TSTP Solution File: SYO068^4.005 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SYO068^4.005 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n015.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 09:02:42 EDT 2024
% Result : Theorem 0.23s 0.43s
% Output : Refutation 0.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SYO068^4.005 : TPTP v8.2.0. Released v4.0.0.
% 0.13/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.15/0.36 % Computer : n015.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Mon May 20 09:50:38 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 This is a TH0_THM_EQU_NAR problem
% 0.15/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.38 % (32350)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.39 % (32354)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)
% 0.15/0.39 % (32354)Instruction limit reached!
% 0.15/0.39 % (32354)------------------------------
% 0.15/0.39 % (32354)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (32354)Termination reason: Unknown
% 0.15/0.39 % (32354)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (32354)Memory used [KB]: 1023
% 0.15/0.39 % (32354)Time elapsed: 0.003 s
% 0.15/0.39 % (32354)Instructions burned: 2 (million)
% 0.15/0.39 % (32354)------------------------------
% 0.15/0.39 % (32354)------------------------------
% 0.15/0.39 % (32352)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)
% 0.15/0.39 % (32351)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)
% 0.15/0.39 % (32353)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.39 % (32355)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)
% 0.15/0.39 % (32356)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.39 % (32357)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)
% 0.15/0.39 % (32353)Instruction limit reached!
% 0.15/0.39 % (32353)------------------------------
% 0.15/0.39 % (32353)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.39 % (32353)Termination reason: Unknown
% 0.15/0.39 % (32353)Termination phase: shuffling
% 0.15/0.39
% 0.15/0.39 % (32353)Memory used [KB]: 1023
% 0.15/0.39 % (32353)Time elapsed: 0.004 s
% 0.15/0.39 % (32353)Instructions burned: 2 (million)
% 0.15/0.39 % (32353)------------------------------
% 0.15/0.39 % (32353)------------------------------
% 0.15/0.40 % (32357)Instruction limit reached!
% 0.15/0.40 % (32357)------------------------------
% 0.15/0.40 % (32357)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (32357)Termination reason: Unknown
% 0.15/0.40 % (32357)Termination phase: shuffling
% 0.15/0.40
% 0.15/0.40 % (32357)Memory used [KB]: 1023
% 0.15/0.40 % (32357)Time elapsed: 0.005 s
% 0.15/0.40 % (32357)Instructions burned: 3 (million)
% 0.15/0.40 % (32357)------------------------------
% 0.15/0.40 % (32357)------------------------------
% 0.15/0.40 % (32351)Instruction limit reached!
% 0.15/0.40 % (32351)------------------------------
% 0.15/0.40 % (32351)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (32351)Termination reason: Unknown
% 0.15/0.40 % (32351)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (32351)Memory used [KB]: 1023
% 0.15/0.40 % (32351)Time elapsed: 0.006 s
% 0.15/0.40 % (32351)Instructions burned: 4 (million)
% 0.15/0.40 % (32351)------------------------------
% 0.15/0.40 % (32351)------------------------------
% 0.15/0.40 % (32355)Refutation not found, incomplete strategy
% 0.15/0.40 % (32355)------------------------------
% 0.15/0.40 % (32355)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (32355)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.40
% 0.15/0.40
% 0.15/0.40 % (32355)Memory used [KB]: 5500
% 0.15/0.40 % (32355)Time elapsed: 0.007 s
% 0.15/0.40 % (32355)Instructions burned: 4 (million)
% 0.15/0.40 % (32355)------------------------------
% 0.15/0.40 % (32355)------------------------------
% 0.15/0.41 % (32356)Instruction limit reached!
% 0.15/0.41 % (32356)------------------------------
% 0.15/0.41 % (32356)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.41 % (32356)Termination reason: Unknown
% 0.15/0.41 % (32356)Termination phase: Saturation
% 0.15/0.41
% 0.15/0.41 % (32356)Memory used [KB]: 5628
% 0.15/0.41 % (32356)Time elapsed: 0.018 s
% 0.15/0.41 % (32356)Instructions burned: 18 (million)
% 0.15/0.41 % (32356)------------------------------
% 0.15/0.41 % (32356)------------------------------
% 0.15/0.42 % (32352)Instruction limit reached!
% 0.15/0.42 % (32352)------------------------------
% 0.15/0.42 % (32352)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (32352)Termination reason: Unknown
% 0.15/0.42 % (32352)Termination phase: Saturation
% 0.15/0.42
% 0.15/0.42 % (32352)Memory used [KB]: 5756
% 0.15/0.42 % (32352)Time elapsed: 0.027 s
% 0.15/0.42 % (32352)Instructions burned: 27 (million)
% 0.15/0.42 % (32352)------------------------------
% 0.15/0.42 % (32352)------------------------------
% 0.15/0.42 % (32358)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)
% 0.15/0.42 % (32359)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)
% 0.15/0.42 % (32350)First to succeed.
% 0.15/0.42 % (32360)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)
% 0.15/0.42 % (32361)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)
% 0.15/0.42 % (32360)Instruction limit reached!
% 0.15/0.42 % (32360)------------------------------
% 0.15/0.42 % (32360)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.42 % (32360)Termination reason: Unknown
% 0.15/0.42 % (32360)Termination phase: Naming
% 0.15/0.42
% 0.15/0.42 % (32360)Memory used [KB]: 1023
% 0.15/0.42 % (32360)Time elapsed: 0.004 s
% 0.15/0.42 % (32360)Instructions burned: 4 (million)
% 0.15/0.42 % (32360)------------------------------
% 0.15/0.42 % (32360)------------------------------
% 0.15/0.43 % (32359)Refutation not found, incomplete strategy
% 0.15/0.43 % (32359)------------------------------
% 0.15/0.43 % (32359)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.43 % (32359)Termination reason: Refutation not found, incomplete strategy
% 0.15/0.43
% 0.15/0.43
% 0.15/0.43 % (32359)Memory used [KB]: 5628
% 0.15/0.43 % (32359)Time elapsed: 0.008 s
% 0.15/0.43 % (32359)Instructions burned: 12 (million)
% 0.15/0.43 % (32359)------------------------------
% 0.15/0.43 % (32359)------------------------------
% 0.15/0.43 % (32363)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on theBenchmark for (2999ds/16Mi)
% 0.15/0.43 % (32362)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.23/0.43 % (32350)Refutation found. Thanks to Tanya!
% 0.23/0.43 % SZS status Theorem for theBenchmark
% 0.23/0.43 % SZS output start Proof for theBenchmark
% 0.23/0.43 thf(func_def_0, type, irel: $i > $i > $o).
% 0.23/0.43 thf(func_def_2, type, mnot: ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_3, type, mor: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_4, type, mand: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_5, type, mimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_6, type, mbox_s4: ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_7, type, iatom: ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_8, type, inot: ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_9, type, itrue: $i > $o).
% 0.23/0.43 thf(func_def_10, type, ifalse: $i > $o).
% 0.23/0.43 thf(func_def_11, type, iand: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_12, type, ior: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_13, type, iimplies: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_14, type, iimplied: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_15, type, iequiv: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_16, type, ixor: ($i > $o) > ($i > $o) > $i > $o).
% 0.23/0.43 thf(func_def_17, type, ivalid: ($i > $o) > $o).
% 0.23/0.43 thf(func_def_18, type, isatisfiable: ($i > $o) > $o).
% 0.23/0.43 thf(func_def_19, type, icountersatisfiable: ($i > $o) > $o).
% 0.23/0.43 thf(func_def_20, type, iinvalid: ($i > $o) > $o).
% 0.23/0.43 thf(func_def_21, type, p0: $i > $o).
% 0.23/0.43 thf(func_def_22, type, p1: $i > $o).
% 0.23/0.43 thf(func_def_23, type, p2: $i > $o).
% 0.23/0.43 thf(func_def_24, type, p3: $i > $o).
% 0.23/0.43 thf(func_def_25, type, p4: $i > $o).
% 0.23/0.43 thf(func_def_26, type, p5: $i > $o).
% 0.23/0.43 thf(func_def_40, type, sK1: $i > $i).
% 0.23/0.43 thf(func_def_41, type, sK2: $i > $i).
% 0.23/0.43 thf(func_def_42, type, sK3: $i > $i).
% 0.23/0.43 thf(func_def_43, type, sK4: $i > $i).
% 0.23/0.43 thf(func_def_44, type, sK5: $i > $i).
% 0.23/0.43 thf(func_def_45, type, sK6: $i > $i).
% 0.23/0.43 thf(func_def_47, type, sK8: $i > $i).
% 0.23/0.43 thf(func_def_48, type, sK9: $i > $i).
% 0.23/0.43 thf(func_def_49, type, sK10: $i > $i).
% 0.23/0.43 thf(func_def_50, type, sK11: $i > $i).
% 0.23/0.43 thf(func_def_51, type, sK12: $i > $i).
% 0.23/0.43 thf(func_def_52, type, sK13: $i > $i).
% 0.23/0.43 thf(func_def_53, type, sK14: $i > $i).
% 0.23/0.43 thf(func_def_54, type, sK15: $i > $i).
% 0.23/0.43 thf(func_def_55, type, sK16: $i > $i).
% 0.23/0.43 thf(f469,plain,(
% 0.23/0.43 $false),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f468])).
% 0.23/0.43 thf(f468,plain,(
% 0.23/0.43 ($false = $true)),
% 0.23/0.43 inference(superposition,[],[f199,f466])).
% 0.23/0.43 thf(f466,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p0 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f464])).
% 0.23/0.43 thf(f464,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = $true) | ((p0 @ X0) = $true)) )),
% 0.23/0.43 inference(superposition,[],[f417,f462])).
% 0.23/0.43 thf(f462,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p1 @ (sK1 @ X0)) = $false) | ((p0 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f460])).
% 0.23/0.43 thf(f460,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p1 @ (sK1 @ X0)) = $false) | ((p0 @ X0) = $true) | ($false = $true)) )),
% 0.23/0.43 inference(superposition,[],[f305,f417])).
% 0.23/0.43 thf(f305,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = (p1 @ (sK3 @ X0))) | ((p1 @ (sK1 @ X0)) = $false) | ((p0 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f298])).
% 0.23/0.43 thf(f298,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p0 @ X0) = $true) | ($false = $true) | ((p1 @ (sK1 @ X0)) = $false) | ($false = (p1 @ (sK3 @ X0)))) )),
% 0.23/0.43 inference(superposition,[],[f296,f109])).
% 0.23/0.43 thf(f109,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((irel @ X0 @ X0) = $true)) )),
% 0.23/0.43 inference(cnf_transformation,[],[f68])).
% 0.23/0.43 thf(f68,plain,(
% 0.23/0.43 ! [X0] : ((irel @ X0 @ X0) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f67])).
% 0.23/0.43 thf(f67,plain,(
% 0.23/0.43 ! [X0] : (irel @ X0 @ X0)),
% 0.23/0.43 inference(rectify,[],[f1])).
% 0.23/0.43 thf(f1,axiom,(
% 0.23/0.43 ! [X0] : (irel @ X0 @ X0)),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',refl_axiom)).
% 0.23/0.43 thf(f296,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p1 @ (sK1 @ X0)) = $false) | ($false = (p1 @ (sK3 @ X1))) | ((p0 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f290])).
% 0.23/0.43 thf(f290,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((p1 @ (sK1 @ X0)) = $false) | ($false = $true) | ((irel @ X1 @ X0) = $false) | ($false = (p1 @ (sK3 @ X1))) | ((p0 @ X0) = $true)) )),
% 0.23/0.43 inference(superposition,[],[f109,f165])).
% 0.23/0.43 thf(f165,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p0 @ X3) = $true) | ($false = (p1 @ (sK1 @ X2))) | ((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK3 @ X1)))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f164])).
% 0.23/0.43 thf(f164,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p1 @ (sK3 @ X1))) | ((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK1 @ X2))) | (((irel @ X2 @ X3) => (p0 @ X3)) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f163])).
% 0.23/0.43 thf(f163,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p1 @ (sK3 @ X1))) | ((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK1 @ X2))) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))) @ X3))) )),
% 0.23/0.43 inference(pi_clausification,[],[f158])).
% 0.23/0.43 thf(f158,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (p1 @ (sK3 @ X1))) | ($false = (p1 @ (sK1 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f157])).
% 0.23/0.43 thf(f157,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((irel @ X1 @ (sK3 @ X1)) => (p1 @ (sK3 @ X1))) = $false) | ($false = (p1 @ (sK1 @ X2))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f156])).
% 0.23/0.43 thf(f156,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))))) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))) @ (sK3 @ X1)) = $false) | ($false = (p1 @ (sK1 @ X2)))) )),
% 0.23/0.43 inference(sigma_clausification,[],[f144])).
% 0.23/0.43 thf(f144,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($false = (p1 @ (sK1 @ X2))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))))) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f143])).
% 0.23/0.43 thf(f143,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((irel @ X2 @ (sK1 @ X2)) => (p1 @ (sK1 @ X2))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))))) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f142])).
% 0.23/0.43 thf(f142,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true) | (((irel @ X2 @ (sK1 @ X2)) => (p1 @ (sK1 @ X2))) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f141])).
% 0.23/0.43 thf(f141,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))))) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ (sK1 @ X2)) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(sigma_clausification,[],[f140])).
% 0.23/0.43 thf(f140,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f139])).
% 0.23/0.43 thf(f139,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true) | ($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f138])).
% 0.23/0.43 thf(f138,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))))) = $true) | ((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f137])).
% 0.23/0.43 thf(f137,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p0 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f136])).
% 0.23/0.43 thf(f136,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))))))) @ X2) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f135])).
% 0.23/0.43 thf(f135,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f134])).
% 0.23/0.43 thf(f134,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p0 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p1 @ Y0)))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f133])).
% 0.23/0.43 thf(f133,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1))))))) @ X1) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f132])).
% 0.23/0.43 thf(f132,plain,(
% 0.23/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p0 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))))))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f128])).
% 0.23/0.43 thf(f128,plain,(
% 0.23/0.43 ($true = ((^[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 > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[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)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p1) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)))))),
% 0.23/0.43 inference(definition_unfolding,[],[f101,f106,f121,f99,f121,f99,f99])).
% 0.23/0.43 thf(f99,plain,(
% 0.23/0.43 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.23/0.43 inference(cnf_transformation,[],[f78])).
% 0.23/0.43 thf(f78,plain,(
% 0.23/0.43 (iatom = (^[Y0 : $i > $o]: (Y0)))),
% 0.23/0.43 inference(fool_elimination,[],[f77])).
% 0.23/0.43 thf(f77,plain,(
% 0.23/0.43 (iatom = (^[X0 : $i > $o] : (X0)))),
% 0.23/0.43 inference(rectify,[],[f8])).
% 0.23/0.43 thf(f8,axiom,(
% 0.23/0.43 (iatom = (^[X5 : $i > $o] : (X5)))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iatom)).
% 0.23/0.43 thf(f121,plain,(
% 0.23/0.43 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[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)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))))),
% 0.23/0.43 inference(definition_unfolding,[],[f97,f116,f92,f92])).
% 0.23/0.43 thf(f92,plain,(
% 0.23/0.43 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.23/0.43 inference(cnf_transformation,[],[f48])).
% 0.23/0.43 thf(f48,plain,(
% 0.23/0.43 (mbox_s4 = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.23/0.43 inference(fool_elimination,[],[f47])).
% 0.23/0.43 thf(f47,plain,(
% 0.23/0.43 ((^[X0 : $i > $o, X1 : $i] : (! [X2] : ((irel @ X1 @ X2) => (X0 @ X2)))) = mbox_s4)),
% 0.23/0.43 inference(rectify,[],[f7])).
% 0.23/0.43 thf(f7,axiom,(
% 0.23/0.43 ((^[X5 : $i > $o, X0 : $i] : (! [X1] : ((irel @ X0 @ X1) => (X5 @ X1)))) = mbox_s4)),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mbox_s4)).
% 0.23/0.43 thf(f116,plain,(
% 0.23/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (~ (Y2 @ Y3))))) @ Y0) @ Y1)))))),
% 0.23/0.43 inference(definition_unfolding,[],[f100,f107,f103])).
% 0.23/0.43 thf(f103,plain,(
% 0.23/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.23/0.43 inference(cnf_transformation,[],[f46])).
% 0.23/0.43 thf(f46,plain,(
% 0.23/0.43 (mnot = (^[Y0 : $i > $o]: ((^[Y1 : $i]: (~ (Y0 @ Y1))))))),
% 0.23/0.43 inference(fool_elimination,[],[f45])).
% 0.23/0.43 thf(f45,plain,(
% 0.23/0.43 (mnot = (^[X0 : $i > $o, X1 : $i] : (~(X0 @ X1))))),
% 0.23/0.43 inference(rectify,[],[f3])).
% 0.23/0.43 thf(f3,axiom,(
% 0.23/0.43 (mnot = (^[X0 : $i > $o, X3 : $i] : (~(X0 @ X3))))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mnot)).
% 0.23/0.43 thf(f107,plain,(
% 0.23/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.23/0.43 inference(cnf_transformation,[],[f32])).
% 0.23/0.43 thf(f32,plain,(
% 0.23/0.43 (mor = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 0.23/0.43 inference(fool_elimination,[],[f31])).
% 0.23/0.43 thf(f31,plain,(
% 0.23/0.43 (mor = (^[X0 : $i > $o, X1 : $i > $o, X2 : $i] : ((X0 @ X2) | (X1 @ X2))))),
% 0.23/0.43 inference(rectify,[],[f4])).
% 0.23/0.43 thf(f4,axiom,(
% 0.23/0.43 (mor = (^[X0 : $i > $o, X1 : $i > $o, X3 : $i] : ((X0 @ X3) | (X1 @ X3))))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mor)).
% 0.23/0.43 thf(f100,plain,(
% 0.23/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.23/0.43 inference(cnf_transformation,[],[f76])).
% 0.23/0.43 thf(f76,plain,(
% 0.23/0.43 (mimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mor @ (mnot @ Y0) @ Y1)))))),
% 0.23/0.43 inference(fool_elimination,[],[f75])).
% 0.23/0.43 thf(f75,plain,(
% 0.23/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mor @ (mnot @ X0) @ X1)) = mimplies)),
% 0.23/0.43 inference(rectify,[],[f6])).
% 0.23/0.43 thf(f6,axiom,(
% 0.23/0.43 ((^[X3 : $i > $o, X4 : $i > $o] : (mor @ (mnot @ X3) @ X4)) = mimplies)),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mimplies)).
% 0.23/0.43 thf(f97,plain,(
% 0.23/0.43 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.23/0.43 inference(cnf_transformation,[],[f44])).
% 0.23/0.43 thf(f44,plain,(
% 0.23/0.43 (iimplies = (^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: (mimplies @ (mbox_s4 @ Y0) @ (mbox_s4 @ Y1))))))),
% 0.23/0.43 inference(fool_elimination,[],[f43])).
% 0.23/0.43 thf(f43,plain,(
% 0.23/0.43 ((^[X0 : $i > $o, X1 : $i > $o] : (mimplies @ (mbox_s4 @ X0) @ (mbox_s4 @ X1))) = iimplies)),
% 0.23/0.43 inference(rectify,[],[f14])).
% 0.23/0.43 thf(f14,axiom,(
% 0.23/0.43 ((^[X5 : $i > $o, X7 : $i > $o] : (mimplies @ (mbox_s4 @ X5) @ (mbox_s4 @ X7))) = iimplies)),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iimplies)).
% 0.23/0.43 thf(f106,plain,(
% 0.23/0.43 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.23/0.43 inference(cnf_transformation,[],[f40])).
% 0.23/0.43 thf(f40,plain,(
% 0.23/0.43 (ivalid = (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))))),
% 0.23/0.43 inference(fool_elimination,[],[f39])).
% 0.23/0.43 thf(f39,plain,(
% 0.23/0.43 ((^[X0 : $i > $o] : (! [X1] : (X0 @ X1))) = ivalid)),
% 0.23/0.43 inference(rectify,[],[f18])).
% 0.23/0.43 thf(f18,axiom,(
% 0.23/0.43 ((^[X8 : $i > $o] : (! [X6] : (X8 @ X6))) = ivalid)),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ivalid)).
% 0.23/0.43 thf(f101,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f56])).
% 0.23/0.43 thf(f56,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0)))) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f55])).
% 0.23/0.43 thf(f55,plain,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 0.23/0.43 inference(rectify,[],[f23])).
% 0.23/0.43 thf(f23,axiom,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p1) @ (iimplies @ (iatom @ p1) @ (iatom @ p0))))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom2)).
% 0.23/0.43 thf(f417,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p1 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f414])).
% 0.23/0.43 thf(f414,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p1 @ X0) = $true) | ($false = $true)) )),
% 0.23/0.43 inference(superposition,[],[f413,f409])).
% 0.23/0.43 thf(f409,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p2 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f407])).
% 0.23/0.43 thf(f407,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = $true) | ((p2 @ X0) = $true)) )),
% 0.23/0.43 inference(superposition,[],[f401,f405])).
% 0.23/0.43 thf(f405,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p3 @ (sK10 @ X0)) = $false) | ((p2 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f402])).
% 0.23/0.43 thf(f402,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p2 @ X0) = $true) | ((p3 @ (sK10 @ X0)) = $false) | ($false = $true)) )),
% 0.23/0.43 inference(superposition,[],[f401,f347])).
% 0.23/0.43 thf(f347,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = (p3 @ (sK8 @ X0))) | ((p3 @ (sK10 @ X0)) = $false) | ((p2 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f342])).
% 0.23/0.43 thf(f342,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = $true) | ((p3 @ (sK10 @ X0)) = $false) | ($false = (p3 @ (sK8 @ X0))) | ((p2 @ X0) = $true)) )),
% 0.23/0.43 inference(superposition,[],[f332,f109])).
% 0.23/0.43 thf(f332,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p2 @ X0) = $true) | ((p3 @ (sK10 @ X0)) = $false) | ((p3 @ (sK8 @ X1)) = $false)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f326])).
% 0.23/0.43 thf(f326,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p2 @ X0) = $true) | ($false = $true) | ((p3 @ (sK10 @ X0)) = $false) | ((p3 @ (sK8 @ X1)) = $false)) )),
% 0.23/0.43 inference(superposition,[],[f109,f233])).
% 0.23/0.43 thf(f233,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($true = (p2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p3 @ (sK8 @ X1)) = $false) | ($false = (p3 @ (sK10 @ X2)))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f230])).
% 0.23/0.43 thf(f230,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = ((irel @ X2 @ X3) => (p2 @ X3))) | ((p3 @ (sK8 @ X1)) = $false) | ($false = (p3 @ (sK10 @ X2)))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f229])).
% 0.23/0.43 thf(f229,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ X2 @ (sK10 @ X2)) => (p3 @ (sK10 @ X2)))) | ($true = ((irel @ X2 @ X3) => (p2 @ X3))) | ((p3 @ (sK8 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f228])).
% 0.23/0.43 thf(f228,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p3 @ (sK8 @ X1)) = $false) | ($true = ((irel @ X2 @ X3) => (p2 @ X3))) | ((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))) @ (sK10 @ X2)) = $false)) )),
% 0.23/0.43 inference(sigma_clausification,[],[f227])).
% 0.23/0.43 thf(f227,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))) | ((p3 @ (sK8 @ X1)) = $false) | ($true = ((irel @ X2 @ X3) => (p2 @ X3)))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f226])).
% 0.23/0.43 thf(f226,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))) @ X3)) | ((p3 @ (sK8 @ X1)) = $false)) )),
% 0.23/0.43 inference(pi_clausification,[],[f225])).
% 0.23/0.43 thf(f225,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true) | ((p3 @ (sK8 @ X1)) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f224])).
% 0.23/0.43 thf(f224,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))))) | ((p3 @ (sK8 @ X1)) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f223])).
% 0.23/0.43 thf(f223,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK8 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f211])).
% 0.23/0.43 thf(f211,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((p3 @ (sK8 @ X1)) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f210])).
% 0.23/0.43 thf(f210,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ X1 @ (sK8 @ X1)) => (p3 @ (sK8 @ X1)))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f209])).
% 0.23/0.43 thf(f209,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))) = $true) | ($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0))) @ (sK8 @ X1)))) )),
% 0.23/0.43 inference(sigma_clausification,[],[f208])).
% 0.23/0.43 thf(f208,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))) = $false) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))) = $true)) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f207])).
% 0.23/0.43 thf(f207,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))))) | (((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f206])).
% 0.23/0.43 thf(f206,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))) @ X2) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0))))))) )),
% 0.23/0.43 inference(pi_clausification,[],[f205])).
% 0.23/0.43 thf(f205,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0))))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f204])).
% 0.23/0.43 thf(f204,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p3 @ Y0)))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f203])).
% 0.23/0.43 thf(f203,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1))))))) @ X1) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f202])).
% 0.23/0.43 thf(f202,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))))))) = $true)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f125])).
% 0.23/0.43 thf(f125,plain,(
% 0.23/0.43 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p3) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[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)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p3) @ ((^[Y0 : $i > $o]: (Y0)) @ p2)))) = $true)),
% 0.23/0.43 inference(definition_unfolding,[],[f88,f106,f121,f99,f121,f99,f99])).
% 0.23/0.43 thf(f88,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2)))) = $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f52])).
% 0.23/0.43 thf(f52,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2)))) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f51])).
% 0.23/0.43 thf(f51,plain,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),
% 0.23/0.43 inference(rectify,[],[f25])).
% 0.23/0.43 thf(f25,axiom,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p3) @ (iimplies @ (iatom @ p3) @ (iatom @ p2))))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom4)).
% 0.23/0.43 thf(f401,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p3 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f399])).
% 0.23/0.43 thf(f399,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = $true) | ((p3 @ X0) = $true)) )),
% 0.23/0.43 inference(superposition,[],[f341,f397])).
% 0.23/0.43 thf(f397,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p4 @ (sK14 @ X0)) = $false) | ((p3 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f394])).
% 0.23/0.43 thf(f394,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p4 @ (sK14 @ X0)) = $false) | ($false = $true) | ((p3 @ X0) = $true)) )),
% 0.23/0.43 inference(superposition,[],[f391,f341])).
% 0.23/0.43 thf(f391,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p4 @ (sK16 @ X0)) = $false) | ((p4 @ (sK14 @ X0)) = $false) | ((p3 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f388])).
% 0.23/0.43 thf(f388,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p4 @ (sK14 @ X0)) = $false) | ((p3 @ X0) = $true) | ($false = $true) | ((p4 @ (sK16 @ X0)) = $false)) )),
% 0.23/0.43 inference(superposition,[],[f109,f377])).
% 0.23/0.43 thf(f377,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ((p4 @ (sK14 @ X1)) = $false) | ((p4 @ (sK16 @ X0)) = $false) | ((p3 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f368])).
% 0.23/0.43 thf(f368,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((p4 @ (sK16 @ X0)) = $false) | ((p3 @ X0) = $true) | ($false = $true) | ((p4 @ (sK14 @ X1)) = $false) | ((irel @ X1 @ X0) = $false)) )),
% 0.23/0.43 inference(superposition,[],[f286,f109])).
% 0.23/0.43 thf(f286,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ($false = (p4 @ (sK16 @ X2))) | ((p3 @ X3) = $true) | ((p4 @ (sK14 @ X1)) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f285])).
% 0.23/0.43 thf(f285,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p4 @ (sK14 @ X1)) = $false) | ((p3 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | (((irel @ X2 @ (sK16 @ X2)) => (p4 @ (sK16 @ X2))) = $false) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f284])).
% 0.23/0.43 thf(f284,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))) @ (sK16 @ X2)) = $false) | ($false = (irel @ X2 @ X3)) | ((p4 @ (sK14 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p3 @ X3) = $true)) )),
% 0.23/0.43 inference(sigma_clausification,[],[f278])).
% 0.23/0.43 thf(f278,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $false) | ((p4 @ (sK14 @ X1)) = $false) | ((p3 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f277])).
% 0.23/0.43 thf(f277,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ X1 @ (sK14 @ X1)) => (p4 @ (sK14 @ X1)))) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $false) | ((p3 @ X3) = $true)) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f276])).
% 0.23/0.43 thf(f276,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p3 @ X3) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true) | ($false = ((irel @ X1 @ (sK14 @ X1)) => (p4 @ (sK14 @ X1))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f275])).
% 0.23/0.43 thf(f275,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))) @ (sK14 @ X1))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true) | ((p3 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(sigma_clausification,[],[f274])).
% 0.23/0.43 thf(f274,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p3 @ X3) = $true) | ($false = (irel @ X2 @ X3)) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f273])).
% 0.23/0.43 thf(f273,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p3 @ X3))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f272])).
% 0.23/0.43 thf(f272,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0))) @ X3))) )),
% 0.23/0.43 inference(pi_clausification,[],[f271])).
% 0.23/0.43 thf(f271,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f270])).
% 0.23/0.43 thf(f270,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))))) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f269])).
% 0.23/0.43 thf(f269,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) = $true) | (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f268])).
% 0.23/0.43 thf(f268,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p3 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))))))) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f267])).
% 0.23/0.43 thf(f267,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))))))) @ X2) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f266])).
% 0.23/0.43 thf(f266,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))) = $true) | ((~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0))))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f265])).
% 0.23/0.43 thf(f265,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p3 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p4 @ Y0)))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f264])).
% 0.23/0.43 thf(f264,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1))))))) @ X1))) )),
% 0.23/0.43 inference(pi_clausification,[],[f263])).
% 0.23/0.43 thf(f263,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p3 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))))))) = $true)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f126])).
% 0.23/0.43 thf(f126,plain,(
% 0.23/0.43 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p4) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[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)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p4) @ ((^[Y0 : $i > $o]: (Y0)) @ p3)))) = $true)),
% 0.23/0.43 inference(definition_unfolding,[],[f94,f106,f121,f99,f121,f99,f99])).
% 0.23/0.43 thf(f94,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3)))) = $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f34])).
% 0.23/0.43 thf(f34,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3)))) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f33])).
% 0.23/0.43 thf(f33,plain,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),
% 0.23/0.43 inference(rectify,[],[f26])).
% 0.23/0.43 thf(f26,axiom,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p4) @ (iimplies @ (iatom @ p4) @ (iatom @ p3))))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom5)).
% 0.23/0.43 thf(f341,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($true = (p4 @ X0))) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f339])).
% 0.23/0.43 thf(f339,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($true = (p4 @ X0)) | ($false = $true)) )),
% 0.23/0.43 inference(superposition,[],[f201,f337])).
% 0.23/0.43 thf(f337,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p5 @ (sK4 @ X0)) = $false) | ($true = (p4 @ X0))) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f334])).
% 0.23/0.43 thf(f334,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($true = (p4 @ X0)) | ($false = $true) | ((p5 @ (sK4 @ X0)) = $false)) )),
% 0.23/0.43 inference(superposition,[],[f322,f201])).
% 0.23/0.43 thf(f322,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = (p5 @ (sK6 @ X0))) | ($true = (p4 @ X0)) | ((p5 @ (sK4 @ X0)) = $false)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f316])).
% 0.23/0.43 thf(f316,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = $true) | ($false = (p5 @ (sK6 @ X0))) | ($true = (p4 @ X0)) | ((p5 @ (sK4 @ X0)) = $false)) )),
% 0.23/0.43 inference(superposition,[],[f313,f109])).
% 0.23/0.43 thf(f313,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($false = (p5 @ (sK6 @ X0))) | ($true = (p4 @ X0)) | ((p5 @ (sK4 @ X1)) = $false)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f306])).
% 0.23/0.43 thf(f306,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (($true = (p4 @ X0)) | ($false = $true) | ((p5 @ (sK4 @ X1)) = $false) | ($false = (p5 @ (sK6 @ X0))) | ((irel @ X1 @ X0) = $false)) )),
% 0.23/0.43 inference(superposition,[],[f196,f109])).
% 0.23/0.43 thf(f196,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p5 @ (sK4 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ((p4 @ X3) = $true) | ($false = (p5 @ (sK6 @ X2)))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f195])).
% 0.23/0.43 thf(f195,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((p5 @ (sK4 @ X1)) = $false) | ($false = ((irel @ X2 @ (sK6 @ X2)) => (p5 @ (sK6 @ X2)))) | ((irel @ X1 @ X2) = $false) | ((p4 @ X3) = $true) | ($false = (irel @ X2 @ X3))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f194])).
% 0.23/0.43 thf(f194,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p4 @ X3) = $true) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))) @ (sK6 @ X2)) = $false) | ((p5 @ (sK4 @ X1)) = $false)) )),
% 0.23/0.43 inference(sigma_clausification,[],[f193])).
% 0.23/0.43 thf(f193,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p5 @ (sK4 @ X1)) = $false) | ((p4 @ X3) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f192])).
% 0.23/0.43 thf(f192,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((irel @ X2 @ X3) => (p4 @ X3))) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))) | ((irel @ X1 @ X2) = $false) | ((p5 @ (sK4 @ X1)) = $false)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f191])).
% 0.23/0.43 thf(f191,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | (((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0))) @ X3) = $true) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))) | ((p5 @ (sK4 @ X1)) = $false)) )),
% 0.23/0.43 inference(pi_clausification,[],[f190])).
% 0.23/0.43 thf(f190,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))) | ((p5 @ (sK4 @ X1)) = $false)) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f177])).
% 0.23/0.43 thf(f177,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((p5 @ (sK4 @ X1)) = $false) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f176])).
% 0.23/0.43 thf(f176,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ X1 @ (sK4 @ X1)) => (p5 @ (sK4 @ X1)))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f175])).
% 0.23/0.43 thf(f175,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))) @ (sK4 @ X1))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(sigma_clausification,[],[f174])).
% 0.23/0.43 thf(f174,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f173])).
% 0.23/0.43 thf(f173,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))))) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f172])).
% 0.23/0.43 thf(f172,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f171])).
% 0.23/0.43 thf(f171,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p4 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p5 @ Y0)))))))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f170])).
% 0.23/0.43 thf(f170,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))))))) @ X2) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f169])).
% 0.23/0.43 thf(f169,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1))))))))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0))))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f168])).
% 0.23/0.43 thf(f168,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p4 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p5 @ Y0)))))) = $true)) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f167])).
% 0.23/0.43 thf(f167,plain,(
% 0.23/0.43 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1))))))) @ X1) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f166])).
% 0.23/0.43 thf(f166,plain,(
% 0.23/0.43 ((!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p4 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p5 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p5 @ Y1)))))))) = $true)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f129])).
% 0.23/0.43 thf(f129,plain,(
% 0.23/0.43 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p5) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[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)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p5) @ ((^[Y0 : $i > $o]: (Y0)) @ p4)))) = $true)),
% 0.23/0.43 inference(definition_unfolding,[],[f111,f106,f121,f99,f121,f99,f99])).
% 0.23/0.43 thf(f111,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4)))) = $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f82])).
% 0.23/0.43 thf(f82,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4)))) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f81])).
% 0.23/0.43 thf(f81,plain,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),
% 0.23/0.43 inference(rectify,[],[f27])).
% 0.23/0.43 thf(f27,axiom,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p5) @ (iimplies @ (iatom @ p5) @ (iatom @ p4))))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom6)).
% 0.23/0.43 thf(f201,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($true = (p5 @ X1))) )),
% 0.23/0.43 inference(pi_clausification,[],[f200])).
% 0.23/0.43 thf(f200,plain,(
% 0.23/0.43 ($true = (!! @ $i @ p5))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f130])).
% 0.23/0.43 thf(f130,plain,(
% 0.23/0.43 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p5)) = $true)),
% 0.23/0.43 inference(definition_unfolding,[],[f112,f106,f99])).
% 0.23/0.43 thf(f112,plain,(
% 0.23/0.43 ((ivalid @ (iatom @ p5)) = $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f60])).
% 0.23/0.43 thf(f60,plain,(
% 0.23/0.43 ((ivalid @ (iatom @ p5)) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f59])).
% 0.23/0.43 thf(f59,plain,(
% 0.23/0.43 (ivalid @ (iatom @ p5))),
% 0.23/0.43 inference(rectify,[],[f22])).
% 0.23/0.43 thf(f22,axiom,(
% 0.23/0.43 (ivalid @ (iatom @ p5))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom1)).
% 0.23/0.43 thf(f413,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p2 @ (sK13 @ X0)) = $false) | ((p1 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f411])).
% 0.23/0.43 thf(f411,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (((p1 @ X0) = $true) | ($false = $true) | ((p2 @ (sK13 @ X0)) = $false)) )),
% 0.23/0.43 inference(superposition,[],[f367,f409])).
% 0.23/0.43 thf(f367,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = (p2 @ (sK11 @ X0))) | ((p2 @ (sK13 @ X0)) = $false) | ((p1 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f362])).
% 0.23/0.43 thf(f362,plain,(
% 0.23/0.43 ( ! [X0 : $i] : (($false = $true) | ((p2 @ (sK13 @ X0)) = $false) | ((p1 @ X0) = $true) | ($false = (p2 @ (sK11 @ X0)))) )),
% 0.23/0.43 inference(superposition,[],[f109,f357])).
% 0.23/0.43 thf(f357,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((irel @ X1 @ X0) = $false) | ($false = (p2 @ (sK11 @ X1))) | ((p2 @ (sK13 @ X0)) = $false) | ((p1 @ X0) = $true)) )),
% 0.23/0.43 inference(trivial_inequality_removal,[],[f350])).
% 0.23/0.43 thf(f350,plain,(
% 0.23/0.43 ( ! [X0 : $i,X1 : $i] : (((p1 @ X0) = $true) | ((irel @ X1 @ X0) = $false) | ((p2 @ (sK13 @ X0)) = $false) | ($false = (p2 @ (sK11 @ X1))) | ($false = $true)) )),
% 0.23/0.43 inference(superposition,[],[f261,f109])).
% 0.23/0.43 thf(f261,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (irel @ X2 @ X3)) | ((p2 @ (sK13 @ X2)) = $false) | ((p1 @ X3) = $true) | ($false = (p2 @ (sK11 @ X1))) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f260])).
% 0.23/0.43 thf(f260,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((irel @ X2 @ (sK13 @ X2)) => (p2 @ (sK13 @ X2)))) | ($false = (irel @ X2 @ X3)) | ((irel @ X1 @ X2) = $false) | ((p1 @ X3) = $true) | ($false = (p2 @ (sK11 @ X1)))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f259])).
% 0.23/0.43 thf(f259,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((irel @ X2 @ X3) => (p1 @ X3)) = $true) | ($false = (p2 @ (sK11 @ X1))) | ((irel @ X1 @ X2) = $false) | ($false = ((irel @ X2 @ (sK13 @ X2)) => (p2 @ (sK13 @ X2))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f258])).
% 0.23/0.43 thf(f258,plain,(
% 0.23/0.43 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (p2 @ (sK11 @ X1))) | ($false = ((irel @ X2 @ (sK13 @ X2)) => (p2 @ (sK13 @ X2)))) | ((irel @ X1 @ X2) = $false) | ($true = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0))) @ X3))) )),
% 0.23/0.43 inference(pi_clausification,[],[f257])).
% 0.23/0.43 thf(f257,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true) | ($false = (p2 @ (sK11 @ X1))) | ((irel @ X1 @ X2) = $false) | ($false = ((irel @ X2 @ (sK13 @ X2)) => (p2 @ (sK13 @ X2))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f256])).
% 0.23/0.43 thf(f256,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true) | ($false = (p2 @ (sK11 @ X1))) | ($false = ((^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))) @ (sK13 @ X2)))) )),
% 0.23/0.43 inference(sigma_clausification,[],[f255])).
% 0.23/0.43 thf(f255,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))) | ($false = (p2 @ (sK11 @ X1))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true)) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f245])).
% 0.23/0.43 thf(f245,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | ($false = (p2 @ (sK11 @ X1))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true)) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f244])).
% 0.23/0.43 thf(f244,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($false = ((irel @ X1 @ (sK11 @ X1)) => (p2 @ (sK11 @ X1)))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f243])).
% 0.23/0.43 thf(f243,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true) | ($false = ((^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))) @ (sK11 @ X1))) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0)))))) | ((irel @ X1 @ X2) = $false)) )),
% 0.23/0.43 inference(sigma_clausification,[],[f242])).
% 0.23/0.43 thf(f242,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (((irel @ X1 @ X2) = $false) | ($false = (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))))) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) )),
% 0.23/0.43 inference(not_proxy_clausification,[],[f241])).
% 0.23/0.43 thf(f241,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))))) | ((irel @ X1 @ X2) = $false) | ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f240])).
% 0.23/0.43 thf(f240,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) | ((irel @ X1 @ X2) = $false) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f239])).
% 0.23/0.43 thf(f239,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : ((((irel @ X1 @ X2) => ((!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p1 @ Y0)))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X2 @ Y0) => (p2 @ Y0))))))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f238])).
% 0.23/0.43 thf(f238,plain,(
% 0.23/0.43 ( ! [X2 : $i,X1 : $i] : (($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))))) | (((^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))))))) @ X2) = $true)) )),
% 0.23/0.43 inference(pi_clausification,[],[f237])).
% 0.23/0.43 thf(f237,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) = $true) | ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0))))))) )),
% 0.23/0.43 inference(binary_proxy_clausification,[],[f236])).
% 0.23/0.43 thf(f236,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p1 @ Y1)))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))))) | (~ (!! @ $i @ (^[Y0 : $i]: ((irel @ X1 @ Y0) => (p2 @ Y0)))))))) )),
% 0.23/0.43 inference(beta_eta_normalization,[],[f235])).
% 0.23/0.43 thf(f235,plain,(
% 0.23/0.43 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1))))))) @ X1))) )),
% 0.23/0.43 inference(pi_clausification,[],[f234])).
% 0.23/0.43 thf(f234,plain,(
% 0.23/0.43 ($true = (!! @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => ((!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p1 @ Y2)))) | (~ (!! @ $i @ (^[Y2 : $i]: ((irel @ Y1 @ Y2) => (p2 @ Y2))))))))) | (~ (!! @ $i @ (^[Y1 : $i]: ((irel @ Y0 @ Y1) => (p2 @ Y1)))))))))),
% 0.23/0.43 inference(beta_eta_normalization,[],[f131])).
% 0.23/0.43 thf(f131,plain,(
% 0.23/0.43 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[Y2 : $i > $o]: ((^[Y3 : $i > $o]: ((^[Y4 : $i > $o]: ((^[Y5 : $i > $o]: ((^[Y6 : $i]: ((Y5 @ Y6) | (Y4 @ Y6))))))) @ ((^[Y4 : $i > $o]: ((^[Y5 : $i]: (~ (Y4 @ Y5))))) @ Y2) @ Y3)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p2) @ ((^[Y0 : $i > $o]: ((^[Y1 : $i > $o]: ((^[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)))) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y0) @ ((^[Y2 : $i > $o]: ((^[Y3 : $i]: (!! @ $i @ (^[Y4 : $i]: ((irel @ Y3 @ Y4) => (Y2 @ Y4))))))) @ Y1))))) @ ((^[Y0 : $i > $o]: (Y0)) @ p2) @ ((^[Y0 : $i > $o]: (Y0)) @ p1)))) = $true)),
% 0.23/0.43 inference(definition_unfolding,[],[f114,f106,f121,f99,f121,f99,f99])).
% 0.23/0.43 thf(f114,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1)))) = $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f36])).
% 0.23/0.43 thf(f36,plain,(
% 0.23/0.43 ((ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1)))) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f35])).
% 0.23/0.43 thf(f35,plain,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),
% 0.23/0.43 inference(rectify,[],[f24])).
% 0.23/0.43 thf(f24,axiom,(
% 0.23/0.43 (ivalid @ (iimplies @ (iatom @ p2) @ (iimplies @ (iatom @ p2) @ (iatom @ p1))))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom3)).
% 0.23/0.43 thf(f199,plain,(
% 0.23/0.43 ($false = (p0 @ sK7))),
% 0.23/0.43 inference(sigma_clausification,[],[f198])).
% 0.23/0.43 thf(f198,plain,(
% 0.23/0.43 ((!! @ $i @ p0) != $true)),
% 0.23/0.43 inference(beta_eta_normalization,[],[f127])).
% 0.23/0.43 thf(f127,plain,(
% 0.23/0.43 (((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1)))) @ ((^[Y0 : $i > $o]: (Y0)) @ p0)) != $true)),
% 0.23/0.43 inference(definition_unfolding,[],[f96,f106,f99])).
% 0.23/0.43 thf(f96,plain,(
% 0.23/0.43 ((ivalid @ (iatom @ p0)) != $true)),
% 0.23/0.43 inference(cnf_transformation,[],[f85])).
% 0.23/0.43 thf(f85,plain,(
% 0.23/0.43 ((ivalid @ (iatom @ p0)) != $true)),
% 0.23/0.43 inference(flattening,[],[f70])).
% 0.23/0.43 thf(f70,plain,(
% 0.23/0.43 ~((ivalid @ (iatom @ p0)) = $true)),
% 0.23/0.43 inference(fool_elimination,[],[f69])).
% 0.23/0.43 thf(f69,plain,(
% 0.23/0.43 ~(ivalid @ (iatom @ p0))),
% 0.23/0.43 inference(rectify,[],[f29])).
% 0.23/0.43 thf(f29,negated_conjecture,(
% 0.23/0.43 ~(ivalid @ (iatom @ p0))),
% 0.23/0.43 inference(negated_conjecture,[],[f28])).
% 0.23/0.43 thf(f28,conjecture,(
% 0.23/0.43 (ivalid @ (iatom @ p0))),
% 0.23/0.43 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con)).
% 0.23/0.43 % SZS output end Proof for theBenchmark
% 0.23/0.43 % (32350)------------------------------
% 0.23/0.43 % (32350)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.23/0.43 % (32350)Termination reason: Refutation
% 0.23/0.43
% 0.23/0.43 % (32350)Memory used [KB]: 5884
% 0.23/0.43 % (32350)Time elapsed: 0.047 s
% 0.23/0.43 % (32350)Instructions burned: 57 (million)
% 0.23/0.43 % (32350)------------------------------
% 0.23/0.43 % (32350)------------------------------
% 0.23/0.43 % (32349)Success in time 0.057 s
% 0.23/0.43 % Vampire---4.8 exiting
%------------------------------------------------------------------------------