TSTP Solution File: SYO444^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO444^1 : 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 : n019.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 09:04:27 EDT 2024
% Result : Theorem 0.22s 0.45s
% Output : Refutation 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO444^1 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15 % 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
% 0.15/0.36 % Computer : n019.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 08:58:53 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 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
% 0.15/0.39 % (1667)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)
% 0.15/0.39 % (1670)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)
% 0.15/0.39 % (1668)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)
% 0.15/0.39 % (1671)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)
% 0.15/0.39 % (1669)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (1666)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (1673)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39 % (1674)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)
% 0.15/0.39 % (1669)Instruction limit reached!
% 0.15/0.39 % (1669)------------------------------
% 0.15/0.39 % (1669)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (1669)Termination reason: Unknown
% 0.15/0.39 % (1669)Termination phase: shuffling
% 0.15/0.39 % (1670)Instruction limit reached!
% 0.15/0.39 % (1670)------------------------------
% 0.15/0.39 % (1670)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39
% 0.15/0.39 % (1669)Memory used [KB]: 1023
% 0.15/0.39 % (1669)Time elapsed: 0.003 s
% 0.15/0.39 % (1669)Instructions burned: 2 (million)
% 0.15/0.39 % (1669)------------------------------
% 0.15/0.39 % (1669)------------------------------
% 0.15/0.39 % (1670)Termination reason: Unknown
% 0.15/0.39 % (1670)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (1670)Memory used [KB]: 1023
% 0.15/0.39 % (1670)Time elapsed: 0.003 s
% 0.15/0.39 % (1670)Instructions burned: 2 (million)
% 0.15/0.39 % (1670)------------------------------
% 0.15/0.39 % (1670)------------------------------
% 0.15/0.39 % (1667)Instruction limit reached!
% 0.15/0.39 % (1667)------------------------------
% 0.15/0.39 % (1667)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (1667)Termination reason: Unknown
% 0.15/0.39 % (1667)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (1667)Memory used [KB]: 1023
% 0.15/0.39 % (1667)Time elapsed: 0.004 s
% 0.15/0.39 % (1667)Instructions burned: 4 (million)
% 0.15/0.39 % (1667)------------------------------
% 0.15/0.39 % (1667)------------------------------
% 0.15/0.39 % (1674)Instruction limit reached!
% 0.15/0.39 % (1674)------------------------------
% 0.15/0.39 % (1674)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (1674)Termination reason: Unknown
% 0.15/0.39 % (1674)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (1674)Memory used [KB]: 1023
% 0.15/0.39 % (1674)Time elapsed: 0.003 s
% 0.15/0.39 % (1674)Instructions burned: 4 (million)
% 0.15/0.39 % (1674)------------------------------
% 0.15/0.39 % (1674)------------------------------
% 0.15/0.39 % (1671)Refutation not found, incomplete strategy
% 0.15/0.39 % (1671)------------------------------
% 0.15/0.39 % (1671)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (1671)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.39
% 0.15/0.39
% 0.15/0.39 % (1671)Memory used [KB]: 5628
% 0.15/0.39 % (1671)Time elapsed: 0.006 s
% 0.15/0.39 % (1671)Instructions burned: 8 (million)
% 0.15/0.39 % (1671)------------------------------
% 0.15/0.39 % (1671)------------------------------
% 0.15/0.39 % (1673)Instruction limit reached!
% 0.15/0.39 % (1673)------------------------------
% 0.15/0.39 % (1673)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (1673)Termination reason: Unknown
% 0.15/0.39 % (1673)Termination phase: Saturation
% 0.15/0.39
% 0.15/0.39 % (1673)Memory used [KB]: 5628
% 0.15/0.39 % (1673)Time elapsed: 0.010 s
% 0.15/0.39 % (1673)Instructions burned: 19 (million)
% 0.15/0.39 % (1673)------------------------------
% 0.15/0.39 % (1673)------------------------------
% 0.15/0.40 % (1668)Instruction limit reached!
% 0.15/0.40 % (1668)------------------------------
% 0.15/0.40 % (1668)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1668)Termination reason: Unknown
% 0.15/0.40 % (1668)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (1668)Memory used [KB]: 5756
% 0.15/0.40 % (1668)Time elapsed: 0.016 s
% 0.15/0.40 % (1668)Instructions burned: 28 (million)
% 0.15/0.40 % (1668)------------------------------
% 0.15/0.40 % (1668)------------------------------
% 0.15/0.40 % (1679)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)
% 0.15/0.40 % (1680)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)
% 0.15/0.40 % (1681)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)
% 0.15/0.40 % (1682)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)
% 0.15/0.40 % (1681)Instruction limit reached!
% 0.15/0.40 % (1681)------------------------------
% 0.15/0.40 % (1681)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1681)Termination reason: Unknown
% 0.15/0.40 % (1681)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (1681)Memory used [KB]: 1023
% 0.15/0.40 % (1681)Time elapsed: 0.003 s
% 0.15/0.40 % (1681)Instructions burned: 3 (million)
% 0.15/0.40 % (1681)------------------------------
% 0.15/0.40 % (1681)------------------------------
% 0.15/0.41 % (1684)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.15/0.41 % (1680)Instruction limit reached!
% 0.15/0.41 % (1680)------------------------------
% 0.15/0.41 % (1680)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (1680)Termination reason: Unknown
% 0.15/0.41 % (1680)Termination phase: Saturation
% 0.15/0.41
% 0.15/0.41 % (1680)Memory used [KB]: 5628
% 0.15/0.41 % (1680)Time elapsed: 0.009 s
% 0.15/0.41 % (1680)Instructions burned: 16 (million)
% 0.15/0.41 % (1680)------------------------------
% 0.15/0.41 % (1680)------------------------------
% 0.15/0.41 % (1684)Instruction limit reached!
% 0.15/0.41 % (1684)------------------------------
% 0.15/0.41 % (1684)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (1684)Termination reason: Unknown
% 0.15/0.41 % (1684)Termination phase: Property scanning
% 0.15/0.41
% 0.15/0.41 % (1684)Memory used [KB]: 1023
% 0.15/0.41 % (1684)Time elapsed: 0.005 s
% 0.15/0.41 % (1684)Instructions burned: 7 (million)
% 0.15/0.41 % (1684)------------------------------
% 0.15/0.41 % (1684)------------------------------
% 0.15/0.41 % (1686)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.41 % (1687)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)
% 0.15/0.42 % (1687)Instruction limit reached!
% 0.15/0.42 % (1687)------------------------------
% 0.15/0.42 % (1687)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (1687)Termination reason: Unknown
% 0.15/0.42 % (1687)Termination phase: Property scanning
% 0.15/0.42
% 0.15/0.42 % (1687)Memory used [KB]: 1023
% 0.15/0.42 % (1687)Time elapsed: 0.004 s
% 0.15/0.42 % (1687)Instructions burned: 4 (million)
% 0.15/0.42 % (1687)------------------------------
% 0.15/0.42 % (1687)------------------------------
% 0.15/0.42 % (1688)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)
% 0.15/0.42 % (1686)Instruction limit reached!
% 0.15/0.42 % (1686)------------------------------
% 0.15/0.42 % (1686)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (1686)Termination reason: Unknown
% 0.15/0.42 % (1688)Instruction limit reached!
% 0.15/0.42 % (1688)------------------------------
% 0.15/0.42 % (1688)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (1686)Termination phase: Saturation
% 0.15/0.42
% 0.15/0.42 % (1686)Memory used [KB]: 5884
% 0.15/0.42 % (1686)Time elapsed: 0.011 s
% 0.15/0.42 % (1686)Instructions burned: 17 (million)
% 0.15/0.42 % (1686)------------------------------
% 0.15/0.42 % (1686)------------------------------
% 0.15/0.42 % (1688)Termination reason: Unknown
% 0.15/0.42 % (1688)Termination phase: shuffling
% 0.15/0.42
% 0.15/0.42 % (1688)Memory used [KB]: 1023
% 0.15/0.42 % (1688)Time elapsed: 0.003 s
% 0.15/0.42 % (1688)Instructions burned: 3 (million)
% 0.15/0.42 % (1688)------------------------------
% 0.15/0.42 % (1688)------------------------------
% 0.15/0.42 % (1679)Instruction limit reached!
% 0.15/0.42 % (1679)------------------------------
% 0.15/0.42 % (1679)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (1679)Termination reason: Unknown
% 0.15/0.42 % (1679)Termination phase: Saturation
% 0.15/0.42
% 0.15/0.42 % (1679)Memory used [KB]: 5756
% 0.15/0.42 % (1679)Time elapsed: 0.020 s
% 0.15/0.42 % (1679)Instructions burned: 38 (million)
% 0.15/0.42 % (1679)------------------------------
% 0.15/0.42 % (1679)------------------------------
% 0.15/0.42 % (1690)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)
% 0.15/0.42 % (1689)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)
% 0.15/0.42 % (1690)Instruction limit reached!
% 0.15/0.42 % (1690)------------------------------
% 0.15/0.42 % (1690)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (1690)Termination reason: Unknown
% 0.15/0.42 % (1690)Termination phase: Property scanning
% 0.15/0.42
% 0.15/0.42 % (1690)Memory used [KB]: 1023
% 0.15/0.42 % (1690)Time elapsed: 0.004 s
% 0.15/0.43 % (1690)Instructions burned: 4 (million)
% 0.15/0.43 % (1690)------------------------------
% 0.15/0.43 % (1690)------------------------------
% 0.15/0.43 % (1689)Instruction limit reached!
% 0.15/0.43 % (1689)------------------------------
% 0.15/0.43 % (1689)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (1689)Termination reason: Unknown
% 0.15/0.43 % (1689)Termination phase: shuffling
% 0.15/0.43
% 0.15/0.43 % (1689)Memory used [KB]: 1023
% 0.15/0.43 % (1689)Time elapsed: 0.006 s
% 0.15/0.43 % (1689)Instructions burned: 8 (million)
% 0.15/0.43 % (1689)------------------------------
% 0.15/0.43 % (1689)------------------------------
% 0.22/0.43 % (1693)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.22/0.43 % (1693)Instruction limit reached!
% 0.22/0.43 % (1693)------------------------------
% 0.22/0.43 % (1693)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.43 % (1694)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)
% 0.22/0.43 % (1693)Termination reason: Unknown
% 0.22/0.43 % (1693)Termination phase: Property scanning
% 0.22/0.43
% 0.22/0.43 % (1693)Memory used [KB]: 1023
% 0.22/0.43 % (1693)Time elapsed: 0.004 s
% 0.22/0.43 % (1693)Instructions burned: 5 (million)
% 0.22/0.43 % (1693)------------------------------
% 0.22/0.43 % (1693)------------------------------
% 0.22/0.43 % (1695)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.22/0.43 % (1696)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.22/0.44 % (1696)Instruction limit reached!
% 0.22/0.44 % (1696)------------------------------
% 0.22/0.44 % (1696)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (1696)Termination reason: Unknown
% 0.22/0.44 % (1696)Termination phase: Property scanning
% 0.22/0.44
% 0.22/0.44 % (1696)Memory used [KB]: 1023
% 0.22/0.44 % (1696)Time elapsed: 0.005 s
% 0.22/0.44 % (1696)Instructions burned: 7 (million)
% 0.22/0.44 % (1696)------------------------------
% 0.22/0.44 % (1696)------------------------------
% 0.22/0.44 % (1695)Refutation not found, incomplete strategy
% 0.22/0.44 % (1695)------------------------------
% 0.22/0.44 % (1695)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (1695)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 % (1695)Memory used [KB]: 5628
% 0.22/0.44 % (1695)Time elapsed: 0.007 s
% 0.22/0.44 % (1695)Instructions burned: 11 (million)
% 0.22/0.44 % (1695)------------------------------
% 0.22/0.44 % (1695)------------------------------
% 0.22/0.44 % (1697)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)
% 0.22/0.44 % (1701)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)
% 0.22/0.44 % (1694)Instruction limit reached!
% 0.22/0.44 % (1694)------------------------------
% 0.22/0.44 % (1694)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (1694)Termination reason: Unknown
% 0.22/0.44 % (1694)Termination phase: Saturation
% 0.22/0.44
% 0.22/0.44 % (1694)Memory used [KB]: 5628
% 0.22/0.44 % (1694)Time elapsed: 0.012 s
% 0.22/0.44 % (1694)Instructions burned: 18 (million)
% 0.22/0.44 % (1694)------------------------------
% 0.22/0.44 % (1694)------------------------------
% 0.22/0.44 % (1697)Refutation not found, incomplete strategy
% 0.22/0.44 % (1697)------------------------------
% 0.22/0.44 % (1697)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.44 % (1697)Termination reason: Refutation not found, incomplete strategy
% 0.22/0.44
% 0.22/0.44
% 0.22/0.44 % (1697)Memory used [KB]: 5628
% 0.22/0.44 % (1697)Time elapsed: 0.007 s
% 0.22/0.44 % (1697)Instructions burned: 9 (million)
% 0.22/0.44 % (1697)------------------------------
% 0.22/0.44 % (1697)------------------------------
% 0.22/0.45 % (1682)First to succeed.
% 0.22/0.45 % (1705)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on theBenchmark for (2999ds/5Mi)
% 0.22/0.45 % (1705)Instruction limit reached!
% 0.22/0.45 % (1705)------------------------------
% 0.22/0.45 % (1705)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (1705)Termination reason: Unknown
% 0.22/0.45 % (1705)Termination phase: Property scanning
% 0.22/0.45
% 0.22/0.45 % (1705)Memory used [KB]: 1023
% 0.22/0.45 % (1705)Time elapsed: 0.005 s
% 0.22/0.45 % (1705)Instructions burned: 6 (million)
% 0.22/0.45 % (1705)------------------------------
% 0.22/0.45 % (1705)------------------------------
% 0.22/0.45 % (1706)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)
% 0.22/0.45 % (1701)Instruction limit reached!
% 0.22/0.45 % (1701)------------------------------
% 0.22/0.45 % (1701)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.45 % (1701)Termination reason: Unknown
% 0.22/0.45 % (1701)Termination phase: Saturation
% 0.22/0.45
% 0.22/0.45 % (1701)Memory used [KB]: 5628
% 0.22/0.45 % (1701)Time elapsed: 0.013 s
% 0.22/0.45 % (1701)Instructions burned: 21 (million)
% 0.22/0.45 % (1701)------------------------------
% 0.22/0.45 % (1701)------------------------------
% 0.22/0.45 % (1707)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on theBenchmark for (2999ds/377Mi)
% 0.22/0.45 % (1682)Refutation found. Thanks to Tanya!
% 0.22/0.45 % SZS status Theorem for theBenchmark
% 0.22/0.45 % SZS output start Proof for theBenchmark
% 0.22/0.45 thf(type_def_5, type, mu: $tType).
% 0.22/0.45 thf(func_def_0, type, mu: $tType).
% 0.22/0.45 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.22/0.45 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_15, type, mtrue: $i > $o).
% 0.22/0.45 thf(func_def_16, type, mfalse: $i > $o).
% 0.22/0.45 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.22/0.45 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.22/0.45 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.22/0.45 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.22/0.45 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.22/0.45 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.22/0.45 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.22/0.45 thf(func_def_36, type, p: $i > $o).
% 0.22/0.45 thf(func_def_37, type, q: $i > $o).
% 0.22/0.45 thf(func_def_54, type, ph1: !>[X0: $tType]:(X0)).
% 0.22/0.45 thf(f637,plain,(
% 0.22/0.45 $false),
% 0.22/0.45 inference(avatar_sat_refutation,[],[f208,f416,f558,f611,f636])).
% 0.22/0.45 thf(f636,plain,(
% 0.22/0.45 ~spl0_1 | ~spl0_3),
% 0.22/0.45 inference(avatar_contradiction_clause,[],[f635])).
% 0.22/0.45 thf(f635,plain,(
% 0.22/0.45 $false | (~spl0_1 | ~spl0_3)),
% 0.22/0.45 inference(trivial_inequality_removal,[],[f634])).
% 0.22/0.45 thf(f634,plain,(
% 0.22/0.45 ($true = $false) | (~spl0_1 | ~spl0_3)),
% 0.22/0.45 inference(boolean_simplification,[],[f633])).
% 0.22/0.45 thf(f633,plain,(
% 0.22/0.45 ($true = (~ $true)) | (~spl0_1 | ~spl0_3)),
% 0.22/0.45 inference(forward_demodulation,[],[f624,f486])).
% 0.22/0.45 thf(f486,plain,(
% 0.22/0.45 ((p @ sK5) = $true) | ~spl0_1),
% 0.22/0.45 inference(not_proxy_clausification,[],[f482])).
% 0.22/0.45 thf(f482,plain,(
% 0.22/0.45 ($false = (~ (p @ sK5))) | ~spl0_1),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f428])).
% 0.22/0.45 thf(f428,plain,(
% 0.22/0.45 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))))) | (~ (p @ sK5)))) | ~spl0_1),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f427])).
% 0.22/0.45 thf(f427,plain,(
% 0.22/0.45 ($false = ((~ (rel_s5 @ sK2 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))))) | (~ (p @ sK5))))) | ~spl0_1),
% 0.22/0.45 inference(beta_eta_normalization,[],[f426])).
% 0.22/0.45 thf(f426,plain,(
% 0.22/0.45 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0))))) @ sK5)) | ~spl0_1),
% 0.22/0.45 inference(sigma_clausification,[],[f425])).
% 0.22/0.45 thf(f425,plain,(
% 0.22/0.45 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) = $false) | ~spl0_1),
% 0.22/0.45 inference(boolean_simplification,[],[f424])).
% 0.22/0.45 thf(f424,plain,(
% 0.22/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) | $false)) | ~spl0_1),
% 0.22/0.45 inference(backward_demodulation,[],[f419,f422])).
% 0.22/0.45 thf(f422,plain,(
% 0.22/0.45 ($false = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))))) | ~spl0_1),
% 0.22/0.45 inference(binary_proxy_clausification,[],[f419])).
% 0.22/0.45 thf(f419,plain,(
% 0.22/0.45 ($false = ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))))) | ~spl0_1),
% 0.22/0.45 inference(not_proxy_clausification,[],[f204])).
% 0.22/0.45 thf(f204,plain,(
% 0.22/0.45 ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))))))) | ~spl0_1),
% 0.22/0.45 inference(avatar_component_clause,[],[f203])).
% 0.22/0.45 thf(f203,plain,(
% 0.22/0.45 spl0_1 <=> ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))))))),
% 0.22/0.45 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.22/0.45 thf(f624,plain,(
% 0.22/0.45 ($true = (~ (p @ sK5))) | (~spl0_1 | ~spl0_3)),
% 0.22/0.45 inference(boolean_simplification,[],[f623])).
% 0.22/0.45 thf(f623,plain,(
% 0.22/0.45 ($true = ($false | (~ (p @ sK5)))) | (~spl0_1 | ~spl0_3)),
% 0.22/0.45 inference(boolean_simplification,[],[f620])).
% 0.22/0.45 thf(f620,plain,(
% 0.22/0.45 ($true = ((~ $true) | (~ (p @ sK5)))) | (~spl0_1 | ~spl0_3)),
% 0.22/0.45 inference(superposition,[],[f615,f432])).
% 0.22/0.45 thf(f432,plain,(
% 0.22/0.45 ((rel_s5 @ sK2 @ sK5) = $true) | ~spl0_1),
% 0.22/0.45 inference(not_proxy_clausification,[],[f431])).
% 0.22/0.45 thf(f431,plain,(
% 0.22/0.45 ($false = (~ (rel_s5 @ sK2 @ sK5))) | ~spl0_1),
% 0.22/0.45 inference(boolean_simplification,[],[f430])).
% 0.22/0.45 thf(f430,plain,(
% 0.22/0.45 (((~ (rel_s5 @ sK2 @ sK5)) | $false) = $false) | ~spl0_1),
% 0.22/0.45 inference(backward_demodulation,[],[f427,f428])).
% 0.22/0.45 thf(f615,plain,(
% 0.22/0.45 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (~ (p @ X1))))) ) | ~spl0_3),
% 0.22/0.45 inference(beta_eta_normalization,[],[f614])).
% 0.22/0.45 thf(f614,plain,(
% 0.22/0.45 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))) @ X1))) ) | ~spl0_3),
% 0.22/0.45 inference(pi_clausification,[],[f554])).
% 0.22/0.45 thf(f554,plain,(
% 0.22/0.45 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | ~spl0_3),
% 0.22/0.45 inference(avatar_component_clause,[],[f553])).
% 0.22/0.45 thf(f553,plain,(
% 0.22/0.45 spl0_3 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))),
% 0.22/0.45 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.22/0.45 thf(f611,plain,(
% 0.22/0.45 ~spl0_1 | ~spl0_4),
% 0.22/0.45 inference(avatar_contradiction_clause,[],[f610])).
% 0.22/0.45 thf(f610,plain,(
% 0.22/0.45 $false | (~spl0_1 | ~spl0_4)),
% 0.22/0.45 inference(trivial_inequality_removal,[],[f609])).
% 0.22/0.45 thf(f609,plain,(
% 0.22/0.45 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 0.22/0.45 inference(boolean_simplification,[],[f608])).
% 0.22/0.46 thf(f608,plain,(
% 0.22/0.46 ($true = (~ $true)) | (~spl0_1 | ~spl0_4)),
% 0.22/0.46 inference(backward_demodulation,[],[f583,f604])).
% 0.22/0.46 thf(f604,plain,(
% 0.22/0.46 ((rel_s5 @ sK5 @ sK6) = $true) | (~spl0_1 | ~spl0_4)),
% 0.22/0.46 inference(boolean_simplification,[],[f594])).
% 0.22/0.46 thf(f594,plain,(
% 0.22/0.46 ($true = ($true => (rel_s5 @ sK5 @ sK6))) | (~spl0_1 | ~spl0_4)),
% 0.22/0.46 inference(superposition,[],[f450,f589])).
% 0.22/0.46 thf(f589,plain,(
% 0.22/0.46 ($true = (rel_s5 @ sK2 @ sK6)) | ~spl0_4),
% 0.22/0.46 inference(not_proxy_clausification,[],[f575])).
% 0.22/0.46 thf(f575,plain,(
% 0.22/0.46 ($false = (~ (rel_s5 @ sK2 @ sK6))) | ~spl0_4),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f573])).
% 0.22/0.46 thf(f573,plain,(
% 0.22/0.46 (((~ (rel_s5 @ sK2 @ sK6)) | (~ (q @ sK6))) = $false) | ~spl0_4),
% 0.22/0.46 inference(beta_eta_normalization,[],[f572])).
% 0.22/0.46 thf(f572,plain,(
% 0.22/0.46 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))) @ sK6)) | ~spl0_4),
% 0.22/0.46 inference(sigma_clausification,[],[f566])).
% 0.22/0.46 thf(f566,plain,(
% 0.22/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | ~spl0_4),
% 0.22/0.46 inference(not_proxy_clausification,[],[f557])).
% 0.22/0.46 thf(f557,plain,(
% 0.22/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0))))))) | ~spl0_4),
% 0.22/0.46 inference(avatar_component_clause,[],[f556])).
% 0.22/0.46 thf(f556,plain,(
% 0.22/0.46 spl0_4 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.22/0.46 thf(f450,plain,(
% 0.22/0.46 ( ! [X0 : $i] : (($true = ((rel_s5 @ sK2 @ X0) => (rel_s5 @ sK5 @ X0)))) ) | ~spl0_1),
% 0.22/0.46 inference(boolean_simplification,[],[f445])).
% 0.22/0.46 thf(f445,plain,(
% 0.22/0.46 ( ! [X0 : $i] : (($true = (($true & (rel_s5 @ sK2 @ X0)) => (rel_s5 @ sK5 @ X0)))) ) | ~spl0_1),
% 0.22/0.46 inference(superposition,[],[f183,f442])).
% 0.22/0.46 thf(f442,plain,(
% 0.22/0.46 ($true = (rel_s5 @ sK5 @ sK2)) | ~spl0_1),
% 0.22/0.46 inference(boolean_simplification,[],[f438])).
% 0.22/0.46 thf(f438,plain,(
% 0.22/0.46 ($true = ($true => (rel_s5 @ sK5 @ sK2))) | ~spl0_1),
% 0.22/0.46 inference(superposition,[],[f172,f432])).
% 0.22/0.46 thf(f172,plain,(
% 0.22/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_s5 @ X1 @ X2) => (rel_s5 @ X2 @ X1)))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f171])).
% 0.22/0.46 thf(f171,plain,(
% 0.22/0.46 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1))) @ X2))) )),
% 0.22/0.46 inference(pi_clausification,[],[f170])).
% 0.22/0.46 thf(f170,plain,(
% 0.22/0.46 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1)))))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f169])).
% 0.22/0.46 thf(f169,plain,(
% 0.22/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0))))) @ X1) = $true)) )),
% 0.22/0.46 inference(pi_clausification,[],[f162])).
% 0.22/0.46 thf(f162,plain,(
% 0.22/0.46 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))) = $true)),
% 0.22/0.46 inference(beta_eta_normalization,[],[f159])).
% 0.22/0.46 thf(f159,plain,(
% 0.22/0.46 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_s5))),
% 0.22/0.46 inference(definition_unfolding,[],[f132,f114])).
% 0.22/0.46 thf(f114,plain,(
% 0.22/0.46 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f72])).
% 0.22/0.46 thf(f72,plain,(
% 0.22/0.46 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.22/0.46 inference(fool_elimination,[],[f71])).
% 0.22/0.46 thf(f71,plain,(
% 0.22/0.46 ((^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))) = msymmetric)),
% 0.22/0.46 inference(rectify,[],[f19])).
% 0.22/0.46 thf(f19,axiom,(
% 0.22/0.46 ((^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))) = msymmetric)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',msymmetric)).
% 0.22/0.46 thf(f132,plain,(
% 0.22/0.46 ((msymmetric @ rel_s5) = $true)),
% 0.22/0.46 inference(cnf_transformation,[],[f102])).
% 0.22/0.46 thf(f102,plain,(
% 0.22/0.46 ((msymmetric @ rel_s5) = $true)),
% 0.22/0.46 inference(fool_elimination,[],[f101])).
% 0.22/0.46 thf(f101,plain,(
% 0.22/0.46 (msymmetric @ rel_s5)),
% 0.22/0.46 inference(rectify,[],[f36])).
% 0.22/0.46 thf(f36,axiom,(
% 0.22/0.46 (msymmetric @ rel_s5)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3)).
% 0.22/0.46 thf(f183,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((((rel_s5 @ X2 @ X3) & (rel_s5 @ X3 @ X1)) => (rel_s5 @ X2 @ X1)) = $true)) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f182])).
% 0.22/0.46 thf(f182,plain,(
% 0.22/0.46 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ X2 @ X1))) @ X3))) )),
% 0.22/0.46 inference(pi_clausification,[],[f181])).
% 0.22/0.46 thf(f181,plain,(
% 0.22/0.46 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X2 @ Y0) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ X2 @ X1)))))) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f180])).
% 0.22/0.46 thf(f180,plain,(
% 0.22/0.46 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y0 @ X1))))) @ X2) = $true)) )),
% 0.22/0.46 inference(pi_clausification,[],[f179])).
% 0.22/0.46 thf(f179,plain,(
% 0.22/0.46 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y0 @ X1)))))) = $true)) )),
% 0.22/0.46 inference(beta_eta_normalization,[],[f178])).
% 0.22/0.46 thf(f178,plain,(
% 0.22/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y2) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y1 @ Y0))))))) @ X1) = $true)) )),
% 0.22/0.46 inference(pi_clausification,[],[f166])).
% 0.22/0.46 thf(f166,plain,(
% 0.22/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y1 @ Y2) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y1 @ Y0)))))))))),
% 0.22/0.46 inference(beta_eta_normalization,[],[f161])).
% 0.22/0.46 thf(f161,plain,(
% 0.22/0.46 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))) @ rel_s5) = $true)),
% 0.22/0.46 inference(definition_unfolding,[],[f139,f140])).
% 0.22/0.46 thf(f140,plain,(
% 0.22/0.46 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f58])).
% 0.22/0.46 thf(f58,plain,(
% 0.22/0.46 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y2 @ Y3) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y2 @ Y1))))))))))),
% 0.22/0.46 inference(fool_elimination,[],[f57])).
% 0.22/0.46 thf(f57,plain,(
% 0.22/0.46 (mtransitive = (^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X2 @ X1)) => (X0 @ X2 @ X3)))))),
% 0.22/0.46 inference(rectify,[],[f21])).
% 0.22/0.46 thf(f21,axiom,(
% 0.22/0.46 (mtransitive = (^[X6 : $i > $i > $o] : (! [X9,X8,X10] : (((X6 @ X9 @ X10) & (X6 @ X8 @ X9)) => (X6 @ X8 @ X10)))))),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mtransitive)).
% 0.22/0.46 thf(f139,plain,(
% 0.22/0.46 ((mtransitive @ rel_s5) = $true)),
% 0.22/0.46 inference(cnf_transformation,[],[f74])).
% 0.22/0.46 thf(f74,plain,(
% 0.22/0.46 ((mtransitive @ rel_s5) = $true)),
% 0.22/0.46 inference(fool_elimination,[],[f73])).
% 0.22/0.46 thf(f73,plain,(
% 0.22/0.46 (mtransitive @ rel_s5)),
% 0.22/0.46 inference(rectify,[],[f35])).
% 0.22/0.46 thf(f35,axiom,(
% 0.22/0.46 (mtransitive @ rel_s5)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2)).
% 0.22/0.46 thf(f583,plain,(
% 0.22/0.46 ($true = (~ (rel_s5 @ sK5 @ sK6))) | (~spl0_1 | ~spl0_4)),
% 0.22/0.46 inference(boolean_simplification,[],[f582])).
% 0.22/0.46 thf(f582,plain,(
% 0.22/0.46 ($true = ((~ (rel_s5 @ sK5 @ sK6)) | $false)) | (~spl0_1 | ~spl0_4)),
% 0.22/0.46 inference(superposition,[],[f493,f580])).
% 0.22/0.46 thf(f580,plain,(
% 0.22/0.46 ($false = (~ (q @ sK6))) | ~spl0_4),
% 0.22/0.46 inference(boolean_simplification,[],[f579])).
% 0.22/0.46 thf(f579,plain,(
% 0.22/0.46 ($false = ($false | (~ (q @ sK6)))) | ~spl0_4),
% 0.22/0.46 inference(backward_demodulation,[],[f573,f575])).
% 0.22/0.46 thf(f493,plain,(
% 0.22/0.46 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK5 @ X1)) | (~ (q @ X1))))) ) | ~spl0_1),
% 0.22/0.46 inference(beta_eta_normalization,[],[f492])).
% 0.22/0.46 thf(f492,plain,(
% 0.22/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))) @ X1))) ) | ~spl0_1),
% 0.22/0.46 inference(pi_clausification,[],[f489])).
% 0.22/0.46 thf(f489,plain,(
% 0.22/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))))) | ~spl0_1),
% 0.22/0.46 inference(not_proxy_clausification,[],[f485])).
% 0.22/0.46 thf(f485,plain,(
% 0.22/0.46 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0))))))) | ~spl0_1),
% 0.22/0.46 inference(boolean_simplification,[],[f484])).
% 0.22/0.46 thf(f484,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))))) | $false)) | ~spl0_1),
% 0.22/0.46 inference(backward_demodulation,[],[f428,f482])).
% 0.22/0.46 thf(f558,plain,(
% 0.22/0.46 spl0_3 | spl0_4 | ~spl0_1),
% 0.22/0.46 inference(avatar_split_clause,[],[f551,f203,f556,f553])).
% 0.22/0.46 thf(f551,plain,(
% 0.22/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0))))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | ~spl0_1),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f515])).
% 0.22/0.46 thf(f515,plain,(
% 0.22/0.46 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) | ~spl0_1),
% 0.22/0.46 inference(not_proxy_clausification,[],[f422])).
% 0.22/0.46 thf(f416,plain,(
% 0.22/0.46 ~spl0_2),
% 0.22/0.46 inference(avatar_contradiction_clause,[],[f415])).
% 0.22/0.46 thf(f415,plain,(
% 0.22/0.46 $false | ~spl0_2),
% 0.22/0.46 inference(trivial_inequality_removal,[],[f414])).
% 0.22/0.46 thf(f414,plain,(
% 0.22/0.46 ($true = $false) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f413])).
% 0.22/0.46 thf(f413,plain,(
% 0.22/0.46 ($true = (~ $true)) | ~spl0_2),
% 0.22/0.46 inference(backward_demodulation,[],[f390,f411])).
% 0.22/0.46 thf(f411,plain,(
% 0.22/0.46 ((rel_s5 @ sK2 @ sK4) = $true) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f400])).
% 0.22/0.46 thf(f400,plain,(
% 0.22/0.46 ($true = ($true => (rel_s5 @ sK2 @ sK4))) | ~spl0_2),
% 0.22/0.46 inference(superposition,[],[f307,f396])).
% 0.22/0.46 thf(f396,plain,(
% 0.22/0.46 ($true = (rel_s5 @ sK3 @ sK4)) | ~spl0_2),
% 0.22/0.46 inference(not_proxy_clausification,[],[f385])).
% 0.22/0.46 thf(f385,plain,(
% 0.22/0.46 ($false = (~ (rel_s5 @ sK3 @ sK4))) | ~spl0_2),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f380])).
% 0.22/0.46 thf(f380,plain,(
% 0.22/0.46 ($false = ((~ (rel_s5 @ sK3 @ sK4)) | (~ (q @ sK4)))) | ~spl0_2),
% 0.22/0.46 inference(beta_eta_normalization,[],[f378])).
% 0.22/0.46 thf(f378,plain,(
% 0.22/0.46 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))) @ sK4)) | ~spl0_2),
% 0.22/0.46 inference(sigma_clausification,[],[f372])).
% 0.22/0.46 thf(f372,plain,(
% 0.22/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))) | ~spl0_2),
% 0.22/0.46 inference(not_proxy_clausification,[],[f253])).
% 0.22/0.46 thf(f253,plain,(
% 0.22/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0))))))) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f252])).
% 0.22/0.46 thf(f252,plain,(
% 0.22/0.46 ($true = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))))) | ~spl0_2),
% 0.22/0.46 inference(forward_demodulation,[],[f251,f232])).
% 0.22/0.46 thf(f232,plain,(
% 0.22/0.46 ($false = (~ (rel_s5 @ sK2 @ sK3))) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f231])).
% 0.22/0.46 thf(f231,plain,(
% 0.22/0.46 ($false = ((~ (rel_s5 @ sK2 @ sK3)) | $false)) | ~spl0_2),
% 0.22/0.46 inference(backward_demodulation,[],[f226,f229])).
% 0.22/0.46 thf(f229,plain,(
% 0.22/0.46 ($false = (~ (p @ sK3))) | ~spl0_2),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f226])).
% 0.22/0.46 thf(f226,plain,(
% 0.22/0.46 ($false = ((~ (rel_s5 @ sK2 @ sK3)) | (~ (p @ sK3)))) | ~spl0_2),
% 0.22/0.46 inference(beta_eta_normalization,[],[f225])).
% 0.22/0.46 thf(f225,plain,(
% 0.22/0.46 ($false = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))) @ sK3)) | ~spl0_2),
% 0.22/0.46 inference(sigma_clausification,[],[f218])).
% 0.22/0.46 thf(f218,plain,(
% 0.22/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | ~spl0_2),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f215])).
% 0.22/0.46 thf(f215,plain,(
% 0.22/0.46 ($false = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))) | ~spl0_2),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f211])).
% 0.22/0.46 thf(f211,plain,(
% 0.22/0.46 ($false = (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0))))))))) | ~spl0_2),
% 0.22/0.46 inference(not_proxy_clausification,[],[f207])).
% 0.22/0.46 thf(f207,plain,(
% 0.22/0.46 ($true = (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))))))) | ~spl0_2),
% 0.22/0.46 inference(avatar_component_clause,[],[f206])).
% 0.22/0.46 thf(f206,plain,(
% 0.22/0.46 spl0_2 <=> ($true = (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0))))))))))),
% 0.22/0.46 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.22/0.46 thf(f251,plain,(
% 0.22/0.46 (((~ (rel_s5 @ sK2 @ sK3)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0))))))) = $true) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f250])).
% 0.22/0.46 thf(f250,plain,(
% 0.22/0.46 ($true = ((~ (rel_s5 @ sK2 @ sK3)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))) | $false))) | ~spl0_2),
% 0.22/0.46 inference(superposition,[],[f228,f229])).
% 0.22/0.46 thf(f228,plain,(
% 0.22/0.46 ( ! [X1 : $i] : ((((~ (rel_s5 @ sK2 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (q @ Y0)))))) | (~ (p @ X1)))) = $true)) ) | ~spl0_2),
% 0.22/0.46 inference(beta_eta_normalization,[],[f227])).
% 0.22/0.46 thf(f227,plain,(
% 0.22/0.46 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0))))) @ X1))) ) | ~spl0_2),
% 0.22/0.46 inference(pi_clausification,[],[f222])).
% 0.22/0.46 thf(f222,plain,(
% 0.22/0.46 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) = $true) | ~spl0_2),
% 0.22/0.46 inference(not_proxy_clausification,[],[f217])).
% 0.22/0.46 thf(f217,plain,(
% 0.22/0.46 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))))) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f216])).
% 0.22/0.46 thf(f216,plain,(
% 0.22/0.46 ($false = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0))))))))) | ~spl0_2),
% 0.22/0.46 inference(backward_demodulation,[],[f211,f215])).
% 0.22/0.46 thf(f307,plain,(
% 0.22/0.46 ( ! [X0 : $i] : (($true = ((rel_s5 @ sK3 @ X0) => (rel_s5 @ sK2 @ X0)))) ) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f302])).
% 0.22/0.46 thf(f302,plain,(
% 0.22/0.46 ( ! [X0 : $i] : (($true = (($true & (rel_s5 @ sK3 @ X0)) => (rel_s5 @ sK2 @ X0)))) ) | ~spl0_2),
% 0.22/0.46 inference(superposition,[],[f183,f281])).
% 0.22/0.46 thf(f281,plain,(
% 0.22/0.46 ($true = (rel_s5 @ sK2 @ sK3)) | ~spl0_2),
% 0.22/0.46 inference(not_proxy_clausification,[],[f232])).
% 0.22/0.46 thf(f390,plain,(
% 0.22/0.46 ($true = (~ (rel_s5 @ sK2 @ sK4))) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f389])).
% 0.22/0.46 thf(f389,plain,(
% 0.22/0.46 ($true = ((~ (rel_s5 @ sK2 @ sK4)) | $false)) | ~spl0_2),
% 0.22/0.46 inference(superposition,[],[f273,f387])).
% 0.22/0.46 thf(f387,plain,(
% 0.22/0.46 ($false = (~ (q @ sK4))) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f386])).
% 0.22/0.46 thf(f386,plain,(
% 0.22/0.46 ($false = ($false | (~ (q @ sK4)))) | ~spl0_2),
% 0.22/0.46 inference(backward_demodulation,[],[f380,f385])).
% 0.22/0.46 thf(f273,plain,(
% 0.22/0.46 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (~ (q @ X1))))) ) | ~spl0_2),
% 0.22/0.46 inference(beta_eta_normalization,[],[f271])).
% 0.22/0.46 thf(f271,plain,(
% 0.22/0.46 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))) @ X1) = $true)) ) | ~spl0_2),
% 0.22/0.46 inference(pi_clausification,[],[f256])).
% 0.22/0.46 thf(f256,plain,(
% 0.22/0.46 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | ~spl0_2),
% 0.22/0.46 inference(not_proxy_clausification,[],[f221])).
% 0.22/0.46 thf(f221,plain,(
% 0.22/0.46 ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0))))))) | ~spl0_2),
% 0.22/0.46 inference(boolean_simplification,[],[f220])).
% 0.22/0.46 thf(f220,plain,(
% 0.22/0.46 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | $false) = $false) | ~spl0_2),
% 0.22/0.46 inference(backward_demodulation,[],[f215,f218])).
% 0.22/0.46 thf(f208,plain,(
% 0.22/0.46 spl0_1 | spl0_2),
% 0.22/0.46 inference(avatar_split_clause,[],[f201,f206,f203])).
% 0.22/0.46 thf(f201,plain,(
% 0.22/0.46 ($true = (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))))))) | ($true = (~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))))))),
% 0.22/0.46 inference(binary_proxy_clausification,[],[f198])).
% 0.22/0.46 thf(f198,plain,(
% 0.22/0.46 ($true = ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))))) | (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))))))))),
% 0.22/0.46 inference(not_proxy_clausification,[],[f197])).
% 0.22/0.46 thf(f197,plain,(
% 0.22/0.46 ($false = (~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0))))))))) | (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (p @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (p @ Y0))))))))))))),
% 0.22/0.46 inference(beta_eta_normalization,[],[f196])).
% 0.22/0.46 thf(f196,plain,(
% 0.22/0.46 ($false = ((^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (q @ Y2)))))) | (~ (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (q @ Y2)))))) | (~ (p @ Y1)))))))))))) @ sK2))),
% 0.22/0.46 inference(sigma_clausification,[],[f193])).
% 0.22/0.46 thf(f193,plain,(
% 0.22/0.46 ($false = (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (q @ Y2)))))) | (~ (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (q @ Y2)))))) | (~ (p @ Y1))))))))))))))),
% 0.22/0.46 inference(not_proxy_clausification,[],[f165])).
% 0.22/0.46 thf(f165,plain,(
% 0.22/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (q @ Y2)))))) | (~ (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (q @ Y2)))))) | (~ (p @ Y1)))))))))))))))),
% 0.22/0.46 inference(boolean_simplification,[],[f164])).
% 0.22/0.46 thf(f164,plain,(
% 0.22/0.46 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (q @ Y2)))))) | (~ (p @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1))))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (p @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (~ (q @ Y2)))))) | (~ (p @ Y1)))))))))))))))),
% 0.22/0.46 inference(beta_eta_normalization,[],[f160])).
% 0.22/0.46 thf(f160,plain,(
% 0.22/0.46 ($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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ 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]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q))))))),
% 0.22/0.46 inference(definition_unfolding,[],[f137,f136,f151,f115,f129,f133,f157,f129,f133,f157,f157])).
% 0.22/0.46 thf(f157,plain,(
% 0.22/0.46 (mdia_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_s5 @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.22/0.46 inference(definition_unfolding,[],[f146,f133,f115,f133])).
% 0.22/0.46 thf(f146,plain,(
% 0.22/0.46 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.22/0.46 inference(cnf_transformation,[],[f66])).
% 0.22/0.46 thf(f66,plain,(
% 0.22/0.46 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.22/0.46 inference(fool_elimination,[],[f65])).
% 0.22/0.46 thf(f65,plain,(
% 0.22/0.46 ((^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))) = mdia_s5)),
% 0.22/0.46 inference(rectify,[],[f33])).
% 0.22/0.46 thf(f33,axiom,(
% 0.22/0.46 ((^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))) = mdia_s5)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mdia_s5)).
% 0.22/0.46 thf(f133,plain,(
% 0.22/0.46 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f89])).
% 0.22/0.46 thf(f89,plain,(
% 0.22/0.46 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.22/0.46 inference(fool_elimination,[],[f88])).
% 0.22/0.46 thf(f88,plain,(
% 0.22/0.46 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.22/0.46 inference(rectify,[],[f3])).
% 0.22/0.46 thf(f3,axiom,(
% 0.22/0.46 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.22/0.46 thf(f129,plain,(
% 0.22/0.46 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f91])).
% 0.22/0.46 thf(f91,plain,(
% 0.22/0.46 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.22/0.46 inference(fool_elimination,[],[f90])).
% 0.22/0.46 thf(f90,plain,(
% 0.22/0.46 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.22/0.46 inference(rectify,[],[f4])).
% 0.22/0.46 thf(f4,axiom,(
% 0.22/0.46 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.22/0.46 thf(f115,plain,(
% 0.22/0.46 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f84])).
% 0.22/0.46 thf(f84,plain,(
% 0.22/0.46 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.22/0.46 inference(fool_elimination,[],[f83])).
% 0.22/0.46 thf(f83,plain,(
% 0.22/0.46 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.22/0.46 inference(rectify,[],[f32])).
% 0.22/0.46 thf(f32,axiom,(
% 0.22/0.46 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s5)).
% 0.22/0.46 thf(f151,plain,(
% 0.22/0.46 (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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ 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]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.22/0.46 inference(definition_unfolding,[],[f112,f148,f149,f149])).
% 0.22/0.46 thf(f149,plain,(
% 0.22/0.46 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.22/0.46 inference(definition_unfolding,[],[f113,f129,f133])).
% 0.22/0.46 thf(f113,plain,(
% 0.22/0.46 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.46 inference(cnf_transformation,[],[f54])).
% 0.22/0.46 thf(f54,plain,(
% 0.22/0.46 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.22/0.46 inference(fool_elimination,[],[f53])).
% 0.22/0.46 thf(f53,plain,(
% 0.22/0.46 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.22/0.46 inference(rectify,[],[f6])).
% 0.22/0.46 thf(f6,axiom,(
% 0.22/0.46 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.22/0.46 thf(f148,plain,(
% 0.22/0.46 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.22/0.46 inference(definition_unfolding,[],[f147,f133,f129,f133,f133])).
% 0.22/0.46 thf(f147,plain,(
% 0.22/0.46 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f68])).
% 0.22/0.46 thf(f68,plain,(
% 0.22/0.46 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.22/0.46 inference(fool_elimination,[],[f67])).
% 0.22/0.46 thf(f67,plain,(
% 0.22/0.46 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.22/0.46 inference(rectify,[],[f5])).
% 0.22/0.46 thf(f5,axiom,(
% 0.22/0.46 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.22/0.46 thf(f112,plain,(
% 0.22/0.46 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f44])).
% 0.22/0.46 thf(f44,plain,(
% 0.22/0.46 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.22/0.46 inference(fool_elimination,[],[f43])).
% 0.22/0.46 thf(f43,plain,(
% 0.22/0.46 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.22/0.46 inference(rectify,[],[f8])).
% 0.22/0.46 thf(f8,axiom,(
% 0.22/0.46 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.22/0.46 thf(f136,plain,(
% 0.22/0.46 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.46 inference(cnf_transformation,[],[f97])).
% 0.22/0.46 thf(f97,plain,(
% 0.22/0.46 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.22/0.46 inference(fool_elimination,[],[f96])).
% 0.22/0.46 thf(f96,plain,(
% 0.22/0.46 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.22/0.46 inference(rectify,[],[f28])).
% 0.22/0.46 thf(f28,axiom,(
% 0.22/0.46 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.22/0.46 thf(f137,plain,(
% 0.22/0.46 ($true = (~ (mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mdia_s5 @ q))) @ (mor @ (mnot @ (mdia_s5 @ p)) @ (mdia_s5 @ q))))))),
% 0.22/0.46 inference(cnf_transformation,[],[f52])).
% 0.22/0.46 thf(f52,plain,(
% 0.22/0.46 ($true = (~ (mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mdia_s5 @ q))) @ (mor @ (mnot @ (mdia_s5 @ p)) @ (mdia_s5 @ q))))))),
% 0.22/0.46 inference(fool_elimination,[],[f51])).
% 0.22/0.46 thf(f51,plain,(
% 0.22/0.46 ~(mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mdia_s5 @ q))) @ (mor @ (mnot @ (mdia_s5 @ p)) @ (mdia_s5 @ q))))),
% 0.22/0.46 inference(rectify,[],[f38])).
% 0.22/0.46 thf(f38,negated_conjecture,(
% 0.22/0.46 ~(mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mdia_s5 @ q))) @ (mor @ (mnot @ (mdia_s5 @ p)) @ (mdia_s5 @ q))))),
% 0.22/0.46 inference(negated_conjecture,[],[f37])).
% 0.22/0.46 thf(f37,conjecture,(
% 0.22/0.46 (mvalid @ (mequiv @ (mbox_s5 @ (mor @ (mnot @ p) @ (mdia_s5 @ q))) @ (mor @ (mnot @ (mdia_s5 @ p)) @ (mdia_s5 @ q))))),
% 0.22/0.46 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove)).
% 0.22/0.46 % SZS output end Proof for theBenchmark
% 0.22/0.46 % (1682)------------------------------
% 0.22/0.46 % (1682)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.22/0.46 % (1682)Termination reason: Refutation
% 0.22/0.46
% 0.22/0.46 % (1682)Memory used [KB]: 6012
% 0.22/0.46 % (1682)Time elapsed: 0.052 s
% 0.22/0.46 % (1682)Instructions burned: 77 (million)
% 0.22/0.46 % (1682)------------------------------
% 0.22/0.46 % (1682)------------------------------
% 0.22/0.46 % (1665)Success in time 0.072 s
% 0.22/0.46 % Vampire---4.8 exiting
%------------------------------------------------------------------------------