @ paris)))))) = $true)), 0.23/0.49 inference(cnf_transformation,[],[f93])). 0.23/0.49 thf(f93,plain,( 0.23/0.49 ((~ (mvalid @ (mbox @ a @ (^[Y0 : $i]: (~ (eq @ catalunya @ paris)))))) = $true)), 0.23/0.49 inference(fool_elimination,[],[f92])). 0.23/0.49 thf(f92,plain,( 0.23/0.49 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (~(eq @ catalunya @ paris)))))), 0.23/0.49 inference(rectify,[],[f44])). 0.23/0.49 thf(f44,negated_conjecture,( 0.23/0.49 ~(mvalid @ (mbox @ a @ (^[X0 : $i] : (~(eq @ catalunya @ paris)))))), 0.23/0.49 inference(negated_conjecture,[],[f43])). 0.23/0.49 thf(f43,conjecture,( 0.23/0.49 (mvalid @ (mbox @ a @ (^[X0 : $i] : (~(eq @ catalunya @ paris)))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',con)). 0.23/0.49 thf(f695,plain,( 0.23/0.49 ( ! [X1 : reg] : (($true = ((c @ X1 @ paris) => (c @ X1 @ france)))) )), 0.23/0.49 inference(beta_eta_normalization,[],[f692])). 0.23/0.49 thf(f692,plain,( 0.23/0.49 ( ! [X1 : reg] : ((((^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))) @ X1) = $true)) )), 0.23/0.49 inference(pi_clausification,[],[f687])). 0.23/0.49 thf(f687,plain,( 0.23/0.49 ($true = (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france)))))), 0.23/0.49 inference(boolean_simplification,[],[f686])). 0.23/0.49 thf(f686,plain,( 0.23/0.49 (($true & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) = $true)), 0.23/0.49 inference(backward_demodulation,[],[f597,f685])). 0.23/0.49 thf(f685,plain,( 0.23/0.49 ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) = $true)), 0.23/0.49 inference(binary_proxy_clausification,[],[f597])). 0.23/0.49 thf(f597,plain,( 0.23/0.49 ($true = ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))))), 0.23/0.49 inference(binary_proxy_clausification,[],[f450])). 0.23/0.49 thf(f450,plain,( 0.23/0.49 ($true = (((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))))))) & (c @ Y0 @ paris)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))) & (c @ Y0 @ france))))))))), 0.23/0.49 inference(boolean_simplification,[],[f449])). 0.23/0.49 thf(f449,plain,( 0.23/0.49 (((((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))))))) & (c @ Y0 @ paris)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))) & (c @ Y0 @ france))))))) | $false) = $true)), 0.23/0.49 inference(boolean_simplification,[],[f446])). 0.23/0.49 thf(f446,plain,( 0.23/0.49 ($true = ((((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))))))) & (c @ Y0 @ paris)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))) & (c @ Y0 @ france))))))) | (~ $true)))), 0.23/0.49 inference(superposition,[],[f437,f267])). 0.23/0.49 thf(f267,plain,( 0.23/0.49 ($true = (a @ sK2 @ sK4))), 0.23/0.49 inference(not_proxy_clausification,[],[f264])). 0.23/0.49 thf(f264,plain,( 0.23/0.49 ($false = (~ (a @ sK2 @ sK4)))), 0.23/0.49 inference(beta_eta_normalization,[],[f263])). 0.23/0.49 thf(f263,plain,( 0.23/0.49 (((^[Y0 : $i]: (~ (a @ sK2 @ Y0))) @ sK4) = $false)), 0.23/0.49 inference(sigma_clausification,[],[f259])). 0.23/0.49 thf(f259,plain,( 0.23/0.49 ($false = (!! @ $i @ (^[Y0 : $i]: (~ (a @ sK2 @ Y0)))))), 0.23/0.49 inference(boolean_simplification,[],[f258])). 0.23/0.49 thf(f258,plain,( 0.23/0.49 ($false = (!! @ $i @ (^[Y0 : $i]: ($false | (~ (a @ sK2 @ Y0))))))), 0.23/0.49 inference(backward_demodulation,[],[f251,f257])). 0.23/0.49 thf(f437,plain,( 0.23/0.49 ( ! [X2 : $i,X1 : $i] : ((((((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ france) => (c @ Y0 @ paris))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ paris) => (c @ Y0 @ france))))) & (~ (?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ paris)))))))) & (c @ Y0 @ paris)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))) & (c @ Y0 @ france))))))) | (~ (a @ X1 @ X2))) = $true)) )), 0.23/0.49 inference(beta_eta_normalization,[],[f436])). 0.23/0.49 thf(f436,plain,( 0.23/0.49 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france))))) & (~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))))))) & (c @ Y1 @ paris)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))))))) & (c @ Y1 @ france))))))) | (~ (a @ X1 @ Y0)))) @ X2) = $true)) )), 0.23/0.49 inference(pi_clausification,[],[f429])). 0.23/0.49 thf(f429,plain,( 0.23/0.49 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ france) => (c @ Y1 @ paris))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ paris) => (c @ Y1 @ france))))) & (~ (?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ paris)))))))) & (c @ Y1 @ paris)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))))))) & (c @ Y1 @ france))))))) | (~ (a @ X1 @ Y0))))) = $true)) )), 0.23/0.49 inference(beta_eta_normalization,[],[f428])). 0.23/0.49 thf(f428,plain,( 0.23/0.49 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france))))) & (~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))))))) & (c @ Y2 @ paris)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))))))) & (c @ Y2 @ france))))))) | (~ (a @ Y0 @ Y1)))))) @ X1) = $true)) )), 0.23/0.49 inference(pi_clausification,[],[f225])). 0.23/0.49 thf(f225,plain,( 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ france) => (c @ Y2 @ paris))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ paris) => (c @ Y2 @ france))))) & (~ (?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ paris)))))))) & (c @ Y2 @ paris)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ france)))))))) & (c @ Y2 @ france))))))) | (~ (a @ Y0 @ Y1))))))) = $true)), 0.23/0.49 inference(beta_eta_normalization,[],[f217])). 0.23/0.49 thf(f217,plain,( 0.23/0.49 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4))))) @ Y1 @ Y2) & (~ (?? @ reg @ (^[Y3 : reg]: (((^[Y4 : reg]: ((^[Y5 : reg]: ((~ ((^[Y6 : reg]: ((^[Y7 : reg]: (?? @ reg @ (^[Y8 : reg]: (((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)) & (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 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y2))))))))) @ paris @ france)))))), 0.23/0.49 inference(definition_unfolding,[],[f183,f180,f152,f211])). 0.23/0.49 thf(f211,plain,( 0.23/0.49 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: (((^[Y2 : reg]: ((^[Y3 : reg]: ((~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)) & ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3))))) @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (?? @ reg @ (^[Y7 : reg]: (((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)) & (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 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y1))))))))))), 0.23/0.49 inference(definition_unfolding,[],[f162,f209,f208,f208])). 0.23/0.49 thf(f208,plain,( 0.23/0.49 (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 @ Y2) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3))))))) @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))), 0.23/0.49 inference(definition_unfolding,[],[f176,f206])). 0.23/0.49 thf(f206,plain,( 0.23/0.49 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: (((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y0) & ((^[Y3 : reg]: ((^[Y4 : reg]: (!! @ reg @ (^[Y5 : reg]: ((c @ Y5 @ Y3) => (c @ Y5 @ Y4))))))) @ Y2 @ Y1))))))))), 0.23/0.49 inference(definition_unfolding,[],[f155,f184,f184])). 0.23/0.49 thf(f155,plain,( 0.23/0.49 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))), 0.23/0.49 inference(cnf_transformation,[],[f53])). 0.23/0.49 thf(f53,plain,( 0.23/0.49 (o = (^[Y0 : reg]: ((^[Y1 : reg]: (?? @ reg @ (^[Y2 : reg]: ((p @ Y2 @ Y0) & (p @ Y2 @ Y1))))))))), 0.23/0.49 inference(fool_elimination,[],[f52])). 0.23/0.49 thf(f52,plain,( 0.23/0.49 ((^[X0 : reg, X1 : reg] : (? 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[X11 : reg] : ((p @ X11 @ X1) & (p @ X11 @ X0)))) = o)), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',o)). 0.23/0.49 thf(f176,plain,( 0.23/0.49 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))), 0.23/0.49 inference(cnf_transformation,[],[f110])). 0.23/0.49 thf(f110,plain,( 0.23/0.49 (ec = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (o @ Y0 @ Y1)) & (c @ Y0 @ Y1))))))), 0.23/0.49 inference(fool_elimination,[],[f109])). 0.23/0.49 thf(f109,plain,( 0.23/0.49 ((^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))) = ec)), 0.23/0.49 inference(rectify,[],[f37])). 0.23/0.49 thf(f37,axiom,( 0.23/0.49 ((^[X0 : reg, X1 : reg] : ((c @ X0 @ X1) & ~(o @ X0 @ X1))) = ec)), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',ec)). 0.23/0.49 thf(f209,plain,( 0.23/0.49 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y1 @ Y0)) & ((^[Y2 : reg]: ((^[Y3 : reg]: (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y2) => (c @ Y4 @ Y3))))))) @ Y0 @ Y1))))))), 0.23/0.49 inference(definition_unfolding,[],[f157,f184,f184])). 0.23/0.49 thf(f157,plain,( 0.23/0.49 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (p @ Y1 @ Y0)) & (p @ Y0 @ Y1))))))), 0.23/0.49 inference(cnf_transformation,[],[f146])). 0.23/0.49 thf(f146,plain,( 0.23/0.49 (pp = (^[Y0 : reg]: ((^[Y1 : reg]: ((~ (p @ Y1 @ Y0)) & (p @ Y0 @ Y1))))))), 0.23/0.49 inference(fool_elimination,[],[f145])). 0.23/0.49 thf(f145,plain,( 0.23/0.49 (pp = (^[X0 : reg, X1 : reg] : ((p @ X0 @ X1) & ~(p @ X1 @ X0))))), 0.23/0.49 inference(rectify,[],[f38])). 0.23/0.49 thf(f38,axiom,( 0.23/0.49 (pp = (^[X0 : reg, X1 : reg] : ((p @ X0 @ X1) & ~(p @ X1 @ X0))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',pp)). 0.23/0.49 thf(f162,plain,( 0.23/0.49 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))), 0.23/0.49 inference(cnf_transformation,[],[f98])). 0.23/0.49 thf(f98,plain,( 0.23/0.49 (ntpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((pp @ Y0 @ Y1) & (~ (?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1))))))))))), 0.23/0.49 inference(fool_elimination,[],[f97])). 0.23/0.49 thf(f97,plain,( 0.23/0.49 (ntpp = (^[X0 : reg, X1 : reg] : (~? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)) & (pp @ X0 @ X1))))), 0.23/0.49 inference(rectify,[],[f40])). 0.23/0.49 thf(f40,axiom,( 0.23/0.49 (ntpp = (^[X0 : reg, X1 : reg] : (~? [X11 : reg] : ((ec @ X11 @ X1) & (ec @ X11 @ X0)) & (pp @ X0 @ X1))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',ntpp)). 0.23/0.49 thf(f183,plain,( 0.23/0.49 ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))) = $true)), 0.23/0.49 inference(cnf_transformation,[],[f116])). 0.23/0.49 thf(f116,plain,( 0.23/0.49 ((mvalid @ (mbox @ a @ (^[Y0 : $i]: (ntpp @ paris @ france)))) = $true)), 0.23/0.49 inference(fool_elimination,[],[f115])). 0.23/0.49 thf(f115,plain,( 0.23/0.49 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))), 0.23/0.49 inference(rectify,[],[f49])). 0.23/0.49 thf(f49,axiom,( 0.23/0.49 (mvalid @ (mbox @ a @ (^[X0 : $i] : (ntpp @ paris @ france))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',ax3)). 0.23/0.49 thf(f402,plain,( 0.23/0.49 spl0_3), 0.23/0.49 inference(avatar_split_clause,[],[f391,f395])). 0.23/0.49 thf(f391,plain,( 0.23/0.49 (((?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) & (c @ Y0 @ spain))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) = $true)), 0.23/0.49 inference(boolean_simplification,[],[f390])). 0.23/0.49 thf(f390,plain,( 0.23/0.49 ((((?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) & (c @ Y0 @ spain))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) | $false) = $true)), 0.23/0.49 inference(boolean_simplification,[],[f388])). 0.23/0.49 thf(f388,plain,( 0.23/0.49 ((((?? @ reg @ (^[Y0 : reg]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ catalunya)))))))) & (c @ Y0 @ catalunya)) & ((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ Y0)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))))))) & (c @ Y0 @ spain))))) & ((~ (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ spain) => (c @ Y0 @ catalunya))))) & (!! @ reg @ (^[Y0 : reg]: ((c @ Y0 @ catalunya) => (c @ Y0 @ spain)))))) | (~ $true)) = $true)), 0.23/0.49 inference(superposition,[],[f345,f260])). 0.23/0.49 thf(f260,plain,( 0.23/0.49 ((a @ sK2 @ sK3) = $true)), 0.23/0.49 inference(not_proxy_clausification,[],[f254])). 0.23/0.49 thf(f345,plain,( 0.23/0.49 ( ! 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[X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((?? @ reg @ (^[Y1 : reg]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ catalunya)))))))) & (c @ Y1 @ catalunya)) & ((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ Y1)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))))))) & (c @ Y1 @ spain))))) & ((~ (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ spain) => (c @ Y1 @ catalunya))))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ catalunya) => (c @ Y1 @ spain)))))) | (~ (a @ X1 @ Y0)))) @ X2))) )), 0.23/0.49 inference(pi_clausification,[],[f334])). 0.23/0.49 thf(f334,plain,( 0.23/0.49 ( ! 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[X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))))))) & (c @ Y2 @ catalunya)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))))))) & (c @ Y2 @ spain))))) & ((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))))) | (~ (a @ Y0 @ Y1)))))) @ X1))) )), 0.23/0.49 inference(pi_clausification,[],[f224])). 0.23/0.49 thf(f224,plain,( 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((?? @ reg @ (^[Y2 : reg]: (((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ catalunya)))))))) & (c @ Y2 @ catalunya)) & ((~ (?? @ reg @ (^[Y3 : reg]: ((!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ Y2)))) & (!! @ reg @ (^[Y4 : reg]: ((c @ Y4 @ Y3) => (c @ Y4 @ spain)))))))) & (c @ Y2 @ spain))))) & ((~ (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ spain) => (c @ Y2 @ catalunya))))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ catalunya) => (c @ Y2 @ spain)))))) | (~ (a @ Y0 @ Y1))))))) = $true)), 0.23/0.49 inference(beta_eta_normalization,[],[f212])). 0.23/0.49 thf(f212,plain,( 0.23/0.49 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))) @ a @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((?? @ 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 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ 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 @ Y6) & ((^[Y9 : reg]: ((^[Y10 : reg]: (!! @ reg @ (^[Y11 : reg]: ((c @ Y11 @ Y9) => (c @ Y11 @ Y10))))))) @ Y8 @ Y7))))))) @ Y4 @ Y5)) & (c @ Y4 @ Y5))))) @ Y3 @ Y2)))) & ((^[Y3 : reg]: ((^[Y4 : reg]: ((~ ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y4 @ Y3)) & ((^[Y5 : reg]: ((^[Y6 : reg]: (!! @ reg @ (^[Y7 : reg]: ((c @ Y7 @ Y5) => (c @ Y7 @ Y6))))))) @ Y3 @ Y4))))) @ Y1 @ Y2))))) @ catalunya @ spain)))) = $true)), 0.23/0.49 inference(definition_unfolding,[],[f147,f180,f152,f210])). 0.23/0.49 thf(f210,plain,( 0.23/0.49 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ 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 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ 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 @ Y5) & ((^[Y8 : reg]: ((^[Y9 : reg]: (!! @ reg @ (^[Y10 : reg]: ((c @ Y10 @ Y8) => (c @ Y10 @ Y9))))))) @ Y7 @ Y6))))))) @ Y3 @ Y4)) & (c @ Y3 @ Y4))))) @ Y2 @ Y1)))) & ((^[Y2 : reg]: ((^[Y3 : reg]: ((~ ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y3 @ Y2)) & ((^[Y4 : reg]: ((^[Y5 : reg]: (!! @ reg @ (^[Y6 : reg]: ((c @ Y6 @ Y4) => (c @ Y6 @ Y5))))))) @ Y2 @ Y3))))) @ Y0 @ Y1))))))), 0.23/0.49 inference(definition_unfolding,[],[f167,f208,f208,f209])). 0.23/0.49 thf(f167,plain,( 0.23/0.49 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))) & (pp @ Y0 @ Y1))))))), 0.23/0.49 inference(cnf_transformation,[],[f130])). 0.23/0.49 thf(f130,plain,( 0.23/0.49 (tpp = (^[Y0 : reg]: ((^[Y1 : reg]: ((?? @ reg @ (^[Y2 : reg]: ((ec @ Y2 @ Y0) & (ec @ Y2 @ Y1)))) & (pp @ Y0 @ Y1))))))), 0.23/0.49 inference(fool_elimination,[],[f129])). 0.23/0.49 thf(f129,plain,( 0.23/0.49 (tpp = (^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ? [X2 : reg] : ((ec @ X2 @ X1) & (ec @ X2 @ X0)))))), 0.23/0.49 inference(rectify,[],[f39])). 0.23/0.49 thf(f39,axiom,( 0.23/0.49 (tpp = (^[X0 : reg, X1 : reg] : ((pp @ X0 @ X1) & ? [X11 : reg] : ((ec @ X11 @ X1) & (ec @ X11 @ X0)))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',tpp)). 0.23/0.49 thf(f147,plain,( 0.23/0.49 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))))), 0.23/0.49 inference(cnf_transformation,[],[f120])). 0.23/0.49 thf(f120,plain,( 0.23/0.49 ($true = (mvalid @ (mbox @ a @ (^[Y0 : $i]: (tpp @ catalunya @ spain)))))), 0.23/0.49 inference(fool_elimination,[],[f119])). 0.23/0.49 thf(f119,plain,( 0.23/0.49 (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))), 0.23/0.49 inference(rectify,[],[f50])). 0.23/0.49 thf(f50,axiom,( 0.23/0.49 (mvalid @ (mbox @ a @ (^[X0 : $i] : (tpp @ catalunya @ spain))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',ax1)). 0.23/0.49 thf(f362,plain,( 0.23/0.49 ~spl0_2), 0.23/0.49 inference(avatar_contradiction_clause,[],[f361])). 0.23/0.49 thf(f361,plain,( 0.23/0.49 $false | ~spl0_2), 0.23/0.49 inference(trivial_inequality_removal,[],[f360])). 0.23/0.49 thf(f360,plain,( 0.23/0.49 ($false = $true) | ~spl0_2), 0.23/0.49 inference(boolean_simplification,[],[f359])). 0.23/0.49 thf(f359,plain,( 0.23/0.49 ($false = (~ $false)) | ~spl0_2), 0.23/0.49 inference(forward_demodulation,[],[f358,f328])). 0.23/0.49 thf(f328,plain,( 0.23/0.49 ( ! [X2 : $i,X1 : $i] : (($false = (fool @ X1 @ X2))) ) | ~spl0_2), 0.23/0.49 inference(not_proxy_clausification,[],[f324])). 0.23/0.49 thf(f324,plain,( 0.23/0.49 ( ! [X2 : $i,X1 : $i] : (((~ (fool @ X1 @ X2)) = $true)) ) | ~spl0_2), 0.23/0.49 inference(avatar_component_clause,[],[f323])). 0.23/0.49 thf(f323,plain,( 0.23/0.49 spl0_2 <=> ! [X2,X1] : ((~ (fool @ X1 @ X2)) = $true)), 0.23/0.49 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 0.23/0.49 thf(f358,plain,( 0.23/0.49 ( ! [X0 : $i,X1 : $i] : (((~ (fool @ X1 @ (sK5 @ X1 @ X0))) = $false)) ) | ~spl0_2), 0.23/0.49 inference(boolean_simplification,[],[f357])). 0.23/0.49 thf(f357,plain,( 0.23/0.49 ( ! [X0 : $i,X1 : $i] : (($false = ($false | (~ (fool @ X1 @ (sK5 @ X1 @ X0)))))) ) | ~spl0_2), 0.23/0.49 inference(forward_demodulation,[],[f356,f328])). 0.23/0.49 thf(f356,plain,( 0.23/0.49 ( ! [X0 : $i,X1 : $i] : (($false = ((fool @ X0 @ (sK5 @ X1 @ X0)) | (~ (fool @ X1 @ (sK5 @ X1 @ X0)))))) ) | ~spl0_2), 0.23/0.49 inference(beta_eta_normalization,[],[f346])). 0.23/0.49 thf(f346,plain,( 0.23/0.49 ( ! [X0 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((fool @ X0 @ Y0) | (~ (fool @ X1 @ Y0)))) @ (sK5 @ X1 @ X0)))) ) | ~spl0_2), 0.23/0.49 inference(sigma_clausification,[],[f335])). 0.23/0.49 thf(f335,plain,( 0.23/0.49 ( ! [X0 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((fool @ X0 @ Y0) | (~ (fool @ X1 @ Y0))))))) ) | ~spl0_2), 0.23/0.49 inference(not_proxy_clausification,[],[f332])). 0.23/0.49 thf(f332,plain,( 0.23/0.49 ( ! [X0 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((fool @ X0 @ Y0) | (~ (fool @ X1 @ Y0)))))))) ) | ~spl0_2), 0.23/0.49 inference(boolean_simplification,[],[f331])). 0.23/0.49 thf(f331,plain,( 0.23/0.49 ( ! [X0 : $i,X1 : $i] : (($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((fool @ X0 @ Y0) | (~ (fool @ X1 @ Y0)))))) | $false))) ) | ~spl0_2), 0.23/0.49 inference(superposition,[],[f240,f328])). 0.23/0.49 thf(f240,plain,( 0.23/0.49 ( ! [X2 : $i > $o,X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((X2 @ Y0) | (~ (fool @ X1 @ Y0)))))) | (X2 @ X1)) = $true)) )), 0.23/0.49 inference(beta_eta_normalization,[],[f239])). 0.23/0.49 thf(f239,plain,( 0.23/0.49 ( ! [X2 : $i > $o,X1 : $i] : ((((^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (fool @ X1 @ Y1)))))) | (Y0 @ X1))) @ X2) = $true)) )), 0.23/0.49 inference(pi_clausification,[],[f238])). 0.23/0.49 thf(f238,plain,( 0.23/0.49 ( ! [X1 : $i] : (((!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (!! @ $i @ (^[Y1 : $i]: ((Y0 @ Y1) | (~ (fool @ X1 @ Y1)))))) | (Y0 @ X1)))) = $true)) )), 0.23/0.49 inference(beta_eta_normalization,[],[f237])). 0.23/0.49 thf(f237,plain,( 0.23/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (fool @ Y0 @ Y2)))))) | (Y1 @ Y0))))) @ X1))) )), 0.23/0.49 inference(pi_clausification,[],[f222])). 0.23/0.49 thf(f222,plain,( 0.23/0.49 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (!! @ $i @ (^[Y2 : $i]: ((Y1 @ Y2) | (~ (fool @ Y0 @ Y2)))))) | (Y1 @ Y0)))))) = $true)), 0.23/0.49 inference(beta_eta_normalization,[],[f215])). 0.23/0.49 thf(f215,plain,( 0.23/0.49 ($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]: ((Y3 @ Y5) | (Y4 @ Y5))))))) @ ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (~ (Y3 @ Y4))))) @ Y1) @ Y2)))) @ ((^[Y1 : $i > $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((Y2 @ Y4) | (~ (Y1 @ Y3 @ Y4)))))))))) @ fool @ Y0) @ Y0)))))), 0.23/0.49 inference(definition_unfolding,[],[f164,f180,f159,f197,f152])). 0.23/0.49 thf(f197,plain,( 0.23/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))), 0.23/0.49 inference(definition_unfolding,[],[f187,f171,f173])). 0.23/0.49 thf(f173,plain,( 0.23/0.49 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))), 0.23/0.49 inference(cnf_transformation,[],[f85])). 0.23/0.49 thf(f85,plain,( 0.23/0.49 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))), 0.23/0.49 inference(fool_elimination,[],[f84])). 0.23/0.49 thf(f84,plain,( 0.23/0.49 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)), 0.23/0.49 inference(rectify,[],[f3])). 0.23/0.49 thf(f3,axiom,( 0.23/0.49 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',mnot)). 0.23/0.49 thf(f171,plain,( 0.23/0.49 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))), 0.23/0.49 inference(cnf_transformation,[],[f108])). 0.23/0.49 thf(f108,plain,( 0.23/0.49 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))), 0.23/0.49 inference(fool_elimination,[],[f107])). 0.23/0.49 thf(f107,plain,( 0.23/0.49 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))), 0.23/0.49 inference(rectify,[],[f4])). 0.23/0.49 thf(f4,axiom,( 0.23/0.49 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',mor)). 0.23/0.49 thf(f187,plain,( 0.23/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))), 0.23/0.49 inference(cnf_transformation,[],[f83])). 0.23/0.49 thf(f83,plain,( 0.23/0.49 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))), 0.23/0.49 inference(fool_elimination,[],[f82])). 0.23/0.49 thf(f82,plain,( 0.23/0.49 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))), 0.23/0.49 inference(rectify,[],[f6])). 0.23/0.49 thf(f6,axiom,( 0.23/0.49 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',mimplies)). 0.23/0.49 thf(f159,plain,( 0.23/0.49 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))), 0.23/0.49 inference(cnf_transformation,[],[f95])). 0.23/0.49 thf(f95,plain,( 0.23/0.49 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))), 0.23/0.49 inference(fool_elimination,[],[f94])). 0.23/0.49 thf(f94,plain,( 0.23/0.49 (mforall_prop = (^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))))), 0.23/0.49 inference(rectify,[],[f11])). 0.23/0.49 thf(f11,axiom,( 0.23/0.49 (mforall_prop = (^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',mforall_prop)). 0.23/0.49 thf(f164,plain,( 0.23/0.49 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)))) = $true)), 0.23/0.49 inference(cnf_transformation,[],[f77])). 0.23/0.49 thf(f77,plain,( 0.23/0.49 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mimplies @ (mbox @ fool @ Y0) @ Y0)))) = $true)), 0.23/0.49 inference(fool_elimination,[],[f76])). 0.23/0.49 thf(f76,plain,( 0.23/0.49 (mvalid @ (mforall_prop @ (^[X0 : $i > $o] : (mimplies @ (mbox @ fool @ X0) @ X0))))), 0.23/0.49 inference(rectify,[],[f48])). 0.23/0.49 thf(f48,axiom,( 0.23/0.49 (mvalid @ (mforall_prop @ (^[X12 : $i > $o] : (mimplies @ (mbox @ fool @ X12) @ X12))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',t_axiom_for_fool)). 0.23/0.49 thf(f325,plain,( 0.23/0.49 spl0_1 | spl0_2), 0.23/0.49 inference(avatar_split_clause,[],[f318,f323,f320])). 0.23/0.49 thf(f318,plain,( 0.23/0.49 ( ! [X2 : $i,X1 : $i] : (((~ (fool @ X1 @ X2)) = $true) | (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))) & (c @ spain @ france)) = $true)) )), 0.23/0.49 inference(binary_proxy_clausification,[],[f317])). 0.23/0.49 thf(f317,plain,( 0.23/0.49 ( ! [X2 : $i,X1 : $i] : (($true = (((~ (?? @ reg @ (^[Y0 : reg]: ((!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ spain)))) & (!! @ reg @ (^[Y1 : reg]: ((c @ Y1 @ Y0) => (c @ Y1 @ france)))))))) & (c @ spain @ france)) | (~ (fool @ X1 @ X2))))) )), 0.23/0.49 inference(beta_eta_normalization,[],[f316])). 0.23/0.49 thf(f316,plain,( 0.23/0.49 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))) & (c @ spain @ france)) | (~ (fool @ X1 @ Y0)))) @ X2))) )), 0.23/0.49 inference(pi_clausification,[],[f306])). 0.23/0.49 thf(f306,plain,( 0.23/0.49 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((~ (?? @ reg @ (^[Y1 : reg]: ((!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ spain)))) & (!! @ reg @ (^[Y2 : reg]: ((c @ Y2 @ Y1) => (c @ Y2 @ france)))))))) & (c @ spain @ france)) | (~ (fool @ X1 @ Y0))))))) )), 0.23/0.49 inference(beta_eta_normalization,[],[f305])). 0.23/0.49 thf(f305,plain,( 0.23/0.49 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))))))) & (c @ spain @ france)) | (~ (fool @ Y0 @ Y1)))))) @ X1))) )), 0.23/0.49 inference(pi_clausification,[],[f221])). 0.23/0.49 thf(f221,plain,( 0.23/0.49 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((~ (?? @ reg @ (^[Y2 : reg]: ((!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ spain)))) & (!! @ reg @ (^[Y3 : reg]: ((c @ Y3 @ Y2) => (c @ Y3 @ france)))))))) & (c @ spain @ france)) | (~ (fool @ Y0 @ Y1))))))))), 0.23/0.49 inference(beta_eta_normalization,[],[f213])). 0.23/0.49 thf(f213,plain,( 0.23/0.49 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))) @ fool @ (^[Y0 : $i]: ((^[Y1 : reg]: ((^[Y2 : reg]: ((~ ((^[Y3 : reg]: ((^[Y4 : reg]: (?? @ reg @ (^[Y5 : reg]: (((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y3) & ((^[Y6 : reg]: ((^[Y7 : reg]: (!! @ reg @ (^[Y8 : reg]: ((c @ Y8 @ Y6) => (c @ Y8 @ Y7))))))) @ Y5 @ Y4))))))) @ Y1 @ Y2)) & (c @ Y1 @ Y2))))) @ spain @ france)))))), 0.23/0.49 inference(definition_unfolding,[],[f153,f180,f152,f208])). 0.23/0.49 thf(f153,plain,( 0.23/0.49 ($true = (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)))))), 0.23/0.49 inference(cnf_transformation,[],[f140])). 0.23/0.49 thf(f140,plain,( 0.23/0.49 ($true = (mvalid @ (mbox @ fool @ (^[Y0 : $i]: (ec @ spain @ france)))))), 0.23/0.49 inference(fool_elimination,[],[f139])). 0.23/0.49 thf(f139,plain,( 0.23/0.49 (mvalid @ (mbox @ fool @ (^[X0 : $i] : (ec @ spain @ france))))), 0.23/0.49 inference(rectify,[],[f45])). 0.23/0.49 thf(f45,axiom,( 0.23/0.49 (mvalid @ (mbox @ fool @ (^[X0 : $i] : (ec @ spain @ france))))), 0.23/0.49 file('/export/starexec/sandbox/tmp/tmp.vOWwveS4ME/E---3.1_12845.p',ax2)). 0.23/0.49 % SZS output end Proof for E---3.1_12845 0.23/0.49 % (12963)------------------------------ 0.23/0.49 % (12963)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.49 % (12963)Termination reason: Refutation 0.23/0.49 0.23/0.49 % (12963)Memory used [KB]: 6268 0.23/0.49 % (12963)Time elapsed: 0.068 s 0.23/0.49 % (12963)Instructions burned: 101 (million) 0.23/0.49 % (12963)------------------------------ 0.23/0.49 % (12963)------------------------------ 0.23/0.49 % (12951)Success in time 0.105 s 0.23/0.49 EOF