TSTP Solution File: SYO446^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO446^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 09:04:28 EDT 2024
% Result : Theorem 0.19s 0.45s
% Output : Refutation 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYO446^1 : TPTP v8.2.0. Released v4.0.0.
% 0.12/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.34 % Computer : n008.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon May 20 10:35:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.37 % (12535)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (12542)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.37 % (12542)Instruction limit reached!
% 0.13/0.37 % (12542)------------------------------
% 0.13/0.37 % (12542)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (12542)Termination reason: Unknown
% 0.13/0.37 % (12542)Termination phase: shuffling
% 0.13/0.37
% 0.13/0.37 % (12542)Memory used [KB]: 1023
% 0.13/0.37 % (12542)Time elapsed: 0.004 s
% 0.13/0.37 % (12542)Instructions burned: 4 (million)
% 0.13/0.37 % (12542)------------------------------
% 0.13/0.37 % (12542)------------------------------
% 0.13/0.37 % (12536)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 theBenchmark for (2999ds/4Mi)
% 0.13/0.37 % (12536)Instruction limit reached!
% 0.13/0.37 % (12536)------------------------------
% 0.13/0.37 % (12536)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (12536)Termination reason: Unknown
% 0.13/0.37 % (12536)Termination phase: Property scanning
% 0.13/0.37
% 0.13/0.37 % (12536)Memory used [KB]: 1023
% 0.13/0.37 % (12536)Time elapsed: 0.005 s
% 0.13/0.37 % (12536)Instructions burned: 5 (million)
% 0.13/0.37 % (12536)------------------------------
% 0.13/0.37 % (12536)------------------------------
% 0.13/0.37 % (12537)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 theBenchmark for (2999ds/27Mi)
% 0.13/0.38 % (12538)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (12538)Instruction limit reached!
% 0.13/0.38 % (12538)------------------------------
% 0.13/0.38 % (12538)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (12538)Termination reason: Unknown
% 0.13/0.38 % (12538)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (12538)Memory used [KB]: 1023
% 0.13/0.38 % (12538)Time elapsed: 0.003 s
% 0.13/0.38 % (12538)Instructions burned: 2 (million)
% 0.13/0.38 % (12538)------------------------------
% 0.13/0.38 % (12538)------------------------------
% 0.13/0.38 % (12539)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.38 % (12540)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.13/0.38 % (12541)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.38 % (12539)Instruction limit reached!
% 0.13/0.38 % (12539)------------------------------
% 0.13/0.38 % (12539)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (12539)Termination reason: Unknown
% 0.13/0.38 % (12539)Termination phase: shuffling
% 0.13/0.38
% 0.13/0.38 % (12539)Memory used [KB]: 1023
% 0.13/0.38 % (12539)Time elapsed: 0.003 s
% 0.13/0.38 % (12539)Instructions burned: 2 (million)
% 0.13/0.38 % (12539)------------------------------
% 0.13/0.38 % (12539)------------------------------
% 0.13/0.38 % (12543)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 theBenchmark for (2999ds/37Mi)
% 0.13/0.38 % (12540)Refutation not found, incomplete strategy
% 0.13/0.38 % (12540)------------------------------
% 0.13/0.38 % (12540)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (12540)Termination reason: Refutation not found, incomplete strategy
% 0.13/0.38
% 0.13/0.38
% 0.13/0.38 % (12540)Memory used [KB]: 5628
% 0.13/0.38 % (12540)Time elapsed: 0.007 s
% 0.13/0.38 % (12540)Instructions burned: 8 (million)
% 0.13/0.38 % (12540)------------------------------
% 0.13/0.38 % (12540)------------------------------
% 0.13/0.39 % (12544)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 theBenchmark for (2999ds/15Mi)
% 0.13/0.39 % (12537)Instruction limit reached!
% 0.13/0.39 % (12537)------------------------------
% 0.13/0.39 % (12537)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (12537)Termination reason: Unknown
% 0.13/0.39 % (12537)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (12537)Memory used [KB]: 5756
% 0.13/0.39 % (12537)Time elapsed: 0.016 s
% 0.13/0.39 % (12537)Instructions burned: 28 (million)
% 0.13/0.39 % (12537)------------------------------
% 0.13/0.39 % (12537)------------------------------
% 0.13/0.39 % (12541)Instruction limit reached!
% 0.13/0.39 % (12541)------------------------------
% 0.13/0.39 % (12541)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (12541)Termination reason: Unknown
% 0.13/0.39 % (12541)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (12541)Memory used [KB]: 5628
% 0.13/0.39 % (12541)Time elapsed: 0.011 s
% 0.13/0.39 % (12541)Instructions burned: 19 (million)
% 0.13/0.39 % (12541)------------------------------
% 0.13/0.39 % (12541)------------------------------
% 0.13/0.39 % (12545)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.13/0.39 % (12544)Instruction limit reached!
% 0.13/0.39 % (12544)------------------------------
% 0.13/0.39 % (12544)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (12544)Termination reason: Unknown
% 0.13/0.39 % (12544)Termination phase: Saturation
% 0.13/0.39
% 0.13/0.39 % (12544)Memory used [KB]: 5628
% 0.13/0.39 % (12544)Time elapsed: 0.008 s
% 0.13/0.39 % (12544)Instructions burned: 15 (million)
% 0.13/0.39 % (12544)------------------------------
% 0.13/0.39 % (12544)------------------------------
% 0.13/0.39 % (12545)Instruction limit reached!
% 0.13/0.39 % (12545)------------------------------
% 0.13/0.39 % (12545)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (12545)Termination reason: Unknown
% 0.13/0.39 % (12545)Termination phase: shuffling
% 0.13/0.39
% 0.13/0.39 % (12545)Memory used [KB]: 1023
% 0.13/0.39 % (12545)Time elapsed: 0.003 s
% 0.13/0.39 % (12545)Instructions burned: 3 (million)
% 0.13/0.39 % (12545)------------------------------
% 0.13/0.39 % (12545)------------------------------
% 0.13/0.40 % (12546)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 theBenchmark for (2999ds/1041Mi)
% 0.13/0.40 % (12547)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.13/0.40 % (12543)Instruction limit reached!
% 0.13/0.40 % (12543)------------------------------
% 0.13/0.40 % (12543)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (12543)Termination reason: Unknown
% 0.13/0.40 % (12543)Termination phase: Saturation
% 0.13/0.40
% 0.13/0.40 % (12543)Memory used [KB]: 5756
% 0.13/0.40 % (12543)Time elapsed: 0.018 s
% 0.13/0.40 % (12543)Instructions burned: 38 (million)
% 0.13/0.40 % (12543)------------------------------
% 0.13/0.40 % (12543)------------------------------
% 0.13/0.40 % (12548)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.13/0.40 % (12549)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 theBenchmark for (2999ds/3Mi)
% 0.13/0.40 % (12547)Instruction limit reached!
% 0.13/0.40 % (12547)------------------------------
% 0.13/0.40 % (12547)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.40 % (12547)Termination reason: Unknown
% 0.13/0.40 % (12547)Termination phase: Function definition elimination
% 0.13/0.40
% 0.13/0.40 % (12547)Memory used [KB]: 1151
% 0.13/0.40 % (12547)Time elapsed: 0.006 s
% 0.13/0.40 % (12547)Instructions burned: 9 (million)
% 0.13/0.40 % (12547)------------------------------
% 0.13/0.40 % (12547)------------------------------
% 0.19/0.41 % (12549)Instruction limit reached!
% 0.19/0.41 % (12549)------------------------------
% 0.19/0.41 % (12549)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (12549)Termination reason: Unknown
% 0.19/0.41 % (12549)Termination phase: shuffling
% 0.19/0.41
% 0.19/0.41 % (12549)Memory used [KB]: 1023
% 0.19/0.41 % (12549)Time elapsed: 0.004 s
% 0.19/0.41 % (12549)Instructions burned: 4 (million)
% 0.19/0.41 % (12549)------------------------------
% 0.19/0.41 % (12549)------------------------------
% 0.19/0.41 % (12551)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.41 % (12551)Instruction limit reached!
% 0.19/0.41 % (12551)------------------------------
% 0.19/0.41 % (12551)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (12551)Termination reason: Unknown
% 0.19/0.41 % (12551)Termination phase: Function definition elimination
% 0.19/0.41
% 0.19/0.41 % (12551)Memory used [KB]: 1023
% 0.19/0.41 % (12551)Time elapsed: 0.005 s
% 0.19/0.41 % (12551)Instructions burned: 8 (million)
% 0.19/0.41 % (12551)------------------------------
% 0.19/0.41 % (12551)------------------------------
% 0.19/0.41 % (12548)Instruction limit reached!
% 0.19/0.41 % (12548)------------------------------
% 0.19/0.41 % (12548)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (12548)Termination reason: Unknown
% 0.19/0.41 % (12548)Termination phase: Saturation
% 0.19/0.41
% 0.19/0.41 % (12548)Memory used [KB]: 5884
% 0.19/0.41 % (12548)Time elapsed: 0.011 s
% 0.19/0.41 % (12548)Instructions burned: 16 (million)
% 0.19/0.41 % (12548)------------------------------
% 0.19/0.41 % (12548)------------------------------
% 0.19/0.41 % (12552)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.41 % (12552)Instruction limit reached!
% 0.19/0.41 % (12552)------------------------------
% 0.19/0.41 % (12552)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.41 % (12552)Termination reason: Unknown
% 0.19/0.41 % (12552)Termination phase: shuffling
% 0.19/0.41
% 0.19/0.41 % (12552)Memory used [KB]: 1023
% 0.19/0.41 % (12552)Time elapsed: 0.003 s
% 0.19/0.41 % (12552)Instructions burned: 4 (million)
% 0.19/0.41 % (12552)------------------------------
% 0.19/0.41 % (12552)------------------------------
% 0.19/0.42 % (12550)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 theBenchmark for (2999ds/3Mi)
% 0.19/0.42 % (12550)Instruction limit reached!
% 0.19/0.42 % (12550)------------------------------
% 0.19/0.42 % (12550)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (12550)Termination reason: Unknown
% 0.19/0.42 % (12550)Termination phase: shuffling
% 0.19/0.42
% 0.19/0.42 % (12550)Memory used [KB]: 1023
% 0.19/0.42 % (12550)Time elapsed: 0.003 s
% 0.19/0.42 % (12550)Instructions burned: 3 (million)
% 0.19/0.42 % (12550)------------------------------
% 0.19/0.42 % (12550)------------------------------
% 0.19/0.42 % (12553)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.19/0.42 % (12554)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.19/0.42 % (12553)Instruction limit reached!
% 0.19/0.42 % (12553)------------------------------
% 0.19/0.42 % (12553)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.42 % (12553)Termination reason: Unknown
% 0.19/0.42 % (12553)Termination phase: Property scanning
% 0.19/0.42
% 0.19/0.42 % (12553)Memory used [KB]: 1023
% 0.19/0.42 % (12553)Time elapsed: 0.004 s
% 0.19/0.42 % (12553)Instructions burned: 4 (million)
% 0.19/0.42 % (12553)------------------------------
% 0.19/0.42 % (12553)------------------------------
% 0.19/0.43 % (12556)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.19/0.43 % (12555)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.19/0.43 % (12556)Instruction limit reached!
% 0.19/0.43 % (12556)------------------------------
% 0.19/0.43 % (12556)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.43 % (12556)Termination reason: Unknown
% 0.19/0.43 % (12556)Termination phase: Property scanning
% 0.19/0.43
% 0.19/0.43 % (12556)Memory used [KB]: 1023
% 0.19/0.43 % (12556)Time elapsed: 0.005 s
% 0.19/0.43 % (12556)Instructions burned: 7 (million)
% 0.19/0.43 % (12556)------------------------------
% 0.19/0.43 % (12556)------------------------------
% 0.19/0.43 % (12554)Instruction limit reached!
% 0.19/0.43 % (12554)------------------------------
% 0.19/0.43 % (12554)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.43 % (12554)Termination reason: Unknown
% 0.19/0.43 % (12554)Termination phase: Saturation
% 0.19/0.43
% 0.19/0.43 % (12554)Memory used [KB]: 5628
% 0.19/0.43 % (12554)Time elapsed: 0.013 s
% 0.19/0.43 % (12554)Instructions burned: 18 (million)
% 0.19/0.43 % (12554)------------------------------
% 0.19/0.43 % (12554)------------------------------
% 0.19/0.43 % (12558)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 theBenchmark for (2999ds/21Mi)
% 0.19/0.43 % (12555)Refutation not found, incomplete strategy
% 0.19/0.43 % (12555)------------------------------
% 0.19/0.43 % (12555)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.43 % (12555)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.43
% 0.19/0.43
% 0.19/0.43 % (12555)Memory used [KB]: 5628
% 0.19/0.43 % (12555)Time elapsed: 0.006 s
% 0.19/0.43 % (12555)Instructions burned: 9 (million)
% 0.19/0.43 % (12555)------------------------------
% 0.19/0.43 % (12555)------------------------------
% 0.19/0.44 % (12559)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.19/0.44 % (12559)Instruction limit reached!
% 0.19/0.44 % (12559)------------------------------
% 0.19/0.44 % (12559)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (12559)Termination reason: Unknown
% 0.19/0.44 % (12559)Termination phase: Property scanning
% 0.19/0.44
% 0.19/0.44 % (12559)Memory used [KB]: 1023
% 0.19/0.44 % (12559)Time elapsed: 0.005 s
% 0.19/0.44 % (12559)Instructions burned: 6 (million)
% 0.19/0.44 % (12559)------------------------------
% 0.19/0.44 % (12559)------------------------------
% 0.19/0.44 % (12558)Instruction limit reached!
% 0.19/0.44 % (12558)------------------------------
% 0.19/0.44 % (12558)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.44 % (12558)Termination reason: Unknown
% 0.19/0.44 % (12558)Termination phase: Saturation
% 0.19/0.44
% 0.19/0.44 % (12558)Memory used [KB]: 5628
% 0.19/0.44 % (12558)Time elapsed: 0.012 s
% 0.19/0.44 % (12558)Instructions burned: 22 (million)
% 0.19/0.44 % (12558)------------------------------
% 0.19/0.44 % (12558)------------------------------
% 0.19/0.44 % (12557)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 theBenchmark for (2999ds/902Mi)
% 0.19/0.45 % (12546)First to succeed.
% 0.19/0.45 % (12561)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.19/0.45 % (12562)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 theBenchmark for (2999ds/779Mi)
% 0.19/0.45 % (12560)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 theBenchmark for (2999ds/6Mi)
% 0.19/0.45 % (12557)Refutation not found, incomplete strategy
% 0.19/0.45 % (12557)------------------------------
% 0.19/0.45 % (12557)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.45 % (12557)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.45
% 0.19/0.45
% 0.19/0.45 % (12557)Memory used [KB]: 5628
% 0.19/0.45 % (12557)Time elapsed: 0.033 s
% 0.19/0.45 % (12557)Instructions burned: 10 (million)
% 0.19/0.45 % (12557)------------------------------
% 0.19/0.45 % (12557)------------------------------
% 0.19/0.45 % (12560)Instruction limit reached!
% 0.19/0.45 % (12560)------------------------------
% 0.19/0.45 % (12560)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.45 % (12560)Termination reason: Unknown
% 0.19/0.45 % (12560)Termination phase: Property scanning
% 0.19/0.45
% 0.19/0.45 % (12560)Memory used [KB]: 1023
% 0.19/0.45 % (12560)Time elapsed: 0.005 s
% 0.19/0.45 % (12560)Instructions burned: 6 (million)
% 0.19/0.45 % (12560)------------------------------
% 0.19/0.45 % (12560)------------------------------
% 0.19/0.45 % (12546)Refutation found. Thanks to Tanya!
% 0.19/0.45 % SZS status Theorem for theBenchmark
% 0.19/0.45 % SZS output start Proof for theBenchmark
% 0.19/0.45 thf(type_def_5, type, mu: $tType).
% 0.19/0.45 thf(func_def_0, type, mu: $tType).
% 0.19/0.45 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.19/0.45 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_15, type, mtrue: $i > $o).
% 0.19/0.45 thf(func_def_16, type, mfalse: $i > $o).
% 0.19/0.45 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.19/0.45 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.19/0.45 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.19/0.45 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.19/0.45 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.19/0.45 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.19/0.45 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.19/0.45 thf(func_def_36, type, p: $i > $o).
% 0.19/0.45 thf(func_def_37, type, q: $i > $o).
% 0.19/0.45 thf(func_def_54, type, ph1: !>[X0: $tType]:(X0)).
% 0.19/0.45 thf(f625,plain,(
% 0.19/0.45 $false),
% 0.19/0.45 inference(avatar_sat_refutation,[],[f212,f401,f500,f547,f624])).
% 0.19/0.45 thf(f624,plain,(
% 0.19/0.45 ~spl0_1 | ~spl0_3),
% 0.19/0.45 inference(avatar_contradiction_clause,[],[f623])).
% 0.19/0.45 thf(f623,plain,(
% 0.19/0.45 $false | (~spl0_1 | ~spl0_3)),
% 0.19/0.45 inference(trivial_inequality_removal,[],[f622])).
% 0.19/0.45 thf(f622,plain,(
% 0.19/0.45 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.19/0.45 inference(boolean_simplification,[],[f621])).
% 0.19/0.45 thf(f621,plain,(
% 0.19/0.45 ((~ $true) = $true) | (~spl0_1 | ~spl0_3)),
% 0.19/0.45 inference(forward_demodulation,[],[f608,f417])).
% 0.19/0.45 thf(f417,plain,(
% 0.19/0.45 ($true = (rel_s5 @ sK2 @ sK5)) | ~spl0_1),
% 0.19/0.45 inference(not_proxy_clausification,[],[f413])).
% 0.19/0.45 thf(f413,plain,(
% 0.19/0.45 ((~ (rel_s5 @ sK2 @ sK5)) = $false) | ~spl0_1),
% 0.19/0.45 inference(binary_proxy_clausification,[],[f412])).
% 0.19/0.45 thf(f412,plain,(
% 0.19/0.45 ($false = (((~ (p @ sK5)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))))) | (~ (rel_s5 @ sK2 @ sK5)))) | ~spl0_1),
% 0.19/0.45 inference(beta_eta_normalization,[],[f411])).
% 0.19/0.45 thf(f411,plain,(
% 0.19/0.45 (((^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK5) = $false) | ~spl0_1),
% 0.19/0.45 inference(sigma_clausification,[],[f410])).
% 0.19/0.45 thf(f410,plain,(
% 0.19/0.45 ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) = $false) | ~spl0_1),
% 0.19/0.45 inference(boolean_simplification,[],[f409])).
% 0.19/0.45 thf(f409,plain,(
% 0.19/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | $false)) | ~spl0_1),
% 0.19/0.45 inference(backward_demodulation,[],[f404,f407])).
% 0.19/0.45 thf(f407,plain,(
% 0.19/0.45 ($false = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))))) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f404])).
% 0.19/0.46 thf(f404,plain,(
% 0.19/0.46 (((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $false) | ~spl0_1),
% 0.19/0.46 inference(not_proxy_clausification,[],[f208])).
% 0.19/0.46 thf(f208,plain,(
% 0.19/0.46 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))))))) | ~spl0_1),
% 0.19/0.46 inference(avatar_component_clause,[],[f207])).
% 0.19/0.46 thf(f207,plain,(
% 0.19/0.46 spl0_1 <=> ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))))))),
% 0.19/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.19/0.46 thf(f608,plain,(
% 0.19/0.46 ((~ (rel_s5 @ sK2 @ sK5)) = $true) | (~spl0_1 | ~spl0_3)),
% 0.19/0.46 inference(boolean_simplification,[],[f607])).
% 0.19/0.46 thf(f607,plain,(
% 0.19/0.46 (($false | (~ (rel_s5 @ sK2 @ sK5))) = $true) | (~spl0_1 | ~spl0_3)),
% 0.19/0.46 inference(boolean_simplification,[],[f606])).
% 0.19/0.46 thf(f606,plain,(
% 0.19/0.46 ($true = ((~ $true) | (~ (rel_s5 @ sK2 @ sK5)))) | (~spl0_1 | ~spl0_3)),
% 0.19/0.46 inference(superposition,[],[f583,f424])).
% 0.19/0.46 thf(f424,plain,(
% 0.19/0.46 ($true = (p @ sK5)) | ~spl0_1),
% 0.19/0.46 inference(not_proxy_clausification,[],[f423])).
% 0.19/0.46 thf(f423,plain,(
% 0.19/0.46 ((~ (p @ sK5)) = $false) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f422])).
% 0.19/0.46 thf(f422,plain,(
% 0.19/0.46 (((~ (p @ sK5)) | $false) = $false) | ~spl0_1),
% 0.19/0.46 inference(backward_demodulation,[],[f416,f420])).
% 0.19/0.46 thf(f420,plain,(
% 0.19/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))))) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f416])).
% 0.19/0.46 thf(f416,plain,(
% 0.19/0.46 ($false = ((~ (p @ sK5)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0))))))) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f415])).
% 0.19/0.46 thf(f415,plain,(
% 0.19/0.46 ($false = (((~ (p @ sK5)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))))) | $false)) | ~spl0_1),
% 0.19/0.46 inference(backward_demodulation,[],[f412,f413])).
% 0.19/0.46 thf(f583,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((~ (p @ X1)) | (~ (rel_s5 @ sK2 @ X1))))) ) | ~spl0_3),
% 0.19/0.46 inference(beta_eta_normalization,[],[f582])).
% 0.19/0.46 thf(f582,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1))) ) | ~spl0_3),
% 0.19/0.46 inference(pi_clausification,[],[f496])).
% 0.19/0.46 thf(f496,plain,(
% 0.19/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | ~spl0_3),
% 0.19/0.46 inference(avatar_component_clause,[],[f495])).
% 0.19/0.46 thf(f495,plain,(
% 0.19/0.46 spl0_3 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))),
% 0.19/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.19/0.46 thf(f547,plain,(
% 0.19/0.46 ~spl0_1 | ~spl0_4),
% 0.19/0.46 inference(avatar_contradiction_clause,[],[f546])).
% 0.19/0.46 thf(f546,plain,(
% 0.19/0.46 $false | (~spl0_1 | ~spl0_4)),
% 0.19/0.46 inference(trivial_inequality_removal,[],[f545])).
% 0.19/0.46 thf(f545,plain,(
% 0.19/0.46 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 0.19/0.46 inference(boolean_simplification,[],[f544])).
% 0.19/0.46 thf(f544,plain,(
% 0.19/0.46 ((~ $true) = $true) | (~spl0_1 | ~spl0_4)),
% 0.19/0.46 inference(forward_demodulation,[],[f533,f491])).
% 0.19/0.46 thf(f491,plain,(
% 0.19/0.46 ($true = (rel_s5 @ sK2 @ sK6)) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f487])).
% 0.19/0.46 thf(f487,plain,(
% 0.19/0.46 ($true = ($true => (rel_s5 @ sK2 @ sK6))) | ~spl0_1),
% 0.19/0.46 inference(superposition,[],[f433,f456])).
% 0.19/0.46 thf(f456,plain,(
% 0.19/0.46 ($true = (rel_s5 @ sK5 @ sK6)) | ~spl0_1),
% 0.19/0.46 inference(not_proxy_clausification,[],[f452])).
% 0.19/0.46 thf(f452,plain,(
% 0.19/0.46 ($false = (~ (rel_s5 @ sK5 @ sK6))) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f451])).
% 0.19/0.46 thf(f451,plain,(
% 0.19/0.46 (($false | (~ (rel_s5 @ sK5 @ sK6))) = $false) | ~spl0_1),
% 0.19/0.46 inference(backward_demodulation,[],[f438,f450])).
% 0.19/0.46 thf(f450,plain,(
% 0.19/0.46 ($false = (~ (q @ sK6))) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f438])).
% 0.19/0.46 thf(f438,plain,(
% 0.19/0.46 (((~ (q @ sK6)) | (~ (rel_s5 @ sK5 @ sK6))) = $false) | ~spl0_1),
% 0.19/0.46 inference(beta_eta_normalization,[],[f437])).
% 0.19/0.46 thf(f437,plain,(
% 0.19/0.46 ($false = ((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK5 @ Y0)))) @ sK6)) | ~spl0_1),
% 0.19/0.46 inference(sigma_clausification,[],[f420])).
% 0.19/0.46 thf(f433,plain,(
% 0.19/0.46 ( ! [X0 : $i] : (($true = ((rel_s5 @ sK5 @ X0) => (rel_s5 @ sK2 @ X0)))) ) | ~spl0_1),
% 0.19/0.46 inference(boolean_simplification,[],[f428])).
% 0.19/0.46 thf(f428,plain,(
% 0.19/0.46 ( ! [X0 : $i] : (($true = (((rel_s5 @ sK5 @ X0) & $true) => (rel_s5 @ sK2 @ X0)))) ) | ~spl0_1),
% 0.19/0.46 inference(superposition,[],[f187,f417])).
% 0.19/0.46 thf(f187,plain,(
% 0.19/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s5 @ X2 @ X1) & (rel_s5 @ X3 @ X2)) => (rel_s5 @ X3 @ X1)))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f186])).
% 0.19/0.46 thf(f186,plain,(
% 0.19/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s5 @ X2 @ X1) & (rel_s5 @ Y0 @ X2)) => (rel_s5 @ Y0 @ X1))) @ X3))) )),
% 0.19/0.46 inference(pi_clausification,[],[f185])).
% 0.19/0.46 thf(f185,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X2 @ X1) & (rel_s5 @ Y0 @ X2)) => (rel_s5 @ Y0 @ X1)))))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f184])).
% 0.19/0.46 thf(f184,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ X1) & (rel_s5 @ Y1 @ Y0)) => (rel_s5 @ Y1 @ X1))))) @ X2) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f183])).
% 0.19/0.46 thf(f183,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ X1) & (rel_s5 @ Y1 @ Y0)) => (rel_s5 @ Y1 @ X1)))))))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f182])).
% 0.19/0.46 thf(f182,plain,(
% 0.19/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ Y2 @ Y1)) => (rel_s5 @ Y2 @ Y0))))))) @ X1) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f162])).
% 0.19/0.46 thf(f162,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y0) & (rel_s5 @ Y2 @ Y1)) => (rel_s5 @ Y2 @ Y0)))))))) = $true)),
% 0.19/0.46 inference(beta_eta_normalization,[],[f160])).
% 0.19/0.46 thf(f160,plain,(
% 0.19/0.46 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))) @ rel_s5))),
% 0.19/0.46 inference(definition_unfolding,[],[f129,f136])).
% 0.19/0.46 thf(f136,plain,(
% 0.19/0.46 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f47])).
% 0.19/0.46 thf(f47,plain,(
% 0.19/0.46 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y1) & (Y0 @ Y3 @ Y2)) => (Y0 @ Y3 @ Y1))))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f46])).
% 0.19/0.46 thf(f46,plain,(
% 0.19/0.46 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X2) & (X0 @ X2 @ X3)) => (X0 @ X1 @ X3)))))),
% 0.19/0.46 inference(rectify,[],[f21])).
% 0.19/0.46 thf(f21,axiom,(
% 0.19/0.46 (mtransitive = (^[X6 : $i > $i > $o] : (! [X8,X9,X10] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.19/0.46 thf(f129,plain,(
% 0.19/0.46 ((mtransitive @ rel_s5) = $true)),
% 0.19/0.46 inference(cnf_transformation,[],[f61])).
% 0.19/0.46 thf(f61,plain,(
% 0.19/0.46 ((mtransitive @ rel_s5) = $true)),
% 0.19/0.46 inference(fool_elimination,[],[f60])).
% 0.19/0.46 thf(f60,plain,(
% 0.19/0.46 (mtransitive @ rel_s5)),
% 0.19/0.46 inference(rectify,[],[f35])).
% 0.19/0.46 thf(f35,axiom,(
% 0.19/0.46 (mtransitive @ rel_s5)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.19/0.46 thf(f533,plain,(
% 0.19/0.46 ((~ (rel_s5 @ sK2 @ sK6)) = $true) | (~spl0_1 | ~spl0_4)),
% 0.19/0.46 inference(boolean_simplification,[],[f532])).
% 0.19/0.46 thf(f532,plain,(
% 0.19/0.46 ($true = ($false | (~ (rel_s5 @ sK2 @ sK6)))) | (~spl0_1 | ~spl0_4)),
% 0.19/0.46 inference(boolean_simplification,[],[f531])).
% 0.19/0.46 thf(f531,plain,(
% 0.19/0.46 ($true = ((~ $true) | (~ (rel_s5 @ sK2 @ sK6)))) | (~spl0_1 | ~spl0_4)),
% 0.19/0.46 inference(superposition,[],[f516,f453])).
% 0.19/0.46 thf(f453,plain,(
% 0.19/0.46 ($true = (q @ sK6)) | ~spl0_1),
% 0.19/0.46 inference(not_proxy_clausification,[],[f450])).
% 0.19/0.46 thf(f516,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((~ (q @ X1)) | (~ (rel_s5 @ sK2 @ X1))))) ) | ~spl0_4),
% 0.19/0.46 inference(beta_eta_normalization,[],[f515])).
% 0.19/0.46 thf(f515,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1))) ) | ~spl0_4),
% 0.19/0.46 inference(pi_clausification,[],[f499])).
% 0.19/0.46 thf(f499,plain,(
% 0.19/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | ~spl0_4),
% 0.19/0.46 inference(avatar_component_clause,[],[f498])).
% 0.19/0.46 thf(f498,plain,(
% 0.19/0.46 spl0_4 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))),
% 0.19/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.19/0.46 thf(f500,plain,(
% 0.19/0.46 spl0_3 | spl0_4 | ~spl0_1),
% 0.19/0.46 inference(avatar_split_clause,[],[f493,f207,f498,f495])).
% 0.19/0.46 thf(f493,plain,(
% 0.19/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | ~spl0_1),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f479])).
% 0.19/0.46 thf(f479,plain,(
% 0.19/0.46 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))) | ~spl0_1),
% 0.19/0.46 inference(not_proxy_clausification,[],[f407])).
% 0.19/0.46 thf(f401,plain,(
% 0.19/0.46 ~spl0_2),
% 0.19/0.46 inference(avatar_contradiction_clause,[],[f400])).
% 0.19/0.46 thf(f400,plain,(
% 0.19/0.46 $false | ~spl0_2),
% 0.19/0.46 inference(trivial_inequality_removal,[],[f399])).
% 0.19/0.46 thf(f399,plain,(
% 0.19/0.46 ($true = $false) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f398])).
% 0.19/0.46 thf(f398,plain,(
% 0.19/0.46 ((~ $true) = $true) | ~spl0_2),
% 0.19/0.46 inference(forward_demodulation,[],[f389,f264])).
% 0.19/0.46 thf(f264,plain,(
% 0.19/0.46 ($true = (q @ sK4)) | ~spl0_2),
% 0.19/0.46 inference(not_proxy_clausification,[],[f263])).
% 0.19/0.46 thf(f263,plain,(
% 0.19/0.46 ((~ (q @ sK4)) = $false) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f262])).
% 0.19/0.46 thf(f262,plain,(
% 0.19/0.46 ($false = ((~ (q @ sK4)) | $false)) | ~spl0_2),
% 0.19/0.46 inference(backward_demodulation,[],[f249,f260])).
% 0.19/0.46 thf(f260,plain,(
% 0.19/0.46 ($false = (~ (rel_s5 @ sK2 @ sK4))) | ~spl0_2),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f249])).
% 0.19/0.46 thf(f249,plain,(
% 0.19/0.46 (((~ (q @ sK4)) | (~ (rel_s5 @ sK2 @ sK4))) = $false) | ~spl0_2),
% 0.19/0.46 inference(beta_eta_normalization,[],[f248])).
% 0.19/0.46 thf(f248,plain,(
% 0.19/0.46 (((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK4) = $false) | ~spl0_2),
% 0.19/0.46 inference(sigma_clausification,[],[f222])).
% 0.19/0.46 thf(f222,plain,(
% 0.19/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | ~spl0_2),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f221])).
% 0.19/0.46 thf(f221,plain,(
% 0.19/0.46 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f220])).
% 0.19/0.46 thf(f220,plain,(
% 0.19/0.46 ((((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | $false) = $false) | ~spl0_2),
% 0.19/0.46 inference(backward_demodulation,[],[f215,f218])).
% 0.19/0.46 thf(f218,plain,(
% 0.19/0.46 ($false = (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))))) | ~spl0_2),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f215])).
% 0.19/0.46 thf(f215,plain,(
% 0.19/0.46 ($false = (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))) | ~spl0_2),
% 0.19/0.46 inference(not_proxy_clausification,[],[f211])).
% 0.19/0.46 thf(f211,plain,(
% 0.19/0.46 ((~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $true) | ~spl0_2),
% 0.19/0.46 inference(avatar_component_clause,[],[f210])).
% 0.19/0.46 thf(f210,plain,(
% 0.19/0.46 spl0_2 <=> ((~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $true)),
% 0.19/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.19/0.46 thf(f389,plain,(
% 0.19/0.46 ($true = (~ (q @ sK4))) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f388])).
% 0.19/0.46 thf(f388,plain,(
% 0.19/0.46 ($true = ((~ (q @ sK4)) | $false)) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f384])).
% 0.19/0.46 thf(f384,plain,(
% 0.19/0.46 ($true = ((~ (q @ sK4)) | (~ $true))) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f368,f359])).
% 0.19/0.46 thf(f359,plain,(
% 0.19/0.46 ($true = (rel_s5 @ sK3 @ sK4)) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f356])).
% 0.19/0.46 thf(f356,plain,(
% 0.19/0.46 ($true = ($true => (rel_s5 @ sK3 @ sK4))) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f176,f336])).
% 0.19/0.46 thf(f336,plain,(
% 0.19/0.46 ($true = (rel_s5 @ sK4 @ sK3)) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f334])).
% 0.19/0.46 thf(f334,plain,(
% 0.19/0.46 ($true = ($true => (rel_s5 @ sK4 @ sK3))) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f245,f280])).
% 0.19/0.46 thf(f280,plain,(
% 0.19/0.46 ($true = (rel_s5 @ sK4 @ sK2)) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f276])).
% 0.19/0.46 thf(f276,plain,(
% 0.19/0.46 ($true = ($true => (rel_s5 @ sK4 @ sK2))) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f176,f267])).
% 0.19/0.46 thf(f267,plain,(
% 0.19/0.46 ($true = (rel_s5 @ sK2 @ sK4)) | ~spl0_2),
% 0.19/0.46 inference(not_proxy_clausification,[],[f260])).
% 0.19/0.46 thf(f245,plain,(
% 0.19/0.46 ( ! [X0 : $i] : (($true = ((rel_s5 @ X0 @ sK2) => (rel_s5 @ X0 @ sK3)))) ) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f238])).
% 0.19/0.46 thf(f238,plain,(
% 0.19/0.46 ( ! [X0 : $i] : (($true = (($true & (rel_s5 @ X0 @ sK2)) => (rel_s5 @ X0 @ sK3)))) ) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f187,f235])).
% 0.19/0.46 thf(f235,plain,(
% 0.19/0.46 ((rel_s5 @ sK2 @ sK3) = $true) | ~spl0_2),
% 0.19/0.46 inference(not_proxy_clausification,[],[f228])).
% 0.19/0.46 thf(f228,plain,(
% 0.19/0.46 ($false = (~ (rel_s5 @ sK2 @ sK3))) | ~spl0_2),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f227])).
% 0.19/0.46 thf(f227,plain,(
% 0.19/0.46 ($false = ((~ (p @ sK3)) | (~ (rel_s5 @ sK2 @ sK3)))) | ~spl0_2),
% 0.19/0.46 inference(beta_eta_normalization,[],[f226])).
% 0.19/0.46 thf(f226,plain,(
% 0.19/0.46 (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))) @ sK3) = $false) | ~spl0_2),
% 0.19/0.46 inference(sigma_clausification,[],[f225])).
% 0.19/0.46 thf(f225,plain,(
% 0.19/0.46 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) = $false) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f224])).
% 0.19/0.46 thf(f224,plain,(
% 0.19/0.46 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | $false)) | ~spl0_2),
% 0.19/0.46 inference(backward_demodulation,[],[f221,f222])).
% 0.19/0.46 thf(f176,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_s5 @ X2 @ X1) => (rel_s5 @ X1 @ X2)))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f175])).
% 0.19/0.46 thf(f175,plain,(
% 0.19/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0))) @ X2) = $true)) )),
% 0.19/0.46 inference(pi_clausification,[],[f174])).
% 0.19/0.46 thf(f174,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ Y0 @ X1) => (rel_s5 @ X1 @ Y0)))))) )),
% 0.19/0.46 inference(beta_eta_normalization,[],[f173])).
% 0.19/0.46 thf(f173,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1))))) @ X1))) )),
% 0.19/0.46 inference(pi_clausification,[],[f169])).
% 0.19/0.46 thf(f169,plain,(
% 0.19/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y1 @ Y0) => (rel_s5 @ Y0 @ Y1)))))))),
% 0.19/0.46 inference(beta_eta_normalization,[],[f159])).
% 0.19/0.46 thf(f159,plain,(
% 0.19/0.46 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))) @ rel_s5))),
% 0.19/0.46 inference(definition_unfolding,[],[f125,f145])).
% 0.19/0.46 thf(f145,plain,(
% 0.19/0.46 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f108])).
% 0.19/0.46 thf(f108,plain,(
% 0.19/0.46 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) => (Y0 @ Y1 @ Y2))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f107])).
% 0.19/0.46 thf(f107,plain,(
% 0.19/0.46 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X1 @ X2) => (X0 @ X2 @ X1)))))),
% 0.19/0.46 inference(rectify,[],[f19])).
% 0.19/0.46 thf(f19,axiom,(
% 0.19/0.46 (msymmetric = (^[X6 : $i > $i > $o] : (! [X8,X9] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.19/0.46 thf(f125,plain,(
% 0.19/0.46 ((msymmetric @ rel_s5) = $true)),
% 0.19/0.46 inference(cnf_transformation,[],[f69])).
% 0.19/0.46 thf(f69,plain,(
% 0.19/0.46 ((msymmetric @ rel_s5) = $true)),
% 0.19/0.46 inference(fool_elimination,[],[f68])).
% 0.19/0.46 thf(f68,plain,(
% 0.19/0.46 (msymmetric @ rel_s5)),
% 0.19/0.46 inference(rectify,[],[f36])).
% 0.19/0.46 thf(f36,axiom,(
% 0.19/0.46 (msymmetric @ rel_s5)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 0.19/0.46 thf(f368,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((~ (q @ X1)) | (~ (rel_s5 @ sK3 @ X1))))) ) | ~spl0_2),
% 0.19/0.46 inference(beta_eta_normalization,[],[f364])).
% 0.19/0.46 thf(f364,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0)))) @ X1))) ) | ~spl0_2),
% 0.19/0.46 inference(pi_clausification,[],[f314])).
% 0.19/0.46 thf(f314,plain,(
% 0.19/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0)))))) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f313])).
% 0.19/0.46 thf(f313,plain,(
% 0.19/0.46 (((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0))))) | $false) = $true) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f312])).
% 0.19/0.46 thf(f312,plain,(
% 0.19/0.46 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0))))) | (~ $true))) | ~spl0_2),
% 0.19/0.46 inference(forward_demodulation,[],[f307,f235])).
% 0.19/0.46 thf(f307,plain,(
% 0.19/0.46 ($true = ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0))))) | (~ (rel_s5 @ sK2 @ sK3)))) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f306])).
% 0.19/0.46 thf(f306,plain,(
% 0.19/0.46 ((($false | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0)))))) | (~ (rel_s5 @ sK2 @ sK3))) = $true) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f300])).
% 0.19/0.46 thf(f300,plain,(
% 0.19/0.46 ($true = (((~ $true) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK3 @ Y0)))))) | (~ (rel_s5 @ sK2 @ sK3)))) | ~spl0_2),
% 0.19/0.46 inference(superposition,[],[f284,f232])).
% 0.19/0.46 thf(f232,plain,(
% 0.19/0.46 ($true = (p @ sK3)) | ~spl0_2),
% 0.19/0.46 inference(not_proxy_clausification,[],[f231])).
% 0.19/0.46 thf(f231,plain,(
% 0.19/0.46 ($false = (~ (p @ sK3))) | ~spl0_2),
% 0.19/0.46 inference(boolean_simplification,[],[f230])).
% 0.19/0.46 thf(f230,plain,(
% 0.19/0.46 (((~ (p @ sK3)) | $false) = $false) | ~spl0_2),
% 0.19/0.46 inference(backward_demodulation,[],[f227,f228])).
% 0.19/0.46 thf(f284,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (((((~ (p @ X1)) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ X1 @ Y0)))))) | (~ (rel_s5 @ sK2 @ X1))) = $true)) ) | ~spl0_2),
% 0.19/0.46 inference(beta_eta_normalization,[],[f283])).
% 0.19/0.46 thf(f283,plain,(
% 0.19/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))) @ X1))) ) | ~spl0_2),
% 0.19/0.46 inference(pi_clausification,[],[f270])).
% 0.19/0.46 thf(f270,plain,(
% 0.19/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))) | ~spl0_2),
% 0.19/0.46 inference(not_proxy_clausification,[],[f218])).
% 0.19/0.46 thf(f212,plain,(
% 0.19/0.46 spl0_1 | spl0_2),
% 0.19/0.46 inference(avatar_split_clause,[],[f205,f210,f207])).
% 0.19/0.46 thf(f205,plain,(
% 0.19/0.46 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))))))) | ((~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))) = $true)),
% 0.19/0.46 inference(binary_proxy_clausification,[],[f202])).
% 0.19/0.46 thf(f202,plain,(
% 0.19/0.46 ($true = ((~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))))) | (~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))))))))),
% 0.19/0.46 inference(not_proxy_clausification,[],[f201])).
% 0.19/0.46 thf(f201,plain,(
% 0.19/0.46 ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0))))) | (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))))))) | (~ (((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_s5 @ sK2 @ Y0))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_s5 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: (((~ (p @ Y0)) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (rel_s5 @ sK2 @ Y0)))))))))) = $false)),
% 0.19/0.46 inference(beta_eta_normalization,[],[f200])).
% 0.19/0.46 thf(f200,plain,(
% 0.19/0.46 ($false = ((^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))) @ sK2))),
% 0.19/0.46 inference(sigma_clausification,[],[f197])).
% 0.19/0.46 thf(f197,plain,(
% 0.19/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1)))))))))))))),
% 0.19/0.46 inference(not_proxy_clausification,[],[f168])).
% 0.19/0.46 thf(f168,plain,(
% 0.19/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.19/0.46 inference(boolean_simplification,[],[f167])).
% 0.19/0.46 thf(f167,plain,(
% 0.19/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.19/0.46 inference(boolean_simplification,[],[f166])).
% 0.19/0.46 thf(f166,plain,(
% 0.19/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ (((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.19/0.46 inference(boolean_simplification,[],[f165])).
% 0.19/0.46 thf(f165,plain,(
% 0.19/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))) | (~ ((~ (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.19/0.46 inference(boolean_simplification,[],[f164])).
% 0.19/0.46 thf(f164,plain,(
% 0.19/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))))) | (~ ((~ (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: (((~ (p @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.19/0.46 inference(boolean_simplification,[],[f163])).
% 0.19/0.46 thf(f163,plain,(
% 0.19/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))))))) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))))))) | (~ ((~ (~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_s5 @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_s5 @ Y0 @ Y1)))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (~ ((~ (p @ Y1)) | (~ (~ (!! @ $i @ (^[Y2 : $i]: ((~ (q @ Y2)) | (~ (rel_s5 @ Y1 @ Y2)))))))))) | (~ (rel_s5 @ Y0 @ Y1))))))))))))))),
% 0.19/0.46 inference(beta_eta_normalization,[],[f158])).
% 0.19/0.46 thf(f158,plain,(
% 0.19/0.46 ($true = (~ ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ p @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))))))),
% 0.19/0.46 inference(definition_unfolding,[],[f119,f138,f151,f157,f148,f157,f148,f157,f157])).
% 0.19/0.46 thf(f148,plain,(
% 0.19/0.46 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.19/0.46 inference(definition_unfolding,[],[f140,f134,f132,f134,f134])).
% 0.19/0.46 thf(f132,plain,(
% 0.19/0.46 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f96])).
% 0.19/0.46 thf(f96,plain,(
% 0.19/0.46 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f95])).
% 0.19/0.46 thf(f95,plain,(
% 0.19/0.46 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.19/0.46 inference(rectify,[],[f4])).
% 0.19/0.46 thf(f4,axiom,(
% 0.19/0.46 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.19/0.46 thf(f134,plain,(
% 0.19/0.46 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f77])).
% 0.19/0.46 thf(f77,plain,(
% 0.19/0.46 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.19/0.46 inference(fool_elimination,[],[f76])).
% 0.19/0.46 thf(f76,plain,(
% 0.19/0.46 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.19/0.46 inference(rectify,[],[f3])).
% 0.19/0.46 thf(f3,axiom,(
% 0.19/0.46 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.19/0.46 thf(f140,plain,(
% 0.19/0.46 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f73])).
% 0.19/0.46 thf(f73,plain,(
% 0.19/0.46 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.19/0.46 inference(fool_elimination,[],[f72])).
% 0.19/0.46 thf(f72,plain,(
% 0.19/0.46 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.19/0.46 inference(rectify,[],[f5])).
% 0.19/0.46 thf(f5,axiom,(
% 0.19/0.46 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.19/0.46 thf(f157,plain,(
% 0.19/0.46 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_s5 @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.19/0.46 inference(definition_unfolding,[],[f135,f134,f122,f134])).
% 0.19/0.46 thf(f122,plain,(
% 0.19/0.46 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f63])).
% 0.19/0.46 thf(f63,plain,(
% 0.19/0.46 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_s5 @ Y1 @ Y2)))))))))),
% 0.19/0.46 inference(fool_elimination,[],[f62])).
% 0.19/0.46 thf(f62,plain,(
% 0.19/0.46 (mbox_s5 = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_s5 @ X1 @ X2) | (X0 @ X2)))))),
% 0.19/0.46 inference(rectify,[],[f32])).
% 0.19/0.46 thf(f32,axiom,(
% 0.19/0.46 (mbox_s5 = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_s5 @ X2 @ X7) | (X3 @ X7)))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.19/0.46 thf(f135,plain,(
% 0.19/0.46 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.19/0.46 inference(cnf_transformation,[],[f53])).
% 0.19/0.46 thf(f53,plain,(
% 0.19/0.46 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.19/0.46 inference(fool_elimination,[],[f52])).
% 0.19/0.46 thf(f52,plain,(
% 0.19/0.46 ((^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))) = mdia_s5)),
% 0.19/0.46 inference(rectify,[],[f33])).
% 0.19/0.46 thf(f33,axiom,(
% 0.19/0.46 ((^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))) = mdia_s5)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5)).
% 0.19/0.46 thf(f151,plain,(
% 0.19/0.46 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.19/0.46 inference(definition_unfolding,[],[f127,f148,f149,f149])).
% 0.19/0.46 thf(f149,plain,(
% 0.19/0.46 (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)))))),
% 0.19/0.46 inference(definition_unfolding,[],[f137,f132,f134])).
% 0.19/0.46 thf(f137,plain,(
% 0.19/0.46 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.19/0.46 inference(cnf_transformation,[],[f88])).
% 0.19/0.46 thf(f88,plain,(
% 0.19/0.46 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.19/0.46 inference(fool_elimination,[],[f87])).
% 0.19/0.46 thf(f87,plain,(
% 0.19/0.46 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.19/0.46 inference(rectify,[],[f6])).
% 0.19/0.46 thf(f6,axiom,(
% 0.19/0.46 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.19/0.46 thf(f127,plain,(
% 0.19/0.46 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f45])).
% 0.19/0.46 thf(f45,plain,(
% 0.19/0.46 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.19/0.46 inference(fool_elimination,[],[f44])).
% 0.19/0.46 thf(f44,plain,(
% 0.19/0.46 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.19/0.46 inference(rectify,[],[f8])).
% 0.19/0.46 thf(f8,axiom,(
% 0.19/0.46 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.19/0.46 thf(f138,plain,(
% 0.19/0.46 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.46 inference(cnf_transformation,[],[f71])).
% 0.19/0.46 thf(f71,plain,(
% 0.19/0.46 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.19/0.46 inference(fool_elimination,[],[f70])).
% 0.19/0.46 thf(f70,plain,(
% 0.19/0.46 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.19/0.46 inference(rectify,[],[f28])).
% 0.19/0.46 thf(f28,axiom,(
% 0.19/0.46 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.19/0.46 thf(f119,plain,(
% 0.19/0.46 ($true = (~ (mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))))),
% 0.19/0.46 inference(cnf_transformation,[],[f86])).
% 0.19/0.46 thf(f86,plain,(
% 0.19/0.46 ($true = (~ (mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))))),
% 0.19/0.46 inference(fool_elimination,[],[f85])).
% 0.19/0.46 thf(f85,plain,(
% 0.19/0.46 ~(mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))),
% 0.19/0.46 inference(rectify,[],[f38])).
% 0.19/0.46 thf(f38,negated_conjecture,(
% 0.19/0.46 ~(mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))),
% 0.19/0.46 inference(negated_conjecture,[],[f37])).
% 0.19/0.46 thf(f37,conjecture,(
% 0.19/0.46 (mvalid @ (mequiv @ (mdia_s5 @ (mand @ p @ (mdia_s5 @ q))) @ (mand @ (mdia_s5 @ p) @ (mdia_s5 @ q))))),
% 0.19/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.19/0.46 % SZS output end Proof for theBenchmark
% 0.19/0.46 % (12546)------------------------------
% 0.19/0.46 % (12546)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.19/0.46 % (12546)Termination reason: Refutation
% 0.19/0.46
% 0.19/0.46 % (12546)Memory used [KB]: 6140
% 0.19/0.46 % (12546)Time elapsed: 0.057 s
% 0.19/0.46 % (12546)Instructions burned: 78 (million)
% 0.19/0.46 % (12546)------------------------------
% 0.19/0.46 % (12546)------------------------------
% 0.19/0.46 % (12534)Success in time 0.09 s
% 0.19/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------