TSTP Solution File: SET926^7 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET926^7 : TPTP v8.2.0. Released v5.5.0.
% 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 : n027.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 03:13:58 EDT 2024
% Result : Theorem 0.16s 0.39s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SET926^7 : TPTP v8.2.0. Released v5.5.0.
% 0.05/0.11 % 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
% 0.10/0.31 % Computer : n027.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon May 20 13:29:38 EDT 2024
% 0.16/0.31 % CPUTime :
% 0.16/0.31 This is a TH0_THM_EQU_NAR problem
% 0.16/0.32 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
% 0.16/0.33 % (6072)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)
% 0.16/0.33 % (6074)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.33 % (6076)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)
% 0.16/0.33 % (6073)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)
% 0.16/0.33 % (6075)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)
% 0.16/0.33 % (6071)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.33 % (6077)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.34 % (6078)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)
% 0.16/0.34 % (6074)Instruction limit reached!
% 0.16/0.34 % (6074)------------------------------
% 0.16/0.34 % (6074)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (6074)Termination reason: Unknown
% 0.16/0.34 % (6074)Termination phase: shuffling
% 0.16/0.34
% 0.16/0.34 % (6074)Memory used [KB]: 1023
% 0.16/0.34 % (6074)Time elapsed: 0.003 s
% 0.16/0.34 % (6074)Instructions burned: 3 (million)
% 0.16/0.34 % (6074)------------------------------
% 0.16/0.34 % (6074)------------------------------
% 0.16/0.34 % (6075)Instruction limit reached!
% 0.16/0.34 % (6075)------------------------------
% 0.16/0.34 % (6075)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (6075)Termination reason: Unknown
% 0.16/0.34 % (6075)Termination phase: shuffling
% 0.16/0.34
% 0.16/0.34 % (6075)Memory used [KB]: 1023
% 0.16/0.34 % (6075)Time elapsed: 0.003 s
% 0.16/0.34 % (6075)Instructions burned: 3 (million)
% 0.16/0.34 % (6075)------------------------------
% 0.16/0.34 % (6075)------------------------------
% 0.16/0.34 % (6078)Instruction limit reached!
% 0.16/0.34 % (6078)------------------------------
% 0.16/0.34 % (6078)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (6078)Termination reason: Unknown
% 0.16/0.34 % (6078)Termination phase: shuffling
% 0.16/0.34
% 0.16/0.34 % (6078)Memory used [KB]: 1023
% 0.16/0.34 % (6078)Time elapsed: 0.003 s
% 0.16/0.34 % (6078)Instructions burned: 3 (million)
% 0.16/0.34 % (6078)------------------------------
% 0.16/0.34 % (6078)------------------------------
% 0.16/0.34 % (6072)Instruction limit reached!
% 0.16/0.34 % (6072)------------------------------
% 0.16/0.34 % (6072)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (6072)Termination reason: Unknown
% 0.16/0.34 % (6072)Termination phase: shuffling
% 0.16/0.34
% 0.16/0.34 % (6072)Memory used [KB]: 1151
% 0.16/0.34 % (6072)Time elapsed: 0.004 s
% 0.16/0.34 % (6072)Instructions burned: 5 (million)
% 0.16/0.34 % (6072)------------------------------
% 0.16/0.34 % (6072)------------------------------
% 0.16/0.34 % (6077)Instruction limit reached!
% 0.16/0.34 % (6077)------------------------------
% 0.16/0.34 % (6077)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.34 % (6077)Termination reason: Unknown
% 0.16/0.34 % (6077)Termination phase: Saturation
% 0.16/0.34
% 0.16/0.34 % (6077)Memory used [KB]: 5628
% 0.16/0.34 % (6077)Time elapsed: 0.010 s
% 0.16/0.34 % (6077)Instructions burned: 19 (million)
% 0.16/0.34 % (6077)------------------------------
% 0.16/0.34 % (6077)------------------------------
% 0.16/0.35 % (6076)Refutation not found, incomplete strategy
% 0.16/0.35 % (6076)------------------------------
% 0.16/0.35 % (6076)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (6076)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.35
% 0.16/0.35
% 0.16/0.35 % (6076)Memory used [KB]: 5756
% 0.16/0.35 % (6076)Time elapsed: 0.013 s
% 0.16/0.35 % (6076)Instructions burned: 23 (million)
% 0.16/0.35 % (6076)------------------------------
% 0.16/0.35 % (6076)------------------------------
% 0.16/0.35 % (6073)Instruction limit reached!
% 0.16/0.35 % (6073)------------------------------
% 0.16/0.35 % (6073)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (6073)Termination reason: Unknown
% 0.16/0.35 % (6073)Termination phase: Saturation
% 0.16/0.35
% 0.16/0.35 % (6073)Memory used [KB]: 5756
% 0.16/0.35 % (6073)Time elapsed: 0.014 s
% 0.16/0.35 % (6073)Instructions burned: 28 (million)
% 0.16/0.35 % (6073)------------------------------
% 0.16/0.35 % (6073)------------------------------
% 0.16/0.35 % (6079)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)
% 0.16/0.35 % (6080)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)
% 0.16/0.35 % (6081)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)
% 0.16/0.35 % (6082)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)
% 0.16/0.35 % (6081)Instruction limit reached!
% 0.16/0.35 % (6081)------------------------------
% 0.16/0.35 % (6081)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.35 % (6081)Termination reason: Unknown
% 0.16/0.35 % (6081)Termination phase: shuffling
% 0.16/0.35
% 0.16/0.35 % (6081)Memory used [KB]: 1023
% 0.16/0.35 % (6081)Time elapsed: 0.003 s
% 0.16/0.35 % (6081)Instructions burned: 4 (million)
% 0.16/0.35 % (6081)------------------------------
% 0.16/0.35 % (6081)------------------------------
% 0.16/0.36 % (6080)Instruction limit reached!
% 0.16/0.36 % (6080)------------------------------
% 0.16/0.36 % (6080)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (6080)Termination reason: Unknown
% 0.16/0.36 % (6080)Termination phase: Property scanning
% 0.16/0.36
% 0.16/0.36 % (6080)Memory used [KB]: 1151
% 0.16/0.36 % (6080)Time elapsed: 0.008 s
% 0.16/0.36 % (6080)Instructions burned: 15 (million)
% 0.16/0.36 % (6080)------------------------------
% 0.16/0.36 % (6080)------------------------------
% 0.16/0.36 % (6083)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.16/0.36 % (6084)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.16/0.36 % (6083)Instruction limit reached!
% 0.16/0.36 % (6083)------------------------------
% 0.16/0.36 % (6083)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (6083)Termination reason: Unknown
% 0.16/0.36 % (6083)Termination phase: Property scanning
% 0.16/0.36
% 0.16/0.36 % (6083)Memory used [KB]: 1151
% 0.16/0.36 % (6083)Time elapsed: 0.005 s
% 0.16/0.36 % (6083)Instructions burned: 8 (million)
% 0.16/0.36 % (6083)------------------------------
% 0.16/0.36 % (6083)------------------------------
% 0.16/0.36 % (6085)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)
% 0.16/0.36 % (6085)Instruction limit reached!
% 0.16/0.36 % (6085)------------------------------
% 0.16/0.36 % (6085)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.36 % (6085)Termination reason: Unknown
% 0.16/0.36 % (6085)Termination phase: shuffling
% 0.16/0.36
% 0.16/0.36 % (6085)Memory used [KB]: 1023
% 0.16/0.36 % (6085)Time elapsed: 0.003 s
% 0.16/0.36 % (6085)Instructions burned: 3 (million)
% 0.16/0.36 % (6085)------------------------------
% 0.16/0.36 % (6085)------------------------------
% 0.16/0.36 % (6086)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)
% 0.16/0.37 % (6086)Instruction limit reached!
% 0.16/0.37 % (6086)------------------------------
% 0.16/0.37 % (6086)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (6086)Termination reason: Unknown
% 0.16/0.37 % (6086)Termination phase: shuffling
% 0.16/0.37
% 0.16/0.37 % (6086)Memory used [KB]: 1023
% 0.16/0.37 % (6086)Time elapsed: 0.003 s
% 0.16/0.37 % (6086)Instructions burned: 4 (million)
% 0.16/0.37 % (6086)------------------------------
% 0.16/0.37 % (6086)------------------------------
% 0.16/0.37 % (6079)Instruction limit reached!
% 0.16/0.37 % (6079)------------------------------
% 0.16/0.37 % (6079)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (6079)Termination reason: Unknown
% 0.16/0.37 % (6079)Termination phase: Saturation
% 0.16/0.37
% 0.16/0.37 % (6079)Memory used [KB]: 5884
% 0.16/0.37 % (6079)Time elapsed: 0.018 s
% 0.16/0.37 % (6079)Instructions burned: 38 (million)
% 0.16/0.37 % (6079)------------------------------
% 0.16/0.37 % (6079)------------------------------
% 0.16/0.37 % (6084)Instruction limit reached!
% 0.16/0.37 % (6084)------------------------------
% 0.16/0.37 % (6084)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (6084)Termination reason: Unknown
% 0.16/0.37 % (6084)Termination phase: Property scanning
% 0.16/0.37
% 0.16/0.37 % (6084)Memory used [KB]: 1151
% 0.16/0.37 % (6084)Time elapsed: 0.009 s
% 0.16/0.37 % (6084)Instructions burned: 17 (million)
% 0.16/0.37 % (6084)------------------------------
% 0.16/0.37 % (6084)------------------------------
% 0.16/0.37 % (6087)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)
% 0.16/0.37 % (6087)Instruction limit reached!
% 0.16/0.37 % (6087)------------------------------
% 0.16/0.37 % (6087)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (6087)Termination reason: Unknown
% 0.16/0.37 % (6087)Termination phase: Property scanning
% 0.16/0.37
% 0.16/0.37 % (6087)Memory used [KB]: 1151
% 0.16/0.37 % (6087)Time elapsed: 0.005 s
% 0.16/0.37 % (6087)Instructions burned: 8 (million)
% 0.16/0.37 % (6087)------------------------------
% 0.16/0.37 % (6087)------------------------------
% 0.16/0.37 % (6088)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)
% 0.16/0.37 % (6088)Instruction limit reached!
% 0.16/0.37 % (6088)------------------------------
% 0.16/0.37 % (6088)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.37 % (6088)Termination reason: Unknown
% 0.16/0.37 % (6088)Termination phase: shuffling
% 0.16/0.37
% 0.16/0.37 % (6088)Memory used [KB]: 1023
% 0.16/0.37 % (6088)Time elapsed: 0.003 s
% 0.16/0.37 % (6088)Instructions burned: 3 (million)
% 0.16/0.37 % (6088)------------------------------
% 0.16/0.37 % (6088)------------------------------
% 0.16/0.37 % (6089)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.16/0.38 % (6089)Instruction limit reached!
% 0.16/0.38 % (6089)------------------------------
% 0.16/0.38 % (6089)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (6089)Termination reason: Unknown
% 0.16/0.38 % (6089)Termination phase: shuffling
% 0.16/0.38
% 0.16/0.38 % (6089)Memory used [KB]: 1023
% 0.16/0.38 % (6089)Time elapsed: 0.003 s
% 0.16/0.38 % (6089)Instructions burned: 4 (million)
% 0.16/0.38 % (6089)------------------------------
% 0.16/0.38 % (6089)------------------------------
% 0.16/0.38 % (6090)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)
% 0.16/0.38 % (6091)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on theBenchmark for (2999ds/710Mi)
% 0.16/0.38 % (6071)First to succeed.
% 0.16/0.38 % (6092)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.16/0.38 % (6092)Instruction limit reached!
% 0.16/0.38 % (6092)------------------------------
% 0.16/0.38 % (6092)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.38 % (6092)Termination reason: Unknown
% 0.16/0.38 % (6092)Termination phase: shuffling
% 0.16/0.38
% 0.16/0.38 % (6092)Memory used [KB]: 1151
% 0.16/0.38 % (6092)Time elapsed: 0.004 s
% 0.16/0.38 % (6092)Instructions burned: 6 (million)
% 0.16/0.38 % (6092)------------------------------
% 0.16/0.38 % (6092)------------------------------
% 0.16/0.39 % (6093)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)
% 0.16/0.39 % (6071)Refutation found. Thanks to Tanya!
% 0.16/0.39 % SZS status Theorem for theBenchmark
% 0.16/0.39 % SZS output start Proof for theBenchmark
% 0.16/0.39 thf(type_def_5, type, mu: $tType).
% 0.16/0.39 thf(func_def_0, type, mu: $tType).
% 0.16/0.39 thf(func_def_1, type, qmltpeq: mu > mu > $i > $o).
% 0.16/0.39 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_6, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_7, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_8, type, mtrue: $i > $o).
% 0.16/0.39 thf(func_def_9, type, mfalse: $i > $o).
% 0.16/0.39 thf(func_def_10, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_11, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_12, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_13, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_14, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_15, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_16, type, exists_in_world: mu > $i > $o).
% 0.16/0.39 thf(func_def_17, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_18, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_19, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_20, type, mreflexive: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_21, type, msymmetric: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_22, type, mserial: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_23, type, mtransitive: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_24, type, meuclidean: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_25, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_26, type, mfunctional: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_27, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_28, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_29, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.16/0.39 thf(func_def_30, type, mvalid: ($i > $o) > $o).
% 0.16/0.39 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.16/0.39 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.16/0.39 thf(func_def_33, type, minvalid: ($i > $o) > $o).
% 0.16/0.39 thf(func_def_34, type, rel_s4: $i > $i > $o).
% 0.16/0.39 thf(func_def_35, type, mbox_s4: ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_36, type, mdia_s4: ($i > $o) > $i > $o).
% 0.16/0.39 thf(func_def_37, type, in: mu > mu > $i > $o).
% 0.16/0.39 thf(func_def_38, type, empty: mu > $i > $o).
% 0.16/0.39 thf(func_def_39, type, empty_set: mu).
% 0.16/0.39 thf(func_def_40, type, singleton: mu > mu).
% 0.16/0.39 thf(func_def_41, type, set_difference: mu > mu > mu).
% 0.16/0.39 thf(func_def_57, type, sK0: $i > mu).
% 0.16/0.39 thf(func_def_59, type, sK2: $i > mu).
% 0.16/0.39 thf(func_def_60, type, sK3: $i > mu).
% 0.16/0.39 thf(func_def_62, type, sK5: mu).
% 0.16/0.39 thf(func_def_63, type, sK6: mu).
% 0.16/0.39 thf(f693,plain,(
% 0.16/0.39 $false),
% 0.16/0.39 inference(avatar_sat_refutation,[],[f608,f648,f657,f678,f690])).
% 0.16/0.39 thf(f690,plain,(
% 0.16/0.39 ~spl1_6 | ~spl1_9),
% 0.16/0.39 inference(avatar_contradiction_clause,[],[f689])).
% 0.16/0.39 thf(f689,plain,(
% 0.16/0.39 $false | (~spl1_6 | ~spl1_9)),
% 0.16/0.39 inference(trivial_inequality_removal,[],[f681])).
% 0.16/0.39 thf(f681,plain,(
% 0.16/0.39 ($true = $false) | (~spl1_6 | ~spl1_9)),
% 0.16/0.39 inference(superposition,[],[f646,f598])).
% 0.16/0.39 thf(f598,plain,(
% 0.16/0.39 ((in @ sK5 @ sK6 @ sK4) = $false) | ~spl1_6),
% 0.16/0.39 inference(avatar_component_clause,[],[f596])).
% 0.16/0.39 thf(f596,plain,(
% 0.16/0.39 spl1_6 <=> ((in @ sK5 @ sK6 @ sK4) = $false)),
% 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.16/0.39 thf(f646,plain,(
% 0.16/0.39 ($true = (in @ sK5 @ sK6 @ sK4)) | ~spl1_9),
% 0.16/0.39 inference(avatar_component_clause,[],[f644])).
% 0.16/0.39 thf(f644,plain,(
% 0.16/0.39 spl1_9 <=> ($true = (in @ sK5 @ sK6 @ sK4))),
% 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_9])])).
% 0.16/0.39 thf(f678,plain,(
% 0.16/0.39 ~spl1_8),
% 0.16/0.39 inference(avatar_contradiction_clause,[],[f677])).
% 0.16/0.39 thf(f677,plain,(
% 0.16/0.39 $false | ~spl1_8),
% 0.16/0.39 inference(trivial_inequality_removal,[],[f669])).
% 0.16/0.39 thf(f669,plain,(
% 0.16/0.39 ($true = $false) | ~spl1_8),
% 0.16/0.39 inference(superposition,[],[f606,f413])).
% 0.16/0.39 thf(f413,plain,(
% 0.16/0.39 ((exists_in_world @ sK5 @ sK4) = $true)),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f411])).
% 0.16/0.39 thf(f411,plain,(
% 0.16/0.39 ($false = ((exists_in_world @ sK5 @ sK4) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => ((qmltpeq @ (set_difference @ (singleton @ sK5) @ Y0) @ empty_set @ sK4) | (qmltpeq @ (set_difference @ (singleton @ sK5) @ Y0) @ (singleton @ sK5) @ sK4)))))))),
% 0.16/0.39 inference(beta_eta_normalization,[],[f410])).
% 0.16/0.39 thf(f410,plain,(
% 0.16/0.39 (((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK4) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ sK4) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ sK4))))))) @ sK5) = $false)),
% 0.16/0.39 inference(sigma_clausification,[],[f409])).
% 0.16/0.39 thf(f409,plain,(
% 0.16/0.39 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ sK4) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ sK4) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ sK4)))))))))),
% 0.16/0.39 inference(beta_eta_normalization,[],[f408])).
% 0.16/0.39 thf(f408,plain,(
% 0.16/0.39 (((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => ((qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ empty_set @ Y0) | (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ (singleton @ Y1) @ Y0))))))))) @ sK4) = $false)),
% 0.16/0.39 inference(sigma_clausification,[],[f407])).
% 0.16/0.39 thf(f407,plain,(
% 0.16/0.39 ((!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => ((qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ empty_set @ Y0) | (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ (singleton @ Y1) @ Y0)))))))))) != $true)),
% 0.16/0.39 inference(beta_eta_normalization,[],[f249])).
% 0.16/0.39 thf(f249,plain,(
% 0.16/0.39 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 0.16/0.39 inference(definition_unfolding,[],[f212,f188,f182,f182,f219])).
% 0.16/0.39 thf(f219,plain,(
% 0.16/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f160])).
% 0.16/0.39 thf(f160,plain,(
% 0.16/0.39 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.16/0.39 inference(fool_elimination,[],[f159])).
% 0.16/0.39 thf(f159,plain,(
% 0.16/0.39 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.16/0.39 inference(rectify,[],[f3])).
% 0.16/0.39 thf(f3,axiom,(
% 0.16/0.39 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))) = mor)),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.16/0.39 thf(f182,plain,(
% 0.16/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f152])).
% 0.16/0.39 thf(f152,plain,(
% 0.16/0.39 (mforall_ind = (^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.16/0.39 inference(fool_elimination,[],[f151])).
% 0.16/0.39 thf(f151,plain,(
% 0.16/0.39 (mforall_ind = (^[X0 : mu > $i > $o, X1 : $i] : (! [X2 : mu] : ((exists_in_world @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 0.16/0.39 inference(rectify,[],[f15])).
% 0.16/0.39 thf(f15,axiom,(
% 0.16/0.39 (mforall_ind = (^[X3 : mu > $i > $o, X2 : $i] : (! [X0 : mu] : ((exists_in_world @ X0 @ X2) => (X3 @ X0 @ X2)))))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mforall_ind)).
% 0.16/0.39 thf(f188,plain,(
% 0.16/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.39 inference(cnf_transformation,[],[f69])).
% 0.16/0.39 thf(f69,plain,(
% 0.16/0.39 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.39 inference(fool_elimination,[],[f68])).
% 0.16/0.39 thf(f68,plain,(
% 0.16/0.39 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.16/0.39 inference(rectify,[],[f28])).
% 0.16/0.39 thf(f28,axiom,(
% 0.16/0.39 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mvalid)).
% 0.16/0.39 thf(f212,plain,(
% 0.16/0.39 ($true != (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f165])).
% 0.16/0.39 thf(f165,plain,(
% 0.16/0.39 ($true != (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 0.16/0.39 inference(flattening,[],[f110])).
% 0.16/0.39 thf(f110,plain,(
% 0.16/0.39 ~($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 0.16/0.39 inference(fool_elimination,[],[f109])).
% 0.16/0.39 thf(f109,plain,(
% 0.16/0.39 ~(mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mor @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ (singleton @ X0))))))))),
% 0.16/0.39 inference(rectify,[],[f56])).
% 0.16/0.39 thf(f56,negated_conjecture,(
% 0.16/0.39 ~(mvalid @ (mforall_ind @ (^[X14 : mu] : (mforall_ind @ (^[X15 : mu] : (mor @ (qmltpeq @ (set_difference @ (singleton @ X14) @ X15) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ X14) @ X15) @ (singleton @ X14))))))))),
% 0.16/0.39 inference(negated_conjecture,[],[f55])).
% 0.16/0.39 thf(f55,conjecture,(
% 0.16/0.39 (mvalid @ (mforall_ind @ (^[X14 : mu] : (mforall_ind @ (^[X15 : mu] : (mor @ (qmltpeq @ (set_difference @ (singleton @ X14) @ X15) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ X14) @ X15) @ (singleton @ X14))))))))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_zfmisc_1)).
% 0.16/0.39 thf(f606,plain,(
% 0.16/0.39 ((exists_in_world @ sK5 @ sK4) = $false) | ~spl1_8),
% 0.16/0.39 inference(avatar_component_clause,[],[f604])).
% 0.16/0.39 thf(f604,plain,(
% 0.16/0.39 spl1_8 <=> ((exists_in_world @ sK5 @ sK4) = $false)),
% 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_8])])).
% 0.16/0.39 thf(f657,plain,(
% 0.16/0.39 ~spl1_7),
% 0.16/0.39 inference(avatar_contradiction_clause,[],[f656])).
% 0.16/0.39 thf(f656,plain,(
% 0.16/0.39 $false | ~spl1_7),
% 0.16/0.39 inference(trivial_inequality_removal,[],[f651])).
% 0.16/0.39 thf(f651,plain,(
% 0.16/0.39 ($true = $false) | ~spl1_7),
% 0.16/0.39 inference(superposition,[],[f417,f602])).
% 0.16/0.39 thf(f602,plain,(
% 0.16/0.39 ($false = (exists_in_world @ sK6 @ sK4)) | ~spl1_7),
% 0.16/0.39 inference(avatar_component_clause,[],[f600])).
% 0.16/0.39 thf(f600,plain,(
% 0.16/0.39 spl1_7 <=> ($false = (exists_in_world @ sK6 @ sK4))),
% 0.16/0.39 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 0.16/0.39 thf(f417,plain,(
% 0.16/0.39 ($true = (exists_in_world @ sK6 @ sK4))),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f415])).
% 0.16/0.39 thf(f415,plain,(
% 0.16/0.39 ($false = ((exists_in_world @ sK6 @ sK4) => ((qmltpeq @ (set_difference @ (singleton @ sK5) @ sK6) @ empty_set @ sK4) | (qmltpeq @ (set_difference @ (singleton @ sK5) @ sK6) @ (singleton @ sK5) @ sK4))))),
% 0.16/0.39 inference(beta_eta_normalization,[],[f414])).
% 0.16/0.39 thf(f414,plain,(
% 0.16/0.39 ($false = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => ((qmltpeq @ (set_difference @ (singleton @ sK5) @ Y0) @ empty_set @ sK4) | (qmltpeq @ (set_difference @ (singleton @ sK5) @ Y0) @ (singleton @ sK5) @ sK4)))) @ sK6))),
% 0.16/0.39 inference(sigma_clausification,[],[f412])).
% 0.16/0.39 thf(f412,plain,(
% 0.16/0.39 ($false = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ sK4) => ((qmltpeq @ (set_difference @ (singleton @ sK5) @ Y0) @ empty_set @ sK4) | (qmltpeq @ (set_difference @ (singleton @ sK5) @ Y0) @ (singleton @ sK5) @ sK4))))))),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f411])).
% 0.16/0.39 thf(f648,plain,(
% 0.16/0.39 spl1_9 | spl1_7 | spl1_8),
% 0.16/0.39 inference(avatar_split_clause,[],[f637,f604,f600,f644])).
% 0.16/0.39 thf(f637,plain,(
% 0.16/0.39 ((exists_in_world @ sK5 @ sK4) = $false) | ($false = (exists_in_world @ sK6 @ sK4)) | ($true = (in @ sK5 @ sK6 @ sK4))),
% 0.16/0.39 inference(trivial_inequality_removal,[],[f628])).
% 0.16/0.39 thf(f628,plain,(
% 0.16/0.39 ($false = (exists_in_world @ sK6 @ sK4)) | ((exists_in_world @ sK5 @ sK4) = $false) | ($true = $false) | ($true = (in @ sK5 @ sK6 @ sK4))),
% 0.16/0.39 inference(superposition,[],[f383,f418])).
% 0.16/0.39 thf(f418,plain,(
% 0.16/0.39 ((qmltpeq @ (set_difference @ (singleton @ sK5) @ sK6) @ (singleton @ sK5) @ sK4) = $false)),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f416])).
% 0.16/0.39 thf(f416,plain,(
% 0.16/0.39 (((qmltpeq @ (set_difference @ (singleton @ sK5) @ sK6) @ empty_set @ sK4) | (qmltpeq @ (set_difference @ (singleton @ sK5) @ sK6) @ (singleton @ sK5) @ sK4)) = $false)),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f415])).
% 0.16/0.39 thf(f383,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1)) | ($true = (in @ X2 @ X3 @ X1)) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f382])).
% 0.16/0.39 thf(f382,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X3 @ X1) = $false) | ($true = ((in @ X2 @ X3 @ X1) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1))) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(not_proxy_clausification,[],[f376])).
% 0.16/0.39 thf(f376,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((exists_in_world @ X3 @ X1) = $false) | ($false = (~ ((in @ X2 @ X3 @ X1) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1)))) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f375])).
% 0.16/0.39 thf(f375,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1)) | (~ (in @ X2 @ X3 @ X1)))) | (~ ((in @ X2 @ X3 @ X1) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1))))) | ($false = (exists_in_world @ X2 @ X1)) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.16/0.39 inference(not_proxy_clausification,[],[f374])).
% 0.16/0.39 thf(f374,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1)) | (~ (in @ X2 @ X3 @ X1)))) | (~ ((in @ X2 @ X3 @ X1) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1)))))) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f373])).
% 0.16/0.39 thf(f373,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | (((exists_in_world @ X3 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1)) | (~ (in @ X2 @ X3 @ X1)))) | (~ ((in @ X2 @ X3 @ X1) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ (singleton @ X2) @ X1)))))) = $true)) )),
% 0.16/0.39 inference(beta_eta_normalization,[],[f372])).
% 0.16/0.39 thf(f372,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ (singleton @ X2) @ X1)) | (~ (in @ X2 @ Y0 @ X1)))) | (~ ((in @ X2 @ Y0 @ X1) | (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ (singleton @ X2) @ X1))))))) @ X3))) )),
% 0.16/0.39 inference(pi_clausification,[],[f371])).
% 0.16/0.39 thf(f371,plain,(
% 0.16/0.39 ( ! [X2 : mu,X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ (singleton @ X2) @ X1)) | (~ (in @ X2 @ Y0 @ X1)))) | (~ ((in @ X2 @ Y0 @ X1) | (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ (singleton @ X2) @ X1))))))))) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f370])).
% 0.16/0.39 thf(f370,plain,(
% 0.16/0.39 ( ! [X2 : mu,X1 : $i] : ((((exists_in_world @ X2 @ X1) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ (singleton @ X2) @ X1)) | (~ (in @ X2 @ Y0 @ X1)))) | (~ ((in @ X2 @ Y0 @ X1) | (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ (singleton @ X2) @ X1))))))))) = $true)) )),
% 0.16/0.39 inference(beta_eta_normalization,[],[f369])).
% 0.16/0.39 thf(f369,plain,(
% 0.16/0.39 ( ! [X2 : mu,X1 : $i] : ((((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ X1)) | (~ (in @ Y0 @ Y1 @ X1)))) | (~ ((in @ Y0 @ Y1 @ X1) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ X1)))))))))) @ X2) = $true)) )),
% 0.16/0.39 inference(pi_clausification,[],[f368])).
% 0.16/0.39 thf(f368,plain,(
% 0.16/0.39 ( ! [X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ X1)) | (~ (in @ Y0 @ Y1 @ X1)))) | (~ ((in @ Y0 @ Y1 @ X1) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ X1))))))))))))) )),
% 0.16/0.39 inference(beta_eta_normalization,[],[f367])).
% 0.16/0.39 thf(f367,plain,(
% 0.16/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ (singleton @ Y1) @ Y0)) | (~ (in @ Y1 @ Y2 @ Y0)))) | (~ ((in @ Y1 @ Y2 @ Y0) | (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ (singleton @ Y1) @ Y0)))))))))))) @ X1))) )),
% 0.16/0.39 inference(pi_clausification,[],[f366])).
% 0.16/0.39 thf(f366,plain,(
% 0.16/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ (singleton @ Y1) @ Y0)) | (~ (in @ Y1 @ Y2 @ Y0)))) | (~ ((in @ Y1 @ Y2 @ Y0) | (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ (singleton @ Y1) @ Y0))))))))))))))),
% 0.16/0.39 inference(boolean_simplification,[],[f365])).
% 0.16/0.39 thf(f365,plain,(
% 0.16/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ (singleton @ Y1) @ Y0)) | (~ (in @ Y1 @ Y2 @ Y0)))) | (~ ((~ (~ (in @ Y1 @ Y2 @ Y0))) | (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ (singleton @ Y1) @ Y0))))))))))))))),
% 0.16/0.39 inference(beta_eta_normalization,[],[f250])).
% 0.16/0.39 thf(f250,plain,(
% 0.16/0.39 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y2 @ Y3) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y3 @ Y2))))) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ (in @ Y0 @ Y1)))))))))),
% 0.16/0.39 inference(definition_unfolding,[],[f216,f188,f182,f182,f229,f206])).
% 0.16/0.39 thf(f206,plain,(
% 0.16/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f146])).
% 0.16/0.39 thf(f146,plain,(
% 0.16/0.39 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.39 inference(fool_elimination,[],[f145])).
% 0.16/0.39 thf(f145,plain,(
% 0.16/0.39 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.16/0.39 inference(rectify,[],[f2])).
% 0.16/0.39 thf(f2,axiom,(
% 0.16/0.39 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.16/0.39 thf(f229,plain,(
% 0.16/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.16/0.39 inference(definition_unfolding,[],[f218,f226,f227,f227])).
% 0.16/0.39 thf(f227,plain,(
% 0.16/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.16/0.39 inference(definition_unfolding,[],[f176,f219,f206])).
% 0.16/0.39 thf(f176,plain,(
% 0.16/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.39 inference(cnf_transformation,[],[f65])).
% 0.16/0.39 thf(f65,plain,(
% 0.16/0.39 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.39 inference(fool_elimination,[],[f64])).
% 0.16/0.39 thf(f64,plain,(
% 0.16/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.16/0.39 inference(rectify,[],[f9])).
% 0.16/0.39 thf(f9,axiom,(
% 0.16/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.16/0.39 thf(f226,plain,(
% 0.16/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y2 @ Y4) | (Y3 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.16/0.39 inference(definition_unfolding,[],[f215,f206,f219,f206,f206])).
% 0.16/0.39 thf(f215,plain,(
% 0.16/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f136])).
% 0.16/0.39 thf(f136,plain,(
% 0.16/0.39 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.39 inference(fool_elimination,[],[f135])).
% 0.16/0.39 thf(f135,plain,(
% 0.16/0.39 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.16/0.39 inference(rectify,[],[f8])).
% 0.16/0.39 thf(f8,axiom,(
% 0.16/0.39 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mand)).
% 0.16/0.39 thf(f218,plain,(
% 0.16/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f106])).
% 0.16/0.39 thf(f106,plain,(
% 0.16/0.39 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.16/0.39 inference(fool_elimination,[],[f105])).
% 0.16/0.39 thf(f105,plain,(
% 0.16/0.39 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.16/0.39 inference(rectify,[],[f11])).
% 0.16/0.39 thf(f11,axiom,(
% 0.16/0.39 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mequiv)).
% 0.16/0.39 thf(f216,plain,(
% 0.16/0.39 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))) = $true)),
% 0.16/0.39 inference(cnf_transformation,[],[f79])).
% 0.16/0.39 thf(f79,plain,(
% 0.16/0.39 ((mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))) = $true)),
% 0.16/0.39 inference(fool_elimination,[],[f78])).
% 0.16/0.39 thf(f78,plain,(
% 0.16/0.39 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ (singleton @ X0)) @ (mnot @ (in @ X0 @ X1))))))))),
% 0.16/0.39 inference(rectify,[],[f51])).
% 0.16/0.39 thf(f51,axiom,(
% 0.16/0.39 (mvalid @ (mforall_ind @ (^[X14 : mu] : (mforall_ind @ (^[X15 : mu] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X14) @ X15) @ (singleton @ X14)) @ (mnot @ (in @ X14 @ X15))))))))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l34_zfmisc_1)).
% 0.16/0.39 thf(f608,plain,(
% 0.16/0.39 spl1_8 | spl1_6 | spl1_7),
% 0.16/0.39 inference(avatar_split_clause,[],[f585,f600,f596,f604])).
% 0.16/0.39 thf(f585,plain,(
% 0.16/0.39 ((exists_in_world @ sK5 @ sK4) = $false) | ((in @ sK5 @ sK6 @ sK4) = $false) | ($false = (exists_in_world @ sK6 @ sK4))),
% 0.16/0.39 inference(trivial_inequality_removal,[],[f580])).
% 0.16/0.39 thf(f580,plain,(
% 0.16/0.39 ($true = $false) | ($false = (exists_in_world @ sK6 @ sK4)) | ((in @ sK5 @ sK6 @ sK4) = $false) | ((exists_in_world @ sK5 @ sK4) = $false)),
% 0.16/0.39 inference(superposition,[],[f350,f419])).
% 0.16/0.39 thf(f419,plain,(
% 0.16/0.39 ((qmltpeq @ (set_difference @ (singleton @ sK5) @ sK6) @ empty_set @ sK4) = $false)),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f416])).
% 0.16/0.39 thf(f350,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1)) | ($false = (exists_in_world @ X2 @ X1)) | ($false = (in @ X2 @ X3 @ X1)) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.16/0.39 inference(not_proxy_clausification,[],[f349])).
% 0.16/0.39 thf(f349,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = (~ (in @ X2 @ X3 @ X1))) | ($true = (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1)) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f348])).
% 0.16/0.39 thf(f348,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ((exists_in_world @ X3 @ X1) = $false) | (((~ (in @ X2 @ X3 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1)) = $true)) )),
% 0.16/0.39 inference(not_proxy_clausification,[],[f343])).
% 0.16/0.39 thf(f343,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (((~ ((~ (in @ X2 @ X3 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1))) = $false) | ((exists_in_world @ X3 @ X1) = $false) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f342])).
% 0.16/0.39 thf(f342,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ((exists_in_world @ X3 @ X1) = $false) | ($false = ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1)) | (in @ X2 @ X3 @ X1))) | (~ ((~ (in @ X2 @ X3 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1)))))) )),
% 0.16/0.39 inference(not_proxy_clausification,[],[f341])).
% 0.16/0.39 thf(f341,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ($true = (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1)) | (in @ X2 @ X3 @ X1))) | (~ ((~ (in @ X2 @ X3 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1)))))) | ((exists_in_world @ X3 @ X1) = $false)) )),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f340])).
% 0.16/0.39 thf(f340,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($true = ((exists_in_world @ X3 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1)) | (in @ X2 @ X3 @ X1))) | (~ ((~ (in @ X2 @ X3 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ X2) @ X3) @ empty_set @ X1))))))) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(beta_eta_normalization,[],[f339])).
% 0.16/0.39 thf(f339,plain,(
% 0.16/0.39 ( ! [X2 : mu,X3 : mu,X1 : $i] : (($false = (exists_in_world @ X2 @ X1)) | ($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ empty_set @ X1)) | (in @ X2 @ Y0 @ X1))) | (~ ((~ (in @ X2 @ Y0 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ empty_set @ X1))))))) @ X3))) )),
% 0.16/0.39 inference(pi_clausification,[],[f338])).
% 0.16/0.39 thf(f338,plain,(
% 0.16/0.39 ( ! [X2 : mu,X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ empty_set @ X1)) | (in @ X2 @ Y0 @ X1))) | (~ ((~ (in @ X2 @ Y0 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ empty_set @ X1))))))))) | ($false = (exists_in_world @ X2 @ X1))) )),
% 0.16/0.39 inference(binary_proxy_clausification,[],[f337])).
% 0.16/0.39 thf(f337,plain,(
% 0.16/0.39 ( ! [X2 : mu,X1 : $i] : (($true = ((exists_in_world @ X2 @ X1) => (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ empty_set @ X1)) | (in @ X2 @ Y0 @ X1))) | (~ ((~ (in @ X2 @ Y0 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ X2) @ Y0) @ empty_set @ X1))))))))))) )),
% 0.16/0.39 inference(beta_eta_normalization,[],[f336])).
% 0.16/0.39 thf(f336,plain,(
% 0.16/0.39 ( ! [X2 : mu,X1 : $i] : (($true = ((^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ X1)) | (in @ Y0 @ Y1 @ X1))) | (~ ((~ (in @ Y0 @ Y1 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ X1)))))))))) @ X2))) )),
% 0.16/0.39 inference(pi_clausification,[],[f335])).
% 0.16/0.39 thf(f335,plain,(
% 0.16/0.39 ( ! [X1 : $i] : (($true = (!! @ mu @ (^[Y0 : mu]: ((exists_in_world @ Y0 @ X1) => (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ X1) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ X1)) | (in @ Y0 @ Y1 @ X1))) | (~ ((~ (in @ Y0 @ Y1 @ X1)) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ X1))))))))))))) )),
% 0.16/0.39 inference(beta_eta_normalization,[],[f334])).
% 0.16/0.39 thf(f334,plain,(
% 0.16/0.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ empty_set @ Y0)) | (in @ Y1 @ Y2 @ Y0))) | (~ ((~ (in @ Y1 @ Y2 @ Y0)) | (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ empty_set @ Y0)))))))))))) @ X1))) )),
% 0.16/0.39 inference(pi_clausification,[],[f333])).
% 0.16/0.39 thf(f333,plain,(
% 0.16/0.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ mu @ (^[Y1 : mu]: ((exists_in_world @ Y1 @ Y0) => (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y0) => (~ ((~ ((~ (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ empty_set @ Y0)) | (in @ Y1 @ Y2 @ Y0))) | (~ ((~ (in @ Y1 @ Y2 @ Y0)) | (qmltpeq @ (set_difference @ (singleton @ Y1) @ Y2) @ empty_set @ Y0))))))))))))))),
% 0.16/0.39 inference(beta_eta_normalization,[],[f242])).
% 0.16/0.39 thf(f242,plain,(
% 0.16/0.39 ($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : mu > $i > $o]: ((^[Y1 : $i]: (!! @ mu @ (^[Y2 : mu]: ((exists_in_world @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : mu]: ((^[Y1 : mu > $i > $o]: ((^[Y2 : $i]: (!! @ mu @ (^[Y3 : mu]: ((exists_in_world @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : mu]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y2 @ Y3) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y6 @ Y8) | (Y7 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y3 @ Y2))))) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 0.16/0.39 inference(definition_unfolding,[],[f198,f188,f182,f182,f229])).
% 0.16/0.39 thf(f198,plain,(
% 0.16/0.39 ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 0.16/0.39 inference(cnf_transformation,[],[f73])).
% 0.16/0.39 thf(f73,plain,(
% 0.16/0.39 ($true = (mvalid @ (mforall_ind @ (^[Y0 : mu]: (mforall_ind @ (^[Y1 : mu]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 0.16/0.39 inference(fool_elimination,[],[f72])).
% 0.16/0.39 thf(f72,plain,(
% 0.16/0.39 (mvalid @ (mforall_ind @ (^[X0 : mu] : (mforall_ind @ (^[X1 : mu] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ empty_set) @ (in @ X0 @ X1)))))))),
% 0.16/0.39 inference(rectify,[],[f52])).
% 0.16/0.39 thf(f52,axiom,(
% 0.16/0.39 (mvalid @ (mforall_ind @ (^[X14 : mu] : (mforall_ind @ (^[X15 : mu] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X14) @ X15) @ empty_set) @ (in @ X14 @ X15)))))))),
% 0.16/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1)).
% 0.16/0.39 % SZS output end Proof for theBenchmark
% 0.16/0.39 % (6071)------------------------------
% 0.16/0.39 % (6071)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.39 % (6071)Termination reason: Refutation
% 0.16/0.39
% 0.16/0.39 % (6071)Memory used [KB]: 6396
% 0.16/0.39 % (6071)Time elapsed: 0.051 s
% 0.16/0.39 % (6071)Instructions burned: 91 (million)
% 0.16/0.39 % (6071)------------------------------
% 0.16/0.39 % (6071)------------------------------
% 0.16/0.39 % (6070)Success in time 0.047 s
% 0.16/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------