TSTP Solution File: SYO049^1 by Vampire---4.9
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.9
% Problem : SYO049^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d THM
% Computer : n029.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 : Mon Jun 24 21:00:17 EDT 2024
% Result : Theorem 0.21s 0.40s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO049^1 : TPTP v8.2.0. Released v4.0.0.
% 0.03/0.12 % Command : run_vampire %s %d THM
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sun Jun 23 06:52:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.21/0.35 This is a TH0_THM_EQU_NAR problem
% 0.21/0.35 Running higher-order theorem proving
% 0.21/0.35 Running /export/starexec/sandbox/solver/bin/vampire_ho --cores 7 --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol /export/starexec/sandbox/benchmark/theBenchmark.p -m 16384 -t 300
% 0.21/0.37 % (12192)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)
% 0.21/0.37 % (12187)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (12189)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)
% 0.21/0.37 % (12188)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)
% 0.21/0.37 % (12190)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.37 % (12191)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)
% 0.21/0.37 % (12193)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (12190)Instruction limit reached!
% 0.21/0.38 % (12190)------------------------------
% 0.21/0.38 % (12190)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (12191)Instruction limit reached!
% 0.21/0.38 % (12191)------------------------------
% 0.21/0.38 % (12191)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (12190)Termination reason: Unknown
% 0.21/0.38 % (12190)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (12190)Memory used [KB]: 1023
% 0.21/0.38 % (12190)Time elapsed: 0.004 s
% 0.21/0.38 % (12190)Instructions burned: 3 (million)
% 0.21/0.38 % (12190)------------------------------
% 0.21/0.38 % (12190)------------------------------
% 0.21/0.38 % (12191)Termination reason: Unknown
% 0.21/0.38 % (12191)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (12191)Memory used [KB]: 1023
% 0.21/0.38 % (12191)Time elapsed: 0.004 s
% 0.21/0.38 % (12191)Instructions burned: 3 (million)
% 0.21/0.38 % (12191)------------------------------
% 0.21/0.38 % (12191)------------------------------
% 0.21/0.38 % (12188)Instruction limit reached!
% 0.21/0.38 % (12188)------------------------------
% 0.21/0.38 % (12188)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (12188)Termination reason: Unknown
% 0.21/0.38 % (12188)Termination phase: Property scanning
% 0.21/0.38
% 0.21/0.38 % (12188)Memory used [KB]: 1023
% 0.21/0.38 % (12188)Time elapsed: 0.005 s
% 0.21/0.38 % (12188)Instructions burned: 5 (million)
% 0.21/0.38 % (12188)------------------------------
% 0.21/0.38 % (12188)------------------------------
% 0.21/0.38 % (12192)Refutation not found, incomplete strategy
% 0.21/0.38 % (12192)------------------------------
% 0.21/0.38 % (12192)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (12192)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.38
% 0.21/0.38
% 0.21/0.38 % (12192)Memory used [KB]: 5628
% 0.21/0.38 % (12192)Time elapsed: 0.007 s
% 0.21/0.38 % (12192)Instructions burned: 8 (million)
% 0.21/0.38 % (12192)------------------------------
% 0.21/0.38 % (12192)------------------------------
% 0.21/0.38 % (12193)Instruction limit reached!
% 0.21/0.38 % (12193)------------------------------
% 0.21/0.38 % (12193)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.38 % (12193)Termination reason: Unknown
% 0.21/0.38 % (12193)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (12193)Memory used [KB]: 5628
% 0.21/0.38 % (12193)Time elapsed: 0.012 s
% 0.21/0.38 % (12193)Instructions burned: 19 (million)
% 0.21/0.38 % (12193)------------------------------
% 0.21/0.38 % (12193)------------------------------
% 0.21/0.39 % (12189)Instruction limit reached!
% 0.21/0.39 % (12189)------------------------------
% 0.21/0.39 % (12189)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (12189)Termination reason: Unknown
% 0.21/0.39 % (12189)Termination phase: Saturation
% 0.21/0.39
% 0.21/0.39 % (12189)Memory used [KB]: 5756
% 0.21/0.39 % (12189)Time elapsed: 0.018 s
% 0.21/0.39 % (12189)Instructions burned: 27 (million)
% 0.21/0.39 % (12189)------------------------------
% 0.21/0.39 % (12189)------------------------------
% 0.21/0.39 % (12195)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)
% 0.21/0.39 % (12194)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)
% 0.21/0.39 % (12196)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)
% 0.21/0.39 % (12187)First to succeed.
% 0.21/0.39 % (12194)Instruction limit reached!
% 0.21/0.39 % (12194)------------------------------
% 0.21/0.39 % (12194)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.39 % (12194)Termination reason: Unknown
% 0.21/0.39 % (12194)Termination phase: Property scanning
% 0.21/0.39
% 0.21/0.39 % (12194)Memory used [KB]: 1023
% 0.21/0.39 % (12194)Time elapsed: 0.004 s
% 0.21/0.39 % (12194)Instructions burned: 4 (million)
% 0.21/0.39 % (12194)------------------------------
% 0.21/0.39 % (12194)------------------------------
% 0.21/0.40 % (12197)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)
% 0.21/0.40 % (12197)Instruction limit reached!
% 0.21/0.40 % (12197)------------------------------
% 0.21/0.40 % (12197)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (12197)Termination reason: Unknown
% 0.21/0.40 % (12197)Termination phase: Property scanning
% 0.21/0.40
% 0.21/0.40 % (12197)Memory used [KB]: 1023
% 0.21/0.40 % (12197)Time elapsed: 0.004 s
% 0.21/0.40 % (12197)Instructions burned: 4 (million)
% 0.21/0.40 % (12197)------------------------------
% 0.21/0.40 % (12197)------------------------------
% 0.21/0.40 % (12196)Instruction limit reached!
% 0.21/0.40 % (12196)------------------------------
% 0.21/0.40 % (12196)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (12196)Termination reason: Unknown
% 0.21/0.40 % (12196)Termination phase: Saturation
% 0.21/0.40
% 0.21/0.40 % (12196)Memory used [KB]: 5628
% 0.21/0.40 % (12196)Time elapsed: 0.010 s
% 0.21/0.40 % (12196)Instructions burned: 15 (million)
% 0.21/0.40 % (12196)------------------------------
% 0.21/0.40 % (12196)------------------------------
% 0.21/0.40 % (12198)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)
% 0.21/0.40 % (12187)Refutation found. Thanks to Tanya!
% 0.21/0.40 % SZS status Theorem for theBenchmark
% 0.21/0.40 % SZS output start Proof for theBenchmark
% 0.21/0.40 thf(type_def_5, type, mu: $tType).
% 0.21/0.40 thf(func_def_0, type, mu: $tType).
% 0.21/0.40 thf(func_def_1, type, meq_ind: mu > mu > $i > $o).
% 0.21/0.40 thf(func_def_2, type, meq_prop: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_4, type, mnot: ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_5, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_6, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_7, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_8, type, mimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_9, type, mequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_10, type, mxor: ($i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_11, type, mforall_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_12, type, mforall_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_13, type, mexists_ind: (mu > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_14, type, mexists_prop: (($i > $o) > $i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_15, type, mtrue: $i > $o).
% 0.21/0.40 thf(func_def_16, type, mfalse: $i > $o).
% 0.21/0.40 thf(func_def_17, type, mbox: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_18, type, mdia: ($i > $i > $o) > ($i > $o) > $i > $o).
% 0.21/0.40 thf(func_def_19, type, mreflexive: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_20, type, msymmetric: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_21, type, mserial: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_22, type, mtransitive: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_23, type, meuclidean: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_24, type, mpartially_functional: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_25, type, mfunctional: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_26, type, mweakly_dense: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_27, type, mweakly_connected: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_28, type, mweakly_directed: ($i > $i > $o) > $o).
% 0.21/0.40 thf(func_def_29, type, mvalid: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_30, type, minvalid: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_31, type, msatisfiable: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_32, type, mcountersatisfiable: ($i > $o) > $o).
% 0.21/0.40 thf(func_def_48, type, sK0: $i > $i > $o).
% 0.21/0.40 thf(func_def_51, type, sK3: $i > $o).
% 0.21/0.40 thf(func_def_52, type, sK4: $i > $o).
% 0.21/0.40 thf(f592,plain,(
% 0.21/0.40 $false),
% 0.21/0.40 inference(avatar_sat_refutation,[],[f338,f343,f352,f357,f374,f379,f388,f393,f464,f467,f481,f488,f503,f519,f544,f559,f585,f591])).
% 0.21/0.40 thf(f591,plain,(
% 0.21/0.40 ~spl1_1 | ~spl1_6 | ~spl1_16),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f590])).
% 0.21/0.40 thf(f590,plain,(
% 0.21/0.40 $false | (~spl1_1 | ~spl1_6 | ~spl1_16)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f586])).
% 0.21/0.40 thf(f586,plain,(
% 0.21/0.40 ($true = $false) | (~spl1_1 | ~spl1_6 | ~spl1_16)),
% 0.21/0.40 inference(superposition,[],[f351,f565])).
% 0.21/0.40 thf(f565,plain,(
% 0.21/0.40 ($false = (sK3 @ sK15)) | (~spl1_1 | ~spl1_16)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f563])).
% 0.21/0.40 thf(f563,plain,(
% 0.21/0.40 ($false = (sK3 @ sK15)) | ($true = $false) | (~spl1_1 | ~spl1_16)),
% 0.21/0.40 inference(superposition,[],[f396,f329])).
% 0.21/0.40 thf(f329,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK15) = $true) | ~spl1_1),
% 0.21/0.40 inference(avatar_component_clause,[],[f327])).
% 0.21/0.40 thf(f327,plain,(
% 0.21/0.40 spl1_1 <=> ((sK0 @ sK2 @ sK15) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_1])])).
% 0.21/0.40 thf(f396,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ((sK3 @ X1) = $false)) ) | ~spl1_16),
% 0.21/0.40 inference(avatar_component_clause,[],[f395])).
% 0.21/0.40 thf(f395,plain,(
% 0.21/0.40 spl1_16 <=> ! [X1] : (($false = (sK0 @ sK2 @ X1)) | ((sK3 @ X1) = $false))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_16])])).
% 0.21/0.40 thf(f351,plain,(
% 0.21/0.40 ($true = (sK3 @ sK15)) | ~spl1_6),
% 0.21/0.40 inference(avatar_component_clause,[],[f349])).
% 0.21/0.40 thf(f349,plain,(
% 0.21/0.40 spl1_6 <=> ($true = (sK3 @ sK15))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_6])])).
% 0.21/0.40 thf(f585,plain,(
% 0.21/0.40 ~spl1_5 | ~spl1_7 | ~spl1_23),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f584])).
% 0.21/0.40 thf(f584,plain,(
% 0.21/0.40 $false | (~spl1_5 | ~spl1_7 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f581])).
% 0.21/0.40 thf(f581,plain,(
% 0.21/0.40 ($true = $false) | (~spl1_5 | ~spl1_7 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f356,f578])).
% 0.21/0.40 thf(f578,plain,(
% 0.21/0.40 ((sK4 @ sK16) = $false) | (~spl1_5 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f574])).
% 0.21/0.40 thf(f574,plain,(
% 0.21/0.40 ((sK4 @ sK16) = $false) | ($true = $false) | (~spl1_5 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f427,f347])).
% 0.21/0.40 thf(f347,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK16)) | ~spl1_5),
% 0.21/0.40 inference(avatar_component_clause,[],[f345])).
% 0.21/0.40 thf(f345,plain,(
% 0.21/0.40 spl1_5 <=> ($true = (sK0 @ sK2 @ sK16))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_5])])).
% 0.21/0.40 thf(f427,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ((sK4 @ X1) = $false)) ) | ~spl1_23),
% 0.21/0.40 inference(avatar_component_clause,[],[f426])).
% 0.21/0.40 thf(f426,plain,(
% 0.21/0.40 spl1_23 <=> ! [X1] : (($false = (sK0 @ sK2 @ X1)) | ((sK4 @ X1) = $false))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_23])])).
% 0.21/0.40 thf(f356,plain,(
% 0.21/0.40 ($true = (sK4 @ sK16)) | ~spl1_7),
% 0.21/0.40 inference(avatar_component_clause,[],[f354])).
% 0.21/0.40 thf(f354,plain,(
% 0.21/0.40 spl1_7 <=> ($true = (sK4 @ sK16))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_7])])).
% 0.21/0.40 thf(f559,plain,(
% 0.21/0.40 ~spl1_2 | ~spl1_4 | ~spl1_23),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f558])).
% 0.21/0.40 thf(f558,plain,(
% 0.21/0.40 $false | (~spl1_2 | ~spl1_4 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f554])).
% 0.21/0.40 thf(f554,plain,(
% 0.21/0.40 ($true = $false) | (~spl1_2 | ~spl1_4 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f553,f342])).
% 0.21/0.40 thf(f342,plain,(
% 0.21/0.40 ($true = (sK4 @ sK17)) | ~spl1_4),
% 0.21/0.40 inference(avatar_component_clause,[],[f340])).
% 0.21/0.40 thf(f340,plain,(
% 0.21/0.40 spl1_4 <=> ($true = (sK4 @ sK17))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_4])])).
% 0.21/0.40 thf(f553,plain,(
% 0.21/0.40 ((sK4 @ sK17) = $false) | (~spl1_2 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f548])).
% 0.21/0.40 thf(f548,plain,(
% 0.21/0.40 ((sK4 @ sK17) = $false) | ($true = $false) | (~spl1_2 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f427,f333])).
% 0.21/0.40 thf(f333,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK17) = $true) | ~spl1_2),
% 0.21/0.40 inference(avatar_component_clause,[],[f331])).
% 0.21/0.40 thf(f331,plain,(
% 0.21/0.40 spl1_2 <=> ((sK0 @ sK2 @ sK17) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_2])])).
% 0.21/0.40 thf(f544,plain,(
% 0.21/0.40 ~spl1_14 | ~spl1_15 | ~spl1_16),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f543])).
% 0.21/0.40 thf(f543,plain,(
% 0.21/0.40 $false | (~spl1_14 | ~spl1_15 | ~spl1_16)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f540])).
% 0.21/0.40 thf(f540,plain,(
% 0.21/0.40 ($true = $false) | (~spl1_14 | ~spl1_15 | ~spl1_16)),
% 0.21/0.40 inference(superposition,[],[f392,f538])).
% 0.21/0.40 thf(f538,plain,(
% 0.21/0.40 ((sK3 @ sK13) = $false) | (~spl1_14 | ~spl1_16)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f532])).
% 0.21/0.40 thf(f532,plain,(
% 0.21/0.40 ($true = $false) | ((sK3 @ sK13) = $false) | (~spl1_14 | ~spl1_16)),
% 0.21/0.40 inference(superposition,[],[f387,f396])).
% 0.21/0.40 thf(f387,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK13)) | ~spl1_14),
% 0.21/0.40 inference(avatar_component_clause,[],[f385])).
% 0.21/0.40 thf(f385,plain,(
% 0.21/0.40 spl1_14 <=> ($true = (sK0 @ sK2 @ sK13))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_14])])).
% 0.21/0.40 thf(f392,plain,(
% 0.21/0.40 ((sK3 @ sK13) = $true) | ~spl1_15),
% 0.21/0.40 inference(avatar_component_clause,[],[f390])).
% 0.21/0.40 thf(f390,plain,(
% 0.21/0.40 spl1_15 <=> ((sK3 @ sK13) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_15])])).
% 0.21/0.40 thf(f519,plain,(
% 0.21/0.40 ~spl1_9 | ~spl1_12 | ~spl1_16),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f518])).
% 0.21/0.40 thf(f518,plain,(
% 0.21/0.40 $false | (~spl1_9 | ~spl1_12 | ~spl1_16)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f514])).
% 0.21/0.40 thf(f514,plain,(
% 0.21/0.40 ($true = $false) | (~spl1_9 | ~spl1_12 | ~spl1_16)),
% 0.21/0.40 inference(superposition,[],[f513,f378])).
% 0.21/0.40 thf(f378,plain,(
% 0.21/0.40 ($true = (sK3 @ sK14)) | ~spl1_12),
% 0.21/0.40 inference(avatar_component_clause,[],[f376])).
% 0.21/0.40 thf(f376,plain,(
% 0.21/0.40 spl1_12 <=> ($true = (sK3 @ sK14))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_12])])).
% 0.21/0.40 thf(f513,plain,(
% 0.21/0.40 ($false = (sK3 @ sK14)) | (~spl1_9 | ~spl1_16)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f507])).
% 0.21/0.40 thf(f507,plain,(
% 0.21/0.40 ($false = (sK3 @ sK14)) | ($true = $false) | (~spl1_9 | ~spl1_16)),
% 0.21/0.40 inference(superposition,[],[f365,f396])).
% 0.21/0.40 thf(f365,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK14)) | ~spl1_9),
% 0.21/0.40 inference(avatar_component_clause,[],[f363])).
% 0.21/0.40 thf(f363,plain,(
% 0.21/0.40 spl1_9 <=> ($true = (sK0 @ sK2 @ sK14))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_9])])).
% 0.21/0.40 thf(f503,plain,(
% 0.21/0.40 ~spl1_8 | ~spl1_13 | ~spl1_23),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f502])).
% 0.21/0.40 thf(f502,plain,(
% 0.21/0.40 $false | (~spl1_8 | ~spl1_13 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f498])).
% 0.21/0.40 thf(f498,plain,(
% 0.21/0.40 ($true = $false) | (~spl1_8 | ~spl1_13 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f497,f383])).
% 0.21/0.40 thf(f383,plain,(
% 0.21/0.40 ($true = (sK4 @ sK12)) | ~spl1_13),
% 0.21/0.40 inference(avatar_component_clause,[],[f381])).
% 0.21/0.40 thf(f381,plain,(
% 0.21/0.40 spl1_13 <=> ($true = (sK4 @ sK12))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_13])])).
% 0.21/0.40 thf(f497,plain,(
% 0.21/0.40 ($false = (sK4 @ sK12)) | (~spl1_8 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f492])).
% 0.21/0.40 thf(f492,plain,(
% 0.21/0.40 ($false = (sK4 @ sK12)) | ($true = $false) | (~spl1_8 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f427,f361])).
% 0.21/0.40 thf(f361,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK12) = $true) | ~spl1_8),
% 0.21/0.40 inference(avatar_component_clause,[],[f359])).
% 0.21/0.40 thf(f359,plain,(
% 0.21/0.40 spl1_8 <=> ((sK0 @ sK2 @ sK12) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_8])])).
% 0.21/0.40 thf(f488,plain,(
% 0.21/0.40 ~spl1_3 | ~spl1_11 | ~spl1_16),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f487])).
% 0.21/0.40 thf(f487,plain,(
% 0.21/0.40 $false | (~spl1_3 | ~spl1_11 | ~spl1_16)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f484])).
% 0.21/0.40 thf(f484,plain,(
% 0.21/0.40 ($true = $false) | (~spl1_3 | ~spl1_11 | ~spl1_16)),
% 0.21/0.40 inference(superposition,[],[f471,f373])).
% 0.21/0.40 thf(f373,plain,(
% 0.21/0.40 ($true = (sK3 @ sK11)) | ~spl1_11),
% 0.21/0.40 inference(avatar_component_clause,[],[f371])).
% 0.21/0.40 thf(f371,plain,(
% 0.21/0.40 spl1_11 <=> ($true = (sK3 @ sK11))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_11])])).
% 0.21/0.40 thf(f471,plain,(
% 0.21/0.40 ($false = (sK3 @ sK11)) | (~spl1_3 | ~spl1_16)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f469])).
% 0.21/0.40 thf(f469,plain,(
% 0.21/0.40 ($true = $false) | ($false = (sK3 @ sK11)) | (~spl1_3 | ~spl1_16)),
% 0.21/0.40 inference(superposition,[],[f337,f396])).
% 0.21/0.40 thf(f337,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK11)) | ~spl1_3),
% 0.21/0.40 inference(avatar_component_clause,[],[f335])).
% 0.21/0.40 thf(f335,plain,(
% 0.21/0.40 spl1_3 <=> ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_3])])).
% 0.21/0.40 thf(f481,plain,(
% 0.21/0.40 ~spl1_3 | ~spl1_10 | ~spl1_23),
% 0.21/0.40 inference(avatar_contradiction_clause,[],[f480])).
% 0.21/0.40 thf(f480,plain,(
% 0.21/0.40 $false | (~spl1_3 | ~spl1_10 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f476])).
% 0.21/0.40 thf(f476,plain,(
% 0.21/0.40 ($true = $false) | (~spl1_3 | ~spl1_10 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f475,f369])).
% 0.21/0.40 thf(f369,plain,(
% 0.21/0.40 ((sK4 @ sK11) = $true) | ~spl1_10),
% 0.21/0.40 inference(avatar_component_clause,[],[f367])).
% 0.21/0.40 thf(f367,plain,(
% 0.21/0.40 spl1_10 <=> ((sK4 @ sK11) = $true)),
% 0.21/0.40 introduced(avatar_definition,[new_symbols(naming,[spl1_10])])).
% 0.21/0.40 thf(f475,plain,(
% 0.21/0.40 ((sK4 @ sK11) = $false) | (~spl1_3 | ~spl1_23)),
% 0.21/0.40 inference(trivial_inequality_removal,[],[f473])).
% 0.21/0.40 thf(f473,plain,(
% 0.21/0.40 ($true = $false) | ((sK4 @ sK11) = $false) | (~spl1_3 | ~spl1_23)),
% 0.21/0.40 inference(superposition,[],[f337,f427])).
% 0.21/0.40 thf(f467,plain,(
% 0.21/0.40 spl1_23 | spl1_23),
% 0.21/0.40 inference(avatar_split_clause,[],[f171,f426,f426])).
% 0.21/0.40 thf(f171,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK0 @ sK2 @ X2) = $false) | ($false = (sK0 @ sK2 @ X1)) | ((sK4 @ X1) = $false) | ((sK4 @ X2) = $false)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f169])).
% 0.21/0.40 thf(f169,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($false = (sK0 @ sK2 @ X1)) | ((sK4 @ X1) = $false) | ((sK0 @ sK2 @ X2) = $false) | (((sK4 @ X2) | (sK3 @ X2)) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f168])).
% 0.21/0.40 thf(f168,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ sK2 @ X1))) | (((sK4 @ X2) | (sK3 @ X2)) = $false) | ((sK4 @ X1) = $false) | ((sK0 @ sK2 @ X2) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f167])).
% 0.21/0.40 thf(f167,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ ((sK4 @ X2) | (sK3 @ X2)))) | ($true = (~ (sK0 @ sK2 @ X1))) | ((sK0 @ sK2 @ X2) = $false) | ((sK4 @ X1) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f166])).
% 0.21/0.40 thf(f166,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ sK2 @ X2))) | ($true = (~ ((sK4 @ X2) | (sK3 @ X2)))) | ((sK4 @ X1) = $false) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f165])).
% 0.21/0.40 thf(f165,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : ((((~ ((sK4 @ X2) | (sK3 @ X2))) | (~ (sK0 @ sK2 @ X2))) = $true) | ($true = (~ (sK0 @ sK2 @ X1))) | ((sK4 @ X1) = $false)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f164])).
% 0.21/0.40 thf(f164,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ sK2 @ X1))) | ((sK4 @ X1) = $false) | (((^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))) @ X2) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f163])).
% 0.21/0.40 thf(f163,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $true) | ((sK4 @ X1) = $false) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f162])).
% 0.21/0.40 thf(f162,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($true = (~ (sK4 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $true) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f161])).
% 0.21/0.40 thf(f161,plain,(
% 0.21/0.40 ( ! [X1 : $i] : ((((~ (sK4 @ X1)) | (~ (sK0 @ sK2 @ X1))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $true)) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f160])).
% 0.21/0.40 thf(f160,plain,(
% 0.21/0.40 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ X1) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f159])).
% 0.21/0.40 thf(f159,plain,(
% 0.21/0.40 ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f158])).
% 0.21/0.40 thf(f158,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f157])).
% 0.21/0.40 thf(f157,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f155])).
% 0.21/0.40 thf(f155,plain,(
% 0.21/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f153])).
% 0.21/0.40 thf(f153,plain,(
% 0.21/0.40 ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f151])).
% 0.21/0.40 thf(f151,plain,(
% 0.21/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))))) = $false) | ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f150])).
% 0.21/0.40 thf(f150,plain,(
% 0.21/0.40 ((~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))) = $true) | (((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f149])).
% 0.21/0.40 thf(f149,plain,(
% 0.21/0.40 ($true = (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))))))) | ((~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))) = $true)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f148])).
% 0.21/0.40 thf(f148,plain,(
% 0.21/0.40 ($true = ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))))) | (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))))))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f147])).
% 0.21/0.40 thf(f147,plain,(
% 0.21/0.40 ((~ ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) | (~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))))) | (~ (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))))))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f146])).
% 0.21/0.40 thf(f146,plain,(
% 0.21/0.40 ($false = ((^[Y0 : $i > $o]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((Y0 @ Y1) | (sK3 @ Y1))) | (~ (sK0 @ sK2 @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK3 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK3 @ Y1)) | (~ (sK0 @ sK2 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ ((Y0 @ Y1) | (sK3 @ Y1))) | (~ (sK0 @ sK2 @ Y1)))))))))) @ sK4))),
% 0.21/0.40 inference(sigma_clausification,[],[f145])).
% 0.21/0.40 thf(f145,plain,(
% 0.21/0.40 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (~ ((~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ ((Y0 @ Y1) | (sK3 @ Y1))) | (~ (sK0 @ sK2 @ Y1)))))) | (~ ((~ (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK3 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))))))) | (~ (((~ (!! @ $i @ (^[Y1 : $i]: ((~ (Y0 @ Y1)) | (~ (sK0 @ sK2 @ Y1)))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((~ (sK3 @ Y1)) | (~ (sK0 @ sK2 @ Y1))))))) | (!! @ $i @ (^[Y1 : $i]: ((~ ((Y0 @ Y1) | (sK3 @ Y1))) | (~ (sK0 @ sK2 @ Y1))))))))))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f144])).
% 0.21/0.40 thf(f144,plain,(
% 0.21/0.40 (((^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ ((Y1 @ Y2) | (Y0 @ Y2))) | (~ (sK0 @ sK2 @ Y2)))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (sK0 @ sK2 @ Y2)))))))))) | (~ (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (sK0 @ sK2 @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ ((Y1 @ Y2) | (Y0 @ Y2))) | (~ (sK0 @ sK2 @ Y2)))))))))))) @ sK3) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f143])).
% 0.21/0.40 thf(f143,plain,(
% 0.21/0.40 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (~ ((~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ ((Y1 @ Y2) | (Y0 @ Y2))) | (~ (sK0 @ sK2 @ Y2)))))) | (~ ((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (sK0 @ sK2 @ Y2)))))))))) | (~ (((~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y1 @ Y2)) | (~ (sK0 @ sK2 @ Y2)))))) | (~ (!! @ $i @ (^[Y2 : $i]: ((~ (Y0 @ Y2)) | (~ (sK0 @ sK2 @ Y2))))))) | (!! @ $i @ (^[Y2 : $i]: ((~ ((Y1 @ Y2) | (Y0 @ Y2))) | (~ (sK0 @ sK2 @ Y2))))))))))))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f142])).
% 0.21/0.40 thf(f142,plain,(
% 0.21/0.40 (((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (Y1 @ Y3))) | (~ (sK0 @ Y0 @ Y3)))))) | (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))))))) | (~ (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y0 @ Y3))))))) | (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (Y1 @ Y3))) | (~ (sK0 @ Y0 @ Y3)))))))))))))) @ sK2) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f141])).
% 0.21/0.40 thf(f141,plain,(
% 0.21/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (Y1 @ Y3))) | (~ (sK0 @ Y0 @ Y3)))))) | (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))))))) | (~ (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y0 @ Y3))))))) | (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (Y1 @ Y3))) | (~ (sK0 @ Y0 @ Y3))))))))))))))))),
% 0.21/0.40 inference(boolean_simplification,[],[f140])).
% 0.21/0.40 thf(f140,plain,(
% 0.21/0.40 ($true != (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (~ ((~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (Y1 @ Y3))) | (~ (sK0 @ Y0 @ Y3)))))) | (~ ((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))))))) | (~ (((~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y2 @ Y3)) | (~ (sK0 @ Y0 @ Y3)))))) | (~ (!! @ $i @ (^[Y3 : $i]: ((~ (Y1 @ Y3)) | (~ (sK0 @ Y0 @ Y3))))))) | (~ (~ (!! @ $i @ (^[Y3 : $i]: ((~ ((Y2 @ Y3) | (Y1 @ Y3))) | (~ (sK0 @ Y0 @ Y3))))))))))))))))))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f139])).
% 0.21/0.40 thf(f139,plain,(
% 0.21/0.40 ($true != ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i > $o]: ((^[Y1 : ($i > $o) > $i > $o]: ((^[Y2 : $i]: (!! @ ($i > $o) @ (^[Y3 : $i > $o]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y5)))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y2 @ Y3) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i > $o]: ((^[Y7 : $i > $o]: ((^[Y8 : $i]: ((Y7 @ Y8) | (Y6 @ Y8))))))) @ ((^[Y6 : $i > $o]: ((^[Y7 : $i]: (~ (Y6 @ Y7))))) @ Y4) @ Y5)))) @ Y3 @ Y2))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ sK0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ Y0 @ Y1)) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ sK0 @ Y0) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ ((^[Y4 : $i > $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: (!! @ $i @ (^[Y7 : $i]: ((Y5 @ Y7) | (~ (Y4 @ Y6 @ Y7)))))))))) @ Y2 @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y3)))))) @ sK0 @ Y1)))))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f115,f119,f120,f120,f133,f138,f124,f124,f138,f138])).
% 0.21/0.40 thf(f124,plain,(
% 0.21/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f50])).
% 0.21/0.40 thf(f50,plain,(
% 0.21/0.40 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f49])).
% 0.21/0.40 thf(f49,plain,(
% 0.21/0.40 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.21/0.40 inference(rectify,[],[f4])).
% 0.21/0.40 thf(f4,axiom,(
% 0.21/0.40 (mor = (^[X3 : $i > $o, X4 : $i > $o, X2 : $i] : ((X3 @ X2) | (X4 @ X2))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mor)).
% 0.21/0.40 thf(f138,plain,(
% 0.21/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ ((^[Y2 : $i > $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: (!! @ $i @ (^[Y5 : $i]: ((Y3 @ Y5) | (~ (Y2 @ Y4 @ Y5)))))))))) @ Y0 @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y1)))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f111,f101,f127,f101])).
% 0.21/0.40 thf(f127,plain,(
% 0.21/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f76])).
% 0.21/0.40 thf(f76,plain,(
% 0.21/0.40 (mbox = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: (!! @ $i @ (^[Y3 : $i]: ((Y1 @ Y3) | (~ (Y0 @ Y2 @ Y3)))))))))))),
% 0.21/0.40 inference(fool_elimination,[],[f75])).
% 0.21/0.40 thf(f75,plain,(
% 0.21/0.40 (mbox = (^[X0 : $i > $i > $o, X1 : $i > $o, X2 : $i] : (! [X3] : (~(X0 @ X2 @ X3) | (X1 @ X3)))))),
% 0.21/0.40 inference(rectify,[],[f16])).
% 0.21/0.40 thf(f16,axiom,(
% 0.21/0.40 (mbox = (^[X6 : $i > $i > $o, X3 : $i > $o, X2 : $i] : (! [X7] : (~(X6 @ X2 @ X7) | (X3 @ X7)))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mbox)).
% 0.21/0.40 thf(f101,plain,(
% 0.21/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f54])).
% 0.21/0.40 thf(f54,plain,(
% 0.21/0.40 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.21/0.40 inference(fool_elimination,[],[f53])).
% 0.21/0.40 thf(f53,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))) = mnot)),
% 0.21/0.40 inference(rectify,[],[f3])).
% 0.21/0.40 thf(f3,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X2 : $i] : (~(X3 @ X2))) = mnot)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mnot)).
% 0.21/0.40 thf(f111,plain,(
% 0.21/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f58])).
% 0.21/0.40 thf(f58,plain,(
% 0.21/0.40 (mdia = (^[Y0 : $i > $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mbox @ Y0 @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f57])).
% 0.21/0.40 thf(f57,plain,(
% 0.21/0.40 ((^[X0 : $i > $i > $o, X1 : $i > $o] : (mnot @ (mbox @ X0 @ (mnot @ X1)))) = mdia)),
% 0.21/0.40 inference(rectify,[],[f17])).
% 0.21/0.40 thf(f17,axiom,(
% 0.21/0.40 ((^[X6 : $i > $i > $o, X3 : $i > $o] : (mnot @ (mbox @ X6 @ (mnot @ X3)))) = mdia)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mdia)).
% 0.21/0.40 thf(f133,plain,(
% 0.21/0.40 (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]: ((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))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f100,f130,f131,f131])).
% 0.21/0.40 thf(f131,plain,(
% 0.21/0.40 (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)))))),
% 0.21/0.40 inference(definition_unfolding,[],[f123,f124,f101])).
% 0.21/0.40 thf(f123,plain,(
% 0.21/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f42])).
% 0.21/0.40 thf(f42,plain,(
% 0.21/0.40 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.21/0.40 inference(fool_elimination,[],[f41])).
% 0.21/0.40 thf(f41,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.21/0.40 inference(rectify,[],[f6])).
% 0.21/0.40 thf(f6,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mimplies)).
% 0.21/0.40 thf(f130,plain,(
% 0.21/0.40 (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)))))))),
% 0.21/0.40 inference(definition_unfolding,[],[f113,f101,f124,f101,f101])).
% 0.21/0.40 thf(f113,plain,(
% 0.21/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f92])).
% 0.21/0.40 thf(f92,plain,(
% 0.21/0.40 (mand = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mnot @ (mor @ (mnot @ Y0) @ (mnot @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f91])).
% 0.21/0.40 thf(f91,plain,(
% 0.21/0.40 (mand = (^[X0 : $i > $o, X1 : $i > $o] : (mnot @ (mor @ (mnot @ X0) @ (mnot @ X1)))))),
% 0.21/0.40 inference(rectify,[],[f5])).
% 0.21/0.40 thf(f5,axiom,(
% 0.21/0.40 (mand = (^[X3 : $i > $o, X4 : $i > $o] : (mnot @ (mor @ (mnot @ X3) @ (mnot @ X4)))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mand)).
% 0.21/0.40 thf(f100,plain,(
% 0.21/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f52])).
% 0.21/0.40 thf(f52,plain,(
% 0.21/0.40 (mequiv = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mand @ (mimplies @ Y0 @ Y1) @ (mimplies @ Y1 @ Y0))))))),
% 0.21/0.40 inference(fool_elimination,[],[f51])).
% 0.21/0.40 thf(f51,plain,(
% 0.21/0.40 ((^[X0 : $i > $o, X1 : $i > $o] : (mand @ (mimplies @ X0 @ X1) @ (mimplies @ X1 @ X0))) = mequiv)),
% 0.21/0.40 inference(rectify,[],[f8])).
% 0.21/0.40 thf(f8,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o, X4 : $i > $o] : (mand @ (mimplies @ X3 @ X4) @ (mimplies @ X4 @ X3))) = mequiv)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mequiv)).
% 0.21/0.40 thf(f120,plain,(
% 0.21/0.40 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.40 inference(cnf_transformation,[],[f62])).
% 0.21/0.40 thf(f62,plain,(
% 0.21/0.40 (mforall_prop = (^[Y0 : ($i > $o) > $i > $o]: ((^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: (Y0 @ Y2 @ Y1)))))))),
% 0.21/0.40 inference(fool_elimination,[],[f61])).
% 0.21/0.40 thf(f61,plain,(
% 0.21/0.40 ((^[X0 : ($i > $o) > $i > $o, X1 : $i] : (! [X2 : $i > $o] : (X0 @ X2 @ X1))) = mforall_prop)),
% 0.21/0.40 inference(rectify,[],[f11])).
% 0.21/0.40 thf(f11,axiom,(
% 0.21/0.40 ((^[X3 : ($i > $o) > $i > $o, X2 : $i] : (! [X5 : $i > $o] : (X3 @ X5 @ X2))) = mforall_prop)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mforall_prop)).
% 0.21/0.40 thf(f119,plain,(
% 0.21/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.40 inference(cnf_transformation,[],[f86])).
% 0.21/0.40 thf(f86,plain,(
% 0.21/0.40 (mvalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.21/0.40 inference(fool_elimination,[],[f85])).
% 0.21/0.40 thf(f85,plain,(
% 0.21/0.40 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = mvalid)),
% 0.21/0.40 inference(rectify,[],[f28])).
% 0.21/0.40 thf(f28,axiom,(
% 0.21/0.40 ((^[X3 : $i > $o] : (! [X2] : (X3 @ X2))) = mvalid)),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',mvalid)).
% 0.21/0.40 thf(f115,plain,(
% 0.21/0.40 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ sK0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.21/0.40 inference(cnf_transformation,[],[f97])).
% 0.21/0.40 thf(f97,plain,(
% 0.21/0.40 ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ sK0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.21/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f95,f96])).
% 0.21/0.40 thf(f96,plain,(
% 0.21/0.40 ? [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ X0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ X0 @ Y0) @ (mdia @ X0 @ Y1)))))))) != $true) => ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ sK0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ sK0 @ Y0) @ (mdia @ sK0 @ Y1)))))))) != $true)),
% 0.21/0.40 introduced(choice_axiom,[])).
% 0.21/0.40 thf(f95,plain,(
% 0.21/0.40 ? [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ X0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ X0 @ Y0) @ (mdia @ X0 @ Y1)))))))) != $true)),
% 0.21/0.40 inference(ennf_transformation,[],[f68])).
% 0.21/0.40 thf(f68,plain,(
% 0.21/0.40 ~! [X0 : $i > $i > $o] : ((mvalid @ (mforall_prop @ (^[Y0 : $i > $o]: (mforall_prop @ (^[Y1 : $i > $o]: (mequiv @ (mdia @ X0 @ (mor @ Y0 @ Y1)) @ (mor @ (mdia @ X0 @ Y0) @ (mdia @ X0 @ Y1)))))))) = $true)),
% 0.21/0.40 inference(fool_elimination,[],[f67])).
% 0.21/0.40 thf(f67,plain,(
% 0.21/0.40 ~! [X0 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X1 : $i > $o] : (mforall_prop @ (^[X2 : $i > $o] : (mequiv @ (mdia @ X0 @ (mor @ X1 @ X2)) @ (mor @ (mdia @ X0 @ X1) @ (mdia @ X0 @ X2))))))))),
% 0.21/0.40 inference(rectify,[],[f33])).
% 0.21/0.40 thf(f33,negated_conjecture,(
% 0.21/0.40 ~! [X6 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mequiv @ (mdia @ X6 @ (mor @ X11 @ X12)) @ (mor @ (mdia @ X6 @ X11) @ (mdia @ X6 @ X12))))))))),
% 0.21/0.40 inference(negated_conjecture,[],[f32])).
% 0.21/0.40 thf(f32,conjecture,(
% 0.21/0.40 ! [X6 : $i > $i > $o] : (mvalid @ (mforall_prop @ (^[X11 : $i > $o] : (mforall_prop @ (^[X12 : $i > $o] : (mequiv @ (mdia @ X6 @ (mor @ X11 @ X12)) @ (mor @ (mdia @ X6 @ X11) @ (mdia @ X6 @ X12))))))))),
% 0.21/0.40 file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj)).
% 0.21/0.40 thf(f464,plain,(
% 0.21/0.40 spl1_16 | spl1_16),
% 0.21/0.40 inference(avatar_split_clause,[],[f184,f395,f395])).
% 0.21/0.40 thf(f184,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK3 @ X2) = $false) | ($false = (sK0 @ sK2 @ X1)) | ((sK0 @ sK2 @ X2) = $false) | ((sK3 @ X1) = $false)) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f183])).
% 0.21/0.40 thf(f183,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK0 @ sK2 @ X2) = $false) | (((sK4 @ X1) | (sK3 @ X1)) = $false) | ($false = (sK0 @ sK2 @ X1)) | ((sK3 @ X2) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f182])).
% 0.21/0.40 thf(f182,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ sK2 @ X1))) | ((sK0 @ sK2 @ X2) = $false) | (((sK4 @ X1) | (sK3 @ X1)) = $false) | ((sK3 @ X2) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f181])).
% 0.21/0.40 thf(f181,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((sK0 @ sK2 @ X2) = $false) | ((sK3 @ X2) = $false) | ($true = (~ ((sK4 @ X1) | (sK3 @ X1)))) | ($true = (~ (sK0 @ sK2 @ X1)))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f180])).
% 0.21/0.40 thf(f180,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((~ ((sK4 @ X1) | (sK3 @ X1))) | (~ (sK0 @ sK2 @ X1)))) | ((sK3 @ X2) = $false) | ((sK0 @ sK2 @ X2) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f179])).
% 0.21/0.40 thf(f179,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = (~ (sK0 @ sK2 @ X2))) | ($true = ((~ ((sK4 @ X1) | (sK3 @ X1))) | (~ (sK0 @ sK2 @ X1)))) | ((sK3 @ X2) = $false)) )),
% 0.21/0.40 inference(not_proxy_clausification,[],[f178])).
% 0.21/0.40 thf(f178,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (((~ (sK3 @ X2)) = $true) | ($true = (~ (sK0 @ sK2 @ X2))) | ($true = ((~ ((sK4 @ X1) | (sK3 @ X1))) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f177])).
% 0.21/0.40 thf(f177,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (sK3 @ X2)) | (~ (sK0 @ sK2 @ X2)))) | ($true = ((~ ((sK4 @ X1) | (sK3 @ X1))) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f176])).
% 0.21/0.40 thf(f176,plain,(
% 0.21/0.40 ( ! [X2 : $i,X1 : $i] : (($true = ((~ ((sK4 @ X1) | (sK3 @ X1))) | (~ (sK0 @ sK2 @ X1)))) | ($true = ((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ X2))) )),
% 0.21/0.40 inference(pi_clausification,[],[f175])).
% 0.21/0.40 thf(f175,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | ($true = ((~ ((sK4 @ X1) | (sK3 @ X1))) | (~ (sK0 @ sK2 @ X1))))) )),
% 0.21/0.40 inference(beta_eta_normalization,[],[f174])).
% 0.21/0.40 thf(f174,plain,(
% 0.21/0.40 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (((^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))) @ X1) = $true)) )),
% 0.21/0.40 inference(pi_clausification,[],[f173])).
% 0.21/0.40 thf(f173,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f172])).
% 0.21/0.40 thf(f172,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f156])).
% 0.21/0.40 thf(f156,plain,(
% 0.21/0.40 ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f155])).
% 0.21/0.40 thf(f393,plain,(
% 0.21/0.40 spl1_10 | spl1_11 | spl1_15 | spl1_13),
% 0.21/0.40 inference(avatar_split_clause,[],[f296,f381,f390,f371,f367])).
% 0.21/0.40 thf(f296,plain,(
% 0.21/0.40 ($true = (sK3 @ sK11)) | ((sK3 @ sK13) = $true) | ($true = (sK4 @ sK12)) | ((sK4 @ sK11) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f295])).
% 0.21/0.40 thf(f295,plain,(
% 0.21/0.40 ((sK4 @ sK11) = $true) | ((~ (sK3 @ sK13)) = $false) | ($true = (sK3 @ sK11)) | ($true = (sK4 @ sK12))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f293])).
% 0.21/0.40 thf(f293,plain,(
% 0.21/0.40 ((sK4 @ sK11) = $true) | (((~ (sK3 @ sK13)) | (~ (sK0 @ sK2 @ sK13))) = $false) | ($true = (sK3 @ sK11)) | ($true = (sK4 @ sK12))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f292])).
% 0.21/0.40 thf(f292,plain,(
% 0.21/0.40 ($true = ((sK4 @ sK11) | (sK3 @ sK11))) | ($true = (sK4 @ sK12)) | (((~ (sK3 @ sK13)) | (~ (sK0 @ sK2 @ sK13))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f291])).
% 0.21/0.40 thf(f291,plain,(
% 0.21/0.40 ($true = (sK4 @ sK12)) | (((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK13) = $false) | ($true = ((sK4 @ sK11) | (sK3 @ sK11)))),
% 0.21/0.40 inference(sigma_clausification,[],[f290])).
% 0.21/0.40 thf(f290,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($true = (sK4 @ sK12)) | ($true = ((sK4 @ sK11) | (sK3 @ sK11)))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f289])).
% 0.21/0.40 thf(f289,plain,(
% 0.21/0.40 ($false = (~ (sK4 @ sK12))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($true = ((sK4 @ sK11) | (sK3 @ sK11)))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f287])).
% 0.21/0.40 thf(f287,plain,(
% 0.21/0.40 (((~ (sK4 @ sK12)) | (~ (sK0 @ sK2 @ sK12))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($true = ((sK4 @ sK11) | (sK3 @ sK11)))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f286])).
% 0.21/0.40 thf(f286,plain,(
% 0.21/0.40 ((~ ((sK4 @ sK11) | (sK3 @ sK11))) = $false) | (((~ (sK4 @ sK12)) | (~ (sK0 @ sK2 @ sK12))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f285])).
% 0.21/0.40 thf(f285,plain,(
% 0.21/0.40 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (((~ (sK4 @ sK12)) | (~ (sK0 @ sK2 @ sK12))) = $false) | ((~ ((sK4 @ sK11) | (sK3 @ sK11))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f284])).
% 0.21/0.40 thf(f284,plain,(
% 0.21/0.40 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ((~ ((sK4 @ sK11) | (sK3 @ sK11))) = $false) | (((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK12) = $false)),
% 0.21/0.40 inference(sigma_clausification,[],[f283])).
% 0.21/0.40 thf(f283,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((~ ((sK4 @ sK11) | (sK3 @ sK11))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f281])).
% 0.21/0.40 thf(f281,plain,(
% 0.21/0.40 (((~ ((sK4 @ sK11) | (sK3 @ sK11))) | (~ (sK0 @ sK2 @ sK11))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f280])).
% 0.21/0.40 thf(f280,plain,(
% 0.21/0.40 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (((~ ((sK4 @ sK11) | (sK3 @ sK11))) | (~ (sK0 @ sK2 @ sK11))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f279])).
% 0.21/0.40 thf(f279,plain,(
% 0.21/0.40 (((^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))) @ sK11) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))),
% 0.21/0.40 inference(sigma_clausification,[],[f278])).
% 0.21/0.40 thf(f278,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f277])).
% 0.21/0.40 thf(f277,plain,(
% 0.21/0.40 (((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f206])).
% 0.21/0.40 thf(f206,plain,(
% 0.21/0.40 ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f152])).
% 0.21/0.40 thf(f152,plain,(
% 0.21/0.40 ((((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | (!! @ $i @ (^[Y0 : $i]: ((~ ((sK4 @ Y0) | (sK3 @ Y0))) | (~ (sK0 @ sK2 @ Y0)))))) = $false) | ((~ ((~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f151])).
% 0.21/0.40 thf(f388,plain,(
% 0.21/0.40 spl1_10 | spl1_11 | spl1_13 | spl1_14),
% 0.21/0.40 inference(avatar_split_clause,[],[f297,f385,f381,f371,f367])).
% 0.21/0.40 thf(f297,plain,(
% 0.21/0.40 ((sK4 @ sK11) = $true) | ($true = (sK4 @ sK12)) | ($true = (sK0 @ sK2 @ sK13)) | ($true = (sK3 @ sK11))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f294])).
% 0.21/0.40 thf(f294,plain,(
% 0.21/0.40 ((~ (sK0 @ sK2 @ sK13)) = $false) | ($true = (sK4 @ sK12)) | ((sK4 @ sK11) = $true) | ($true = (sK3 @ sK11))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f293])).
% 0.21/0.40 thf(f379,plain,(
% 0.21/0.40 spl1_11 | spl1_12 | spl1_10 | spl1_8),
% 0.21/0.40 inference(avatar_split_clause,[],[f304,f359,f367,f376,f371])).
% 0.21/0.40 thf(f304,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK12) = $true) | ((sK4 @ sK11) = $true) | ($true = (sK3 @ sK11)) | ($true = (sK3 @ sK14))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f303])).
% 0.21/0.40 thf(f303,plain,(
% 0.21/0.40 ($true = (sK3 @ sK11)) | ((sK4 @ sK11) = $true) | ((sK0 @ sK2 @ sK12) = $true) | ($false = (~ (sK3 @ sK14)))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f301])).
% 0.21/0.40 thf(f301,plain,(
% 0.21/0.40 ($true = (sK3 @ sK11)) | ((sK4 @ sK11) = $true) | ((sK0 @ sK2 @ sK12) = $true) | (((~ (sK3 @ sK14)) | (~ (sK0 @ sK2 @ sK14))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f300])).
% 0.21/0.40 thf(f300,plain,(
% 0.21/0.40 ((sK4 @ sK11) = $true) | ((sK0 @ sK2 @ sK12) = $true) | (((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK14) = $false) | ($true = (sK3 @ sK11))),
% 0.21/0.40 inference(sigma_clausification,[],[f299])).
% 0.21/0.40 thf(f299,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK12) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((sK4 @ sK11) = $true) | ($true = (sK3 @ sK11))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f298])).
% 0.21/0.40 thf(f298,plain,(
% 0.21/0.40 ((~ (sK0 @ sK2 @ sK12)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((sK4 @ sK11) = $true) | ($true = (sK3 @ sK11))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f288])).
% 0.21/0.40 thf(f288,plain,(
% 0.21/0.40 ($true = ((sK4 @ sK11) | (sK3 @ sK11))) | ((~ (sK0 @ sK2 @ sK12)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f287])).
% 0.21/0.40 thf(f374,plain,(
% 0.21/0.40 spl1_8 | spl1_9 | spl1_10 | spl1_11),
% 0.21/0.40 inference(avatar_split_clause,[],[f305,f371,f367,f363,f359])).
% 0.21/0.40 thf(f305,plain,(
% 0.21/0.40 ((sK4 @ sK11) = $true) | ((sK0 @ sK2 @ sK12) = $true) | ($true = (sK0 @ sK2 @ sK14)) | ($true = (sK3 @ sK11))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f302])).
% 0.21/0.40 thf(f302,plain,(
% 0.21/0.40 ($false = (~ (sK0 @ sK2 @ sK14))) | ((sK0 @ sK2 @ sK12) = $true) | ((sK4 @ sK11) = $true) | ($true = (sK3 @ sK11))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f301])).
% 0.21/0.40 thf(f357,plain,(
% 0.21/0.40 spl1_6 | spl1_3 | spl1_7),
% 0.21/0.40 inference(avatar_split_clause,[],[f317,f354,f335,f349])).
% 0.21/0.40 thf(f317,plain,(
% 0.21/0.40 ($true = (sK3 @ sK15)) | ($true = (sK0 @ sK2 @ sK11)) | ($true = (sK4 @ sK16))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f316])).
% 0.21/0.40 thf(f316,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK11)) | ((~ (sK4 @ sK16)) = $false) | ($true = (sK3 @ sK15))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f314])).
% 0.21/0.40 thf(f314,plain,(
% 0.21/0.40 (((~ (sK4 @ sK16)) | (~ (sK0 @ sK2 @ sK16))) = $false) | ($true = (sK3 @ sK15)) | ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 inference(beta_eta_normalization,[],[f313])).
% 0.21/0.40 thf(f313,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK11)) | (((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK16) = $false) | ($true = (sK3 @ sK15))),
% 0.21/0.40 inference(sigma_clausification,[],[f312])).
% 0.21/0.40 thf(f312,plain,(
% 0.21/0.40 ($true = (sK3 @ sK15)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f311])).
% 0.21/0.40 thf(f311,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK11)) | ((~ (sK3 @ sK15)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f309])).
% 0.21/0.40 thf(f309,plain,(
% 0.21/0.40 (((~ (sK3 @ sK15)) | (~ (sK0 @ sK2 @ sK15))) = $false) | ($true = (sK0 @ sK2 @ sK11)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f308])).
% 0.21/0.40 thf(f308,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK11)) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($false = ((^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK15))),
% 0.21/0.40 inference(sigma_clausification,[],[f307])).
% 0.21/0.40 thf(f307,plain,(
% 0.21/0.40 ((!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f306])).
% 0.21/0.40 thf(f306,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK11)) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f282])).
% 0.21/0.40 thf(f282,plain,(
% 0.21/0.40 ((~ (sK0 @ sK2 @ sK11)) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((~ (sK3 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))))) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f281])).
% 0.21/0.40 thf(f352,plain,(
% 0.21/0.40 spl1_5 | spl1_3 | spl1_6),
% 0.21/0.40 inference(avatar_split_clause,[],[f318,f349,f335,f345])).
% 0.21/0.40 thf(f318,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK11)) | ($true = (sK3 @ sK15)) | ($true = (sK0 @ sK2 @ sK16))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f315])).
% 0.21/0.40 thf(f315,plain,(
% 0.21/0.40 ($true = (sK3 @ sK15)) | ($false = (~ (sK0 @ sK2 @ sK16))) | ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f314])).
% 0.21/0.40 thf(f343,plain,(
% 0.21/0.40 spl1_1 | spl1_3 | spl1_4),
% 0.21/0.40 inference(avatar_split_clause,[],[f324,f340,f335,f327])).
% 0.21/0.40 thf(f324,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK15) = $true) | ($true = (sK4 @ sK17)) | ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f323])).
% 0.21/0.40 thf(f323,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK15) = $true) | ((~ (sK4 @ sK17)) = $false) | ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f321])).
% 0.21/0.40 thf(f321,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK15) = $true) | ($true = (sK0 @ sK2 @ sK11)) | (((~ (sK4 @ sK17)) | (~ (sK0 @ sK2 @ sK17))) = $false)),
% 0.21/0.40 inference(beta_eta_normalization,[],[f320])).
% 0.21/0.40 thf(f320,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK15) = $true) | (((^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0)))) @ sK17) = $false) | ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 inference(sigma_clausification,[],[f319])).
% 0.21/0.40 thf(f319,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK15) = $true) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false) | ($true = (sK0 @ sK2 @ sK11))),
% 0.21/0.40 inference(not_proxy_clausification,[],[f310])).
% 0.21/0.40 thf(f310,plain,(
% 0.21/0.40 ($true = (sK0 @ sK2 @ sK11)) | ((~ (sK0 @ sK2 @ sK15)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((~ (sK4 @ Y0)) | (~ (sK0 @ sK2 @ Y0))))) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f309])).
% 0.21/0.40 thf(f338,plain,(
% 0.21/0.40 spl1_1 | spl1_2 | spl1_3),
% 0.21/0.40 inference(avatar_split_clause,[],[f325,f335,f331,f327])).
% 0.21/0.40 thf(f325,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK17) = $true) | ($true = (sK0 @ sK2 @ sK11)) | ((sK0 @ sK2 @ sK15) = $true)),
% 0.21/0.40 inference(not_proxy_clausification,[],[f322])).
% 0.21/0.40 thf(f322,plain,(
% 0.21/0.40 ((sK0 @ sK2 @ sK15) = $true) | ($true = (sK0 @ sK2 @ sK11)) | ((~ (sK0 @ sK2 @ sK17)) = $false)),
% 0.21/0.40 inference(binary_proxy_clausification,[],[f321])).
% 0.21/0.40 % SZS output end Proof for theBenchmark
% 0.21/0.40 % (12187)------------------------------
% 0.21/0.40 % (12187)Version: Vampire 4.8 (commit 11aac991b on 2023-10-04 16:26:07 +0200)
% 0.21/0.40 % (12187)Termination reason: Refutation
% 0.21/0.40
% 0.21/0.40 % (12187)Memory used [KB]: 6012
% 0.21/0.40 % (12187)Time elapsed: 0.028 s
% 0.21/0.40 % (12187)Instructions burned: 31 (million)
% 0.21/0.40 % (12187)------------------------------
% 0.21/0.40 % (12187)------------------------------
% 0.21/0.40 % (12186)Success in time 0.034 s
%------------------------------------------------------------------------------