0.04/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.14 % Command : run_vampire %s %d THM 0.14/0.35 % Computer : n015.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1440 0.14/0.35 % WCLimit : 180 0.14/0.35 % DateTime : Thu Jul 4 07:26:24 EDT 2024 0.14/0.35 % CPUTime : 0.14/0.37 This is a THF_ problem 0.14/0.37 Running higher-order theorem proving 0.23/0.38 Running /export/starexec/sandbox2/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox2/tmp/tmp.FV3o8fGbsI/E---3.1_3848.p -m 16384 -t 180 0.23/0.40 % (3958)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_3848 for (1799ds/27Mi) 0.23/0.40 % (3956)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on E---3.1_3848 for (1799ds/183Mi) 0.23/0.40 % (3959)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on E---3.1_3848 for (1799ds/2Mi) 0.23/0.40 % (3961)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_3848 for (1799ds/275Mi) 0.23/0.40 % (3957)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_3848 for (1799ds/4Mi) 0.23/0.40 % (3960)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_3848 for (1799ds/2Mi) 0.23/0.40 % (3962)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on E---3.1_3848 for (1799ds/18Mi) 0.23/0.40 % (3959)Instruction limit reached! 0.23/0.40 % (3959)------------------------------ 0.23/0.40 % (3959)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.40 % (3960)Instruction limit reached! 0.23/0.40 % (3960)------------------------------ 0.23/0.40 % (3960)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.40 % (3959)Termination reason: Unknown 0.23/0.40 % (3959)Termination phase: Function definition elimination 0.23/0.40 0.23/0.40 % (3959)Memory used [KB]: 1023 0.23/0.40 % (3959)Time elapsed: 0.004 s 0.23/0.40 % (3959)Instructions burned: 2 (million) 0.23/0.40 % (3959)------------------------------ 0.23/0.40 % (3959)------------------------------ 0.23/0.40 % (3960)Termination reason: Unknown 0.23/0.40 % (3960)Termination phase: Property scanning 0.23/0.40 0.23/0.40 % (3960)Memory used [KB]: 1023 0.23/0.40 % (3960)Time elapsed: 0.004 s 0.23/0.40 % (3960)Instructions burned: 3 (million) 0.23/0.40 % (3960)------------------------------ 0.23/0.40 % (3960)------------------------------ 0.23/0.41 % (3957)Instruction limit reached! 0.23/0.41 % (3957)------------------------------ 0.23/0.41 % (3957)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.41 % (3957)Termination reason: Unknown 0.23/0.41 % (3957)Termination phase: Saturation 0.23/0.41 0.23/0.41 % (3957)Memory used [KB]: 5500 0.23/0.41 % (3957)Time elapsed: 0.005 s 0.23/0.41 % (3957)Instructions burned: 4 (million) 0.23/0.41 % (3957)------------------------------ 0.23/0.41 % (3957)------------------------------ 0.23/0.42 % (3962)Instruction limit reached! 0.23/0.42 % (3962)------------------------------ 0.23/0.42 % (3962)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.42 % (3962)Termination reason: Unknown 0.23/0.42 % (3962)Termination phase: Saturation 0.23/0.42 0.23/0.42 % (3962)Memory used [KB]: 5628 0.23/0.42 % (3962)Time elapsed: 0.014 s 0.23/0.42 % (3962)Instructions burned: 19 (million) 0.23/0.42 % (3962)------------------------------ 0.23/0.42 % (3962)------------------------------ 0.23/0.42 % (3958)Instruction limit reached! 0.23/0.42 % (3958)------------------------------ 0.23/0.42 % (3958)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.42 % (3958)Termination reason: Unknown 0.23/0.42 % (3958)Termination phase: Saturation 0.23/0.42 0.23/0.42 % (3958)Memory used [KB]: 5756 0.23/0.42 % (3958)Time elapsed: 0.020 s 0.23/0.42 % (3958)Instructions burned: 27 (million) 0.23/0.42 % (3958)------------------------------ 0.23/0.42 % (3958)------------------------------ 0.23/0.42 % (3963)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_3848 for (1799ds/3Mi) 0.23/0.42 % (3964)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_3848 for (1799ds/37Mi) 0.23/0.42 % (3965)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_3848 for (1799ds/15Mi) 0.23/0.42 % (3963)Instruction limit reached! 0.23/0.42 % (3963)------------------------------ 0.23/0.42 % (3963)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.42 % (3963)Termination reason: Unknown 0.23/0.42 % (3963)Termination phase: Property scanning 0.23/0.42 0.23/0.42 % (3963)Memory used [KB]: 1023 0.23/0.42 % (3963)Time elapsed: 0.004 s 0.23/0.42 % (3963)Instructions burned: 3 (million) 0.23/0.42 % (3963)------------------------------ 0.23/0.42 % (3963)------------------------------ 0.23/0.43 % (3965)Instruction limit reached! 0.23/0.43 % (3965)------------------------------ 0.23/0.43 % (3965)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.43 % (3965)Termination reason: Unknown 0.23/0.43 % (3965)Termination phase: Saturation 0.23/0.43 0.23/0.43 % (3965)Memory used [KB]: 5628 0.23/0.43 % (3966)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_3848 for (1799ds/3Mi) 0.23/0.43 % (3965)Time elapsed: 0.012 s 0.23/0.43 % (3965)Instructions burned: 15 (million) 0.23/0.43 % (3965)------------------------------ 0.23/0.43 % (3965)------------------------------ 0.23/0.43 % (3966)Instruction limit reached! 0.23/0.43 % (3966)------------------------------ 0.23/0.43 % (3966)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.43 % (3966)Termination reason: Unknown 0.23/0.43 % (3966)Termination phase: Function definition elimination 0.23/0.43 0.23/0.43 % (3966)Memory used [KB]: 1023 0.23/0.43 % (3966)Time elapsed: 0.004 s 0.23/0.43 % (3966)Instructions burned: 3 (million) 0.23/0.43 % (3966)------------------------------ 0.23/0.43 % (3966)------------------------------ 0.23/0.44 % (3967)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_3848 for (1799ds/1041Mi) 0.23/0.44 % (3968)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on E---3.1_3848 for (1799ds/7Mi) 0.23/0.44 % (3968)Instruction limit reached! 0.23/0.44 % (3968)------------------------------ 0.23/0.44 % (3968)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.44 % (3968)Termination reason: Unknown 0.23/0.44 % (3968)Termination phase: Saturation 0.23/0.44 0.23/0.44 % (3968)Memory used [KB]: 1023 0.23/0.44 % (3968)Time elapsed: 0.007 s 0.23/0.44 % (3968)Instructions burned: 8 (million) 0.23/0.44 % (3968)------------------------------ 0.23/0.44 % (3968)------------------------------ 0.23/0.44 % (3964)Instruction limit reached! 0.23/0.44 % (3964)------------------------------ 0.23/0.44 % (3964)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.44 % (3964)Termination reason: Unknown 0.23/0.44 % (3964)Termination phase: Saturation 0.23/0.44 0.23/0.44 % (3964)Memory used [KB]: 5756 0.23/0.44 % (3964)Time elapsed: 0.025 s 0.23/0.44 % (3964)Instructions burned: 37 (million) 0.23/0.44 % (3964)------------------------------ 0.23/0.44 % (3964)------------------------------ 0.23/0.45 % (3969)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on E---3.1_3848 for (1799ds/16Mi) 0.23/0.45 % (3970)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_3848 for (1799ds/3Mi) 0.23/0.45 % (3970)Instruction limit reached! 0.23/0.45 % (3970)------------------------------ 0.23/0.45 % (3970)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.45 % (3970)Termination reason: Unknown 0.23/0.45 % (3970)Termination phase: Function definition elimination 0.23/0.45 0.23/0.45 % (3970)Memory used [KB]: 1023 0.23/0.45 % (3970)Time elapsed: 0.004 s 0.23/0.45 % (3970)Instructions burned: 3 (million) 0.23/0.45 % (3970)------------------------------ 0.23/0.45 % (3970)------------------------------ 0.23/0.46 % (3969)Instruction limit reached! 0.23/0.46 % (3969)------------------------------ 0.23/0.46 % (3969)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.46 % (3969)Termination reason: Unknown 0.23/0.46 % (3969)Termination phase: Saturation 0.23/0.46 0.23/0.46 % (3969)Memory used [KB]: 5756 0.23/0.46 % (3969)Time elapsed: 0.014 s 0.23/0.46 % (3969)Instructions burned: 16 (million) 0.23/0.46 % (3969)------------------------------ 0.23/0.46 % (3969)------------------------------ 0.23/0.46 % (3971)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_3848 for (1799ds/3Mi) 0.23/0.46 % (3972)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_3848 for (1799ds/7Mi) 0.23/0.46 % (3971)Instruction limit reached! 0.23/0.46 % (3971)------------------------------ 0.23/0.46 % (3971)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.46 % (3971)Termination reason: Unknown 0.23/0.46 % (3971)Termination phase: Function definition elimination 0.23/0.46 0.23/0.46 % (3971)Memory used [KB]: 1023 0.23/0.46 % (3971)Time elapsed: 0.004 s 0.23/0.46 % (3971)Instructions burned: 3 (million) 0.23/0.46 % (3971)------------------------------ 0.23/0.46 % (3971)------------------------------ 0.23/0.46 % (3972)Instruction limit reached! 0.23/0.46 % (3972)------------------------------ 0.23/0.46 % (3972)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.46 % (3972)Termination reason: Unknown 0.23/0.46 % (3972)Termination phase: Saturation 0.23/0.46 0.23/0.46 % (3972)Memory used [KB]: 5500 0.23/0.46 % (3972)Time elapsed: 0.007 s 0.23/0.46 % (3972)Instructions burned: 8 (million) 0.23/0.46 % (3972)------------------------------ 0.23/0.46 % (3972)------------------------------ 0.23/0.47 % (3973)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_3848 for (1799ds/3Mi) 0.23/0.47 % (3973)Instruction limit reached! 0.23/0.47 % (3973)------------------------------ 0.23/0.47 % (3973)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.47 % (3973)Termination reason: Unknown 0.23/0.47 % (3973)Termination phase: Property scanning 0.23/0.47 0.23/0.47 % (3973)Memory used [KB]: 1023 0.23/0.47 % (3973)Time elapsed: 0.004 s 0.23/0.47 % (3973)Instructions burned: 3 (million) 0.23/0.47 % (3973)------------------------------ 0.23/0.47 % (3973)------------------------------ 0.23/0.48 % (3974)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on E---3.1_3848 for (1799ds/4Mi) 0.23/0.48 % (3975)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_3848 for (1799ds/18Mi) 0.23/0.48 % (3974)Instruction limit reached! 0.23/0.48 % (3974)------------------------------ 0.23/0.48 % (3974)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.48 % (3974)Termination reason: Unknown 0.23/0.48 % (3974)Termination phase: Saturation 0.23/0.48 0.23/0.48 % (3974)Memory used [KB]: 5500 0.23/0.48 % (3974)Time elapsed: 0.005 s 0.23/0.48 % (3974)Instructions burned: 4 (million) 0.23/0.48 % (3974)------------------------------ 0.23/0.48 % (3974)------------------------------ 0.23/0.48 % (3976)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on E---3.1_3848 for (1799ds/710Mi) 0.23/0.48 % (3977)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on E---3.1_3848 for (1799ds/6Mi) 0.23/0.49 % (3977)Instruction limit reached! 0.23/0.49 % (3977)------------------------------ 0.23/0.49 % (3977)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.49 % (3977)Termination reason: Unknown 0.23/0.49 % (3977)Termination phase: Saturation 0.23/0.49 0.23/0.49 % (3977)Memory used [KB]: 5500 0.23/0.49 % (3977)Time elapsed: 0.005 s 0.23/0.49 % (3977)Instructions burned: 8 (million) 0.23/0.49 % (3977)------------------------------ 0.23/0.49 % (3977)------------------------------ 0.23/0.49 % (3975)Instruction limit reached! 0.23/0.49 % (3975)------------------------------ 0.23/0.49 % (3975)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.49 % (3975)Termination reason: Unknown 0.23/0.49 % (3975)Termination phase: Saturation 0.23/0.49 0.23/0.49 % (3975)Memory used [KB]: 5628 0.23/0.49 % (3975)Time elapsed: 0.036 s 0.23/0.49 % (3975)Instructions burned: 18 (million) 0.23/0.49 % (3975)------------------------------ 0.23/0.49 % (3975)------------------------------ 0.23/0.49 % (3978)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_3848 for (1799ds/902Mi) 0.23/0.50 % (3979)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_3848 for (1799ds/21Mi) 0.23/0.50 % (3978)Refutation not found, incomplete strategy 0.23/0.50 % (3978)------------------------------ 0.23/0.50 % (3978)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.50 % (3978)Termination reason: Refutation not found, incomplete strategy 0.23/0.50 0.23/0.50 0.23/0.50 % (3978)Memory used [KB]: 5500 0.23/0.50 % (3978)Time elapsed: 0.027 s 0.23/0.50 % (3978)Instructions burned: 3 (million) 0.23/0.50 % (3978)------------------------------ 0.23/0.50 % (3978)------------------------------ 0.23/0.50 % (3980)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on E---3.1_3848 for (1798ds/5Mi) 0.23/0.50 % (3979)Instruction limit reached! 0.23/0.50 % (3979)------------------------------ 0.23/0.50 % (3979)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.50 % (3979)Termination reason: Unknown 0.23/0.50 % (3979)Termination phase: Saturation 0.23/0.50 0.23/0.50 % (3979)Memory used [KB]: 5628 0.23/0.50 % (3979)Time elapsed: 0.010 s 0.23/0.50 % (3979)Instructions burned: 21 (million) 0.23/0.50 % (3979)------------------------------ 0.23/0.50 % (3979)------------------------------ 0.23/0.51 % (3980)Instruction limit reached! 0.23/0.51 % (3980)------------------------------ 0.23/0.51 % (3980)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.51 % (3980)Termination reason: Unknown 0.23/0.51 % (3980)Termination phase: Saturation 0.23/0.51 0.23/0.51 % (3980)Memory used [KB]: 5500 0.23/0.51 % (3980)Time elapsed: 0.005 s 0.23/0.51 % (3980)Instructions burned: 7 (million) 0.23/0.51 % (3980)------------------------------ 0.23/0.51 % (3980)------------------------------ 0.23/0.51 % (3981)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_3848 for (1798ds/6Mi) 0.23/0.51 % (3982)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on E---3.1_3848 for (1798ds/377Mi) 0.23/0.52 % (3981)Instruction limit reached! 0.23/0.52 % (3981)------------------------------ 0.23/0.52 % (3981)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 0.23/0.52 % (3981)Termination reason: Unknown 0.23/0.52 % (3981)Termination phase: Saturation 0.23/0.52 0.23/0.52 % (3981)Memory used [KB]: 5500 0.23/0.52 % (3981)Time elapsed: 0.005 s 0.23/0.52 % (3981)Instructions burned: 7 (million) 0.23/0.52 % (3981)------------------------------ 0.23/0.52 % (3981)------------------------------ 0.23/0.52 % (3983)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_3848 for (1798ds/779Mi) 1.07/0.53 % (3956)Instruction limit reached! 1.07/0.53 % (3956)------------------------------ 1.07/0.53 % (3956)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.07/0.53 % (3956)Termination reason: Unknown 1.07/0.53 % (3956)Termination phase: Saturation 1.07/0.53 1.07/0.53 % (3956)Memory used [KB]: 6908 1.07/0.53 % (3956)Time elapsed: 0.115 s 1.07/0.53 % (3956)Instructions burned: 184 (million) 1.07/0.53 % (3956)------------------------------ 1.07/0.53 % (3956)------------------------------ 1.07/0.53 % (3984)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_3848 for (1798ds/19Mi) 1.07/0.53 % (3984)Instruction limit reached! 1.07/0.53 % (3984)------------------------------ 1.07/0.53 % (3984)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.07/0.53 % (3984)Termination reason: Unknown 1.07/0.53 % (3984)Termination phase: Saturation 1.07/0.53 1.07/0.53 % (3984)Memory used [KB]: 5628 1.07/0.53 % (3984)Time elapsed: 0.008 s 1.07/0.53 % (3984)Instructions burned: 19 (million) 1.07/0.53 % (3984)------------------------------ 1.07/0.53 % (3984)------------------------------ 1.07/0.54 % (3985)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_3848 for (1798ds/879Mi) 1.07/0.54 % (3961)Instruction limit reached! 1.07/0.54 % (3961)------------------------------ 1.07/0.54 % (3961)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.07/0.54 % (3961)Termination reason: Unknown 1.07/0.54 % (3961)Termination phase: Saturation 1.07/0.54 1.07/0.54 % (3961)Memory used [KB]: 6524 1.07/0.54 % (3961)Time elapsed: 0.137 s 1.07/0.54 % (3961)Instructions burned: 277 (million) 1.07/0.54 % (3961)------------------------------ 1.07/0.54 % (3961)------------------------------ 1.22/0.54 % (3986)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on E---3.1_3848 for (1798ds/17Mi) 1.22/0.55 % (3987)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on E---3.1_3848 for (1798ds/3Mi) 1.22/0.55 % (3987)Instruction limit reached! 1.22/0.55 % (3987)------------------------------ 1.22/0.55 % (3987)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.55 % (3987)Termination reason: Unknown 1.22/0.55 % (3987)Termination phase: Function definition elimination 1.22/0.55 1.22/0.55 % (3987)Memory used [KB]: 1023 1.22/0.55 % (3987)Time elapsed: 0.003 s 1.22/0.55 % (3987)Instructions burned: 3 (million) 1.22/0.55 % (3987)------------------------------ 1.22/0.55 % (3987)------------------------------ 1.22/0.55 % (3986)Instruction limit reached! 1.22/0.55 % (3986)------------------------------ 1.22/0.55 % (3986)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.55 % (3986)Termination reason: Unknown 1.22/0.55 % (3986)Termination phase: Saturation 1.22/0.55 1.22/0.55 % (3986)Memory used [KB]: 5628 1.22/0.55 % (3986)Time elapsed: 0.009 s 1.22/0.55 % (3986)Instructions burned: 19 (million) 1.22/0.55 % (3986)------------------------------ 1.22/0.55 % (3986)------------------------------ 1.22/0.56 % (3988)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on E---3.1_3848 for (1798ds/30Mi) 1.22/0.56 % (3989)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_3848 for (1798ds/127Mi) 1.22/0.56 % (3988)Refutation not found, incomplete strategy 1.22/0.56 % (3988)------------------------------ 1.22/0.56 % (3988)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.56 % (3988)Termination reason: Refutation not found, incomplete strategy 1.22/0.56 1.22/0.56 1.22/0.56 % (3988)Memory used [KB]: 5500 1.22/0.56 % (3988)Time elapsed: 0.005 s 1.22/0.56 % (3988)Instructions burned: 8 (million) 1.22/0.56 % (3988)------------------------------ 1.22/0.56 % (3988)------------------------------ 1.22/0.56 % (3983)First to succeed. 1.22/0.57 % (3983)Refutation found. Thanks to Tanya! 1.22/0.57 % SZS status Theorem for E---3.1_3848 1.22/0.57 % SZS output start Proof for E---3.1_3848 1.22/0.57 thf(type_def_5, type, g: $tType). 1.22/0.57 thf(func_def_0, type, g: $tType). 1.22/0.57 thf(func_def_1, type, cGROUP3: (g > g > g) > g > $o). 1.22/0.57 thf(func_def_2, type, cGROUP4: (g > g > g) > $o). 1.22/0.57 thf(func_def_3, type, cGRP_ASSOC: (g > g > g) > $o). 1.22/0.57 thf(func_def_4, type, cGRP_DIVISORS: (g > g > g) > $o). 1.22/0.57 thf(func_def_5, type, cGRP_RIGHT_INVERSE: (g > g > g) > g > $o). 1.22/0.57 thf(func_def_6, type, cGRP_RIGHT_UNIT: (g > g > g) > g > $o). 1.22/0.57 thf(func_def_23, type, sK1: g > g > g). 1.22/0.57 thf(func_def_24, type, sK2: g). 1.22/0.57 thf(func_def_25, type, sK3: g > g). 1.22/0.57 thf(func_def_26, type, sK4: g > g > g). 1.22/0.57 thf(func_def_27, type, sK5: g > g > g). 1.22/0.57 thf(func_def_28, type, sK6: g). 1.22/0.57 thf(func_def_29, type, sK7: g). 1.22/0.57 thf(func_def_30, type, sK8: g). 1.22/0.57 thf(func_def_31, type, sK9: g). 1.22/0.57 thf(func_def_32, type, sK10: g). 1.22/0.57 thf(func_def_33, type, sK11: g > g). 1.22/0.57 thf(func_def_34, type, sK12: g > g). 1.22/0.57 thf(f657,plain,( 1.22/0.57 $false), 1.22/0.57 inference(avatar_sat_refutation,[],[f87,f109,f116,f128,f134,f209,f217,f337,f345,f351,f380,f591,f656])). 1.22/0.57 thf(f656,plain,( 1.22/0.57 ~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_8), 1.22/0.57 inference(avatar_contradiction_clause,[],[f655])). 1.22/0.57 thf(f655,plain,( 1.22/0.57 $false | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_8)), 1.22/0.57 inference(equality_resolution,[],[f598])). 1.22/0.57 thf(f598,plain,( 1.22/0.57 ( ! [X0 : g] : ((sK6 != X0)) ) | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_8)), 1.22/0.57 inference(superposition,[],[f592,f521])). 1.22/0.57 thf(f521,plain,( 1.22/0.57 ( ! [X0 : g] : (((sK1 @ sK2 @ (sK3 @ (sK3 @ X0))) = X0)) ) | (~spl0_1 | ~spl0_2 | ~spl0_3)), 1.22/0.57 inference(forward_demodulation,[],[f498,f64])). 1.22/0.57 thf(f64,plain,( 1.22/0.57 ( ! [X4 : g] : (((sK1 @ X4 @ sK2) = X4)) ) | ~spl0_2), 1.22/0.57 inference(avatar_component_clause,[],[f63])). 1.22/0.57 thf(f63,plain,( 1.22/0.57 spl0_2 <=> ! [X4 : g] : ((sK1 @ X4 @ sK2) = X4)), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])). 1.22/0.57 thf(f498,plain,( 1.22/0.57 ( ! [X0 : g] : (((sK1 @ X0 @ sK2) = (sK1 @ sK2 @ (sK3 @ (sK3 @ X0))))) ) | (~spl0_1 | ~spl0_3)), 1.22/0.57 inference(superposition,[],[f360,f73])). 1.22/0.57 thf(f73,plain,( 1.22/0.57 ( ! [X4 : g] : (((sK1 @ X4 @ (sK3 @ X4)) = sK2)) ) | ~spl0_3), 1.22/0.57 inference(avatar_component_clause,[],[f72])). 1.22/0.57 thf(f72,plain,( 1.22/0.57 spl0_3 <=> ! [X4 : g] : ((sK1 @ X4 @ (sK3 @ X4)) = sK2)), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])). 1.22/0.57 thf(f360,plain,( 1.22/0.57 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ (sK3 @ X0) @ X1)) = (sK1 @ sK2 @ X1))) ) | (~spl0_1 | ~spl0_3)), 1.22/0.57 inference(superposition,[],[f61,f73])). 1.22/0.57 thf(f61,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ (sK1 @ X1 @ X2) @ X3) = (sK1 @ X1 @ (sK1 @ X2 @ X3)))) ) | ~spl0_1), 1.22/0.57 inference(avatar_component_clause,[],[f60])). 1.22/0.57 thf(f60,plain,( 1.22/0.57 spl0_1 <=> ! [X2 : g,X1 : g,X3 : g] : ((sK1 @ (sK1 @ X1 @ X2) @ X3) = (sK1 @ X1 @ (sK1 @ X2 @ X3)))), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])). 1.22/0.57 thf(f592,plain,( 1.22/0.57 ( ! [X0 : g] : ((sK6 != (sK1 @ sK2 @ X0))) ) | (~spl0_1 | ~spl0_3 | ~spl0_8)), 1.22/0.57 inference(superposition,[],[f205,f360])). 1.22/0.57 thf(f205,plain,( 1.22/0.57 ( ! [X2 : g] : (((sK1 @ sK8 @ X2) != sK6)) ) | ~spl0_8), 1.22/0.57 inference(avatar_component_clause,[],[f204])). 1.22/0.57 thf(f204,plain,( 1.22/0.57 spl0_8 <=> ! [X2 : g] : ((sK1 @ sK8 @ X2) != sK6)), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])). 1.22/0.57 thf(f591,plain,( 1.22/0.57 ~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_9), 1.22/0.57 inference(avatar_contradiction_clause,[],[f590])). 1.22/0.57 thf(f590,plain,( 1.22/0.57 $false | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_9)), 1.22/0.57 inference(equality_resolution,[],[f586])). 1.22/0.57 thf(f586,plain,( 1.22/0.57 ( ! [X0 : g] : ((sK6 != X0)) ) | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_9)), 1.22/0.57 inference(superposition,[],[f561,f64])). 1.22/0.57 thf(f561,plain,( 1.22/0.57 ( ! [X0 : g] : ((sK6 != (sK1 @ X0 @ sK2))) ) | (~spl0_1 | ~spl0_2 | ~spl0_3 | ~spl0_9)), 1.22/0.57 inference(superposition,[],[f381,f547])). 1.22/0.57 thf(f547,plain,( 1.22/0.57 ( ! [X0 : g] : (((sK1 @ (sK3 @ X0) @ X0) = sK2)) ) | (~spl0_1 | ~spl0_2 | ~spl0_3)), 1.22/0.57 inference(superposition,[],[f418,f521])). 1.22/0.57 thf(f418,plain,( 1.22/0.57 ( ! [X0 : g] : (((sK1 @ X0 @ (sK1 @ sK2 @ (sK3 @ X0))) = sK2)) ) | (~spl0_1 | ~spl0_2 | ~spl0_3)), 1.22/0.57 inference(superposition,[],[f358,f64])). 1.22/0.57 thf(f358,plain,( 1.22/0.57 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK1 @ X1 @ (sK3 @ (sK1 @ X0 @ X1)))) = sK2)) ) | (~spl0_1 | ~spl0_3)), 1.22/0.57 inference(superposition,[],[f73,f61])). 1.22/0.57 thf(f381,plain,( 1.22/0.57 ( ! [X0 : g,X1 : g] : ((sK6 != (sK1 @ X0 @ (sK1 @ X1 @ sK8)))) ) | (~spl0_1 | ~spl0_9)), 1.22/0.57 inference(superposition,[],[f208,f61])). 1.22/0.57 thf(f208,plain,( 1.22/0.57 ( ! [X3 : g] : ((sK6 != (sK1 @ X3 @ sK8))) ) | ~spl0_9), 1.22/0.57 inference(avatar_component_clause,[],[f207])). 1.22/0.57 thf(f207,plain,( 1.22/0.57 spl0_9 <=> ! [X3 : g] : (sK6 != (sK1 @ X3 @ sK8))), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])). 1.22/0.57 thf(f380,plain,( 1.22/0.57 ~spl0_2 | ~spl0_3 | ~spl0_6), 1.22/0.57 inference(avatar_contradiction_clause,[],[f379])). 1.22/0.57 thf(f379,plain,( 1.22/0.57 $false | (~spl0_2 | ~spl0_3 | ~spl0_6)), 1.22/0.57 inference(trivial_inequality_removal,[],[f376])). 1.22/0.57 thf(f376,plain,( 1.22/0.57 (sK2 != sK2) | (~spl0_2 | ~spl0_3 | ~spl0_6)), 1.22/0.57 inference(superposition,[],[f370,f73])). 1.22/0.57 thf(f370,plain,( 1.22/0.57 ( ! [X0 : g] : (((sK1 @ (sK11 @ sK2) @ X0) != sK2)) ) | (~spl0_2 | ~spl0_6)), 1.22/0.57 inference(trivial_inequality_removal,[],[f369])). 1.22/0.57 thf(f369,plain,( 1.22/0.57 ( ! [X0 : g] : (((sK1 @ (sK11 @ sK2) @ X0) != sK2) | ((sK12 @ sK2) != (sK12 @ sK2))) ) | (~spl0_2 | ~spl0_6)), 1.22/0.57 inference(superposition,[],[f198,f64])). 1.22/0.57 thf(f198,plain,( 1.22/0.57 ( ! [X1 : g,X4 : g] : (((sK12 @ X1) != (sK1 @ (sK12 @ X1) @ X1)) | ((sK1 @ (sK11 @ X1) @ X4) != X1)) ) | ~spl0_6), 1.22/0.57 inference(avatar_component_clause,[],[f197])). 1.22/0.57 thf(f197,plain,( 1.22/0.57 spl0_6 <=> ! [X4 : g,X1 : g] : (((sK1 @ (sK11 @ X1) @ X4) != X1) | ((sK12 @ X1) != (sK1 @ (sK12 @ X1) @ X1)))), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])). 1.22/0.57 thf(f351,plain,( 1.22/0.57 ~spl0_5 | ~spl0_9), 1.22/0.57 inference(avatar_contradiction_clause,[],[f350])). 1.22/0.57 thf(f350,plain,( 1.22/0.57 $false | (~spl0_5 | ~spl0_9)), 1.22/0.57 inference(equality_resolution,[],[f346])). 1.22/0.57 thf(f346,plain,( 1.22/0.57 ( ! [X0 : g] : ((sK6 != X0)) ) | (~spl0_5 | ~spl0_9)), 1.22/0.57 inference(superposition,[],[f208,f127])). 1.22/0.57 thf(f127,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) ) | ~spl0_5), 1.22/0.57 inference(avatar_component_clause,[],[f126])). 1.22/0.57 thf(f126,plain,( 1.22/0.57 spl0_5 <=> ! [X2 : g,X1 : g] : ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])). 1.22/0.57 thf(f345,plain,( 1.22/0.57 ~spl0_4 | ~spl0_8), 1.22/0.57 inference(avatar_contradiction_clause,[],[f344])). 1.22/0.57 thf(f344,plain,( 1.22/0.57 $false | (~spl0_4 | ~spl0_8)), 1.22/0.57 inference(equality_resolution,[],[f338])). 1.22/0.57 thf(f338,plain,( 1.22/0.57 ( ! [X0 : g] : ((sK6 != X0)) ) | (~spl0_4 | ~spl0_8)), 1.22/0.57 inference(superposition,[],[f205,f108])). 1.22/0.57 thf(f108,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1)) ) | ~spl0_4), 1.22/0.57 inference(avatar_component_clause,[],[f107])). 1.22/0.57 thf(f107,plain,( 1.22/0.57 spl0_4 <=> ! [X2 : g,X1 : g] : ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1)), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])). 1.22/0.57 thf(f337,plain,( 1.22/0.57 ~spl0_1 | ~spl0_4 | ~spl0_5 | ~spl0_6), 1.22/0.57 inference(avatar_contradiction_clause,[],[f336])). 1.22/0.57 thf(f336,plain,( 1.22/0.57 $false | (~spl0_1 | ~spl0_4 | ~spl0_5 | ~spl0_6)), 1.22/0.57 inference(equality_resolution,[],[f330])). 1.22/0.57 thf(f330,plain,( 1.22/0.57 ( ! [X0 : g,X1 : g] : (((sK4 @ X0 @ X0) != X1)) ) | (~spl0_1 | ~spl0_4 | ~spl0_5 | ~spl0_6)), 1.22/0.57 inference(superposition,[],[f308,f108])). 1.22/0.57 thf(f308,plain,( 1.22/0.57 ( ! [X0 : g,X1 : g] : (((sK4 @ X0 @ X0) != (sK1 @ (sK11 @ (sK4 @ X0 @ X0)) @ X1))) ) | (~spl0_1 | ~spl0_4 | ~spl0_5 | ~spl0_6)), 1.22/0.57 inference(trivial_inequality_removal,[],[f307])). 1.22/0.57 thf(f307,plain,( 1.22/0.57 ( ! [X0 : g,X1 : g] : (((sK4 @ X0 @ X0) != (sK1 @ (sK11 @ (sK4 @ X0 @ X0)) @ X1)) | ((sK12 @ (sK4 @ X0 @ X0)) != (sK12 @ (sK4 @ X0 @ X0)))) ) | (~spl0_1 | ~spl0_4 | ~spl0_5 | ~spl0_6)), 1.22/0.57 inference(superposition,[],[f198,f268])). 1.22/0.57 thf(f268,plain,( 1.22/0.57 ( ! [X0 : g,X1 : g] : (((sK1 @ X0 @ (sK4 @ X1 @ X1)) = X0)) ) | (~spl0_1 | ~spl0_4 | ~spl0_5)), 1.22/0.57 inference(superposition,[],[f227,f127])). 1.22/0.57 thf(f227,plain,( 1.22/0.57 ( ! [X2 : g,X0 : g,X1 : g] : (((sK1 @ X2 @ (sK4 @ X1 @ X0)) = (sK1 @ (sK5 @ X2 @ X0) @ X1))) ) | (~spl0_1 | ~spl0_4 | ~spl0_5)), 1.22/0.57 inference(superposition,[],[f211,f108])). 1.22/0.57 thf(f211,plain,( 1.22/0.57 ( ! [X2 : g,X0 : g,X1 : g] : (((sK1 @ X0 @ X2) = (sK1 @ (sK5 @ X0 @ X1) @ (sK1 @ X1 @ X2)))) ) | (~spl0_1 | ~spl0_5)), 1.22/0.57 inference(superposition,[],[f61,f127])). 1.22/0.57 thf(f217,plain,( 1.22/0.57 ~spl0_1 | spl0_7), 1.22/0.57 inference(avatar_contradiction_clause,[],[f216])). 1.22/0.57 thf(f216,plain,( 1.22/0.57 $false | (~spl0_1 | spl0_7)), 1.22/0.57 inference(trivial_inequality_removal,[],[f214])). 1.22/0.57 thf(f214,plain,( 1.22/0.57 ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ sK7 @ (sK1 @ sK9 @ sK10))) | (~spl0_1 | spl0_7)), 1.22/0.57 inference(superposition,[],[f202,f61])). 1.22/0.57 thf(f202,plain,( 1.22/0.57 ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | spl0_7), 1.22/0.57 inference(avatar_component_clause,[],[f200])). 1.22/0.57 thf(f200,plain,( 1.22/0.57 spl0_7 <=> ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) = (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))), 1.22/0.57 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])). 1.22/0.57 thf(f209,plain,( 1.22/0.57 spl0_6 | ~spl0_7 | spl0_8 | spl0_9), 1.22/0.57 inference(avatar_split_clause,[],[f195,f207,f204,f200,f197])). 1.22/0.57 thf(f195,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ sK8 @ X2) != sK6) | (sK6 != (sK1 @ X3 @ sK8)) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((sK1 @ (sK11 @ X1) @ X4) != X1) | ((sK12 @ X1) != (sK1 @ (sK12 @ X1) @ X1))) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f194])). 1.22/0.57 thf(f194,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : ((sK6 != (sK1 @ X3 @ sK8)) | ((sK1 @ (sK11 @ X1) @ X4) != X1) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((sK1 @ sK8 @ X2) != sK6) | (((sK1 @ (sK12 @ X1) @ X1) = (sK12 @ X1)) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f193])). 1.22/0.57 thf(f193,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ sK8 @ X2) != sK6) | ((sK1 @ (sK11 @ X1) @ X4) != X1) | (((^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0)) @ (sK12 @ X1)) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | (sK6 != (sK1 @ X3 @ sK8))) )), 1.22/0.57 inference(sigma_clausification,[],[f192])). 1.22/0.57 thf(f192,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ sK8 @ X2) != sK6) | (sK6 != (sK1 @ X3 @ sK8)) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((sK1 @ (sK11 @ X1) @ X4) != X1) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f191])). 1.22/0.57 thf(f191,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : ((((sK1 @ (sK11 @ X1) @ X4) = X1) = $false) | ((sK1 @ sK8 @ X2) != sK6) | (sK6 != (sK1 @ X3 @ sK8)) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false)) )), 1.22/0.57 inference(duplicate_literal_removal,[],[f190])). 1.22/0.57 thf(f190,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | (sK6 != (sK1 @ X3 @ sK8)) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((sK1 @ sK8 @ X2) != sK6) | (((sK1 @ (sK11 @ X1) @ X4) = X1) = $false)) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f189])). 1.22/0.57 thf(f189,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ sK8 @ X2) != sK6) | (sK6 != (sK1 @ X3 @ sK8)) | ($false = ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) = (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | (((sK1 @ (sK11 @ X1) @ X4) = X1) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f188])). 1.22/0.57 thf(f188,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | (((sK1 @ (sK11 @ X1) @ X4) = X1) = $false) | ($false = ((^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0))) @ sK10)) | (sK6 != (sK1 @ X3 @ sK8)) | ((sK1 @ sK8 @ X2) != sK6) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))) )), 1.22/0.57 inference(sigma_clausification,[],[f187])). 1.22/0.57 thf(f187,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (((sK1 @ sK8 @ X2) != sK6) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false) | (((sK1 @ (sK11 @ X1) @ X4) = X1) = $false) | (sK6 != (sK1 @ X3 @ sK8)) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f186])). 1.22/0.57 thf(f186,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : ((((^[Y0 : g]: ((sK1 @ (sK11 @ X1) @ Y0) = X1)) @ X4) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((sK1 @ sK8 @ X2) != sK6) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | (sK6 != (sK1 @ X3 @ sK8))) )), 1.22/0.57 inference(pi_clausification,[],[f185])). 1.22/0.57 thf(f185,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((sK1 @ sK8 @ X2) != sK6) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ (sK11 @ X1) @ Y0) = X1))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false) | (sK6 != (sK1 @ X3 @ sK8)) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f184])). 1.22/0.57 thf(f184,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ (sK11 @ X1) @ Y0) = X1))) = $false) | (sK6 != (sK1 @ X3 @ sK8)) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1))))) @ sK9) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((sK1 @ sK8 @ X2) != sK6) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))) )), 1.22/0.57 inference(sigma_clausification,[],[f183])). 1.22/0.57 thf(f183,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1)))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((sK1 @ sK8 @ X2) != sK6) | (sK6 != (sK1 @ X3 @ sK8)) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ (sK11 @ X1) @ Y0) = X1))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f182])). 1.22/0.57 thf(f182,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1)))))) = $false) | (sK6 != (sK1 @ X3 @ sK8)) | (((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))) @ (sK11 @ X1)) = $false) | ((sK1 @ sK8 @ X2) != sK6)) )), 1.22/0.57 inference(sigma_clausification,[],[f181])). 1.22/0.57 thf(f181,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | (sK6 != (sK1 @ X3 @ sK8)) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1)))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((sK1 @ sK8 @ X2) != sK6)) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f180])). 1.22/0.57 thf(f180,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ X3 @ sK8) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1)))))) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((sK1 @ sK8 @ X2) != sK6) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false)) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f179])). 1.22/0.57 thf(f179,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : ((((sK1 @ sK8 @ X2) = sK6) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | (((sK1 @ X3 @ sK8) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1)))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f178])). 1.22/0.57 thf(f178,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))) @ sK7) = $false) | (((sK1 @ X3 @ sK8) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | (((sK1 @ sK8 @ X2) = sK6) = $false)) )), 1.22/0.57 inference(sigma_clausification,[],[f177])). 1.22/0.57 thf(f177,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | (((sK1 @ X3 @ sK8) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | (((sK1 @ sK8 @ X2) = sK6) = $false) | ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) != (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f176])). 1.22/0.57 thf(f176,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($false = ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) = (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))) | (((sK1 @ sK8 @ X2) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | (((sK1 @ X3 @ sK8) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f175])). 1.22/0.57 thf(f175,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | ($false = ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) = (sK1 @ (sK1 @ sK7 @ sK9) @ sK10))) | (((^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6)) @ X3) = $false) | (((sK1 @ sK8 @ X2) = sK6) = $false)) )), 1.22/0.57 inference(pi_clausification,[],[f174])). 1.22/0.57 thf(f174,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | (((sK1 @ sK8 @ X2) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ($false = ((sK1 @ sK7 @ (sK1 @ sK9 @ sK10)) = (sK1 @ (sK1 @ sK7 @ sK9) @ sK10)))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f173])). 1.22/0.57 thf(f173,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))) = $false) | (((sK1 @ sK8 @ X2) = sK6) = $false) | ($false = ((^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0))) @ sK10)) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false)) )), 1.22/0.57 inference(sigma_clausification,[],[f172])). 1.22/0.57 thf(f172,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))) = $false) | (((sK1 @ sK8 @ X2) = sK6) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f171])). 1.22/0.57 thf(f171,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false) | (((^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK6)) @ X2) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false)) )), 1.22/0.57 inference(pi_clausification,[],[f170])). 1.22/0.57 thf(f170,plain,( 1.22/0.57 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK6))) = $false) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false)) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f169])). 1.22/0.57 thf(f169,plain,( 1.22/0.57 ( ! [X1 : g] : (($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK6))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))))) | ((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) = $false)) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f168])). 1.22/0.57 thf(f168,plain,( 1.22/0.57 ( ! [X1 : g] : ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) = $false) | ($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK6))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))))) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false)) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f167])). 1.22/0.57 thf(f167,plain,( 1.22/0.57 ( ! [X1 : g] : (((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((sK1 @ sK7 @ (sK1 @ sK9 @ Y0)) = (sK1 @ (sK1 @ sK7 @ sK9) @ Y0)))) = $false) | ($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK6))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6)))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f166])). 1.22/0.57 thf(f166,plain,( 1.22/0.57 ( ! [X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1))))) @ sK9) = $false) | ($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK6))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))))) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false)) )), 1.22/0.57 inference(sigma_clausification,[],[f165])). 1.22/0.57 thf(f165,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1)))))) = $false) | ($false = ((?? @ g @ (^[Y0 : g]: ((sK1 @ sK8 @ Y0) = sK6))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK8) = sK6))))) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f164])). 1.22/0.57 thf(f164,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1)))))) = $false) | (((^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK6))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK6))))) @ sK8) = $false) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false)) )), 1.22/0.57 inference(sigma_clausification,[],[f163])). 1.22/0.57 thf(f163,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK6))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK6)))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ sK7 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ sK7 @ Y0) @ Y1)))))) = $false) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f162])). 1.22/0.57 thf(f162,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK6))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK6)))))) = $false) | (((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))) @ sK7) = $false) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false)) )), 1.22/0.57 inference(sigma_clausification,[],[f161])). 1.22/0.57 thf(f161,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK6))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = sK6)))))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f160])). 1.22/0.57 thf(f160,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ($false = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0))))))) @ sK6)) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false)) )), 1.22/0.57 inference(sigma_clausification,[],[f159])). 1.22/0.57 thf(f159,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0)))))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | ((((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X1) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) = $false)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f158])). 1.22/0.57 thf(f158,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0)))))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false) | (((^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3)))))))))) @ X1) = $false)) )), 1.22/0.57 inference(pi_clausification,[],[f157])). 1.22/0.57 thf(f157,plain,( 1.22/0.57 ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0)))))))) = $false) | ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) = $false)), 1.22/0.57 inference(binary_proxy_clausification,[],[f40])). 1.22/0.57 thf(f40,plain,( 1.22/0.57 (((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0))))))))) = $false) | ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $false)), 1.22/0.57 inference(binary_proxy_clausification,[],[f38])). 1.22/0.57 thf(f38,plain,( 1.22/0.57 ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) != ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0))))))))))), 1.22/0.57 inference(binary_proxy_clausification,[],[f37])). 1.22/0.57 thf(f37,plain,( 1.22/0.57 (((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0)))))))))) = $false)), 1.22/0.57 inference(beta_eta_normalization,[],[f36])). 1.22/0.57 thf(f36,plain,( 1.22/0.57 (((^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (((!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ Y2 @ (Y0 @ Y3 @ Y4)) = (Y0 @ (Y0 @ Y2 @ Y3) @ Y4))))))))))) = ((!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ (Y0 @ Y2 @ Y3)) = (Y0 @ (Y0 @ Y1 @ Y2) @ Y3)))))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1))))))))))) @ sK1) = $false)), 1.22/0.57 inference(sigma_clausification,[],[f35])). 1.22/0.57 thf(f35,plain,( 1.22/0.57 ((!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (((!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ Y2 @ (Y0 @ Y3 @ Y4)) = (Y0 @ (Y0 @ Y2 @ Y3) @ Y4))))))))))) = ((!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ (Y0 @ Y2 @ Y3)) = (Y0 @ (Y0 @ Y1 @ Y2) @ Y3)))))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1)))))))))))) = $false)), 1.22/0.57 inference(not_proxy_clausification,[],[f34])). 1.22/0.57 thf(f34,plain,( 1.22/0.57 ((~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (((!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2))) & (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))) & (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y0 @ Y2 @ (Y0 @ Y3 @ Y4)) = (Y0 @ (Y0 @ Y2 @ Y3) @ Y4))))))))))) = ((!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ (Y0 @ Y2 @ Y3)) = (Y0 @ (Y0 @ Y1 @ Y2) @ Y3)))))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1))))))))))))) = $true)), 1.22/0.57 inference(beta_eta_normalization,[],[f33])). 1.22/0.57 thf(f33,plain,( 1.22/0.57 ($true = (~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: ((^[Y2 : g > g > g]: ((^[Y3 : g]: ((((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: ((Y4 @ Y6 @ Y5) = Y6)))))) @ Y2 @ Y3) & ((^[Y4 : g > g > g]: ((^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (?? @ g @ (^[Y7 : g]: ((Y4 @ Y6 @ Y7) = Y5)))))))) @ Y2 @ Y3)) & ((^[Y4 : g > g > g]: (!! @ g @ (^[Y5 : g]: (!! @ g @ (^[Y6 : g]: (!! @ g @ (^[Y7 : g]: ((Y4 @ Y5 @ (Y4 @ Y6 @ Y7)) = (Y4 @ (Y4 @ Y5 @ Y6) @ Y7))))))))) @ Y2))))) @ Y0 @ Y1))) = ((^[Y1 : g > g > g]: (((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ Y3 @ (Y2 @ Y4 @ Y5)) = (Y2 @ (Y2 @ Y3 @ Y4) @ Y5))))))))) @ Y1) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((?? @ g @ (^[Y5 : g]: ((Y2 @ Y4 @ Y5) = Y3))) & (?? @ g @ (^[Y5 : g]: ((Y2 @ Y5 @ Y4) = Y3))))))))) @ Y1))) @ Y0))))))), 1.22/0.57 inference(definition_unfolding,[],[f26,f31,f32])). 1.22/0.57 thf(f32,plain,( 1.22/0.57 (cGROUP4 = (^[Y0 : g > g > g]: (((^[Y1 : g > g > g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y1 @ Y2 @ (Y1 @ Y3 @ Y4)) = (Y1 @ (Y1 @ Y2 @ Y3) @ Y4))))))))) @ Y0) & ((^[Y1 : g > g > g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((?? @ g @ (^[Y4 : g]: ((Y1 @ Y3 @ Y4) = Y2))) & (?? @ g @ (^[Y4 : g]: ((Y1 @ Y4 @ Y3) = Y2))))))))) @ Y0))))), 1.22/0.57 inference(definition_unfolding,[],[f24,f30,f25])). 1.22/0.57 thf(f25,plain,( 1.22/0.57 (cGRP_DIVISORS = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1))))))))))), 1.22/0.57 inference(cnf_transformation,[],[f21])). 1.22/0.57 thf(f21,plain,( 1.22/0.57 (cGRP_DIVISORS = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1))) & (?? @ g @ (^[Y3 : g]: ((Y0 @ Y3 @ Y2) = Y1))))))))))), 1.22/0.57 inference(fool_elimination,[],[f20])). 1.22/0.57 thf(f20,plain,( 1.22/0.57 (cGRP_DIVISORS = (^[X0 : g > g > g] : (! [X1 : g,X2 : g] : (? [X3 : g] : ((X0 @ X3 @ X1) = X2) & ? [X4 : g] : ((X0 @ X1 @ X4) = X2)))))), 1.22/0.57 inference(rectify,[],[f2])). 1.22/0.57 thf(f2,axiom,( 1.22/0.57 (cGRP_DIVISORS = (^[X0 : g > g > g] : (! [X1 : g,X2 : g] : (? [X5 : g] : ((X0 @ X5 @ X1) = X2) & ? [X4 : g] : ((X0 @ X1 @ X4) = X2)))))), 1.22/0.57 file('/export/starexec/sandbox2/tmp/tmp.FV3o8fGbsI/E---3.1_3848.p',cGRP_DIVISORS_def)). 1.22/0.57 thf(f30,plain,( 1.22/0.57 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ (Y0 @ Y2 @ Y3)) = (Y0 @ (Y0 @ Y1 @ Y2) @ Y3))))))))))), 1.22/0.57 inference(cnf_transformation,[],[f17])). 1.22/0.57 thf(f17,plain,( 1.22/0.57 (cGRP_ASSOC = (^[Y0 : g > g > g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((Y0 @ Y1 @ (Y0 @ Y2 @ Y3)) = (Y0 @ (Y0 @ Y1 @ Y2) @ Y3))))))))))), 1.22/0.57 inference(fool_elimination,[],[f16])). 1.22/0.57 thf(f16,plain,( 1.22/0.57 ((^[X0 : g > g > g] : (! [X1 : g,X2 : g,X3 : g] : ((X0 @ X3 @ (X0 @ X2 @ X1)) = (X0 @ (X0 @ X3 @ X2) @ X1)))) = cGRP_ASSOC)), 1.22/0.57 inference(rectify,[],[f1])). 1.22/0.57 thf(f1,axiom,( 1.22/0.57 ((^[X0 : g > g > g] : (! [X3 : g,X2 : g,X1 : g] : ((X0 @ (X0 @ X1 @ X2) @ X3) = (X0 @ X1 @ (X0 @ X2 @ X3))))) = cGRP_ASSOC)), 1.22/0.57 file('/export/starexec/sandbox2/tmp/tmp.FV3o8fGbsI/E---3.1_3848.p',cGRP_ASSOC_def)). 1.22/0.57 thf(f24,plain,( 1.22/0.57 (cGROUP4 = (^[Y0 : g > g > g]: ((cGRP_ASSOC @ Y0) & (cGRP_DIVISORS @ Y0))))), 1.22/0.57 inference(cnf_transformation,[],[f11])). 1.22/0.57 thf(f11,plain,( 1.22/0.57 (cGROUP4 = (^[Y0 : g > g > g]: ((cGRP_ASSOC @ Y0) & (cGRP_DIVISORS @ Y0))))), 1.22/0.57 inference(fool_elimination,[],[f10])). 1.22/0.57 thf(f10,plain,( 1.22/0.57 (cGROUP4 = (^[X0 : g > g > g] : ((cGRP_DIVISORS @ X0) & (cGRP_ASSOC @ X0))))), 1.22/0.57 inference(rectify,[],[f6])). 1.22/0.57 thf(f6,axiom,( 1.22/0.57 (cGROUP4 = (^[X0 : g > g > g] : ((cGRP_DIVISORS @ X0) & (cGRP_ASSOC @ X0))))), 1.22/0.57 file('/export/starexec/sandbox2/tmp/tmp.FV3o8fGbsI/E---3.1_3848.p',cGROUP4_def)). 1.22/0.57 thf(f31,plain,( 1.22/0.57 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: ((((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: ((Y2 @ Y4 @ Y3) = Y4)))))) @ Y0 @ Y1) & ((^[Y2 : g > g > g]: ((^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (?? @ g @ (^[Y5 : g]: ((Y2 @ Y4 @ Y5) = Y3)))))))) @ Y0 @ Y1)) & ((^[Y2 : g > g > g]: (!! @ g @ (^[Y3 : g]: (!! @ g @ (^[Y4 : g]: (!! @ g @ (^[Y5 : g]: ((Y2 @ Y3 @ (Y2 @ Y4 @ Y5)) = (Y2 @ (Y2 @ Y3 @ Y4) @ Y5))))))))) @ Y0))))))), 1.22/0.57 inference(definition_unfolding,[],[f29,f28,f27,f30])). 1.22/0.57 thf(f27,plain,( 1.22/0.57 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))), 1.22/0.57 inference(cnf_transformation,[],[f13])). 1.22/0.57 thf(f13,plain,( 1.22/0.57 (cGRP_RIGHT_INVERSE = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (?? @ g @ (^[Y3 : g]: ((Y0 @ Y2 @ Y3) = Y1)))))))))), 1.22/0.57 inference(fool_elimination,[],[f12])). 1.22/0.57 thf(f12,plain,( 1.22/0.57 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ? [X3 : g] : ((X0 @ X2 @ X3) = X1))))), 1.22/0.57 inference(rectify,[],[f3])). 1.22/0.57 thf(f3,axiom,( 1.22/0.57 (cGRP_RIGHT_INVERSE = (^[X0 : g > g > g, X6 : g] : (! [X1 : g] : ? [X2 : g] : ((X0 @ X1 @ X2) = X6))))), 1.22/0.57 file('/export/starexec/sandbox2/tmp/tmp.FV3o8fGbsI/E---3.1_3848.p',cGRP_RIGHT_INVERSE_def)). 1.22/0.57 thf(f28,plain,( 1.22/0.57 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))), 1.22/0.57 inference(cnf_transformation,[],[f15])). 1.22/0.57 thf(f15,plain,( 1.22/0.57 (cGRP_RIGHT_UNIT = (^[Y0 : g > g > g]: ((^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((Y0 @ Y2 @ Y1) = Y2)))))))), 1.22/0.57 inference(fool_elimination,[],[f14])). 1.22/0.57 thf(f14,plain,( 1.22/0.57 ((^[X0 : g > g > g, X1 : g] : (! [X2 : g] : ((X0 @ X2 @ X1) = X2))) = cGRP_RIGHT_UNIT)), 1.22/0.57 inference(rectify,[],[f4])). 1.22/0.57 thf(f4,axiom,( 1.22/0.57 ((^[X0 : g > g > g, X6 : g] : (! [X1 : g] : ((X0 @ X1 @ X6) = X1))) = cGRP_RIGHT_UNIT)), 1.22/0.57 file('/export/starexec/sandbox2/tmp/tmp.FV3o8fGbsI/E---3.1_3848.p',cGRP_RIGHT_UNIT_def)). 1.22/0.57 thf(f29,plain,( 1.22/0.57 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_UNIT @ Y0 @ Y1) & (cGRP_RIGHT_INVERSE @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))), 1.22/0.57 inference(cnf_transformation,[],[f19])). 1.22/0.57 thf(f19,plain,( 1.22/0.57 (cGROUP3 = (^[Y0 : g > g > g]: ((^[Y1 : g]: (((cGRP_RIGHT_UNIT @ Y0 @ Y1) & (cGRP_RIGHT_INVERSE @ Y0 @ Y1)) & (cGRP_ASSOC @ Y0))))))), 1.22/0.57 inference(fool_elimination,[],[f18])). 1.22/0.57 thf(f18,plain,( 1.22/0.57 (cGROUP3 = (^[X0 : g > g > g, X1 : g] : ((cGRP_ASSOC @ X0) & (cGRP_RIGHT_INVERSE @ X0 @ X1) & (cGRP_RIGHT_UNIT @ X0 @ X1))))), 1.22/0.57 inference(rectify,[],[f5])). 1.22/0.57 thf(f5,axiom,( 1.22/0.57 (cGROUP3 = (^[X0 : g > g > g, X6 : g] : ((cGRP_ASSOC @ X0) & (cGRP_RIGHT_INVERSE @ X0 @ X6) & (cGRP_RIGHT_UNIT @ X0 @ X6))))), 1.22/0.57 file('/export/starexec/sandbox2/tmp/tmp.FV3o8fGbsI/E---3.1_3848.p',cGROUP3_def)). 1.22/0.57 thf(f26,plain,( 1.22/0.57 ($true = (~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (cGROUP3 @ Y0 @ Y1))) = (cGROUP4 @ Y0))))))), 1.22/0.57 inference(cnf_transformation,[],[f23])). 1.22/0.57 thf(f23,plain,( 1.22/0.57 ($true = (~ (!! @ (g > g > g) @ (^[Y0 : g > g > g]: ((?? @ g @ (^[Y1 : g]: (cGROUP3 @ Y0 @ Y1))) = (cGROUP4 @ Y0))))))), 1.22/0.57 inference(fool_elimination,[],[f22])). 1.22/0.57 thf(f22,plain,( 1.22/0.57 ~! [X0 : g > g > g] : (? [X1 : g] : (cGROUP3 @ X0 @ X1) <=> (cGROUP4 @ X0))), 1.22/0.57 inference(rectify,[],[f8])). 1.22/0.57 thf(f8,negated_conjecture,( 1.22/0.57 ~! [X0 : g > g > g] : (? [X6 : g] : (cGROUP3 @ X0 @ X6) <=> (cGROUP4 @ X0))), 1.22/0.57 inference(negated_conjecture,[],[f7])). 1.22/0.57 thf(f7,conjecture,( 1.22/0.57 ! [X0 : g > g > g] : (? [X6 : g] : (cGROUP3 @ X0 @ X6) <=> (cGROUP4 @ X0))), 1.22/0.57 file('/export/starexec/sandbox2/tmp/tmp.FV3o8fGbsI/E---3.1_3848.p',cEQUIV_03_04)). 1.22/0.57 thf(f134,plain,( 1.22/0.57 spl0_3 | spl0_5), 1.22/0.57 inference(avatar_split_clause,[],[f133,f126,f72])). 1.22/0.57 thf(f133,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : ((sK2 = (sK1 @ X3 @ (sK3 @ X3))) | ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f132])). 1.22/0.57 thf(f132,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ X3 @ (sK3 @ X3)) = sK2)) | ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f131])). 1.22/0.57 thf(f131,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ X3 @ Y0) = sK2)) @ (sK3 @ X3))) | ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) )), 1.22/0.57 inference(sigma_clausification,[],[f130])). 1.22/0.57 thf(f130,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1) | ($true = (?? @ g @ (^[Y0 : g]: ((sK1 @ X3 @ Y0) = sK2))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f129])). 1.22/0.57 thf(f129,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))) @ X3)) | ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) )), 1.22/0.57 inference(pi_clausification,[],[f120])). 1.22/0.57 thf(f120,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true) | ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f119])). 1.22/0.57 thf(f119,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1) | ($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))))) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f118])). 1.22/0.57 thf(f118,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) | ($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f117])). 1.22/0.57 thf(f117,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))))) | (((^[Y0 : g]: ((sK1 @ Y0 @ X2) = X1)) @ (sK5 @ X1 @ X2)) = $true)) )), 1.22/0.57 inference(sigma_clausification,[],[f96])). 1.22/0.57 thf(f96,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X2) = X1)))) | ($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))))) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f95])). 1.22/0.57 thf(f95,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = ((?? @ g @ (^[Y0 : g]: ((sK1 @ X2 @ Y0) = X1))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X2) = X1))))) | ($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))))) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f93])). 1.22/0.57 thf(f93,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))))) | ($true = ((?? @ g @ (^[Y0 : g]: ((sK1 @ X2 @ Y0) = X1))) & (?? @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ X2) = X1)))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f92])). 1.22/0.57 thf(f92,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : ((((^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = X1))))) @ X2) = $true) | ($true = (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))))) )), 1.22/0.57 inference(pi_clausification,[],[f91])). 1.22/0.57 thf(f91,plain,( 1.22/0.57 ( ! [X1 : g] : (((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = X1)))))) = $true) | ($true = (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f90])). 1.22/0.57 thf(f90,plain,( 1.22/0.57 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3)))))))))) @ sK2)) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = X1)))))) = $true)) )), 1.22/0.57 inference(sigma_clausification,[],[f89])). 1.22/0.57 thf(f89,plain,( 1.22/0.57 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $true) | ((!! @ g @ (^[Y0 : g]: ((?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = X1))) & (?? @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = X1)))))) = $true)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f88])). 1.22/0.57 thf(f88,plain,( 1.22/0.57 ( ! [X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0))))))) @ X1) = $true) | ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $true)) )), 1.22/0.57 inference(pi_clausification,[],[f41])). 1.22/0.57 thf(f41,plain,( 1.22/0.57 ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0))))))))) | ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $true)), 1.22/0.57 inference(binary_proxy_clausification,[],[f39])). 1.22/0.57 thf(f39,plain,( 1.22/0.57 ($true = ((!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0))) & (?? @ g @ (^[Y2 : g]: ((sK1 @ Y2 @ Y1) = Y0)))))))))) | ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $true)), 1.22/0.57 inference(binary_proxy_clausification,[],[f38])). 1.22/0.57 thf(f128,plain,( 1.22/0.57 spl0_2 | spl0_5), 1.22/0.57 inference(avatar_split_clause,[],[f124,f126,f63])). 1.22/0.57 thf(f124,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1) | ((sK1 @ X3 @ sK2) = X3)) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f123])). 1.22/0.57 thf(f123,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ X3 @ sK2) = X3)) | ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) )), 1.22/0.57 inference(beta_eta_normalization,[],[f122])). 1.22/0.57 thf(f122,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)) @ X3)) | ((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1)) )), 1.22/0.57 inference(pi_clausification,[],[f121])). 1.22/0.57 thf(f121,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((sK1 @ (sK5 @ X1 @ X2) @ X2) = X1) | ($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))))) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f119])). 1.22/0.57 thf(f116,plain,( 1.22/0.57 spl0_4 | spl0_3), 1.22/0.57 inference(avatar_split_clause,[],[f115,f72,f107])). 1.22/0.57 thf(f115,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1) | (sK2 = (sK1 @ X3 @ (sK3 @ X3)))) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f114])). 1.22/0.57 thf(f114,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1) | ($true = ((sK1 @ X3 @ (sK3 @ X3)) = sK2))) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f113])). 1.22/0.57 thf(f113,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1)) | ($true = ((sK1 @ X3 @ (sK3 @ X3)) = sK2))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f112])). 1.22/0.57 thf(f112,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1)) | ($true = ((^[Y0 : g]: ((sK1 @ X3 @ Y0) = sK2)) @ (sK3 @ X3)))) )), 1.22/0.57 inference(sigma_clausification,[],[f111])). 1.22/0.57 thf(f111,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = (?? @ g @ (^[Y0 : g]: ((sK1 @ X3 @ Y0) = sK2)))) | ($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f110])). 1.22/0.57 thf(f110,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))) @ X3)) | ($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1))) )), 1.22/0.57 inference(pi_clausification,[],[f100])). 1.22/0.57 thf(f100,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (((!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))) = $true) | ($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1))) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f99])). 1.22/0.57 thf(f99,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2))))))) | ($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f98])). 1.22/0.57 thf(f98,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = ((^[Y0 : g]: ((sK1 @ X2 @ Y0) = X1)) @ (sK4 @ X1 @ X2))) | ($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))))) )), 1.22/0.57 inference(sigma_clausification,[],[f97])). 1.22/0.57 thf(f97,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = (?? @ g @ (^[Y0 : g]: ((sK1 @ X2 @ Y0) = X1)))) | ($true = ((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))))) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f95])). 1.22/0.57 thf(f109,plain,( 1.22/0.57 spl0_4 | spl0_2), 1.22/0.57 inference(avatar_split_clause,[],[f105,f63,f107])). 1.22/0.57 thf(f105,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (((sK1 @ X3 @ sK2) = X3) | ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1)) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f104])). 1.22/0.57 thf(f104,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ X3 @ sK2) = X3)) | ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1)) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f103])). 1.22/0.57 thf(f103,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1)) | ($true = ((sK1 @ X3 @ sK2) = X3))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f102])). 1.22/0.57 thf(f102,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1)) | ($true = ((^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)) @ X3))) )), 1.22/0.57 inference(pi_clausification,[],[f101])). 1.22/0.57 thf(f101,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0)))) | ($true = ((sK1 @ X2 @ (sK4 @ X1 @ X2)) = X1))) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f99])). 1.22/0.57 thf(f87,plain,( 1.22/0.57 spl0_1 | spl0_1), 1.22/0.57 inference(avatar_split_clause,[],[f86,f60,f60])). 1.22/0.57 thf(f86,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : (((sK1 @ (sK1 @ X3 @ X5) @ X6) = (sK1 @ X3 @ (sK1 @ X5 @ X6))) | ((sK1 @ X1 @ (sK1 @ X2 @ X4)) = (sK1 @ (sK1 @ X1 @ X2) @ X4))) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f85])). 1.22/0.57 thf(f85,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : ((((sK1 @ X3 @ (sK1 @ X5 @ X6)) = (sK1 @ (sK1 @ X3 @ X5) @ X6)) = $true) | ((sK1 @ X1 @ (sK1 @ X2 @ X4)) = (sK1 @ (sK1 @ X1 @ X2) @ X4))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f84])). 1.22/0.57 thf(f84,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X6 : g,X4 : g,X5 : g] : (((sK1 @ X1 @ (sK1 @ X2 @ X4)) = (sK1 @ (sK1 @ X1 @ X2) @ X4)) | (((^[Y0 : g]: ((sK1 @ X3 @ (sK1 @ X5 @ Y0)) = (sK1 @ (sK1 @ X3 @ X5) @ Y0))) @ X6) = $true)) )), 1.22/0.57 inference(pi_clausification,[],[f83])). 1.22/0.57 thf(f83,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g,X5 : g] : (((sK1 @ X1 @ (sK1 @ X2 @ X4)) = (sK1 @ (sK1 @ X1 @ X2) @ X4)) | ($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ X3 @ (sK1 @ X5 @ Y0)) = (sK1 @ (sK1 @ X3 @ X5) @ Y0)))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f82])). 1.22/0.57 thf(f82,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g,X5 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X3 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X3 @ Y0) @ Y1))))) @ X5) = $true) | ((sK1 @ X1 @ (sK1 @ X2 @ X4)) = (sK1 @ (sK1 @ X1 @ X2) @ X4))) )), 1.22/0.57 inference(pi_clausification,[],[f81])). 1.22/0.57 thf(f81,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X3 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X3 @ Y0) @ Y1))))))) | ((sK1 @ X1 @ (sK1 @ X2 @ X4)) = (sK1 @ (sK1 @ X1 @ X2) @ X4))) )), 1.22/0.57 inference(equality_proxy_clausification,[],[f80])). 1.22/0.57 thf(f80,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : (($true = ((sK1 @ X1 @ (sK1 @ X2 @ X4)) = (sK1 @ (sK1 @ X1 @ X2) @ X4))) | ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X3 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X3 @ Y0) @ Y1)))))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f79])). 1.22/0.57 thf(f79,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g,X4 : g] : ((((^[Y0 : g]: ((sK1 @ X1 @ (sK1 @ X2 @ Y0)) = (sK1 @ (sK1 @ X1 @ X2) @ Y0))) @ X4) = $true) | ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X3 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X3 @ Y0) @ Y1)))))))) )), 1.22/0.57 inference(pi_clausification,[],[f78])). 1.22/0.57 thf(f78,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ X1 @ (sK1 @ X2 @ Y0)) = (sK1 @ (sK1 @ X1 @ X2) @ Y0))))) | ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X3 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X3 @ Y0) @ Y1)))))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f77])). 1.22/0.57 thf(f77,plain,( 1.22/0.57 ( ! [X2 : g,X3 : g,X1 : g] : (($true = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))) @ X3)) | ($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ X1 @ (sK1 @ X2 @ Y0)) = (sK1 @ (sK1 @ X1 @ X2) @ Y0)))))) )), 1.22/0.57 inference(pi_clausification,[],[f76])). 1.22/0.57 thf(f76,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) | ($true = (!! @ g @ (^[Y0 : g]: ((sK1 @ X1 @ (sK1 @ X2 @ Y0)) = (sK1 @ (sK1 @ X1 @ X2) @ Y0)))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f75])). 1.22/0.57 thf(f75,plain,( 1.22/0.57 ( ! [X2 : g,X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) | ($true = ((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X1 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X1 @ Y0) @ Y1))))) @ X2))) )), 1.22/0.57 inference(pi_clausification,[],[f47])). 1.22/0.57 thf(f47,plain,( 1.22/0.57 ( ! [X1 : g] : (($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X1 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X1 @ Y0) @ Y1))))))) | ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))))) )), 1.22/0.57 inference(binary_proxy_clausification,[],[f46])). 1.22/0.57 thf(f46,plain,( 1.22/0.57 ( ! [X1 : g] : (($true = (((!! @ g @ (^[Y0 : g]: ((sK1 @ Y0 @ sK2) = Y0))) & (!! @ g @ (^[Y0 : g]: (?? @ g @ (^[Y1 : g]: ((sK1 @ Y0 @ Y1) = sK2)))))) & (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2)))))))))) | ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X1 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X1 @ Y0) @ Y1)))))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f45])). 1.22/0.57 thf(f45,plain,( 1.22/0.57 ( ! [X1 : g] : (($true = ((^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3)))))))))) @ sK2)) | ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X1 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X1 @ Y0) @ Y1)))))))) )), 1.22/0.57 inference(sigma_clausification,[],[f44])). 1.22/0.57 thf(f44,plain,( 1.22/0.57 ( ! [X1 : g] : (((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $true) | ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: ((sK1 @ X1 @ (sK1 @ Y0 @ Y1)) = (sK1 @ (sK1 @ X1 @ Y0) @ Y1)))))))) )), 1.22/0.57 inference(beta_eta_normalization,[],[f43])). 1.22/0.57 thf(f43,plain,( 1.22/0.57 ( ! [X1 : g] : ((((^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))) @ X1) = $true) | ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $true)) )), 1.22/0.57 inference(pi_clausification,[],[f42])). 1.22/0.57 thf(f42,plain,( 1.22/0.57 ($true = (!! @ g @ (^[Y0 : g]: (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: ((sK1 @ Y0 @ (sK1 @ Y1 @ Y2)) = (sK1 @ (sK1 @ Y0 @ Y1) @ Y2))))))))) | ((?? @ g @ (^[Y0 : g]: (((!! @ g @ (^[Y1 : g]: ((sK1 @ Y1 @ Y0) = Y1))) & (!! @ g @ (^[Y1 : g]: (?? @ g @ (^[Y2 : g]: ((sK1 @ Y1 @ Y2) = Y0)))))) & (!! @ g @ (^[Y1 : g]: (!! @ g @ (^[Y2 : g]: (!! @ g @ (^[Y3 : g]: ((sK1 @ Y1 @ (sK1 @ Y2 @ Y3)) = (sK1 @ (sK1 @ Y1 @ Y2) @ Y3))))))))))) = $true)), 1.22/0.57 inference(binary_proxy_clausification,[],[f39])). 1.22/0.57 % SZS output end Proof for E---3.1_3848 1.22/0.57 % (3983)------------------------------ 1.22/0.57 % (3983)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200) 1.22/0.57 % (3983)Termination reason: Refutation 1.22/0.57 1.22/0.57 % (3983)Memory used [KB]: 6140 1.22/0.57 % (3983)Time elapsed: 0.049 s 1.22/0.57 % (3983)Instructions burned: 119 (million) 1.22/0.57 % (3983)------------------------------ 1.22/0.57 % (3983)------------------------------ 1.22/0.57 % (3955)Success in time 0.175 s 1.22/0.57 EOF