TSTP Solution File: SYO445^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO445^1 : 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n007.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 0.20s 0.43s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYO445^1 : TPTP v8.2.0. Released v4.0.0.
% 0.11/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 08:53:23 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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/sandbox/benchmark/theBenchmark.p
% 0.14/0.37 % (31763)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)
% 0.14/0.37 % (31762)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.37 % (31755)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.37 % (31757)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)
% 0.14/0.37 % (31756)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)
% 0.14/0.37 % (31758)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.37 % (31760)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)
% 0.14/0.37 % (31763)Instruction limit reached!
% 0.14/0.37 % (31763)------------------------------
% 0.14/0.37 % (31763)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (31763)Termination reason: Unknown
% 0.14/0.37 % (31763)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (31763)Memory used [KB]: 1023
% 0.14/0.37 % (31763)Time elapsed: 0.003 s
% 0.14/0.37 % (31763)Instructions burned: 3 (million)
% 0.14/0.37 % (31763)------------------------------
% 0.14/0.37 % (31763)------------------------------
% 0.14/0.37 % (31761)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)
% 0.14/0.37 % (31758)Instruction limit reached!
% 0.14/0.37 % (31758)------------------------------
% 0.14/0.37 % (31758)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (31758)Termination reason: Unknown
% 0.14/0.37 % (31758)Termination phase: shuffling
% 0.14/0.37 % (31760)Instruction limit reached!
% 0.14/0.37 % (31760)------------------------------
% 0.14/0.37 % (31760)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37
% 0.14/0.37 % (31758)Memory used [KB]: 1023
% 0.14/0.37 % (31758)Time elapsed: 0.003 s
% 0.14/0.37 % (31758)Instructions burned: 2 (million)
% 0.14/0.37 % (31758)------------------------------
% 0.14/0.37 % (31758)------------------------------
% 0.14/0.37 % (31760)Termination reason: Unknown
% 0.14/0.37 % (31760)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (31760)Memory used [KB]: 1023
% 0.14/0.37 % (31760)Time elapsed: 0.003 s
% 0.14/0.37 % (31760)Instructions burned: 2 (million)
% 0.14/0.37 % (31760)------------------------------
% 0.14/0.37 % (31760)------------------------------
% 0.14/0.37 % (31756)Instruction limit reached!
% 0.14/0.37 % (31756)------------------------------
% 0.14/0.37 % (31756)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.37 % (31756)Termination reason: Unknown
% 0.14/0.37 % (31756)Termination phase: shuffling
% 0.14/0.37
% 0.14/0.37 % (31756)Memory used [KB]: 1023
% 0.14/0.37 % (31756)Time elapsed: 0.004 s
% 0.14/0.37 % (31756)Instructions burned: 4 (million)
% 0.14/0.37 % (31756)------------------------------
% 0.14/0.37 % (31756)------------------------------
% 0.14/0.38 % (31761)Refutation not found, incomplete strategy
% 0.14/0.38 % (31761)------------------------------
% 0.14/0.38 % (31761)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31761)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (31761)Memory used [KB]: 5628
% 0.14/0.38 % (31761)Time elapsed: 0.007 s
% 0.14/0.38 % (31761)Instructions burned: 7 (million)
% 0.14/0.38 % (31761)------------------------------
% 0.14/0.38 % (31761)------------------------------
% 0.14/0.38 % (31762)Instruction limit reached!
% 0.14/0.38 % (31762)------------------------------
% 0.14/0.38 % (31762)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (31762)Termination reason: Unknown
% 0.14/0.38 % (31762)Termination phase: Saturation
% 0.14/0.38
% 0.14/0.38 % (31762)Memory used [KB]: 5628
% 0.14/0.38 % (31762)Time elapsed: 0.010 s
% 0.14/0.38 % (31762)Instructions burned: 19 (million)
% 0.14/0.38 % (31762)------------------------------
% 0.14/0.38 % (31762)------------------------------
% 0.14/0.39 % (31757)Instruction limit reached!
% 0.14/0.39 % (31757)------------------------------
% 0.14/0.39 % (31757)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (31757)Termination reason: Unknown
% 0.14/0.39 % (31757)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (31757)Memory used [KB]: 5756
% 0.14/0.39 % (31757)Time elapsed: 0.017 s
% 0.14/0.39 % (31757)Instructions burned: 28 (million)
% 0.14/0.39 % (31757)------------------------------
% 0.14/0.39 % (31757)------------------------------
% 0.14/0.39 % (31765)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)
% 0.14/0.39 % (31766)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)
% 0.14/0.39 % (31764)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)
% 0.14/0.39 % (31767)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)
% 0.14/0.39 % (31766)Instruction limit reached!
% 0.14/0.39 % (31766)------------------------------
% 0.14/0.39 % (31766)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (31766)Termination reason: Unknown
% 0.14/0.39 % (31766)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.39 % (31766)Memory used [KB]: 1023
% 0.14/0.39 % (31766)Time elapsed: 0.004 s
% 0.14/0.39 % (31766)Instructions burned: 4 (million)
% 0.14/0.39 % (31766)------------------------------
% 0.14/0.39 % (31766)------------------------------
% 0.14/0.39 % (31768)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.39 % (31765)Instruction limit reached!
% 0.14/0.39 % (31765)------------------------------
% 0.14/0.39 % (31765)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (31765)Termination reason: Unknown
% 0.14/0.39 % (31765)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (31765)Memory used [KB]: 5628
% 0.14/0.39 % (31765)Time elapsed: 0.009 s
% 0.14/0.39 % (31765)Instructions burned: 15 (million)
% 0.14/0.39 % (31765)------------------------------
% 0.14/0.39 % (31765)------------------------------
% 0.14/0.39 % (31768)Instruction limit reached!
% 0.14/0.39 % (31768)------------------------------
% 0.14/0.39 % (31768)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (31768)Termination reason: Unknown
% 0.14/0.39 % (31768)Termination phase: Property scanning
% 0.14/0.39
% 0.14/0.40 % (31768)Memory used [KB]: 1023
% 0.14/0.40 % (31768)Time elapsed: 0.006 s
% 0.14/0.40 % (31768)Instructions burned: 8 (million)
% 0.14/0.40 % (31768)------------------------------
% 0.14/0.40 % (31768)------------------------------
% 0.14/0.40 % (31770)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)
% 0.14/0.40 % (31770)Instruction limit reached!
% 0.14/0.40 % (31770)------------------------------
% 0.14/0.40 % (31770)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (31770)Termination reason: Unknown
% 0.14/0.40 % (31770)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (31770)Memory used [KB]: 1023
% 0.14/0.40 % (31770)Time elapsed: 0.004 s
% 0.14/0.40 % (31770)Instructions burned: 4 (million)
% 0.14/0.40 % (31770)------------------------------
% 0.14/0.40 % (31770)------------------------------
% 0.14/0.40 % (31771)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)
% 0.14/0.40 % (31771)Instruction limit reached!
% 0.14/0.40 % (31771)------------------------------
% 0.14/0.40 % (31771)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (31771)Termination reason: Unknown
% 0.14/0.40 % (31771)Termination phase: Property scanning
% 0.14/0.40
% 0.14/0.40 % (31771)Memory used [KB]: 1023
% 0.14/0.40 % (31771)Time elapsed: 0.004 s
% 0.14/0.40 % (31771)Instructions burned: 4 (million)
% 0.14/0.40 % (31771)------------------------------
% 0.14/0.40 % (31771)------------------------------
% 0.14/0.40 % (31769)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.20/0.41 % (31772)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)
% 0.20/0.41 % (31764)Instruction limit reached!
% 0.20/0.41 % (31764)------------------------------
% 0.20/0.41 % (31764)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (31764)Termination reason: Unknown
% 0.20/0.41 % (31764)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (31764)Memory used [KB]: 5756
% 0.20/0.41 % (31764)Time elapsed: 0.020 s
% 0.20/0.41 % (31764)Instructions burned: 39 (million)
% 0.20/0.41 % (31764)------------------------------
% 0.20/0.41 % (31764)------------------------------
% 0.20/0.41 % (31772)Instruction limit reached!
% 0.20/0.41 % (31772)------------------------------
% 0.20/0.41 % (31772)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (31772)Termination reason: Unknown
% 0.20/0.41 % (31772)Termination phase: Property scanning
% 0.20/0.41
% 0.20/0.41 % (31772)Memory used [KB]: 1151
% 0.20/0.41 % (31772)Time elapsed: 0.006 s
% 0.20/0.41 % (31772)Instructions burned: 8 (million)
% 0.20/0.41 % (31772)------------------------------
% 0.20/0.41 % (31772)------------------------------
% 0.20/0.41 % (31769)Instruction limit reached!
% 0.20/0.41 % (31769)------------------------------
% 0.20/0.41 % (31769)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.41 % (31769)Termination reason: Unknown
% 0.20/0.41 % (31769)Termination phase: Saturation
% 0.20/0.41
% 0.20/0.41 % (31769)Memory used [KB]: 5756
% 0.20/0.41 % (31769)Time elapsed: 0.011 s
% 0.20/0.41 % (31769)Instructions burned: 16 (million)
% 0.20/0.41 % (31769)------------------------------
% 0.20/0.41 % (31769)------------------------------
% 0.20/0.42 % (31774)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.20/0.42 % (31774)Instruction limit reached!
% 0.20/0.42 % (31774)------------------------------
% 0.20/0.42 % (31774)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.42 % (31774)Termination reason: Unknown
% 0.20/0.42 % (31774)Termination phase: Property scanning
% 0.20/0.42
% 0.20/0.42 % (31774)Memory used [KB]: 1023
% 0.20/0.42 % (31774)Time elapsed: 0.004 s
% 0.20/0.42 % (31774)Instructions burned: 4 (million)
% 0.20/0.42 % (31774)------------------------------
% 0.20/0.42 % (31774)------------------------------
% 0.20/0.42 % (31775)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)
% 0.20/0.42 % (31773)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)
% 0.20/0.42 % (31776)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.20/0.43 % (31767)First to succeed.
% 0.20/0.43 % (31773)Instruction limit reached!
% 0.20/0.43 % (31773)------------------------------
% 0.20/0.43 % (31773)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (31773)Termination reason: Unknown
% 0.20/0.43 % (31773)Termination phase: Property scanning
% 0.20/0.43
% 0.20/0.43 % (31773)Memory used [KB]: 1023
% 0.20/0.43 % (31773)Time elapsed: 0.004 s
% 0.20/0.43 % (31773)Instructions burned: 4 (million)
% 0.20/0.43 % (31773)------------------------------
% 0.20/0.43 % (31773)------------------------------
% 0.20/0.43 % (31778)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)
% 0.20/0.43 % (31776)Refutation not found, incomplete strategy
% 0.20/0.43 % (31776)------------------------------
% 0.20/0.43 % (31776)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (31776)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.43
% 0.20/0.43
% 0.20/0.43 % (31776)Memory used [KB]: 5628
% 0.20/0.43 % (31776)Time elapsed: 0.007 s
% 0.20/0.43 % (31776)Instructions burned: 11 (million)
% 0.20/0.43 % (31776)------------------------------
% 0.20/0.43 % (31776)------------------------------
% 0.20/0.43 % (31775)Instruction limit reached!
% 0.20/0.43 % (31775)------------------------------
% 0.20/0.43 % (31775)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (31775)Termination reason: Unknown
% 0.20/0.43 % (31775)Termination phase: Saturation
% 0.20/0.43
% 0.20/0.43 % (31775)Memory used [KB]: 5628
% 0.20/0.43 % (31775)Time elapsed: 0.013 s
% 0.20/0.43 % (31775)Instructions burned: 18 (million)
% 0.20/0.43 % (31775)------------------------------
% 0.20/0.43 % (31775)------------------------------
% 0.20/0.43 % (31767)Refutation found. Thanks to Tanya!
% 0.20/0.43 % SZS status Theorem for theBenchmark
% 0.20/0.43 % SZS output start Proof for theBenchmark
% 0.20/0.43 thf(type_def_5, type, mu: $tType).
% 0.20/0.43 thf(func_def_0, type, mu: $tType).
% 0.20/0.43 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.20/0.43 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_15, type, mtrue: $i > $o).
% 0.20/0.43 thf(func_def_16, type, mfalse: $i > $o).
% 0.20/0.43 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.20/0.43 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.20/0.43 thf(func_def_33, type, rel_s5: $i > $i > $o).
% 0.20/0.43 thf(func_def_34, type, mbox_s5: ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_35, type, mdia_s5: ($i > $o) > $i > $o).
% 0.20/0.43 thf(func_def_36, type, p: $i > $o).
% 0.20/0.43 thf(func_def_37, type, q: $i > $o).
% 0.20/0.43 thf(func_def_54, type, ph1: !>[X0: $tType]:(X0)).
% 0.20/0.43 thf(f629,plain,(
% 0.20/0.43 $false),
% 0.20/0.43 inference(avatar_sat_refutation,[],[f207,f288,f355,f384,f552,f628])).
% 0.20/0.43 thf(f628,plain,(
% 0.20/0.43 ~spl0_1 | ~spl0_6),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f627])).
% 0.20/0.43 thf(f627,plain,(
% 0.20/0.43 $false | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f626])).
% 0.20/0.43 thf(f626,plain,(
% 0.20/0.43 ($true = $false) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(forward_demodulation,[],[f619,f601])).
% 0.20/0.43 thf(f601,plain,(
% 0.20/0.43 ((rel_s5 @ sK2 @ sK6) = $false) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(not_proxy_clausification,[],[f555])).
% 0.20/0.43 thf(f555,plain,(
% 0.20/0.43 ($true = (~ (rel_s5 @ sK2 @ sK6))) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(boolean_simplification,[],[f554])).
% 0.20/0.43 thf(f554,plain,(
% 0.20/0.43 ($true = ((~ (rel_s5 @ sK2 @ sK6)) | $false)) | (~spl0_1 | ~spl0_6)),
% 0.20/0.43 inference(superposition,[],[f441,f547])).
% 0.20/0.43 thf(f547,plain,(
% 0.20/0.43 ((~ (q @ sK6)) = $false) | ~spl0_6),
% 0.20/0.43 inference(avatar_component_clause,[],[f546])).
% 0.20/0.43 thf(f546,plain,(
% 0.20/0.43 spl0_6 <=> ((~ (q @ sK6)) = $false)),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.20/0.43 thf(f441,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (~ (q @ X1))))) ) | ~spl0_1),
% 0.20/0.43 inference(beta_eta_normalization,[],[f439])).
% 0.20/0.43 thf(f439,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))) @ X1))) ) | ~spl0_1),
% 0.20/0.43 inference(pi_clausification,[],[f427])).
% 0.20/0.43 thf(f427,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0))))) = $true) | ~spl0_1),
% 0.20/0.43 inference(not_proxy_clausification,[],[f413])).
% 0.20/0.43 thf(f413,plain,(
% 0.20/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) = $false) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f412])).
% 0.20/0.43 thf(f412,plain,(
% 0.20/0.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | $false) = $false) | ~spl0_1),
% 0.20/0.43 inference(backward_demodulation,[],[f404,f410])).
% 0.20/0.43 thf(f410,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))) = $false) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f404])).
% 0.20/0.43 thf(f404,plain,(
% 0.20/0.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) = $false) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f400])).
% 0.20/0.43 thf(f400,plain,(
% 0.20/0.43 ((((~ (!! @ $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))))))) = $false) | ~spl0_1),
% 0.20/0.43 inference(not_proxy_clausification,[],[f203])).
% 0.20/0.43 thf(f203,plain,(
% 0.20/0.43 ($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 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0))))))))) | ~spl0_1),
% 0.20/0.43 inference(avatar_component_clause,[],[f202])).
% 0.20/0.43 thf(f202,plain,(
% 0.20/0.43 spl0_1 <=> ($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)))))))))),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.20/0.43 thf(f619,plain,(
% 0.20/0.43 ((rel_s5 @ sK2 @ sK6) = $true) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f618])).
% 0.20/0.43 thf(f618,plain,(
% 0.20/0.43 ($true = ($true => (rel_s5 @ sK2 @ sK6))) | ~spl0_1),
% 0.20/0.43 inference(superposition,[],[f484,f561])).
% 0.20/0.43 thf(f561,plain,(
% 0.20/0.43 ($true = (rel_s5 @ sK5 @ sK6)) | ~spl0_1),
% 0.20/0.43 inference(not_proxy_clausification,[],[f538])).
% 0.20/0.43 thf(f538,plain,(
% 0.20/0.43 ((~ (rel_s5 @ sK5 @ sK6)) = $false) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f509])).
% 0.20/0.43 thf(f509,plain,(
% 0.20/0.43 (((~ (rel_s5 @ sK5 @ sK6)) | (~ (q @ sK6))) = $false) | ~spl0_1),
% 0.20/0.43 inference(beta_eta_normalization,[],[f504])).
% 0.20/0.43 thf(f504,plain,(
% 0.20/0.43 (((^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))) @ sK6) = $false) | ~spl0_1),
% 0.20/0.43 inference(sigma_clausification,[],[f495])).
% 0.20/0.43 thf(f495,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0))))) = $false) | ~spl0_1),
% 0.20/0.43 inference(not_proxy_clausification,[],[f450])).
% 0.20/0.43 thf(f450,plain,(
% 0.20/0.43 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0))))))) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f449])).
% 0.20/0.43 thf(f449,plain,(
% 0.20/0.43 ($true = ($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))))))) | ~spl0_1),
% 0.20/0.43 inference(forward_demodulation,[],[f448,f436])).
% 0.20/0.43 thf(f436,plain,(
% 0.20/0.43 ($false = (~ (rel_s5 @ sK2 @ sK5))) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f417])).
% 0.20/0.43 thf(f417,plain,(
% 0.20/0.43 (((~ (rel_s5 @ sK2 @ sK5)) | (p @ sK5)) = $false) | ~spl0_1),
% 0.20/0.43 inference(beta_eta_normalization,[],[f416])).
% 0.20/0.43 thf(f416,plain,(
% 0.20/0.43 (((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))) @ sK5) = $false) | ~spl0_1),
% 0.20/0.43 inference(sigma_clausification,[],[f410])).
% 0.20/0.43 thf(f448,plain,(
% 0.20/0.43 ($true = ((~ (rel_s5 @ sK2 @ sK5)) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))))))) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f447])).
% 0.20/0.43 thf(f447,plain,(
% 0.20/0.43 ($true = ((~ (rel_s5 @ sK2 @ sK5)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK5 @ Y0)) | (~ (q @ Y0)))))) | $false))) | ~spl0_1),
% 0.20/0.43 inference(superposition,[],[f415,f438])).
% 0.20/0.43 thf(f438,plain,(
% 0.20/0.43 ((p @ sK5) = $false) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f437])).
% 0.20/0.43 thf(f437,plain,(
% 0.20/0.43 (($false | (p @ sK5)) = $false) | ~spl0_1),
% 0.20/0.43 inference(backward_demodulation,[],[f417,f436])).
% 0.20/0.43 thf(f415,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ X1 @ Y0)) | (~ (q @ Y0)))))) | (p @ X1))))) ) | ~spl0_1),
% 0.20/0.43 inference(beta_eta_normalization,[],[f414])).
% 0.20/0.43 thf(f414,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0)))) @ X1))) ) | ~spl0_1),
% 0.20/0.43 inference(pi_clausification,[],[f407])).
% 0.20/0.43 thf(f407,plain,(
% 0.20/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0)))))) | ~spl0_1),
% 0.20/0.43 inference(not_proxy_clausification,[],[f406])).
% 0.20/0.43 thf(f406,plain,(
% 0.20/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0)))))) = $false) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f405])).
% 0.20/0.43 thf(f405,plain,(
% 0.20/0.43 (($false | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0))))))) = $false) | ~spl0_1),
% 0.20/0.43 inference(backward_demodulation,[],[f400,f404])).
% 0.20/0.43 thf(f484,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($true = ((rel_s5 @ sK5 @ X0) => (rel_s5 @ sK2 @ X0)))) ) | ~spl0_1),
% 0.20/0.43 inference(boolean_simplification,[],[f475])).
% 0.20/0.43 thf(f475,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($true = (((rel_s5 @ sK5 @ X0) & $true) => (rel_s5 @ sK2 @ X0)))) ) | ~spl0_1),
% 0.20/0.43 inference(superposition,[],[f182,f463])).
% 0.20/0.43 thf(f463,plain,(
% 0.20/0.43 ((rel_s5 @ sK2 @ sK5) = $true) | ~spl0_1),
% 0.20/0.43 inference(not_proxy_clausification,[],[f436])).
% 0.20/0.43 thf(f182,plain,(
% 0.20/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((rel_s5 @ X1 @ X2) & (rel_s5 @ X3 @ X1)) => (rel_s5 @ X3 @ X2)))) )),
% 0.20/0.43 inference(beta_eta_normalization,[],[f181])).
% 0.20/0.43 thf(f181,plain,(
% 0.20/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (((rel_s5 @ X1 @ X2) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ Y0 @ X2))) @ X3))) )),
% 0.20/0.43 inference(pi_clausification,[],[f180])).
% 0.20/0.43 thf(f180,plain,(
% 0.20/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (((rel_s5 @ X1 @ X2) & (rel_s5 @ Y0 @ X1)) => (rel_s5 @ Y0 @ X2)))))) )),
% 0.20/0.43 inference(beta_eta_normalization,[],[f179])).
% 0.20/0.43 thf(f179,plain,(
% 0.20/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ X1 @ Y0) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y1 @ Y0))))) @ X2))) )),
% 0.20/0.43 inference(pi_clausification,[],[f178])).
% 0.20/0.43 thf(f178,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (((rel_s5 @ X1 @ Y0) & (rel_s5 @ Y1 @ X1)) => (rel_s5 @ Y1 @ Y0)))))))) )),
% 0.20/0.43 inference(beta_eta_normalization,[],[f177])).
% 0.20/0.43 thf(f177,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y2 @ Y1))))))) @ X1))) )),
% 0.20/0.43 inference(pi_clausification,[],[f165])).
% 0.20/0.43 thf(f165,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (((rel_s5 @ Y0 @ Y1) & (rel_s5 @ Y2 @ Y0)) => (rel_s5 @ Y2 @ Y1)))))))) = $true)),
% 0.20/0.43 inference(beta_eta_normalization,[],[f158])).
% 0.20/0.43 thf(f158,plain,(
% 0.20/0.43 (((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))) @ rel_s5) = $true)),
% 0.20/0.43 inference(definition_unfolding,[],[f120,f125])).
% 0.20/0.43 thf(f125,plain,(
% 0.20/0.43 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f78])).
% 0.20/0.43 thf(f78,plain,(
% 0.20/0.43 (mtransitive = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: (((Y0 @ Y1 @ Y2) & (Y0 @ Y3 @ Y1)) => (Y0 @ Y3 @ Y2))))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f77])).
% 0.20/0.43 thf(f77,plain,(
% 0.20/0.43 ((^[X0 : $i > $i > $o] : (! [X1,X2,X3] : (((X0 @ X1 @ X3) & (X0 @ X3 @ X2)) => (X0 @ X1 @ X2)))) = mtransitive)),
% 0.20/0.43 inference(rectify,[],[f21])).
% 0.20/0.43 thf(f21,axiom,(
% 0.20/0.43 ((^[X6 : $i > $i > $o] : (! [X8,X10,X9] : (((X6 @ X8 @ X9) & (X6 @ X9 @ X10)) => (X6 @ X8 @ X10)))) = mtransitive)),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mtransitive)).
% 0.20/0.43 thf(f120,plain,(
% 0.20/0.43 ((mtransitive @ rel_s5) = $true)),
% 0.20/0.43 inference(cnf_transformation,[],[f59])).
% 0.20/0.43 thf(f59,plain,(
% 0.20/0.43 ((mtransitive @ rel_s5) = $true)),
% 0.20/0.43 inference(fool_elimination,[],[f58])).
% 0.20/0.43 thf(f58,plain,(
% 0.20/0.43 (mtransitive @ rel_s5)),
% 0.20/0.43 inference(rectify,[],[f35])).
% 0.20/0.43 thf(f35,axiom,(
% 0.20/0.43 (mtransitive @ rel_s5)),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2)).
% 0.20/0.43 thf(f552,plain,(
% 0.20/0.43 spl0_6 | ~spl0_1),
% 0.20/0.43 inference(avatar_split_clause,[],[f537,f202,f546])).
% 0.20/0.43 thf(f537,plain,(
% 0.20/0.43 ((~ (q @ sK6)) = $false) | ~spl0_1),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f509])).
% 0.20/0.43 thf(f384,plain,(
% 0.20/0.43 ~spl0_2 | ~spl0_4),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f383])).
% 0.20/0.43 thf(f383,plain,(
% 0.20/0.43 $false | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f382])).
% 0.20/0.43 thf(f382,plain,(
% 0.20/0.43 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(forward_demodulation,[],[f374,f226])).
% 0.20/0.43 thf(f226,plain,(
% 0.20/0.43 ((p @ sK3) = $false) | ~spl0_2),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f222])).
% 0.20/0.43 thf(f222,plain,(
% 0.20/0.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))) | (p @ sK3)) = $false) | ~spl0_2),
% 0.20/0.43 inference(boolean_simplification,[],[f221])).
% 0.20/0.43 thf(f221,plain,(
% 0.20/0.43 (($false | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))) | (p @ sK3))) = $false) | ~spl0_2),
% 0.20/0.43 inference(backward_demodulation,[],[f218,f220])).
% 0.20/0.43 thf(f220,plain,(
% 0.20/0.43 ((~ (rel_s5 @ sK2 @ sK3)) = $false) | ~spl0_2),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f218])).
% 0.20/0.43 thf(f218,plain,(
% 0.20/0.43 (((~ (rel_s5 @ sK2 @ sK3)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))) | (p @ sK3))) = $false) | ~spl0_2),
% 0.20/0.43 inference(beta_eta_normalization,[],[f217])).
% 0.20/0.43 thf(f217,plain,(
% 0.20/0.43 (((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0)))) @ sK3) = $false) | ~spl0_2),
% 0.20/0.43 inference(sigma_clausification,[],[f216])).
% 0.20/0.43 thf(f216,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0))))) = $false) | ~spl0_2),
% 0.20/0.43 inference(boolean_simplification,[],[f215])).
% 0.20/0.43 thf(f215,plain,(
% 0.20/0.43 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0))))) | $false) = $false) | ~spl0_2),
% 0.20/0.43 inference(backward_demodulation,[],[f210,f213])).
% 0.20/0.43 thf(f213,plain,(
% 0.20/0.43 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))) = $false) | ~spl0_2),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f210])).
% 0.20/0.43 thf(f210,plain,(
% 0.20/0.43 (((!! @ $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))))))) = $false) | ~spl0_2),
% 0.20/0.43 inference(not_proxy_clausification,[],[f206])).
% 0.20/0.43 thf(f206,plain,(
% 0.20/0.43 ($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 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))))))) | ~spl0_2),
% 0.20/0.43 inference(avatar_component_clause,[],[f205])).
% 0.20/0.43 thf(f205,plain,(
% 0.20/0.43 spl0_2 <=> ($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 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))))))),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.20/0.43 thf(f374,plain,(
% 0.20/0.43 ($true = (p @ sK3)) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(boolean_simplification,[],[f373])).
% 0.20/0.43 thf(f373,plain,(
% 0.20/0.43 ($true = ($false | (p @ sK3))) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(boolean_simplification,[],[f372])).
% 0.20/0.43 thf(f372,plain,(
% 0.20/0.43 ($true = ((~ $true) | (p @ sK3))) | (~spl0_2 | ~spl0_4)),
% 0.20/0.43 inference(superposition,[],[f368,f223])).
% 0.20/0.43 thf(f223,plain,(
% 0.20/0.43 ($true = (rel_s5 @ sK2 @ sK3)) | ~spl0_2),
% 0.20/0.43 inference(not_proxy_clausification,[],[f220])).
% 0.20/0.43 thf(f368,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK2 @ X1)) | (p @ X1)))) ) | ~spl0_4),
% 0.20/0.43 inference(beta_eta_normalization,[],[f367])).
% 0.20/0.43 thf(f367,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))) @ X1))) ) | ~spl0_4),
% 0.20/0.43 inference(pi_clausification,[],[f287])).
% 0.20/0.43 thf(f287,plain,(
% 0.20/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | ~spl0_4),
% 0.20/0.43 inference(avatar_component_clause,[],[f286])).
% 0.20/0.43 thf(f286,plain,(
% 0.20/0.43 spl0_4 <=> ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.20/0.43 thf(f355,plain,(
% 0.20/0.43 ~spl0_2 | ~spl0_3),
% 0.20/0.43 inference(avatar_contradiction_clause,[],[f354])).
% 0.20/0.43 thf(f354,plain,(
% 0.20/0.43 $false | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(trivial_inequality_removal,[],[f353])).
% 0.20/0.43 thf(f353,plain,(
% 0.20/0.43 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(boolean_simplification,[],[f352])).
% 0.20/0.43 thf(f352,plain,(
% 0.20/0.43 ((~ $true) = $true) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(backward_demodulation,[],[f329,f351])).
% 0.20/0.43 thf(f351,plain,(
% 0.20/0.43 ($true = (rel_s5 @ sK3 @ sK4)) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(boolean_simplification,[],[f338])).
% 0.20/0.43 thf(f338,plain,(
% 0.20/0.43 ($true = ($true => (rel_s5 @ sK3 @ sK4))) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(superposition,[],[f251,f332])).
% 0.20/0.43 thf(f332,plain,(
% 0.20/0.43 ($true = (rel_s5 @ sK2 @ sK4)) | ~spl0_3),
% 0.20/0.43 inference(not_proxy_clausification,[],[f326])).
% 0.20/0.43 thf(f326,plain,(
% 0.20/0.43 ((~ (rel_s5 @ sK2 @ sK4)) = $false) | ~spl0_3),
% 0.20/0.43 inference(boolean_simplification,[],[f325])).
% 0.20/0.43 thf(f325,plain,(
% 0.20/0.43 (((~ (rel_s5 @ sK2 @ sK4)) | $false) = $false) | ~spl0_3),
% 0.20/0.43 inference(backward_demodulation,[],[f313,f323])).
% 0.20/0.43 thf(f323,plain,(
% 0.20/0.43 ((~ (q @ sK4)) = $false) | ~spl0_3),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f313])).
% 0.20/0.43 thf(f313,plain,(
% 0.20/0.43 (((~ (rel_s5 @ sK2 @ sK4)) | (~ (q @ sK4))) = $false) | ~spl0_3),
% 0.20/0.43 inference(beta_eta_normalization,[],[f312])).
% 0.20/0.43 thf(f312,plain,(
% 0.20/0.43 (((^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))) @ sK4) = $false) | ~spl0_3),
% 0.20/0.43 inference(sigma_clausification,[],[f300])).
% 0.20/0.43 thf(f300,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0))))) = $false) | ~spl0_3),
% 0.20/0.43 inference(not_proxy_clausification,[],[f284])).
% 0.20/0.43 thf(f284,plain,(
% 0.20/0.43 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0))))))) | ~spl0_3),
% 0.20/0.43 inference(avatar_component_clause,[],[f283])).
% 0.20/0.43 thf(f283,plain,(
% 0.20/0.43 spl0_3 <=> ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))))),
% 0.20/0.43 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.20/0.43 thf(f251,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($true = ((rel_s5 @ sK2 @ X0) => (rel_s5 @ sK3 @ X0)))) ) | ~spl0_2),
% 0.20/0.43 inference(boolean_simplification,[],[f246])).
% 0.20/0.43 thf(f246,plain,(
% 0.20/0.43 ( ! [X0 : $i] : (($true = (((rel_s5 @ sK2 @ X0) & $true) => (rel_s5 @ sK3 @ X0)))) ) | ~spl0_2),
% 0.20/0.43 inference(superposition,[],[f182,f240])).
% 0.20/0.43 thf(f240,plain,(
% 0.20/0.43 ($true = (rel_s5 @ sK3 @ sK2)) | ~spl0_2),
% 0.20/0.43 inference(boolean_simplification,[],[f236])).
% 0.20/0.43 thf(f236,plain,(
% 0.20/0.43 ($true = ($true => (rel_s5 @ sK3 @ sK2))) | ~spl0_2),
% 0.20/0.43 inference(superposition,[],[f171,f223])).
% 0.20/0.43 thf(f171,plain,(
% 0.20/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((rel_s5 @ X1 @ X2) => (rel_s5 @ X2 @ X1)))) )),
% 0.20/0.43 inference(beta_eta_normalization,[],[f170])).
% 0.20/0.43 thf(f170,plain,(
% 0.20/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1))) @ X2))) )),
% 0.20/0.43 inference(pi_clausification,[],[f169])).
% 0.20/0.43 thf(f169,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((rel_s5 @ X1 @ Y0) => (rel_s5 @ Y0 @ X1)))))) )),
% 0.20/0.43 inference(beta_eta_normalization,[],[f168])).
% 0.20/0.43 thf(f168,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0))))) @ X1))) )),
% 0.20/0.43 inference(pi_clausification,[],[f162])).
% 0.20/0.43 thf(f162,plain,(
% 0.20/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((rel_s5 @ Y0 @ Y1) => (rel_s5 @ Y1 @ Y0)))))))),
% 0.20/0.43 inference(beta_eta_normalization,[],[f160])).
% 0.20/0.43 thf(f160,plain,(
% 0.20/0.43 ($true = ((^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))) @ rel_s5))),
% 0.20/0.43 inference(definition_unfolding,[],[f144,f127])).
% 0.20/0.43 thf(f127,plain,(
% 0.20/0.43 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f41])).
% 0.20/0.43 thf(f41,plain,(
% 0.20/0.43 (msymmetric = (^[Y0 : $i > $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y1 @ Y2) => (Y0 @ Y2 @ Y1))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f40])).
% 0.20/0.43 thf(f40,plain,(
% 0.20/0.43 (msymmetric = (^[X0 : $i > $i > $o] : (! [X1,X2] : ((X0 @ X2 @ X1) => (X0 @ X1 @ X2)))))),
% 0.20/0.43 inference(rectify,[],[f19])).
% 0.20/0.43 thf(f19,axiom,(
% 0.20/0.43 (msymmetric = (^[X6 : $i > $i > $o] : (! [X9,X8] : ((X6 @ X8 @ X9) => (X6 @ X9 @ X8)))))),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',msymmetric)).
% 0.20/0.43 thf(f144,plain,(
% 0.20/0.43 ((msymmetric @ rel_s5) = $true)),
% 0.20/0.43 inference(cnf_transformation,[],[f108])).
% 0.20/0.43 thf(f108,plain,(
% 0.20/0.43 ((msymmetric @ rel_s5) = $true)),
% 0.20/0.43 inference(fool_elimination,[],[f107])).
% 0.20/0.43 thf(f107,plain,(
% 0.20/0.43 (msymmetric @ rel_s5)),
% 0.20/0.43 inference(rectify,[],[f36])).
% 0.20/0.43 thf(f36,axiom,(
% 0.20/0.43 (msymmetric @ rel_s5)),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3)).
% 0.20/0.43 thf(f329,plain,(
% 0.20/0.43 ($true = (~ (rel_s5 @ sK3 @ sK4))) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(boolean_simplification,[],[f328])).
% 0.20/0.43 thf(f328,plain,(
% 0.20/0.43 ($true = ((~ (rel_s5 @ sK3 @ sK4)) | $false)) | (~spl0_2 | ~spl0_3)),
% 0.20/0.43 inference(superposition,[],[f244,f323])).
% 0.20/0.43 thf(f244,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((~ (rel_s5 @ sK3 @ X1)) | (~ (q @ X1))))) ) | ~spl0_2),
% 0.20/0.43 inference(beta_eta_normalization,[],[f243])).
% 0.20/0.43 thf(f243,plain,(
% 0.20/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))) @ X1))) ) | ~spl0_2),
% 0.20/0.43 inference(pi_clausification,[],[f230])).
% 0.20/0.43 thf(f230,plain,(
% 0.20/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))) | ~spl0_2),
% 0.20/0.43 inference(not_proxy_clausification,[],[f229])).
% 0.20/0.43 thf(f229,plain,(
% 0.20/0.43 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))) = $false) | ~spl0_2),
% 0.20/0.43 inference(boolean_simplification,[],[f228])).
% 0.20/0.43 thf(f228,plain,(
% 0.20/0.43 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK3 @ Y0)) | (~ (q @ Y0)))))) | $false) = $false) | ~spl0_2),
% 0.20/0.43 inference(backward_demodulation,[],[f222,f226])).
% 0.20/0.43 thf(f288,plain,(
% 0.20/0.43 spl0_3 | spl0_4 | ~spl0_2),
% 0.20/0.43 inference(avatar_split_clause,[],[f281,f205,f286,f283])).
% 0.20/0.43 thf(f281,plain,(
% 0.20/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0))))))) | ~spl0_2),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f275])).
% 0.20/0.43 thf(f275,plain,(
% 0.20/0.43 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (~ (q @ Y0)))))) | (!! @ $i @ (^[Y0 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0)))))) | ~spl0_2),
% 0.20/0.43 inference(not_proxy_clausification,[],[f213])).
% 0.20/0.43 thf(f207,plain,(
% 0.20/0.43 spl0_1 | spl0_2),
% 0.20/0.43 inference(avatar_split_clause,[],[f200,f205,f202])).
% 0.20/0.43 thf(f200,plain,(
% 0.20/0.43 ($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 : $i]: ((~ (rel_s5 @ sK2 @ Y0)) | (p @ Y0))))))))) | ($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 : $i]: ((~ (rel_s5 @ Y0 @ Y1)) | (~ (q @ Y1)))))) | (p @ Y0)))))))))),
% 0.20/0.43 inference(binary_proxy_clausification,[],[f197])).
% 0.20/0.43 thf(f197,plain,(
% 0.20/0.43 ($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)))))))) | (~ ((!! @ $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))))))))))),
% 0.20/0.43 inference(not_proxy_clausification,[],[f196])).
% 0.20/0.43 thf(f196,plain,(
% 0.20/0.43 ((~ ((~ (((~ (!! @ $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)))))))) | (~ ((!! @ $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)))))))))) = $false)),
% 0.20/0.43 inference(beta_eta_normalization,[],[f195])).
% 0.20/0.43 thf(f195,plain,(
% 0.20/0.43 (((^[Y0 : $i]: (~ ((~ (((~ (!! @ $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)))))))) | (~ ((!! @ $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))))))))))) @ sK2) = $false)),
% 0.20/0.43 inference(sigma_clausification,[],[f192])).
% 0.20/0.43 thf(f192,plain,(
% 0.20/0.43 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ (((~ (!! @ $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)))))))) | (~ ((!! @ $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)))))))))))) = $false)),
% 0.20/0.43 inference(not_proxy_clausification,[],[f164])).
% 0.20/0.43 thf(f164,plain,(
% 0.20/0.43 ($true = (~ (!! @ $i @ (^[Y0 : $i]: (~ ((~ (((~ (!! @ $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)))))))) | (~ ((!! @ $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))))))))))))))),
% 0.20/0.43 inference(beta_eta_normalization,[],[f159])).
% 0.20/0.43 thf(f159,plain,(
% 0.20/0.43 ((~ ((^[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 > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ 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]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ 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)))))) = $true)),
% 0.20/0.43 inference(definition_unfolding,[],[f135,f115,f151,f132,f137,f157,f137,f132,f157])).
% 0.20/0.43 thf(f157,plain,(
% 0.20/0.43 (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)))))),
% 0.20/0.43 inference(definition_unfolding,[],[f114,f136,f137,f136])).
% 0.20/0.43 thf(f136,plain,(
% 0.20/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f67])).
% 0.20/0.43 thf(f67,plain,(
% 0.20/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.20/0.43 inference(fool_elimination,[],[f66])).
% 0.20/0.43 thf(f66,plain,(
% 0.20/0.43 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.20/0.43 inference(rectify,[],[f3])).
% 0.20/0.43 thf(f3,axiom,(
% 0.20/0.43 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.20/0.43 thf(f114,plain,(
% 0.20/0.43 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.20/0.43 inference(cnf_transformation,[],[f98])).
% 0.20/0.43 thf(f98,plain,(
% 0.20/0.43 (mdia_s5 = (^[Y0 : $i > $o]: (mnot @ (mbox_s5 @ (mnot @ Y0)))))),
% 0.20/0.43 inference(fool_elimination,[],[f97])).
% 0.20/0.43 thf(f97,plain,(
% 0.20/0.43 (mdia_s5 = (^[X0 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X0)))))),
% 0.20/0.43 inference(rectify,[],[f33])).
% 0.20/0.43 thf(f33,axiom,(
% 0.20/0.43 (mdia_s5 = (^[X3 : $i > $o] : (mnot @ (mbox_s5 @ (mnot @ X3)))))),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_s5)).
% 0.20/0.43 thf(f137,plain,(
% 0.20/0.43 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f47])).
% 0.20/0.43 thf(f47,plain,(
% 0.20/0.43 (mbox_s5 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_s5 @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f46])).
% 0.20/0.43 thf(f46,plain,(
% 0.20/0.43 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_s5 @ X1 @ X2)))) = mbox_s5)),
% 0.20/0.43 inference(rectify,[],[f32])).
% 0.20/0.43 thf(f32,axiom,(
% 0.20/0.43 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_s5 @ X2 @ X7)))) = mbox_s5)),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_s5)).
% 0.20/0.43 thf(f132,plain,(
% 0.20/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f63])).
% 0.20/0.43 thf(f63,plain,(
% 0.20/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.20/0.43 inference(fool_elimination,[],[f62])).
% 0.20/0.43 thf(f62,plain,(
% 0.20/0.43 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.20/0.43 inference(rectify,[],[f4])).
% 0.20/0.43 thf(f4,axiom,(
% 0.20/0.43 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.20/0.43 thf(f151,plain,(
% 0.20/0.43 (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))))))),
% 0.20/0.43 inference(definition_unfolding,[],[f130,f148,f149,f149])).
% 0.20/0.43 thf(f149,plain,(
% 0.20/0.43 (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)))))),
% 0.20/0.43 inference(definition_unfolding,[],[f133,f132,f136])).
% 0.20/0.43 thf(f133,plain,(
% 0.20/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.43 inference(cnf_transformation,[],[f110])).
% 0.20/0.43 thf(f110,plain,(
% 0.20/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.20/0.43 inference(fool_elimination,[],[f109])).
% 0.20/0.43 thf(f109,plain,(
% 0.20/0.43 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.20/0.43 inference(rectify,[],[f6])).
% 0.20/0.43 thf(f6,axiom,(
% 0.20/0.43 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.20/0.43 thf(f148,plain,(
% 0.20/0.43 (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)))))))),
% 0.20/0.43 inference(definition_unfolding,[],[f142,f136,f132,f136,f136])).
% 0.20/0.43 thf(f142,plain,(
% 0.20/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f94])).
% 0.20/0.43 thf(f94,plain,(
% 0.20/0.43 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.20/0.43 inference(fool_elimination,[],[f93])).
% 0.20/0.43 thf(f93,plain,(
% 0.20/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.20/0.43 inference(rectify,[],[f5])).
% 0.20/0.43 thf(f5,axiom,(
% 0.20/0.43 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.20/0.43 thf(f130,plain,(
% 0.20/0.43 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f80])).
% 0.20/0.43 thf(f80,plain,(
% 0.20/0.43 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.20/0.43 inference(fool_elimination,[],[f79])).
% 0.20/0.43 thf(f79,plain,(
% 0.20/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.20/0.43 inference(rectify,[],[f8])).
% 0.20/0.43 thf(f8,axiom,(
% 0.20/0.43 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.20/0.43 thf(f115,plain,(
% 0.20/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.43 inference(cnf_transformation,[],[f49])).
% 0.20/0.43 thf(f49,plain,(
% 0.20/0.43 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.20/0.43 inference(fool_elimination,[],[f48])).
% 0.20/0.43 thf(f48,plain,(
% 0.20/0.43 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.20/0.43 inference(rectify,[],[f28])).
% 0.20/0.43 thf(f28,axiom,(
% 0.20/0.43 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.20/0.43 thf(f135,plain,(
% 0.20/0.43 ($true = (~ (mvalid @ (mequiv @ (mor @ (mbox_s5 @ p) @ (mdia_s5 @ q)) @ (mbox_s5 @ (mor @ p @ (mdia_s5 @ q)))))))),
% 0.20/0.43 inference(cnf_transformation,[],[f88])).
% 0.20/0.43 thf(f88,plain,(
% 0.20/0.43 ($true = (~ (mvalid @ (mequiv @ (mor @ (mbox_s5 @ p) @ (mdia_s5 @ q)) @ (mbox_s5 @ (mor @ p @ (mdia_s5 @ q)))))))),
% 0.20/0.43 inference(fool_elimination,[],[f87])).
% 0.20/0.43 thf(f87,plain,(
% 0.20/0.43 ~(mvalid @ (mequiv @ (mor @ (mbox_s5 @ p) @ (mdia_s5 @ q)) @ (mbox_s5 @ (mor @ p @ (mdia_s5 @ q)))))),
% 0.20/0.43 inference(rectify,[],[f38])).
% 0.20/0.43 thf(f38,negated_conjecture,(
% 0.20/0.43 ~(mvalid @ (mequiv @ (mor @ (mbox_s5 @ p) @ (mdia_s5 @ q)) @ (mbox_s5 @ (mor @ p @ (mdia_s5 @ q)))))),
% 0.20/0.43 inference(negated_conjecture,[],[f37])).
% 0.20/0.43 thf(f37,conjecture,(
% 0.20/0.43 (mvalid @ (mequiv @ (mor @ (mbox_s5 @ p) @ (mdia_s5 @ q)) @ (mbox_s5 @ (mor @ p @ (mdia_s5 @ q)))))),
% 0.20/0.43 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.20/0.43 % SZS output end Proof for theBenchmark
% 0.20/0.43 % (31767)------------------------------
% 0.20/0.43 % (31767)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.20/0.43 % (31767)Termination reason: Refutation
% 0.20/0.43
% 0.20/0.43 % (31767)Memory used [KB]: 6012
% 0.20/0.43 % (31767)Time elapsed: 0.067 s
% 0.20/0.43 % (31767)Instructions burned: 75 (million)
% 0.20/0.43 % (31767)------------------------------
% 0.20/0.43 % (31767)------------------------------
% 0.20/0.43 % (31754)Success in time 0.077 s
% 0.20/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------