TSTP Solution File: SYO412^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO412^1 : 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 : n012.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 09:04:20 EDT 2024
% Result : Theorem 0.14s 0.40s
% Output : Refutation 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO412^1 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14 % 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 : n012.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 10:58:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.38 % (26094)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.14/0.38 % (26096)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)
% 0.14/0.38 % (26095)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)
% 0.14/0.38 % (26098)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)
% 0.14/0.38 % (26097)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.14/0.38 % (26099)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)
% 0.14/0.38 % (26100)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.14/0.38 % (26101)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)
% 0.14/0.38 % (26098)Instruction limit reached!
% 0.14/0.38 % (26098)------------------------------
% 0.14/0.38 % (26098)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26098)Termination reason: Unknown
% 0.14/0.38 % (26098)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (26098)Memory used [KB]: 1023
% 0.14/0.38 % (26098)Time elapsed: 0.003 s
% 0.14/0.38 % (26098)Instructions burned: 2 (million)
% 0.14/0.38 % (26098)------------------------------
% 0.14/0.38 % (26098)------------------------------
% 0.14/0.38 % (26097)Instruction limit reached!
% 0.14/0.38 % (26097)------------------------------
% 0.14/0.38 % (26097)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26097)Termination reason: Unknown
% 0.14/0.38 % (26097)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (26097)Memory used [KB]: 1023
% 0.14/0.38 % (26097)Time elapsed: 0.004 s
% 0.14/0.38 % (26097)Instructions burned: 3 (million)
% 0.14/0.38 % (26097)------------------------------
% 0.14/0.38 % (26097)------------------------------
% 0.14/0.38 % (26101)Instruction limit reached!
% 0.14/0.38 % (26101)------------------------------
% 0.14/0.38 % (26101)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26101)Termination reason: Unknown
% 0.14/0.38 % (26101)Termination phase: shuffling
% 0.14/0.38
% 0.14/0.38 % (26101)Memory used [KB]: 1023
% 0.14/0.38 % (26101)Time elapsed: 0.004 s
% 0.14/0.38 % (26101)Instructions burned: 3 (million)
% 0.14/0.38 % (26101)------------------------------
% 0.14/0.38 % (26101)------------------------------
% 0.14/0.38 % (26095)Instruction limit reached!
% 0.14/0.38 % (26095)------------------------------
% 0.14/0.38 % (26095)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26095)Termination reason: Unknown
% 0.14/0.38 % (26095)Termination phase: Property scanning
% 0.14/0.38
% 0.14/0.38 % (26095)Memory used [KB]: 1023
% 0.14/0.38 % (26095)Time elapsed: 0.004 s
% 0.14/0.38 % (26095)Instructions burned: 5 (million)
% 0.14/0.38 % (26095)------------------------------
% 0.14/0.38 % (26095)------------------------------
% 0.14/0.38 % (26099)Refutation not found, incomplete strategy
% 0.14/0.38 % (26099)------------------------------
% 0.14/0.38 % (26099)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.38 % (26099)Termination reason: Refutation not found, incomplete strategy
% 0.14/0.38
% 0.14/0.38
% 0.14/0.38 % (26099)Memory used [KB]: 5628
% 0.14/0.38 % (26099)Time elapsed: 0.007 s
% 0.14/0.38 % (26099)Instructions burned: 7 (million)
% 0.14/0.38 % (26099)------------------------------
% 0.14/0.38 % (26099)------------------------------
% 0.14/0.39 % (26100)Instruction limit reached!
% 0.14/0.39 % (26100)------------------------------
% 0.14/0.39 % (26100)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (26100)Termination reason: Unknown
% 0.14/0.39 % (26100)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (26100)Memory used [KB]: 5628
% 0.14/0.39 % (26100)Time elapsed: 0.012 s
% 0.14/0.39 % (26100)Instructions burned: 19 (million)
% 0.14/0.39 % (26100)------------------------------
% 0.14/0.39 % (26100)------------------------------
% 0.14/0.39 % (26094)First to succeed.
% 0.14/0.39 % (26096)Instruction limit reached!
% 0.14/0.39 % (26096)------------------------------
% 0.14/0.39 % (26096)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.39 % (26096)Termination reason: Unknown
% 0.14/0.39 % (26096)Termination phase: Saturation
% 0.14/0.39
% 0.14/0.39 % (26096)Memory used [KB]: 5756
% 0.14/0.39 % (26096)Time elapsed: 0.018 s
% 0.14/0.39 % (26096)Instructions burned: 27 (million)
% 0.14/0.39 % (26096)------------------------------
% 0.14/0.39 % (26096)------------------------------
% 0.14/0.39 % (26102)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 % (26103)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 % (26104)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 % (26105)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)
% 0.14/0.40 % (26104)Instruction limit reached!
% 0.14/0.40 % (26104)------------------------------
% 0.14/0.40 % (26104)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (26104)Termination reason: Unknown
% 0.14/0.40 % (26104)Termination phase: shuffling
% 0.14/0.40
% 0.14/0.40 % (26104)Memory used [KB]: 1023
% 0.14/0.40 % (26104)Time elapsed: 0.004 s
% 0.14/0.40 % (26104)Instructions burned: 4 (million)
% 0.14/0.40 % (26104)------------------------------
% 0.14/0.40 % (26104)------------------------------
% 0.14/0.40 % (26106)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.14/0.40 % (26094)Refutation found. Thanks to Tanya!
% 0.14/0.40 % SZS status Theorem for theBenchmark
% 0.14/0.40 % SZS output start Proof for theBenchmark
% 0.14/0.40 thf(type_def_5, type, mu: $tType).
% 0.14/0.40 thf(func_def_0, type, mu: $tType).
% 0.14/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.14/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.14/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.14/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.14/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.14/0.40 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.14/0.40 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.14/0.40 thf(func_def_36, type, p: $i > $o).
% 0.14/0.40 thf(func_def_37, type, q: $i > $o).
% 0.14/0.40 thf(f494,plain,(
% 0.14/0.40 $false),
% 0.14/0.40 inference(avatar_sat_refutation,[],[f328,f334,f423,f428,f433,f434,f439,f440,f441,f442,f456,f463,f478,f493])).
% 0.14/0.40 thf(f493,plain,(
% 0.14/0.40 ~spl0_2 | ~spl0_19 | ~spl0_24),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f492])).
% 0.14/0.40 thf(f492,plain,(
% 0.14/0.40 $false | (~spl0_2 | ~spl0_19 | ~spl0_24)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f488])).
% 0.14/0.40 thf(f488,plain,(
% 0.14/0.40 ($true = $false) | (~spl0_2 | ~spl0_19 | ~spl0_24)),
% 0.14/0.40 inference(superposition,[],[f485,f414])).
% 0.14/0.40 thf(f414,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ~spl0_19),
% 0.14/0.40 inference(avatar_component_clause,[],[f412])).
% 0.14/0.40 thf(f412,plain,(
% 0.14/0.40 spl0_19 <=> ($false = (p @ sK3))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_19])])).
% 0.14/0.40 thf(f485,plain,(
% 0.14/0.40 ($true = (p @ sK3)) | (~spl0_2 | ~spl0_24)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f480])).
% 0.14/0.40 thf(f480,plain,(
% 0.14/0.40 ($true = $false) | ($true = (p @ sK3)) | (~spl0_2 | ~spl0_24)),
% 0.14/0.40 inference(superposition,[],[f438,f331])).
% 0.14/0.40 thf(f331,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($true = (p @ X1))) ) | ~spl0_2),
% 0.14/0.40 inference(avatar_component_clause,[],[f330])).
% 0.14/0.40 thf(f330,plain,(
% 0.14/0.40 spl0_2 <=> ! [X1] : (((rel_k @ sK1 @ X1) = $false) | ($true = (p @ X1)))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.14/0.40 thf(f438,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK3) = $true) | ~spl0_24),
% 0.14/0.40 inference(avatar_component_clause,[],[f436])).
% 0.14/0.40 thf(f436,plain,(
% 0.14/0.40 spl0_24 <=> ((rel_k @ sK1 @ sK3) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_24])])).
% 0.14/0.40 thf(f478,plain,(
% 0.14/0.40 ~spl0_1 | ~spl0_18 | ~spl0_23),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f477])).
% 0.14/0.40 thf(f477,plain,(
% 0.14/0.40 $false | (~spl0_1 | ~spl0_18 | ~spl0_23)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f474])).
% 0.14/0.40 thf(f474,plain,(
% 0.14/0.40 ($true = $false) | (~spl0_1 | ~spl0_18 | ~spl0_23)),
% 0.14/0.40 inference(superposition,[],[f410,f472])).
% 0.14/0.40 thf(f472,plain,(
% 0.14/0.40 ((q @ sK2) = $false) | (~spl0_1 | ~spl0_23)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f468])).
% 0.14/0.40 thf(f468,plain,(
% 0.14/0.40 ($true = $false) | ((q @ sK2) = $false) | (~spl0_1 | ~spl0_23)),
% 0.14/0.40 inference(superposition,[],[f327,f432])).
% 0.14/0.40 thf(f432,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK2) = $true) | ~spl0_23),
% 0.14/0.40 inference(avatar_component_clause,[],[f430])).
% 0.14/0.40 thf(f430,plain,(
% 0.14/0.40 spl0_23 <=> ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_23])])).
% 0.14/0.40 thf(f327,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false)) ) | ~spl0_1),
% 0.14/0.40 inference(avatar_component_clause,[],[f326])).
% 0.14/0.40 thf(f326,plain,(
% 0.14/0.40 spl0_1 <=> ! [X1] : (((q @ X1) = $false) | ((rel_k @ sK1 @ X1) = $false))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.14/0.40 thf(f410,plain,(
% 0.14/0.40 ((q @ sK2) = $true) | ~spl0_18),
% 0.14/0.40 inference(avatar_component_clause,[],[f408])).
% 0.14/0.40 thf(f408,plain,(
% 0.14/0.40 spl0_18 <=> ((q @ sK2) = $true)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_18])])).
% 0.14/0.40 thf(f463,plain,(
% 0.14/0.40 ~spl0_1 | ~spl0_21 | ~spl0_22),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f462])).
% 0.14/0.40 thf(f462,plain,(
% 0.14/0.40 $false | (~spl0_1 | ~spl0_21 | ~spl0_22)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f458])).
% 0.14/0.40 thf(f458,plain,(
% 0.14/0.40 ($true = $false) | (~spl0_1 | ~spl0_21 | ~spl0_22)),
% 0.14/0.40 inference(superposition,[],[f422,f446])).
% 0.14/0.40 thf(f446,plain,(
% 0.14/0.40 ($false = (q @ sK4)) | (~spl0_1 | ~spl0_22)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f444])).
% 0.14/0.40 thf(f444,plain,(
% 0.14/0.40 ($true = $false) | ($false = (q @ sK4)) | (~spl0_1 | ~spl0_22)),
% 0.14/0.40 inference(superposition,[],[f327,f427])).
% 0.14/0.40 thf(f427,plain,(
% 0.14/0.40 ($true = (rel_k @ sK1 @ sK4)) | ~spl0_22),
% 0.14/0.40 inference(avatar_component_clause,[],[f425])).
% 0.14/0.40 thf(f425,plain,(
% 0.14/0.40 spl0_22 <=> ($true = (rel_k @ sK1 @ sK4))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_22])])).
% 0.14/0.40 thf(f422,plain,(
% 0.14/0.40 ($true = (q @ sK4)) | ~spl0_21),
% 0.14/0.40 inference(avatar_component_clause,[],[f420])).
% 0.14/0.40 thf(f420,plain,(
% 0.14/0.40 spl0_21 <=> ($true = (q @ sK4))),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_21])])).
% 0.14/0.40 thf(f456,plain,(
% 0.14/0.40 ~spl0_2 | ~spl0_20 | ~spl0_22),
% 0.14/0.40 inference(avatar_contradiction_clause,[],[f455])).
% 0.14/0.40 thf(f455,plain,(
% 0.14/0.40 $false | (~spl0_2 | ~spl0_20 | ~spl0_22)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f451])).
% 0.14/0.40 thf(f451,plain,(
% 0.14/0.40 ($true = $false) | (~spl0_2 | ~spl0_20 | ~spl0_22)),
% 0.14/0.40 inference(superposition,[],[f450,f418])).
% 0.14/0.40 thf(f418,plain,(
% 0.14/0.40 ((p @ sK4) = $false) | ~spl0_20),
% 0.14/0.40 inference(avatar_component_clause,[],[f416])).
% 0.14/0.40 thf(f416,plain,(
% 0.14/0.40 spl0_20 <=> ((p @ sK4) = $false)),
% 0.14/0.40 introduced(avatar_definition,[new_symbols(naming,[spl0_20])])).
% 0.14/0.40 thf(f450,plain,(
% 0.14/0.40 ((p @ sK4) = $true) | (~spl0_2 | ~spl0_22)),
% 0.14/0.40 inference(trivial_inequality_removal,[],[f447])).
% 0.14/0.40 thf(f447,plain,(
% 0.14/0.40 ((p @ sK4) = $true) | ($true = $false) | (~spl0_2 | ~spl0_22)),
% 0.14/0.40 inference(superposition,[],[f331,f427])).
% 0.14/0.40 thf(f442,plain,(
% 0.14/0.40 spl0_22 | spl0_23 | spl0_24),
% 0.14/0.40 inference(avatar_split_clause,[],[f177,f436,f430,f425])).
% 0.14/0.40 thf(f177,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK3) = $true) | ($true = (rel_k @ sK1 @ sK4)) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f176])).
% 0.14/0.40 thf(f176,plain,(
% 0.14/0.40 ($true = (rel_k @ sK1 @ sK4)) | ((rel_k @ sK1 @ sK3) = $true) | ($false = (~ (rel_k @ sK1 @ sK2)))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f175])).
% 0.14/0.40 thf(f175,plain,(
% 0.14/0.40 ((~ (rel_k @ sK1 @ sK4)) = $false) | ((rel_k @ sK1 @ sK3) = $true) | ($false = (~ (rel_k @ sK1 @ sK2)))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f173])).
% 0.14/0.40 thf(f173,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false) | ((rel_k @ sK1 @ sK3) = $true) | ((~ (rel_k @ sK1 @ sK4)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f171])).
% 0.14/0.40 thf(f171,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK4)) | (~ ((~ (p @ sK4)) | (q @ sK4)))) = $false) | ((rel_k @ sK1 @ sK3) = $true) | (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f170])).
% 0.14/0.40 thf(f170,plain,(
% 0.14/0.40 ((~ (rel_k @ sK1 @ sK3)) = $false) | (((~ (rel_k @ sK1 @ sK4)) | (~ ((~ (p @ sK4)) | (q @ sK4)))) = $false) | (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f168])).
% 0.14/0.40 thf(f168,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK3)) | (p @ sK3)) = $false) | (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false) | (((~ (rel_k @ sK1 @ sK4)) | (~ ((~ (p @ sK4)) | (q @ sK4)))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f167])).
% 0.14/0.40 thf(f167,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK3)) | (p @ sK3)) = $false) | ($false = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0))))) @ sK4)) | (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f166])).
% 0.14/0.40 thf(f166,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $false) | (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false) | (((~ (rel_k @ sK1 @ sK3)) | (p @ sK3)) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f165])).
% 0.14/0.40 thf(f165,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $false) | (((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))) @ sK3) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f164])).
% 0.14/0.40 thf(f164,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0)))) = $false) | (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f163])).
% 0.14/0.40 thf(f163,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0)))) = $false) | (((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))) @ sK2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f162])).
% 0.14/0.40 thf(f162,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0)))) = $false)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f161])).
% 0.14/0.40 thf(f161,plain,(
% 0.14/0.40 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0)))) = $false)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f160])).
% 0.14/0.40 thf(f160,plain,(
% 0.14/0.40 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0)))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f159])).
% 0.14/0.40 thf(f159,plain,(
% 0.14/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f157])).
% 0.14/0.40 thf(f157,plain,(
% 0.14/0.40 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f156])).
% 0.14/0.40 thf(f156,plain,(
% 0.14/0.40 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) = $false) | (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) = $false)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f155])).
% 0.14/0.40 thf(f155,plain,(
% 0.14/0.40 ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))))) = $true) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f153])).
% 0.14/0.40 thf(f153,plain,(
% 0.14/0.40 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))))) = $false) | ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f152])).
% 0.14/0.40 thf(f152,plain,(
% 0.14/0.40 ($true = (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))))))) | ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))))) = $true)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f151])).
% 0.14/0.40 thf(f151,plain,(
% 0.14/0.40 ($true = ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))))))))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f150])).
% 0.14/0.40 thf(f150,plain,(
% 0.14/0.40 ((~ ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0))))))))))) = $false)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f149])).
% 0.14/0.40 thf(f149,plain,(
% 0.14/0.40 (((^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (q @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (q @ Y1)))))))))))) @ sK1) = $false)),
% 0.14/0.40 inference(sigma_clausification,[],[f148])).
% 0.14/0.40 thf(f148,plain,(
% 0.14/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (~ ((~ ((!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (q @ Y1)))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (q @ Y1))))))))))))))),
% 0.14/0.40 inference(boolean_simplification,[],[f147])).
% 0.14/0.40 thf(f147,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (q @ Y1)))))))) | ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1))))))))) | (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (p @ Y1))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ (q @ Y1)))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (rel_k @ Y0 @ Y1)) | (~ ((~ (p @ Y1)) | (q @ Y1))))))))))))) != $true)),
% 0.14/0.40 inference(beta_eta_normalization,[],[f146])).
% 0.14/0.40 thf(f146,plain,(
% 0.14/0.40 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y4 @ Y6) | (Y5 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[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)))) @ p @ q)) @ ((^[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)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q)))) != $true)),
% 0.14/0.40 inference(definition_unfolding,[],[f115,f102,f139,f145,f137,f137,f125,f145])).
% 0.14/0.40 thf(f125,plain,(
% 0.14/0.40 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f71])).
% 0.14/0.40 thf(f71,plain,(
% 0.14/0.40 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((~ (rel_k @ Y1 @ Y2)) | (Y0 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f70])).
% 0.14/0.40 thf(f70,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((X0 @ X2) | ~(rel_k @ X1 @ X2)))) = mbox_k)),
% 0.14/0.40 inference(rectify,[],[f32])).
% 0.14/0.40 thf(f32,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X2 : $i] : (! [X7] : ((X3 @ X7) | ~(rel_k @ X2 @ X7)))) = mbox_k)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_k)).
% 0.14/0.40 thf(f137,plain,(
% 0.14/0.40 (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)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f114,f113,f129])).
% 0.14/0.40 thf(f129,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f100])).
% 0.14/0.40 thf(f100,plain,(
% 0.14/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.14/0.40 inference(fool_elimination,[],[f99])).
% 0.14/0.40 thf(f99,plain,(
% 0.14/0.40 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f3])).
% 0.14/0.40 thf(f3,axiom,(
% 0.14/0.40 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.14/0.40 thf(f113,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f81])).
% 0.14/0.40 thf(f81,plain,(
% 0.14/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.14/0.40 inference(fool_elimination,[],[f80])).
% 0.14/0.40 thf(f80,plain,(
% 0.14/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X1 @ X2) | (X0 @ X2))))),
% 0.14/0.40 inference(rectify,[],[f4])).
% 0.14/0.40 thf(f4,axiom,(
% 0.14/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X4 @ X2) | (X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.14/0.40 thf(f114,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f77])).
% 0.14/0.40 thf(f77,plain,(
% 0.14/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f76])).
% 0.14/0.40 thf(f76,plain,(
% 0.14/0.40 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.14/0.40 inference(rectify,[],[f6])).
% 0.14/0.40 thf(f6,axiom,(
% 0.14/0.40 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.14/0.40 thf(f145,plain,(
% 0.14/0.40 (mdia_k = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((~ (rel_k @ Y2 @ Y3)) | (Y1 @ Y3))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.14/0.40 inference(definition_unfolding,[],[f126,f129,f125,f129])).
% 0.14/0.40 thf(f126,plain,(
% 0.14/0.40 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f38])).
% 0.14/0.40 thf(f38,plain,(
% 0.14/0.40 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.14/0.40 inference(fool_elimination,[],[f37])).
% 0.14/0.40 thf(f37,plain,(
% 0.14/0.40 ((^[X0 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X0)))) = mdia_k)),
% 0.14/0.40 inference(rectify,[],[f33])).
% 0.14/0.40 thf(f33,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X3)))) = mdia_k)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_k)).
% 0.14/0.40 thf(f139,plain,(
% 0.14/0.40 (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))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f128,f136,f137,f137])).
% 0.14/0.40 thf(f136,plain,(
% 0.14/0.40 (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)))))))),
% 0.14/0.40 inference(definition_unfolding,[],[f130,f129,f113,f129,f129])).
% 0.14/0.40 thf(f130,plain,(
% 0.14/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f73])).
% 0.14/0.40 thf(f73,plain,(
% 0.14/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.14/0.40 inference(fool_elimination,[],[f72])).
% 0.14/0.40 thf(f72,plain,(
% 0.14/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.14/0.40 inference(rectify,[],[f5])).
% 0.14/0.40 thf(f5,axiom,(
% 0.14/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.14/0.40 thf(f128,plain,(
% 0.14/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.40 inference(cnf_transformation,[],[f59])).
% 0.14/0.40 thf(f59,plain,(
% 0.14/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.14/0.40 inference(fool_elimination,[],[f58])).
% 0.14/0.40 thf(f58,plain,(
% 0.14/0.40 (mequiv = (^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))))),
% 0.14/0.40 inference(rectify,[],[f8])).
% 0.14/0.40 thf(f8,axiom,(
% 0.14/0.40 (mequiv = (^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.14/0.40 thf(f102,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(cnf_transformation,[],[f69])).
% 0.14/0.40 thf(f69,plain,(
% 0.14/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.14/0.40 inference(fool_elimination,[],[f68])).
% 0.14/0.40 thf(f68,plain,(
% 0.14/0.40 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.14/0.40 inference(rectify,[],[f28])).
% 0.14/0.40 thf(f28,axiom,(
% 0.14/0.40 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.14/0.40 thf(f115,plain,(
% 0.14/0.40 ((mvalid @ (mequiv @ (mdia_k @ (mimplies @ p @ q)) @ (mimplies @ (mbox_k @ p) @ (mdia_k @ q)))) != $true)),
% 0.14/0.40 inference(cnf_transformation,[],[f101])).
% 0.14/0.40 thf(f101,plain,(
% 0.14/0.40 ((mvalid @ (mequiv @ (mdia_k @ (mimplies @ p @ q)) @ (mimplies @ (mbox_k @ p) @ (mdia_k @ q)))) != $true)),
% 0.14/0.40 inference(flattening,[],[f91])).
% 0.14/0.40 thf(f91,plain,(
% 0.14/0.40 ~((mvalid @ (mequiv @ (mdia_k @ (mimplies @ p @ q)) @ (mimplies @ (mbox_k @ p) @ (mdia_k @ q)))) = $true)),
% 0.14/0.40 inference(fool_elimination,[],[f90])).
% 0.14/0.40 thf(f90,plain,(
% 0.14/0.40 ~(mvalid @ (mequiv @ (mdia_k @ (mimplies @ p @ q)) @ (mimplies @ (mbox_k @ p) @ (mdia_k @ q))))),
% 0.14/0.40 inference(rectify,[],[f35])).
% 0.14/0.40 thf(f35,negated_conjecture,(
% 0.14/0.40 ~(mvalid @ (mequiv @ (mdia_k @ (mimplies @ p @ q)) @ (mimplies @ (mbox_k @ p) @ (mdia_k @ q))))),
% 0.14/0.40 inference(negated_conjecture,[],[f34])).
% 0.14/0.40 thf(f34,conjecture,(
% 0.14/0.40 (mvalid @ (mequiv @ (mdia_k @ (mimplies @ p @ q)) @ (mimplies @ (mbox_k @ p) @ (mdia_k @ q))))),
% 0.14/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.14/0.40 thf(f441,plain,(
% 0.14/0.40 spl0_18 | spl0_24 | spl0_22),
% 0.14/0.40 inference(avatar_split_clause,[],[f179,f425,f436,f408])).
% 0.14/0.40 thf(f179,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK3) = $true) | ($true = (rel_k @ sK1 @ sK4)) | ((q @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f178])).
% 0.14/0.40 thf(f178,plain,(
% 0.14/0.40 ((q @ sK2) = $true) | ((rel_k @ sK1 @ sK3) = $true) | ((~ (rel_k @ sK1 @ sK4)) = $false)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f174])).
% 0.14/0.40 thf(f174,plain,(
% 0.14/0.40 ((~ (q @ sK2)) = $false) | ((~ (rel_k @ sK1 @ sK4)) = $false) | ((rel_k @ sK1 @ sK3) = $true)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f173])).
% 0.14/0.40 thf(f440,plain,(
% 0.14/0.40 spl0_23 | spl0_20 | spl0_21 | spl0_24),
% 0.14/0.40 inference(avatar_split_clause,[],[f185,f436,f420,f416,f430])).
% 0.14/0.40 thf(f185,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK3) = $true) | ((rel_k @ sK1 @ sK2) = $true) | ((p @ sK4) = $false) | ($true = (q @ sK4))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f184])).
% 0.14/0.40 thf(f184,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK2) = $true) | ($true = (q @ sK4)) | ((rel_k @ sK1 @ sK3) = $true) | ($true = (~ (p @ sK4)))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f183])).
% 0.14/0.40 thf(f183,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK3) = $true) | ((rel_k @ sK1 @ sK2) = $true) | (((~ (p @ sK4)) | (q @ sK4)) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f182])).
% 0.14/0.40 thf(f182,plain,(
% 0.14/0.40 ((~ ((~ (p @ sK4)) | (q @ sK4))) = $false) | ((rel_k @ sK1 @ sK3) = $true) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f181])).
% 0.14/0.40 thf(f181,plain,(
% 0.14/0.40 ($false = (~ (rel_k @ sK1 @ sK2))) | ((~ ((~ (p @ sK4)) | (q @ sK4))) = $false) | ((rel_k @ sK1 @ sK3) = $true)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.40 thf(f172,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false) | ((~ ((~ (p @ sK4)) | (q @ sK4))) = $false) | ((rel_k @ sK1 @ sK3) = $true)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f171])).
% 0.14/0.40 thf(f439,plain,(
% 0.14/0.40 spl0_20 | spl0_18 | spl0_24 | spl0_21),
% 0.14/0.40 inference(avatar_split_clause,[],[f189,f420,f436,f408,f416])).
% 0.14/0.40 thf(f189,plain,(
% 0.14/0.40 ((p @ sK4) = $false) | ($true = (q @ sK4)) | ((q @ sK2) = $true) | ((rel_k @ sK1 @ sK3) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f188])).
% 0.14/0.40 thf(f188,plain,(
% 0.14/0.40 ((q @ sK2) = $true) | ((rel_k @ sK1 @ sK3) = $true) | ($true = (~ (p @ sK4))) | ($true = (q @ sK4))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f187])).
% 0.14/0.40 thf(f187,plain,(
% 0.14/0.40 (((~ (p @ sK4)) | (q @ sK4)) = $true) | ((rel_k @ sK1 @ sK3) = $true) | ((q @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f186])).
% 0.14/0.40 thf(f186,plain,(
% 0.14/0.40 ((q @ sK2) = $true) | ((rel_k @ sK1 @ sK3) = $true) | ((~ ((~ (p @ sK4)) | (q @ sK4))) = $false)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f180])).
% 0.14/0.40 thf(f180,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK3) = $true) | ((~ (q @ sK2)) = $false) | ((~ ((~ (p @ sK4)) | (q @ sK4))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f172])).
% 0.14/0.40 thf(f434,plain,(
% 0.14/0.40 spl0_22 | spl0_19 | spl0_23),
% 0.14/0.40 inference(avatar_split_clause,[],[f195,f430,f412,f425])).
% 0.14/0.40 thf(f195,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK2) = $true) | ($false = (p @ sK3)) | ($true = (rel_k @ sK1 @ sK4))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f194])).
% 0.14/0.40 thf(f194,plain,(
% 0.14/0.40 ((rel_k @ sK1 @ sK2) = $true) | ($false = (p @ sK3)) | ((~ (rel_k @ sK1 @ sK4)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f192])).
% 0.14/0.40 thf(f192,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK4)) | (~ ((~ (p @ sK4)) | (q @ sK4)))) = $false) | ($false = (p @ sK3)) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f191])).
% 0.14/0.40 thf(f191,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ($false = (~ (rel_k @ sK1 @ sK2))) | (((~ (rel_k @ sK1 @ sK4)) | (~ ((~ (p @ sK4)) | (q @ sK4)))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f169])).
% 0.14/0.40 thf(f169,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK2)) | (~ (q @ sK2))) = $false) | ($false = (p @ sK3)) | (((~ (rel_k @ sK1 @ sK4)) | (~ ((~ (p @ sK4)) | (q @ sK4)))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f168])).
% 0.14/0.40 thf(f433,plain,(
% 0.14/0.40 spl0_19 | spl0_23 | spl0_21 | spl0_20),
% 0.14/0.40 inference(avatar_split_clause,[],[f198,f416,f420,f430,f412])).
% 0.14/0.40 thf(f198,plain,(
% 0.14/0.40 ((p @ sK4) = $false) | ($false = (p @ sK3)) | ($true = (q @ sK4)) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f197])).
% 0.14/0.40 thf(f197,plain,(
% 0.14/0.40 ($true = (q @ sK4)) | ($true = (~ (p @ sK4))) | ($false = (p @ sK3)) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f196])).
% 0.14/0.40 thf(f196,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | (((~ (p @ sK4)) | (q @ sK4)) = $true) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f193])).
% 0.14/0.40 thf(f193,plain,(
% 0.14/0.40 ((~ ((~ (p @ sK4)) | (q @ sK4))) = $false) | ($false = (p @ sK3)) | ((rel_k @ sK1 @ sK2) = $true)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f192])).
% 0.14/0.40 thf(f428,plain,(
% 0.14/0.40 spl0_18 | spl0_19 | spl0_22),
% 0.14/0.40 inference(avatar_split_clause,[],[f202,f425,f412,f408])).
% 0.14/0.40 thf(f202,plain,(
% 0.14/0.40 ((q @ sK2) = $true) | ($true = (rel_k @ sK1 @ sK4)) | ($false = (p @ sK3))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f201])).
% 0.14/0.40 thf(f201,plain,(
% 0.14/0.40 ((~ (rel_k @ sK1 @ sK4)) = $false) | ((q @ sK2) = $true) | ($false = (p @ sK3))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f200])).
% 0.14/0.40 thf(f200,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | ((~ (q @ sK2)) = $false) | ((~ (rel_k @ sK1 @ sK4)) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f190])).
% 0.14/0.40 thf(f190,plain,(
% 0.14/0.40 (((~ (rel_k @ sK1 @ sK4)) | (~ ((~ (p @ sK4)) | (q @ sK4)))) = $false) | ((~ (q @ sK2)) = $false) | ($false = (p @ sK3))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f169])).
% 0.14/0.40 thf(f423,plain,(
% 0.14/0.40 spl0_18 | spl0_19 | spl0_20 | spl0_21),
% 0.14/0.40 inference(avatar_split_clause,[],[f206,f420,f416,f412,f408])).
% 0.14/0.40 thf(f206,plain,(
% 0.14/0.40 ((p @ sK4) = $false) | ($false = (p @ sK3)) | ((q @ sK2) = $true) | ($true = (q @ sK4))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f205])).
% 0.14/0.40 thf(f205,plain,(
% 0.14/0.40 ($true = (~ (p @ sK4))) | ($true = (q @ sK4)) | ($false = (p @ sK3)) | ((q @ sK2) = $true)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f204])).
% 0.14/0.40 thf(f204,plain,(
% 0.14/0.40 ($false = (p @ sK3)) | (((~ (p @ sK4)) | (q @ sK4)) = $true) | ((q @ sK2) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f203])).
% 0.14/0.40 thf(f203,plain,(
% 0.14/0.40 ((q @ sK2) = $true) | ((~ ((~ (p @ sK4)) | (q @ sK4))) = $false) | ($false = (p @ sK3))),
% 0.14/0.40 inference(not_proxy_clausification,[],[f199])).
% 0.14/0.40 thf(f199,plain,(
% 0.14/0.40 ((~ (q @ sK2)) = $false) | ((~ ((~ (p @ sK4)) | (q @ sK4))) = $false) | ($false = (p @ sK3))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f190])).
% 0.14/0.40 thf(f334,plain,(
% 0.14/0.40 spl0_2 | spl0_2),
% 0.14/0.40 inference(avatar_split_clause,[],[f310,f330,f330])).
% 0.14/0.40 thf(f310,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((p @ X2) = $true) | ((rel_k @ sK1 @ X2) = $false) | ((rel_k @ sK1 @ X1) = $false) | ($true = (p @ X1))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f309])).
% 0.14/0.40 thf(f309,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X2) = $false) | ((~ (p @ X1)) = $false) | ((p @ X2) = $true) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f307])).
% 0.14/0.40 thf(f307,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X2) = $false) | ((p @ X2) = $true) | ((rel_k @ sK1 @ X1) = $false) | ($false = ((~ (p @ X1)) | (q @ X1)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f306])).
% 0.14/0.40 thf(f306,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((rel_k @ sK1 @ X2) = $false) | ($true = (~ ((~ (p @ X1)) | (q @ X1)))) | ((p @ X2) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f305])).
% 0.14/0.40 thf(f305,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((p @ X2) = $true) | ($true = (~ (rel_k @ sK1 @ X2))) | ($true = (~ ((~ (p @ X1)) | (q @ X1))))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f304])).
% 0.14/0.40 thf(f304,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (rel_k @ sK1 @ X2)) | (p @ X2))) | ($true = (~ ((~ (p @ X1)) | (q @ X1)))) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f303])).
% 0.14/0.40 thf(f303,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ ((~ (p @ X1)) | (q @ X1)))) | ($true = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))) @ X2)) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(pi_clausification,[],[f302])).
% 0.14/0.40 thf(f302,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | ($true = (~ ((~ (p @ X1)) | (q @ X1)))) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f301])).
% 0.14/0.40 thf(f301,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) = $false) | ($true = (~ ((~ (p @ X1)) | (q @ X1)))) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f300])).
% 0.14/0.40 thf(f300,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (rel_k @ sK1 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) = $false) | ($true = (~ ((~ (p @ X1)) | (q @ X1))))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f299])).
% 0.14/0.40 thf(f299,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((~ (rel_k @ sK1 @ X1)) | (~ ((~ (p @ X1)) | (q @ X1))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) = $false)) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f298])).
% 0.14/0.40 thf(f298,plain,(
% 0.14/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0))))) @ X1) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) = $false)) )),
% 0.14/0.40 inference(pi_clausification,[],[f297])).
% 0.14/0.40 thf(f297,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f295])).
% 0.14/0.40 thf(f295,plain,(
% 0.14/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $true)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f269])).
% 0.14/0.40 thf(f269,plain,(
% 0.14/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0))))))) = $false) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f268])).
% 0.14/0.40 thf(f268,plain,(
% 0.14/0.40 (((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0))))))) = $false)),
% 0.14/0.40 inference(not_proxy_clausification,[],[f154])).
% 0.14/0.40 thf(f154,plain,(
% 0.14/0.40 ((~ ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (p @ Y0))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0))))))) = $false)),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f153])).
% 0.14/0.40 thf(f328,plain,(
% 0.14/0.40 spl0_1 | spl0_1),
% 0.14/0.40 inference(avatar_split_clause,[],[f322,f326,f326])).
% 0.14/0.40 thf(f322,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((q @ X1) = $false) | ((rel_k @ sK1 @ X1) = $false) | ((q @ X2) = $false) | ((rel_k @ sK1 @ X2) = $false)) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f321])).
% 0.14/0.40 thf(f321,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X2) = $false) | ((rel_k @ sK1 @ X2) = $false) | ($false = ((~ (p @ X1)) | (q @ X1)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f320])).
% 0.14/0.40 thf(f320,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (q @ X2))) | ((rel_k @ sK1 @ X1) = $false) | ((rel_k @ sK1 @ X2) = $false) | ($false = ((~ (p @ X1)) | (q @ X1)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f319])).
% 0.14/0.40 thf(f319,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($true = (~ (rel_k @ sK1 @ X2))) | ($true = (~ (q @ X2))) | ($false = ((~ (p @ X1)) | (q @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f318])).
% 0.14/0.40 thf(f318,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | (((~ (rel_k @ sK1 @ X2)) | (~ (q @ X2))) = $true) | ($false = ((~ (p @ X1)) | (q @ X1)))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f317])).
% 0.14/0.40 thf(f317,plain,(
% 0.14/0.40 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($false = ((~ (p @ X1)) | (q @ X1))) | ($true = ((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))) @ X2))) )),
% 0.14/0.40 inference(pi_clausification,[],[f316])).
% 0.14/0.40 thf(f316,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))) = $true) | ($false = ((~ (p @ X1)) | (q @ X1)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f315])).
% 0.14/0.40 thf(f315,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ (rel_k @ sK1 @ X1))) | ($false = ((~ (p @ X1)) | (q @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))) = $true)) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f314])).
% 0.14/0.40 thf(f314,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) | ($false = ((~ (p @ X1)) | (q @ X1))) | ($true = (~ (rel_k @ sK1 @ X1)))) )),
% 0.14/0.40 inference(not_proxy_clausification,[],[f313])).
% 0.14/0.40 thf(f313,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = (~ ((~ (p @ X1)) | (q @ X1)))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) | ($true = (~ (rel_k @ sK1 @ X1)))) )),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f312])).
% 0.14/0.40 thf(f312,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($true = ((~ (rel_k @ sK1 @ X1)) | (~ ((~ (p @ X1)) | (q @ X1))))) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))) )),
% 0.14/0.40 inference(beta_eta_normalization,[],[f311])).
% 0.14/0.40 thf(f311,plain,(
% 0.14/0.40 ( ! [X1 : $i] : (($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0))))))) | (((^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0))))) @ X1) = $true)) )),
% 0.14/0.40 inference(pi_clausification,[],[f296])).
% 0.14/0.40 thf(f296,plain,(
% 0.14/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ ((~ (p @ Y0)) | (q @ Y0)))))) = $true) | ($false = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (rel_k @ sK1 @ Y0)) | (~ (q @ Y0)))))))),
% 0.14/0.40 inference(binary_proxy_clausification,[],[f295])).
% 0.14/0.40 % SZS output end Proof for theBenchmark
% 0.14/0.40 % (26094)------------------------------
% 0.14/0.40 % (26094)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.14/0.40 % (26094)Termination reason: Refutation
% 0.14/0.40
% 0.14/0.40 % (26094)Memory used [KB]: 5884
% 0.14/0.40 % (26094)Time elapsed: 0.023 s
% 0.14/0.40 % (26094)Instructions burned: 25 (million)
% 0.14/0.40 % (26094)------------------------------
% 0.14/0.40 % (26094)------------------------------
% 0.14/0.40 % (26093)Success in time 0.044 s
% 0.14/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------