TSTP Solution File: SYO409^1 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO409^1 : 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 : n028.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 0.16s 0.42s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : SYO409^1 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.37 % Computer : n028.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Mon May 20 09:44:38 EDT 2024
% 0.16/0.37 % CPUTime :
% 0.16/0.37 This is a TH0_THM_EQU_NAR problem
% 0.16/0.37 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
% 0.16/0.39 % (16247)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)
% 0.16/0.39 % (16245)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.16/0.39 % (16244)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)
% 0.16/0.39 % (16242)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.16/0.40 % (16246)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)
% 0.16/0.40 % (16249)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)
% 0.16/0.40 % (16245)Instruction limit reached!
% 0.16/0.40 % (16245)------------------------------
% 0.16/0.40 % (16245)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (16245)Termination reason: Unknown
% 0.16/0.40 % (16245)Termination phase: shuffling
% 0.16/0.40
% 0.16/0.40 % (16245)Memory used [KB]: 1023
% 0.16/0.40 % (16245)Time elapsed: 0.003 s
% 0.16/0.40 % (16245)Instructions burned: 2 (million)
% 0.16/0.40 % (16245)------------------------------
% 0.16/0.40 % (16245)------------------------------
% 0.16/0.40 % (16246)Instruction limit reached!
% 0.16/0.40 % (16246)------------------------------
% 0.16/0.40 % (16246)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (16246)Termination reason: Unknown
% 0.16/0.40 % (16246)Termination phase: Property scanning
% 0.16/0.40
% 0.16/0.40 % (16246)Memory used [KB]: 1023
% 0.16/0.40 % (16246)Time elapsed: 0.003 s
% 0.16/0.40 % (16246)Instructions burned: 4 (million)
% 0.16/0.40 % (16246)------------------------------
% 0.16/0.40 % (16246)------------------------------
% 0.16/0.40 % (16249)Instruction limit reached!
% 0.16/0.40 % (16249)------------------------------
% 0.16/0.40 % (16249)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (16249)Termination reason: Unknown
% 0.16/0.40 % (16249)Termination phase: shuffling
% 0.16/0.40
% 0.16/0.40 % (16249)Memory used [KB]: 1023
% 0.16/0.40 % (16249)Time elapsed: 0.004 s
% 0.16/0.40 % (16249)Instructions burned: 4 (million)
% 0.16/0.40 % (16249)------------------------------
% 0.16/0.40 % (16249)------------------------------
% 0.16/0.40 % (16247)Refutation not found, incomplete strategy
% 0.16/0.40 % (16247)------------------------------
% 0.16/0.40 % (16247)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.40 % (16247)Termination reason: Refutation not found, incomplete strategy
% 0.16/0.40
% 0.16/0.40
% 0.16/0.40 % (16247)Memory used [KB]: 5628
% 0.16/0.40 % (16247)Time elapsed: 0.005 s
% 0.16/0.40 % (16247)Instructions burned: 7 (million)
% 0.16/0.40 % (16247)------------------------------
% 0.16/0.40 % (16247)------------------------------
% 0.16/0.40 % (16248)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.16/0.41 % (16243)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)
% 0.16/0.41 % (16243)Instruction limit reached!
% 0.16/0.41 % (16243)------------------------------
% 0.16/0.41 % (16243)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (16243)Termination reason: Unknown
% 0.16/0.41 % (16243)Termination phase: Property scanning
% 0.16/0.41
% 0.16/0.41 % (16243)Memory used [KB]: 1023
% 0.16/0.41 % (16243)Time elapsed: 0.003 s
% 0.16/0.41 % (16243)Instructions burned: 4 (million)
% 0.16/0.41 % (16243)------------------------------
% 0.16/0.41 % (16243)------------------------------
% 0.16/0.41 % (16248)Instruction limit reached!
% 0.16/0.41 % (16248)------------------------------
% 0.16/0.41 % (16248)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (16248)Termination reason: Unknown
% 0.16/0.41 % (16248)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (16248)Memory used [KB]: 5628
% 0.16/0.41 % (16248)Time elapsed: 0.011 s
% 0.16/0.41 % (16248)Instructions burned: 19 (million)
% 0.16/0.41 % (16248)------------------------------
% 0.16/0.41 % (16248)------------------------------
% 0.16/0.41 % (16242)First to succeed.
% 0.16/0.41 % (16244)Instruction limit reached!
% 0.16/0.41 % (16244)------------------------------
% 0.16/0.41 % (16244)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (16244)Termination reason: Unknown
% 0.16/0.41 % (16250)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)
% 0.16/0.41 % (16244)Termination phase: Saturation
% 0.16/0.41
% 0.16/0.41 % (16244)Memory used [KB]: 5756
% 0.16/0.41 % (16244)Time elapsed: 0.018 s
% 0.16/0.41 % (16244)Instructions burned: 27 (million)
% 0.16/0.41 % (16244)------------------------------
% 0.16/0.41 % (16244)------------------------------
% 0.16/0.41 % (16252)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)
% 0.16/0.41 % (16253)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)
% 0.16/0.41 % (16252)Instruction limit reached!
% 0.16/0.41 % (16252)------------------------------
% 0.16/0.41 % (16252)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.41 % (16252)Termination reason: Unknown
% 0.16/0.41 % (16252)Termination phase: Property scanning
% 0.16/0.41
% 0.16/0.41 % (16252)Memory used [KB]: 1023
% 0.16/0.41 % (16252)Time elapsed: 0.004 s
% 0.16/0.41 % (16252)Instructions burned: 4 (million)
% 0.16/0.41 % (16252)------------------------------
% 0.16/0.41 % (16252)------------------------------
% 0.16/0.42 % (16242)Refutation found. Thanks to Tanya!
% 0.16/0.42 % SZS status Theorem for theBenchmark
% 0.16/0.42 % SZS output start Proof for theBenchmark
% 0.16/0.42 thf(type_def_5, type, mu: $tType).
% 0.16/0.42 thf(func_def_0, type, mu: $tType).
% 0.16/0.42 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.16/0.42 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_15, type, mtrue: $i > $o).
% 0.16/0.42 thf(func_def_16, type, mfalse: $i > $o).
% 0.16/0.42 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.16/0.42 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.16/0.42 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.16/0.42 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.16/0.42 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.16/0.42 thf(func_def_33, type, rel_k: $i > $i > $o).
% 0.16/0.42 thf(func_def_34, type, mbox_k: ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_35, type, mdia_k: ($i > $o) > $i > $o).
% 0.16/0.42 thf(func_def_36, type, p: $i > $o).
% 0.16/0.42 thf(func_def_37, type, q: $i > $o).
% 0.16/0.42 thf(f530,plain,(
% 0.16/0.42 $false),
% 0.16/0.42 inference(avatar_sat_refutation,[],[f326,f331,f336,f337,f354,f359,f364,f365,f444,f447,f457,f468,f483,f498,f512,f529])).
% 0.16/0.42 thf(f529,plain,(
% 0.16/0.42 ~spl0_3 | ~spl0_4 | ~spl0_21),
% 0.16/0.42 inference(avatar_contradiction_clause,[],[f528])).
% 0.16/0.42 thf(f528,plain,(
% 0.16/0.42 $false | (~spl0_3 | ~spl0_4 | ~spl0_21)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f524])).
% 0.16/0.42 thf(f524,plain,(
% 0.16/0.42 ($true = $false) | (~spl0_3 | ~spl0_4 | ~spl0_21)),
% 0.16/0.42 inference(superposition,[],[f521,f330])).
% 0.16/0.42 thf(f330,plain,(
% 0.16/0.42 ($true = (q @ sK12)) | ~spl0_4),
% 0.16/0.42 inference(avatar_component_clause,[],[f328])).
% 0.16/0.42 thf(f328,plain,(
% 0.16/0.42 spl0_4 <=> ($true = (q @ sK12))),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_4])])).
% 0.16/0.42 thf(f521,plain,(
% 0.16/0.42 ((q @ sK12) = $false) | (~spl0_3 | ~spl0_21)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f518])).
% 0.16/0.42 thf(f518,plain,(
% 0.16/0.42 ($true = $false) | ((q @ sK12) = $false) | (~spl0_3 | ~spl0_21)),
% 0.16/0.42 inference(superposition,[],[f407,f325])).
% 0.16/0.42 thf(f325,plain,(
% 0.16/0.42 ((rel_k @ sK1 @ sK12) = $true) | ~spl0_3),
% 0.16/0.42 inference(avatar_component_clause,[],[f323])).
% 0.16/0.42 thf(f323,plain,(
% 0.16/0.42 spl0_3 <=> ((rel_k @ sK1 @ sK12) = $true)),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_3])])).
% 0.16/0.42 thf(f407,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false)) ) | ~spl0_21),
% 0.16/0.42 inference(avatar_component_clause,[],[f406])).
% 0.16/0.42 thf(f406,plain,(
% 0.16/0.42 spl0_21 <=> ! [X1] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false))),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_21])])).
% 0.16/0.42 thf(f512,plain,(
% 0.16/0.42 ~spl0_1 | ~spl0_5 | ~spl0_13),
% 0.16/0.42 inference(avatar_contradiction_clause,[],[f511])).
% 0.16/0.42 thf(f511,plain,(
% 0.16/0.42 $false | (~spl0_1 | ~spl0_5 | ~spl0_13)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f507])).
% 0.16/0.42 thf(f507,plain,(
% 0.16/0.42 ($true = $false) | (~spl0_1 | ~spl0_5 | ~spl0_13)),
% 0.16/0.42 inference(superposition,[],[f506,f335])).
% 0.16/0.42 thf(f335,plain,(
% 0.16/0.42 ($true = (p @ sK13)) | ~spl0_5),
% 0.16/0.42 inference(avatar_component_clause,[],[f333])).
% 0.16/0.42 thf(f333,plain,(
% 0.16/0.42 spl0_5 <=> ($true = (p @ sK13))),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_5])])).
% 0.16/0.42 thf(f506,plain,(
% 0.16/0.42 ((p @ sK13) = $false) | (~spl0_1 | ~spl0_13)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f502])).
% 0.16/0.42 thf(f502,plain,(
% 0.16/0.42 ((p @ sK13) = $false) | ($true = $false) | (~spl0_1 | ~spl0_13)),
% 0.16/0.42 inference(superposition,[],[f372,f317])).
% 0.16/0.42 thf(f317,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK13)) | ~spl0_1),
% 0.16/0.42 inference(avatar_component_clause,[],[f315])).
% 0.16/0.42 thf(f315,plain,(
% 0.16/0.42 spl0_1 <=> ($true = (rel_k @ sK1 @ sK13))),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_1])])).
% 0.16/0.42 thf(f372,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($false = (p @ X1))) ) | ~spl0_13),
% 0.16/0.42 inference(avatar_component_clause,[],[f371])).
% 0.16/0.42 thf(f371,plain,(
% 0.16/0.42 spl0_13 <=> ! [X1] : (((rel_k @ sK1 @ X1) = $false) | ($false = (p @ X1)))),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_13])])).
% 0.16/0.42 thf(f498,plain,(
% 0.16/0.42 ~spl0_8 | ~spl0_11 | ~spl0_21),
% 0.16/0.42 inference(avatar_contradiction_clause,[],[f497])).
% 0.16/0.42 thf(f497,plain,(
% 0.16/0.42 $false | (~spl0_8 | ~spl0_11 | ~spl0_21)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f493])).
% 0.16/0.42 thf(f493,plain,(
% 0.16/0.42 ($true = $false) | (~spl0_8 | ~spl0_11 | ~spl0_21)),
% 0.16/0.42 inference(superposition,[],[f491,f363])).
% 0.16/0.42 thf(f363,plain,(
% 0.16/0.42 ((q @ sK10) = $true) | ~spl0_11),
% 0.16/0.42 inference(avatar_component_clause,[],[f361])).
% 0.16/0.42 thf(f361,plain,(
% 0.16/0.42 spl0_11 <=> ((q @ sK10) = $true)),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_11])])).
% 0.16/0.42 thf(f491,plain,(
% 0.16/0.42 ((q @ sK10) = $false) | (~spl0_8 | ~spl0_21)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f485])).
% 0.16/0.42 thf(f485,plain,(
% 0.16/0.42 ((q @ sK10) = $false) | ($true = $false) | (~spl0_8 | ~spl0_21)),
% 0.16/0.42 inference(superposition,[],[f349,f407])).
% 0.16/0.42 thf(f349,plain,(
% 0.16/0.42 ((rel_k @ sK1 @ sK10) = $true) | ~spl0_8),
% 0.16/0.42 inference(avatar_component_clause,[],[f347])).
% 0.16/0.42 thf(f347,plain,(
% 0.16/0.42 spl0_8 <=> ((rel_k @ sK1 @ sK10) = $true)),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_8])])).
% 0.16/0.42 thf(f483,plain,(
% 0.16/0.42 ~spl0_6 | ~spl0_10 | ~spl0_13),
% 0.16/0.42 inference(avatar_contradiction_clause,[],[f482])).
% 0.16/0.42 thf(f482,plain,(
% 0.16/0.42 $false | (~spl0_6 | ~spl0_10 | ~spl0_13)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f478])).
% 0.16/0.42 thf(f478,plain,(
% 0.16/0.42 ($true = $false) | (~spl0_6 | ~spl0_10 | ~spl0_13)),
% 0.16/0.42 inference(superposition,[],[f476,f358])).
% 0.16/0.42 thf(f358,plain,(
% 0.16/0.42 ((p @ sK11) = $true) | ~spl0_10),
% 0.16/0.42 inference(avatar_component_clause,[],[f356])).
% 0.16/0.42 thf(f356,plain,(
% 0.16/0.42 spl0_10 <=> ((p @ sK11) = $true)),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_10])])).
% 0.16/0.42 thf(f476,plain,(
% 0.16/0.42 ((p @ sK11) = $false) | (~spl0_6 | ~spl0_13)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f473])).
% 0.16/0.42 thf(f473,plain,(
% 0.16/0.42 ((p @ sK11) = $false) | ($true = $false) | (~spl0_6 | ~spl0_13)),
% 0.16/0.42 inference(superposition,[],[f372,f341])).
% 0.16/0.42 thf(f341,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK11)) | ~spl0_6),
% 0.16/0.42 inference(avatar_component_clause,[],[f339])).
% 0.16/0.42 thf(f339,plain,(
% 0.16/0.42 spl0_6 <=> ($true = (rel_k @ sK1 @ sK11))),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_6])])).
% 0.16/0.42 thf(f468,plain,(
% 0.16/0.42 ~spl0_2 | ~spl0_9 | ~spl0_21),
% 0.16/0.42 inference(avatar_contradiction_clause,[],[f467])).
% 0.16/0.42 thf(f467,plain,(
% 0.16/0.42 $false | (~spl0_2 | ~spl0_9 | ~spl0_21)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f464])).
% 0.16/0.42 thf(f464,plain,(
% 0.16/0.42 ($true = $false) | (~spl0_2 | ~spl0_9 | ~spl0_21)),
% 0.16/0.42 inference(superposition,[],[f353,f462])).
% 0.16/0.42 thf(f462,plain,(
% 0.16/0.42 ($false = (q @ sK9)) | (~spl0_2 | ~spl0_21)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f459])).
% 0.16/0.42 thf(f459,plain,(
% 0.16/0.42 ($false = (q @ sK9)) | ($true = $false) | (~spl0_2 | ~spl0_21)),
% 0.16/0.42 inference(superposition,[],[f407,f321])).
% 0.16/0.42 thf(f321,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK9)) | ~spl0_2),
% 0.16/0.42 inference(avatar_component_clause,[],[f319])).
% 0.16/0.42 thf(f319,plain,(
% 0.16/0.42 spl0_2 <=> ($true = (rel_k @ sK1 @ sK9))),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_2])])).
% 0.16/0.42 thf(f353,plain,(
% 0.16/0.42 ($true = (q @ sK9)) | ~spl0_9),
% 0.16/0.42 inference(avatar_component_clause,[],[f351])).
% 0.16/0.42 thf(f351,plain,(
% 0.16/0.42 spl0_9 <=> ($true = (q @ sK9))),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_9])])).
% 0.16/0.42 thf(f457,plain,(
% 0.16/0.42 ~spl0_2 | ~spl0_7 | ~spl0_13),
% 0.16/0.42 inference(avatar_contradiction_clause,[],[f456])).
% 0.16/0.42 thf(f456,plain,(
% 0.16/0.42 $false | (~spl0_2 | ~spl0_7 | ~spl0_13)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f452])).
% 0.16/0.42 thf(f452,plain,(
% 0.16/0.42 ($true = $false) | (~spl0_2 | ~spl0_7 | ~spl0_13)),
% 0.16/0.42 inference(superposition,[],[f451,f345])).
% 0.16/0.42 thf(f345,plain,(
% 0.16/0.42 ((p @ sK9) = $true) | ~spl0_7),
% 0.16/0.42 inference(avatar_component_clause,[],[f343])).
% 0.16/0.42 thf(f343,plain,(
% 0.16/0.42 spl0_7 <=> ((p @ sK9) = $true)),
% 0.16/0.42 introduced(avatar_definition,[new_symbols(naming,[spl0_7])])).
% 0.16/0.42 thf(f451,plain,(
% 0.16/0.42 ((p @ sK9) = $false) | (~spl0_2 | ~spl0_13)),
% 0.16/0.42 inference(trivial_inequality_removal,[],[f448])).
% 0.16/0.42 thf(f448,plain,(
% 0.16/0.42 ($true = $false) | ((p @ sK9) = $false) | (~spl0_2 | ~spl0_13)),
% 0.16/0.42 inference(superposition,[],[f372,f321])).
% 0.16/0.42 thf(f447,plain,(
% 0.16/0.42 spl0_21 | spl0_21),
% 0.16/0.42 inference(avatar_split_clause,[],[f174,f406,f406])).
% 0.16/0.42 thf(f174,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X2) = $false) | ((rel_k @ sK1 @ X1) = $false) | ((q @ X2) = $false) | ((q @ X1) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f173])).
% 0.16/0.42 thf(f173,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false) | ((~ (rel_k @ sK1 @ X2)) = $true) | ((q @ X2) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f172])).
% 0.16/0.42 thf(f172,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((q @ X1) = $false) | ((~ (q @ X2)) = $true) | ((~ (rel_k @ sK1 @ X2)) = $true) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f171])).
% 0.16/0.42 thf(f171,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (q @ X2)) | (~ (rel_k @ sK1 @ X2)))) | ((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f170])).
% 0.16/0.42 thf(f170,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X2) = $true) | ((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false)) )),
% 0.16/0.42 inference(pi_clausification,[],[f169])).
% 0.16/0.42 thf(f169,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $true) | ((rel_k @ sK1 @ X1) = $false) | ((q @ X1) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f167])).
% 0.16/0.42 thf(f167,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((q @ X1) | (p @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $true) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f166])).
% 0.16/0.42 thf(f166,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | ((rel_k @ sK1 @ X1) = $false) | (((q @ X1) | (p @ X1)) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f164])).
% 0.16/0.42 thf(f164,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) = $false) | (((q @ X1) | (p @ X1)) = $false) | ((rel_k @ sK1 @ X1) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f162])).
% 0.16/0.42 thf(f162,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | (((q @ X1) | (p @ X1)) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f161])).
% 0.16/0.42 thf(f161,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (($true = (~ (rel_k @ sK1 @ X1))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | (((q @ X1) | (p @ X1)) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f160])).
% 0.16/0.42 thf(f160,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((~ ((q @ X1) | (p @ X1))) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | ($true = (~ (rel_k @ sK1 @ X1)))) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f159])).
% 0.16/0.42 thf(f159,plain,(
% 0.16/0.42 ( ! [X1 : $i] : ((((~ ((q @ X1) | (p @ X1))) | (~ (rel_k @ sK1 @ X1))) = $true) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f158])).
% 0.16/0.42 thf(f158,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | (((^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))) @ X1) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f157])).
% 0.16/0.42 thf(f157,plain,(
% 0.16/0.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f156])).
% 0.16/0.42 thf(f156,plain,(
% 0.16/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f154])).
% 0.16/0.42 thf(f154,plain,(
% 0.16/0.42 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))))) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f153])).
% 0.16/0.42 thf(f153,plain,(
% 0.16/0.42 ($true = (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))))) = $false)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f152])).
% 0.16/0.42 thf(f152,plain,(
% 0.16/0.42 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))))) = $true) | ($true = (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))))),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f151])).
% 0.16/0.42 thf(f151,plain,(
% 0.16/0.42 (((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))))) | (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))))) = $true)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f150])).
% 0.16/0.42 thf(f150,plain,(
% 0.16/0.42 ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))))) | (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0))))))))) = $false)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f149])).
% 0.16/0.42 thf(f149,plain,(
% 0.16/0.42 ($false = ((^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((q @ Y1) | (p @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ ((q @ Y1) | (p @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))))))) @ sK1))),
% 0.16/0.42 inference(sigma_clausification,[],[f148])).
% 0.16/0.42 thf(f148,plain,(
% 0.16/0.42 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((q @ Y1) | (p @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ ((q @ Y1) | (p @ Y1))) | (~ (rel_k @ Y0 @ Y1))))))))))) != $true)),
% 0.16/0.42 inference(boolean_simplification,[],[f147])).
% 0.16/0.42 thf(f147,plain,(
% 0.16/0.42 ((!! @ $i @ (^[Y0 : $i]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((q @ Y1) | (p @ Y1))) | (~ (rel_k @ Y0 @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (q @ Y1)) | (~ (rel_k @ Y0 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (p @ Y1)) | (~ (rel_k @ Y0 @ Y1))))))) | (~ (~ (!! @ $i @ (^[Y1 : $i]: ((~ ((q @ Y1) | (p @ Y1))) | (~ (rel_k @ Y0 @ Y1))))))))))))) != $true)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f146])).
% 0.16/0.42 thf(f146,plain,(
% 0.16/0.42 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ p @ q)) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ p) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))) @ q)))) != $true)),
% 0.16/0.42 inference(definition_unfolding,[],[f131,f127,f139,f145,f103,f103,f145,f145])).
% 0.16/0.42 thf(f103,plain,(
% 0.16/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.42 inference(cnf_transformation,[],[f82])).
% 0.16/0.42 thf(f82,plain,(
% 0.16/0.42 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.16/0.42 inference(fool_elimination,[],[f81])).
% 0.16/0.42 thf(f81,plain,(
% 0.16/0.42 ((^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 0.16/0.42 inference(rectify,[],[f4])).
% 0.16/0.42 thf(f4,axiom,(
% 0.16/0.42 ((^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))) = mor)),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.16/0.42 thf(f145,plain,(
% 0.16/0.42 (mdia_k = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (rel_k @ Y2 @ Y3)))))))) @ ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (~ (Y1 @ Y2))))) @ Y0)))))),
% 0.16/0.42 inference(definition_unfolding,[],[f135,f129,f114,f129])).
% 0.16/0.42 thf(f114,plain,(
% 0.16/0.42 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.16/0.42 inference(cnf_transformation,[],[f100])).
% 0.16/0.42 thf(f100,plain,(
% 0.16/0.42 (mbox_k = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) | (~ (rel_k @ Y1 @ Y2)))))))))),
% 0.16/0.42 inference(fool_elimination,[],[f99])).
% 0.16/0.42 thf(f99,plain,(
% 0.16/0.42 (mbox_k = (^[X0 : $i > $o, X1 : $i] : (! [X2] : (~(rel_k @ X1 @ X2) | (X0 @ X2)))))),
% 0.16/0.42 inference(rectify,[],[f32])).
% 0.16/0.42 thf(f32,axiom,(
% 0.16/0.42 (mbox_k = (^[X3 : $i > $o, X2 : $i] : (! [X7] : (~(rel_k @ X2 @ X7) | (X3 @ X7)))))),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox_k)).
% 0.16/0.42 thf(f129,plain,(
% 0.16/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.42 inference(cnf_transformation,[],[f72])).
% 0.16/0.42 thf(f72,plain,(
% 0.16/0.42 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.16/0.42 inference(fool_elimination,[],[f71])).
% 0.16/0.42 thf(f71,plain,(
% 0.16/0.42 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.16/0.42 inference(rectify,[],[f3])).
% 0.16/0.42 thf(f3,axiom,(
% 0.16/0.42 (mnot = (^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))))),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.16/0.42 thf(f135,plain,(
% 0.16/0.42 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.16/0.42 inference(cnf_transformation,[],[f78])).
% 0.16/0.42 thf(f78,plain,(
% 0.16/0.42 (mdia_k = (^[Y0 : $i > $o]: (mnot @ (mbox_k @ (mnot @ Y0)))))),
% 0.16/0.42 inference(fool_elimination,[],[f77])).
% 0.16/0.42 thf(f77,plain,(
% 0.16/0.42 (mdia_k = (^[X0 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X0)))))),
% 0.16/0.42 inference(rectify,[],[f33])).
% 0.16/0.42 thf(f33,axiom,(
% 0.16/0.42 (mdia_k = (^[X3 : $i > $o] : (mnot @ (mbox_k @ (mnot @ X3)))))),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia_k)).
% 0.16/0.42 thf(f139,plain,(
% 0.16/0.42 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y0 @ Y1) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ Y1 @ Y0))))))),
% 0.16/0.42 inference(definition_unfolding,[],[f122,f136,f137,f137])).
% 0.16/0.42 thf(f137,plain,(
% 0.16/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.16/0.42 inference(definition_unfolding,[],[f124,f103,f129])).
% 0.16/0.42 thf(f124,plain,(
% 0.16/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.42 inference(cnf_transformation,[],[f57])).
% 0.16/0.42 thf(f57,plain,(
% 0.16/0.42 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.16/0.42 inference(fool_elimination,[],[f56])).
% 0.16/0.42 thf(f56,plain,(
% 0.16/0.42 (mimplies = (^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)))),
% 0.16/0.42 inference(rectify,[],[f6])).
% 0.16/0.42 thf(f6,axiom,(
% 0.16/0.42 (mimplies = (^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)))),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.16/0.42 thf(f136,plain,(
% 0.16/0.42 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.16/0.42 inference(definition_unfolding,[],[f126,f129,f103,f129,f129])).
% 0.16/0.42 thf(f126,plain,(
% 0.16/0.42 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.42 inference(cnf_transformation,[],[f42])).
% 0.16/0.42 thf(f42,plain,(
% 0.16/0.42 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.16/0.42 inference(fool_elimination,[],[f41])).
% 0.16/0.42 thf(f41,plain,(
% 0.16/0.42 ((^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))) = mand)),
% 0.16/0.42 inference(rectify,[],[f5])).
% 0.16/0.42 thf(f5,axiom,(
% 0.16/0.42 ((^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))) = mand)),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.16/0.42 thf(f122,plain,(
% 0.16/0.42 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.16/0.42 inference(cnf_transformation,[],[f47])).
% 0.16/0.42 thf(f47,plain,(
% 0.16/0.42 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.16/0.42 inference(fool_elimination,[],[f46])).
% 0.16/0.42 thf(f46,plain,(
% 0.16/0.42 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.16/0.42 inference(rectify,[],[f8])).
% 0.16/0.42 thf(f8,axiom,(
% 0.16/0.42 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.16/0.42 thf(f127,plain,(
% 0.16/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.42 inference(cnf_transformation,[],[f45])).
% 0.16/0.42 thf(f45,plain,(
% 0.16/0.42 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.16/0.42 inference(fool_elimination,[],[f44])).
% 0.16/0.42 thf(f44,plain,(
% 0.16/0.42 (mvalid = (^[X0 : $i > $o] : (! [X1] : (X0 @ X1))))),
% 0.16/0.42 inference(rectify,[],[f28])).
% 0.16/0.42 thf(f28,axiom,(
% 0.16/0.42 (mvalid = (^[X3 : $i > $o] : (! [X2] : (X3 @ X2))))),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.16/0.42 thf(f131,plain,(
% 0.16/0.42 ((mvalid @ (mequiv @ (mdia_k @ (mor @ p @ q)) @ (mor @ (mdia_k @ p) @ (mdia_k @ q)))) != $true)),
% 0.16/0.42 inference(cnf_transformation,[],[f101])).
% 0.16/0.42 thf(f101,plain,(
% 0.16/0.42 ((mvalid @ (mequiv @ (mdia_k @ (mor @ p @ q)) @ (mor @ (mdia_k @ p) @ (mdia_k @ q)))) != $true)),
% 0.16/0.42 inference(flattening,[],[f80])).
% 0.16/0.42 thf(f80,plain,(
% 0.16/0.42 ~((mvalid @ (mequiv @ (mdia_k @ (mor @ p @ q)) @ (mor @ (mdia_k @ p) @ (mdia_k @ q)))) = $true)),
% 0.16/0.42 inference(fool_elimination,[],[f79])).
% 0.16/0.42 thf(f79,plain,(
% 0.16/0.42 ~(mvalid @ (mequiv @ (mdia_k @ (mor @ p @ q)) @ (mor @ (mdia_k @ p) @ (mdia_k @ q))))),
% 0.16/0.42 inference(rectify,[],[f35])).
% 0.16/0.42 thf(f35,negated_conjecture,(
% 0.16/0.42 ~(mvalid @ (mequiv @ (mdia_k @ (mor @ p @ q)) @ (mor @ (mdia_k @ p) @ (mdia_k @ q))))),
% 0.16/0.42 inference(negated_conjecture,[],[f34])).
% 0.16/0.42 thf(f34,conjecture,(
% 0.16/0.42 (mvalid @ (mequiv @ (mdia_k @ (mor @ p @ q)) @ (mor @ (mdia_k @ p) @ (mdia_k @ q))))),
% 0.16/0.42 file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove)).
% 0.16/0.42 thf(f444,plain,(
% 0.16/0.42 spl0_13 | spl0_13),
% 0.16/0.42 inference(avatar_split_clause,[],[f186,f371,f371])).
% 0.16/0.42 thf(f186,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (($false = (p @ X1)) | ((rel_k @ sK1 @ X1) = $false) | ((p @ X2) = $false) | ((rel_k @ sK1 @ X2) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f185])).
% 0.16/0.42 thf(f185,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((p @ X2) = $false) | (((q @ X1) | (p @ X1)) = $false) | ((rel_k @ sK1 @ X2) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f184])).
% 0.16/0.42 thf(f184,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((~ (rel_k @ sK1 @ X2)) = $true) | ((p @ X2) = $false) | (((q @ X1) | (p @ X1)) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f183])).
% 0.16/0.42 thf(f183,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((~ (p @ X2)) = $true) | ((rel_k @ sK1 @ X1) = $false) | (((q @ X1) | (p @ X1)) = $false) | ((~ (rel_k @ sK1 @ X2)) = $true)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f182])).
% 0.16/0.42 thf(f182,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($true = ((~ (p @ X2)) | (~ (rel_k @ sK1 @ X2)))) | (((q @ X1) | (p @ X1)) = $false)) )),
% 0.16/0.42 inference(beta_eta_normalization,[],[f181])).
% 0.16/0.42 thf(f181,plain,(
% 0.16/0.42 ( ! [X2 : $i,X1 : $i] : ((((q @ X1) | (p @ X1)) = $false) | ((rel_k @ sK1 @ X1) = $false) | (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ X2) = $true)) )),
% 0.16/0.42 inference(pi_clausification,[],[f180])).
% 0.16/0.42 thf(f180,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (((q @ X1) | (p @ X1)) = $false)) )),
% 0.16/0.42 inference(not_proxy_clausification,[],[f165])).
% 0.16/0.42 thf(f165,plain,(
% 0.16/0.42 ( ! [X1 : $i] : (((rel_k @ sK1 @ X1) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | (((q @ X1) | (p @ X1)) = $false)) )),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f164])).
% 0.16/0.42 thf(f365,plain,(
% 0.16/0.42 spl0_9 | spl0_7 | spl0_10 | spl0_11),
% 0.16/0.42 inference(avatar_split_clause,[],[f286,f361,f356,f343,f351])).
% 0.16/0.42 thf(f286,plain,(
% 0.16/0.42 ((p @ sK9) = $true) | ((q @ sK10) = $true) | ((p @ sK11) = $true) | ($true = (q @ sK9))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f285])).
% 0.16/0.42 thf(f285,plain,(
% 0.16/0.42 ((p @ sK9) = $true) | ((~ (p @ sK11)) = $false) | ((q @ sK10) = $true) | ($true = (q @ sK9))),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f283])).
% 0.16/0.42 thf(f283,plain,(
% 0.16/0.42 ((q @ sK10) = $true) | ((p @ sK9) = $true) | ($true = (q @ sK9)) | (((~ (p @ sK11)) | (~ (rel_k @ sK1 @ sK11))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f282])).
% 0.16/0.42 thf(f282,plain,(
% 0.16/0.42 (((q @ sK9) | (p @ sK9)) = $true) | (((~ (p @ sK11)) | (~ (rel_k @ sK1 @ sK11))) = $false) | ((q @ sK10) = $true)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f281])).
% 0.16/0.42 thf(f281,plain,(
% 0.16/0.42 ((~ (q @ sK10)) = $false) | (((q @ sK9) | (p @ sK9)) = $true) | (((~ (p @ sK11)) | (~ (rel_k @ sK1 @ sK11))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f279])).
% 0.16/0.42 thf(f279,plain,(
% 0.16/0.42 ($false = ((~ (q @ sK10)) | (~ (rel_k @ sK1 @ sK10)))) | (((q @ sK9) | (p @ sK9)) = $true) | (((~ (p @ sK11)) | (~ (rel_k @ sK1 @ sK11))) = $false)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f278])).
% 0.16/0.42 thf(f278,plain,(
% 0.16/0.42 ((~ ((q @ sK9) | (p @ sK9))) = $false) | ($false = ((~ (q @ sK10)) | (~ (rel_k @ sK1 @ sK10)))) | (((~ (p @ sK11)) | (~ (rel_k @ sK1 @ sK11))) = $false)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f277])).
% 0.16/0.42 thf(f277,plain,(
% 0.16/0.42 ($false = ((~ (q @ sK10)) | (~ (rel_k @ sK1 @ sK10)))) | ((~ ((q @ sK9) | (p @ sK9))) = $false) | (((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK11) = $false)),
% 0.16/0.42 inference(sigma_clausification,[],[f276])).
% 0.16/0.42 thf(f276,plain,(
% 0.16/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ((~ ((q @ sK9) | (p @ sK9))) = $false) | ($false = ((~ (q @ sK10)) | (~ (rel_k @ sK1 @ sK10))))),
% 0.16/0.42 inference(beta_eta_normalization,[],[f275])).
% 0.16/0.42 thf(f275,plain,(
% 0.16/0.42 (((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK10) = $false) | ((~ ((q @ sK9) | (p @ sK9))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.16/0.42 inference(sigma_clausification,[],[f274])).
% 0.16/0.42 thf(f274,plain,(
% 0.16/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ((~ ((q @ sK9) | (p @ sK9))) = $false)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f273])).
% 0.16/0.42 thf(f273,plain,(
% 0.16/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((~ ((q @ sK9) | (p @ sK9))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f272])).
% 0.16/0.42 thf(f272,plain,(
% 0.16/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((~ ((q @ sK9) | (p @ sK9))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f270])).
% 0.16/0.42 thf(f270,plain,(
% 0.16/0.42 (((~ ((q @ sK9) | (p @ sK9))) | (~ (rel_k @ sK1 @ sK9))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f269])).
% 0.16/0.42 thf(f269,plain,(
% 0.16/0.42 ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))) | (((~ ((q @ sK9) | (p @ sK9))) | (~ (rel_k @ sK1 @ sK9))) = $false)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f268])).
% 0.16/0.42 thf(f268,plain,(
% 0.16/0.42 (((^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))) @ sK9) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))))),
% 0.16/0.42 inference(sigma_clausification,[],[f267])).
% 0.16/0.42 thf(f267,plain,(
% 0.16/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ($true = ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f200])).
% 0.16/0.42 thf(f200,plain,(
% 0.16/0.42 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f155])).
% 0.16/0.42 thf(f155,plain,(
% 0.16/0.42 ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((q @ Y0) | (p @ Y0))) | (~ (rel_k @ sK1 @ Y0)))))) = $false) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f154])).
% 0.16/0.42 thf(f364,plain,(
% 0.16/0.42 spl0_9 | spl0_11 | spl0_6 | spl0_7),
% 0.16/0.42 inference(avatar_split_clause,[],[f287,f343,f339,f361,f351])).
% 0.16/0.42 thf(f287,plain,(
% 0.16/0.42 ($true = (q @ sK9)) | ($true = (rel_k @ sK1 @ sK11)) | ((p @ sK9) = $true) | ((q @ sK10) = $true)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f284])).
% 0.16/0.42 thf(f284,plain,(
% 0.16/0.42 ((~ (rel_k @ sK1 @ sK11)) = $false) | ($true = (q @ sK9)) | ((p @ sK9) = $true) | ((q @ sK10) = $true)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f283])).
% 0.16/0.42 thf(f359,plain,(
% 0.16/0.42 spl0_8 | spl0_10 | spl0_9 | spl0_7),
% 0.16/0.42 inference(avatar_split_clause,[],[f292,f343,f351,f356,f347])).
% 0.16/0.42 thf(f292,plain,(
% 0.16/0.42 ((p @ sK11) = $true) | ((p @ sK9) = $true) | ($true = (q @ sK9)) | ((rel_k @ sK1 @ sK10) = $true)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f291])).
% 0.16/0.42 thf(f291,plain,(
% 0.16/0.42 ((~ (p @ sK11)) = $false) | ($true = (q @ sK9)) | ((p @ sK9) = $true) | ((rel_k @ sK1 @ sK10) = $true)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f289])).
% 0.16/0.42 thf(f289,plain,(
% 0.16/0.42 ((p @ sK9) = $true) | ((rel_k @ sK1 @ sK10) = $true) | ($true = (q @ sK9)) | (((~ (p @ sK11)) | (~ (rel_k @ sK1 @ sK11))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f288])).
% 0.16/0.42 thf(f288,plain,(
% 0.16/0.42 (((q @ sK9) | (p @ sK9)) = $true) | (((~ (p @ sK11)) | (~ (rel_k @ sK1 @ sK11))) = $false) | ((rel_k @ sK1 @ sK10) = $true)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f280])).
% 0.16/0.42 thf(f280,plain,(
% 0.16/0.42 ((~ (rel_k @ sK1 @ sK10)) = $false) | (((q @ sK9) | (p @ sK9)) = $true) | (((~ (p @ sK11)) | (~ (rel_k @ sK1 @ sK11))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f279])).
% 0.16/0.42 thf(f354,plain,(
% 0.16/0.42 spl0_6 | spl0_7 | spl0_8 | spl0_9),
% 0.16/0.42 inference(avatar_split_clause,[],[f293,f351,f347,f343,f339])).
% 0.16/0.42 thf(f293,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK11)) | ((rel_k @ sK1 @ sK10) = $true) | ($true = (q @ sK9)) | ((p @ sK9) = $true)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f290])).
% 0.16/0.42 thf(f290,plain,(
% 0.16/0.42 ((rel_k @ sK1 @ sK10) = $true) | ($true = (q @ sK9)) | ((p @ sK9) = $true) | ((~ (rel_k @ sK1 @ sK11)) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f289])).
% 0.16/0.42 thf(f337,plain,(
% 0.16/0.42 spl0_2 | spl0_5 | spl0_4),
% 0.16/0.42 inference(avatar_split_clause,[],[f306,f328,f333,f319])).
% 0.16/0.42 thf(f306,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK9)) | ($true = (p @ sK13)) | ($true = (q @ sK12))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f305])).
% 0.16/0.42 thf(f305,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK9)) | ($true = (p @ sK13)) | ((~ (q @ sK12)) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f303])).
% 0.16/0.42 thf(f303,plain,(
% 0.16/0.42 (((~ (q @ sK12)) | (~ (rel_k @ sK1 @ sK12))) = $false) | ($true = (rel_k @ sK1 @ sK9)) | ($true = (p @ sK13))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f302])).
% 0.16/0.42 thf(f302,plain,(
% 0.16/0.42 ((~ (p @ sK13)) = $false) | ($true = (rel_k @ sK1 @ sK9)) | (((~ (q @ sK12)) | (~ (rel_k @ sK1 @ sK12))) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f300])).
% 0.16/0.42 thf(f300,plain,(
% 0.16/0.42 (((~ (p @ sK13)) | (~ (rel_k @ sK1 @ sK13))) = $false) | ($true = (rel_k @ sK1 @ sK9)) | (((~ (q @ sK12)) | (~ (rel_k @ sK1 @ sK12))) = $false)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f299])).
% 0.16/0.42 thf(f299,plain,(
% 0.16/0.42 ($false = ((^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK13)) | ($true = (rel_k @ sK1 @ sK9)) | (((~ (q @ sK12)) | (~ (rel_k @ sK1 @ sK12))) = $false)),
% 0.16/0.42 inference(sigma_clausification,[],[f298])).
% 0.16/0.42 thf(f298,plain,(
% 0.16/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ($true = (rel_k @ sK1 @ sK9)) | (((~ (q @ sK12)) | (~ (rel_k @ sK1 @ sK12))) = $false)),
% 0.16/0.42 inference(beta_eta_normalization,[],[f297])).
% 0.16/0.42 thf(f297,plain,(
% 0.16/0.42 ($false = ((^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))) @ sK12)) | ($true = (rel_k @ sK1 @ sK9)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.16/0.42 inference(sigma_clausification,[],[f296])).
% 0.16/0.42 thf(f296,plain,(
% 0.16/0.42 ((!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false) | ($true = (rel_k @ sK1 @ sK9))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f295])).
% 0.16/0.42 thf(f295,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK9)) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0))))) = $false)),
% 0.16/0.42 inference(not_proxy_clausification,[],[f294])).
% 0.16/0.42 thf(f294,plain,(
% 0.16/0.42 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ($true = (rel_k @ sK1 @ sK9))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f271])).
% 0.16/0.42 thf(f271,plain,(
% 0.16/0.42 ((~ (rel_k @ sK1 @ sK9)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (p @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (q @ Y0)) | (~ (rel_k @ sK1 @ Y0)))))) = $true)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f270])).
% 0.16/0.42 thf(f336,plain,(
% 0.16/0.42 spl0_3 | spl0_2 | spl0_5),
% 0.16/0.42 inference(avatar_split_clause,[],[f307,f333,f319,f323])).
% 0.16/0.42 thf(f307,plain,(
% 0.16/0.42 ((rel_k @ sK1 @ sK12) = $true) | ($true = (rel_k @ sK1 @ sK9)) | ($true = (p @ sK13))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f304])).
% 0.16/0.42 thf(f304,plain,(
% 0.16/0.42 ((~ (rel_k @ sK1 @ sK12)) = $false) | ($true = (p @ sK13)) | ($true = (rel_k @ sK1 @ sK9))),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f303])).
% 0.16/0.42 thf(f331,plain,(
% 0.16/0.42 spl0_2 | spl0_4 | spl0_1),
% 0.16/0.42 inference(avatar_split_clause,[],[f311,f315,f328,f319])).
% 0.16/0.42 thf(f311,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK13)) | ($true = (q @ sK12)) | ($true = (rel_k @ sK1 @ sK9))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f310])).
% 0.16/0.42 thf(f310,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK9)) | ((~ (rel_k @ sK1 @ sK13)) = $false) | ($true = (q @ sK12))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f309])).
% 0.16/0.42 thf(f309,plain,(
% 0.16/0.42 ($true = (rel_k @ sK1 @ sK9)) | ((~ (q @ sK12)) = $false) | ((~ (rel_k @ sK1 @ sK13)) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f301])).
% 0.16/0.42 thf(f301,plain,(
% 0.16/0.42 (((~ (q @ sK12)) | (~ (rel_k @ sK1 @ sK12))) = $false) | ((~ (rel_k @ sK1 @ sK13)) = $false) | ($true = (rel_k @ sK1 @ sK9))),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f300])).
% 0.16/0.42 thf(f326,plain,(
% 0.16/0.42 spl0_1 | spl0_2 | spl0_3),
% 0.16/0.42 inference(avatar_split_clause,[],[f313,f323,f319,f315])).
% 0.16/0.42 thf(f313,plain,(
% 0.16/0.42 ((rel_k @ sK1 @ sK12) = $true) | ($true = (rel_k @ sK1 @ sK13)) | ($true = (rel_k @ sK1 @ sK9))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f312])).
% 0.16/0.42 thf(f312,plain,(
% 0.16/0.42 ((rel_k @ sK1 @ sK12) = $true) | ((~ (rel_k @ sK1 @ sK13)) = $false) | ($true = (rel_k @ sK1 @ sK9))),
% 0.16/0.42 inference(not_proxy_clausification,[],[f308])).
% 0.16/0.42 thf(f308,plain,(
% 0.16/0.42 ((~ (rel_k @ sK1 @ sK12)) = $false) | ($true = (rel_k @ sK1 @ sK9)) | ((~ (rel_k @ sK1 @ sK13)) = $false)),
% 0.16/0.42 inference(binary_proxy_clausification,[],[f301])).
% 0.16/0.42 % SZS output end Proof for theBenchmark
% 0.16/0.42 % (16242)------------------------------
% 0.16/0.42 % (16242)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.16/0.42 % (16242)Termination reason: Refutation
% 0.16/0.42
% 0.16/0.42 % (16242)Memory used [KB]: 5884
% 0.16/0.42 % (16242)Time elapsed: 0.024 s
% 0.16/0.42 % (16242)Instructions burned: 26 (million)
% 0.16/0.42 % (16242)------------------------------
% 0.16/0.42 % (16242)------------------------------
% 0.16/0.42 % (16241)Success in time 0.035 s
% 0.16/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------