TSTP Solution File: SEU781^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:51:29 EDT 2024
% Result : Theorem 0.13s 0.36s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11 % Problem : SEU781^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.33 % Computer : n022.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Sun May 19 18:18:22 EDT 2024
% 0.13/0.33 % CPUTime :
% 0.13/0.33 This is a TH0_THM_EQU_NAR problem
% 0.13/0.34 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.35 % (26695)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)
% 0.13/0.35 % (26694)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.35 % (26693)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)
% 0.13/0.35 % (26688)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.35 % (26695)Instruction limit reached!
% 0.13/0.35 % (26695)------------------------------
% 0.13/0.35 % (26695)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.35 % (26695)Termination reason: Unknown
% 0.13/0.35 % (26695)Termination phase: Preprocessing 3
% 0.13/0.35
% 0.13/0.35 % (26695)Memory used [KB]: 1023
% 0.13/0.35 % (26695)Time elapsed: 0.003 s
% 0.13/0.35 % (26695)Instructions burned: 3 (million)
% 0.13/0.35 % (26695)------------------------------
% 0.13/0.35 % (26695)------------------------------
% 0.13/0.35 % (26690)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)
% 0.13/0.35 % (26692)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)
% 0.13/0.36 % (26692)Instruction limit reached!
% 0.13/0.36 % (26692)------------------------------
% 0.13/0.36 % (26692)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (26692)Termination reason: Unknown
% 0.13/0.36 % (26692)Termination phase: Function definition elimination
% 0.13/0.36
% 0.13/0.36 % (26692)Memory used [KB]: 1023
% 0.13/0.36 % (26692)Time elapsed: 0.004 s
% 0.13/0.36 % (26692)Instructions burned: 3 (million)
% 0.13/0.36 % (26692)------------------------------
% 0.13/0.36 % (26692)------------------------------
% 0.13/0.36 % (26691)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.36 % (26693)First to succeed.
% 0.13/0.36 % (26689)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)
% 0.13/0.36 % (26691)Instruction limit reached!
% 0.13/0.36 % (26691)------------------------------
% 0.13/0.36 % (26691)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (26691)Termination reason: Unknown
% 0.13/0.36 % (26691)Termination phase: Property scanning
% 0.13/0.36
% 0.13/0.36 % (26691)Memory used [KB]: 1023
% 0.13/0.36 % (26691)Time elapsed: 0.003 s
% 0.13/0.36 % (26691)Instructions burned: 3 (million)
% 0.13/0.36 % (26691)------------------------------
% 0.13/0.36 % (26691)------------------------------
% 0.13/0.36 % (26689)Instruction limit reached!
% 0.13/0.36 % (26689)------------------------------
% 0.13/0.36 % (26689)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (26689)Termination reason: Unknown
% 0.13/0.36 % (26689)Termination phase: Saturation
% 0.13/0.36
% 0.13/0.36 % (26689)Memory used [KB]: 5500
% 0.13/0.36 % (26689)Time elapsed: 0.004 s
% 0.13/0.36 % (26689)Instructions burned: 4 (million)
% 0.13/0.36 % (26689)------------------------------
% 0.13/0.36 % (26689)------------------------------
% 0.13/0.36 % (26694)Instruction limit reached!
% 0.13/0.36 % (26694)------------------------------
% 0.13/0.36 % (26694)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (26694)Termination reason: Unknown
% 0.13/0.36 % (26694)Termination phase: Saturation
% 0.13/0.36
% 0.13/0.36 % (26694)Memory used [KB]: 5628
% 0.13/0.36 % (26694)Time elapsed: 0.011 s
% 0.13/0.36 % (26694)Instructions burned: 18 (million)
% 0.13/0.36 % (26694)------------------------------
% 0.13/0.36 % (26694)------------------------------
% 0.13/0.36 % (26693)Refutation found. Thanks to Tanya!
% 0.13/0.36 % SZS status Theorem for theBenchmark
% 0.13/0.36 % SZS output start Proof for theBenchmark
% 0.13/0.36 thf(func_def_0, type, in: $i > $i > $o).
% 0.13/0.36 thf(func_def_1, type, subset: $i > $i > $o).
% 0.13/0.36 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.13/0.36 thf(func_def_3, type, cartprod: $i > $i > $i).
% 0.13/0.36 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 0.13/0.36 thf(func_def_6, type, breln1: $i > $i > $o).
% 0.13/0.36 thf(func_def_7, type, breln1compset: $i > $i > $i > $i).
% 0.13/0.36 thf(func_def_27, type, sK12: $i > $i > $i > $i > $i > $i).
% 0.13/0.36 thf(f73,plain,(
% 0.13/0.36 $false),
% 0.13/0.36 inference(subsumption_resolution,[],[f72,f36])).
% 0.13/0.36 thf(f36,plain,(
% 0.13/0.36 ($true = (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3)))),
% 0.13/0.36 inference(cnf_transformation,[],[f25])).
% 0.13/0.36 thf(f25,plain,(
% 0.13/0.36 (breln1compE = $true) & (($true = (breln1 @ sK1 @ sK2)) & (($true = (breln1 @ sK1 @ sK3)) & (($true = (in @ sK4 @ sK1)) & ((! [X6] : (($true != (in @ (kpair @ X6 @ sK5) @ sK3)) | ((in @ (kpair @ sK4 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = sK6)) & ($true != sK6)) & ($true = (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3))) & ($true = (in @ sK5 @ sK1))))))),
% 0.13/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4,sK5,sK6])],[f17,f24,f23,f22,f21,f20])).
% 0.13/0.36 thf(f20,plain,(
% 0.13/0.36 ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2] : (($true = (breln1 @ X0 @ X2)) & ? [X3] : (($true = (in @ X3 @ X0)) & ? [X4] : (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ X4) @ X2)) | ($true != (in @ (kpair @ X3 @ X6) @ X1)) | ((in @ X6 @ X0) != $true) | ($true = X5)) & ($true != X5)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) & ($true = (in @ X4 @ X0)))))) => (($true = (breln1 @ sK1 @ sK2)) & ? [X2] : (($true = (breln1 @ sK1 @ X2)) & ? [X3] : (($true = (in @ X3 @ sK1)) & ? [X4] : (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ X4) @ X2)) | ((in @ (kpair @ X3 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = X5)) & ($true != X5)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK2 @ X2)) = $true) & ((in @ X4 @ sK1) = $true)))))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f21,plain,(
% 0.13/0.36 ? [X2] : (($true = (breln1 @ sK1 @ X2)) & ? [X3] : (($true = (in @ X3 @ sK1)) & ? [X4] : (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ X4) @ X2)) | ((in @ (kpair @ X3 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = X5)) & ($true != X5)) & ((in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK2 @ X2)) = $true) & ((in @ X4 @ sK1) = $true)))) => (($true = (breln1 @ sK1 @ sK3)) & ? [X3] : (($true = (in @ X3 @ sK1)) & ? [X4] : (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ X4) @ sK3)) | ((in @ (kpair @ X3 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = X5)) & ($true != X5)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK2 @ sK3))) & ((in @ X4 @ sK1) = $true))))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f22,plain,(
% 0.13/0.36 ? [X3] : (($true = (in @ X3 @ sK1)) & ? [X4] : (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ X4) @ sK3)) | ((in @ (kpair @ X3 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = X5)) & ($true != X5)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK1 @ sK2 @ sK3))) & ((in @ X4 @ sK1) = $true))) => (($true = (in @ sK4 @ sK1)) & ? [X4] : (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ X4) @ sK3)) | ((in @ (kpair @ sK4 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = X5)) & ($true != X5)) & ((in @ (kpair @ sK4 @ X4) @ (breln1compset @ sK1 @ sK2 @ sK3)) = $true) & ((in @ X4 @ sK1) = $true)))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f23,plain,(
% 0.13/0.36 ? [X4] : (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ X4) @ sK3)) | ((in @ (kpair @ sK4 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = X5)) & ($true != X5)) & ((in @ (kpair @ sK4 @ X4) @ (breln1compset @ sK1 @ sK2 @ sK3)) = $true) & ((in @ X4 @ sK1) = $true)) => (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ sK5) @ sK3)) | ((in @ (kpair @ sK4 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = X5)) & ($true != X5)) & ($true = (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3))) & ($true = (in @ sK5 @ sK1)))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f24,plain,(
% 0.13/0.36 ? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ sK5) @ sK3)) | ((in @ (kpair @ sK4 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = X5)) & ($true != X5)) => (! [X6] : (($true != (in @ (kpair @ X6 @ sK5) @ sK3)) | ((in @ (kpair @ sK4 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true) | ($true = sK6)) & ($true != sK6))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f17,plain,(
% 0.13/0.36 (breln1compE = $true) & ? [X0,X1] : (((breln1 @ X0 @ X1) = $true) & ? [X2] : (($true = (breln1 @ X0 @ X2)) & ? [X3] : (($true = (in @ X3 @ X0)) & ? [X4] : (? [X5 : $o] : (! [X6] : (($true != (in @ (kpair @ X6 @ X4) @ X2)) | ($true != (in @ (kpair @ X3 @ X6) @ X1)) | ((in @ X6 @ X0) != $true) | ($true = X5)) & ($true != X5)) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) & ($true = (in @ X4 @ X0))))))),
% 0.13/0.36 inference(flattening,[],[f16])).
% 0.13/0.36 thf(f16,plain,(
% 0.13/0.36 ? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : ((? [X5 : $o] : (($true != X5) & ! [X6] : (((($true = X5) | ($true != (in @ (kpair @ X6 @ X4) @ X2))) | ($true != (in @ (kpair @ X3 @ X6) @ X1))) | ((in @ X6 @ X0) != $true))) & ($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)))) & ($true = (in @ X4 @ X0))) & ($true = (in @ X3 @ X0))) & ($true = (breln1 @ X0 @ X2))) & ((breln1 @ X0 @ X1) = $true)) & (breln1compE = $true)),
% 0.13/0.36 inference(ennf_transformation,[],[f13])).
% 0.13/0.36 thf(f13,plain,(
% 0.13/0.36 ~((breln1compE = $true) => ! [X0,X1] : (((breln1 @ X0 @ X1) = $true) => ! [X2] : (($true = (breln1 @ X0 @ X2)) => ! [X3] : (($true = (in @ X3 @ X0)) => ! [X4] : (($true = (in @ X4 @ X0)) => (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2))) => ! [X5 : $o] : (! [X6] : (((in @ X6 @ X0) = $true) => (($true = (in @ (kpair @ X3 @ X6) @ X1)) => (($true = (in @ (kpair @ X6 @ X4) @ X2)) => ($true = X5)))) => ($true = X5))))))))),
% 0.13/0.36 inference(fool_elimination,[],[f12])).
% 0.13/0.36 thf(f12,plain,(
% 0.13/0.36 ~(breln1compE => ! [X0,X1] : ((breln1 @ X0 @ X1) => ! [X2] : ((breln1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X0) => ! [X4] : ((in @ X4 @ X0) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X0 @ X1 @ X2)) => ! [X5 : $o] : (! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X3 @ X6) @ X1) => ((in @ (kpair @ X6 @ X4) @ X2) => X5))) => X5)))))))),
% 0.13/0.36 inference(rectify,[],[f5])).
% 0.13/0.36 thf(f5,negated_conjecture,(
% 0.13/0.36 ~(breln1compE => ! [X0,X3] : ((breln1 @ X0 @ X3) => ! [X4] : ((breln1 @ X0 @ X4) => ! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ (breln1compset @ X0 @ X3 @ X4)) => ! [X8 : $o] : (! [X7] : ((in @ X7 @ X0) => ((in @ (kpair @ X5 @ X7) @ X3) => ((in @ (kpair @ X7 @ X6) @ X4) => X8))) => X8)))))))),
% 0.13/0.36 inference(negated_conjecture,[],[f4])).
% 0.13/0.36 thf(f4,conjecture,(
% 0.13/0.36 breln1compE => ! [X0,X3] : ((breln1 @ X0 @ X3) => ! [X4] : ((breln1 @ X0 @ X4) => ! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ (breln1compset @ X0 @ X3 @ X4)) => ! [X8 : $o] : (! [X7] : ((in @ X7 @ X0) => ((in @ (kpair @ X5 @ X7) @ X3) => ((in @ (kpair @ X7 @ X6) @ X4) => X8))) => X8))))))),
% 0.13/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compEex)).
% 0.13/0.36 thf(f72,plain,(
% 0.13/0.36 ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3)))),
% 0.13/0.36 inference(subsumption_resolution,[],[f71,f56])).
% 0.13/0.36 thf(f56,plain,(
% 0.13/0.36 (sP0 = $true)),
% 0.13/0.36 inference(trivial_inequality_removal,[],[f55])).
% 0.13/0.36 thf(f55,plain,(
% 0.13/0.36 ($true != $true) | (sP0 = $true)),
% 0.13/0.36 inference(definition_unfolding,[],[f52,f42])).
% 0.13/0.36 thf(f42,plain,(
% 0.13/0.36 (breln1compE = $true)),
% 0.13/0.36 inference(cnf_transformation,[],[f25])).
% 0.13/0.36 thf(f52,plain,(
% 0.13/0.36 (sP0 = $true) | (breln1compE != $true)),
% 0.13/0.36 inference(cnf_transformation,[],[f34])).
% 0.13/0.36 thf(f34,plain,(
% 0.13/0.36 ((breln1compE = $true) | (sP0 != $true)) & ((sP0 = $true) | (breln1compE != $true))),
% 0.13/0.36 inference(nnf_transformation,[],[f19])).
% 0.13/0.36 thf(f19,plain,(
% 0.13/0.36 (breln1compE = $true) <=> (sP0 = $true)),
% 0.13/0.36 inference(definition_folding,[],[f15,f18])).
% 0.13/0.36 thf(f18,plain,(
% 0.13/0.36 (sP0 = $true) <=> ! [X0,X1] : (! [X2] : (! [X3] : (($true != (in @ X3 @ X1)) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true) | ? [X5] : (((in @ (kpair @ X3 @ X5) @ X0) = $true) & ((in @ X5 @ X1) = $true) & ((in @ (kpair @ X5 @ X4) @ X2) = $true)) | ($true != (in @ X4 @ X1)))) | ((breln1 @ X1 @ X2) != $true)) | ((breln1 @ X1 @ X0) != $true))),
% 0.13/0.36 introduced(predicate_definition_introduction,[new_symbols(naming,[=])])).
% 0.13/0.36 thf(f15,plain,(
% 0.13/0.36 (breln1compE = $true) <=> ! [X0,X1] : (! [X2] : (! [X3] : (($true != (in @ X3 @ X1)) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true) | ? [X5] : (((in @ (kpair @ X3 @ X5) @ X0) = $true) & ((in @ X5 @ X1) = $true) & ((in @ (kpair @ X5 @ X4) @ X2) = $true)) | ($true != (in @ X4 @ X1)))) | ((breln1 @ X1 @ X2) != $true)) | ((breln1 @ X1 @ X0) != $true))),
% 0.13/0.36 inference(flattening,[],[f14])).
% 0.13/0.36 thf(f14,plain,(
% 0.13/0.36 ! [X0,X1] : (! [X2] : (! [X3] : (! [X4] : ((? [X5] : (((in @ (kpair @ X3 @ X5) @ X0) = $true) & ((in @ X5 @ X1) = $true) & ((in @ (kpair @ X5 @ X4) @ X2) = $true)) | ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true)) | ($true != (in @ X4 @ X1))) | ($true != (in @ X3 @ X1))) | ((breln1 @ X1 @ X2) != $true)) | ((breln1 @ X1 @ X0) != $true)) <=> (breln1compE = $true)),
% 0.13/0.36 inference(ennf_transformation,[],[f11])).
% 0.13/0.36 thf(f11,plain,(
% 0.13/0.36 ! [X0,X1] : (((breln1 @ X1 @ X0) = $true) => ! [X2] : (((breln1 @ X1 @ X2) = $true) => ! [X3] : (($true = (in @ X3 @ X1)) => ! [X4] : (($true = (in @ X4 @ X1)) => (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) => ? [X5] : (((in @ (kpair @ X3 @ X5) @ X0) = $true) & ((in @ X5 @ X1) = $true) & ((in @ (kpair @ X5 @ X4) @ X2) = $true))))))) <=> (breln1compE = $true)),
% 0.13/0.36 inference(fool_elimination,[],[f10])).
% 0.13/0.36 thf(f10,plain,(
% 0.13/0.36 (breln1compE = ! [X0,X1] : ((breln1 @ X1 @ X0) => ! [X2] : ((breln1 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X1) => ! [X4] : ((in @ X4 @ X1) => ((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) => ? [X5] : ((in @ (kpair @ X5 @ X4) @ X2) & (in @ X5 @ X1) & (in @ (kpair @ X3 @ X5) @ X0))))))))),
% 0.13/0.36 inference(rectify,[],[f3])).
% 0.13/0.36 thf(f3,axiom,(
% 0.13/0.36 (breln1compE = ! [X3,X0] : ((breln1 @ X0 @ X3) => ! [X4] : ((breln1 @ X0 @ X4) => ! [X5] : ((in @ X5 @ X0) => ! [X6] : ((in @ X6 @ X0) => ((in @ (kpair @ X5 @ X6) @ (breln1compset @ X0 @ X3 @ X4)) => ? [X7] : ((in @ (kpair @ X7 @ X6) @ X4) & (in @ X7 @ X0) & (in @ (kpair @ X5 @ X7) @ X3))))))))),
% 0.13/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln1compE)).
% 0.13/0.36 thf(f71,plain,(
% 0.13/0.36 (sP0 != $true) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3)))),
% 0.13/0.36 inference(subsumption_resolution,[],[f70,f35])).
% 0.13/0.36 thf(f35,plain,(
% 0.13/0.36 ($true = (in @ sK5 @ sK1))),
% 0.13/0.36 inference(cnf_transformation,[],[f25])).
% 0.13/0.36 thf(f70,plain,(
% 0.13/0.36 ($true != (in @ sK5 @ sK1)) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3))) | (sP0 != $true)),
% 0.13/0.36 inference(subsumption_resolution,[],[f69,f41])).
% 0.13/0.36 thf(f41,plain,(
% 0.13/0.36 ($true = (breln1 @ sK1 @ sK2))),
% 0.13/0.36 inference(cnf_transformation,[],[f25])).
% 0.13/0.36 thf(f69,plain,(
% 0.13/0.36 ($true != (breln1 @ sK1 @ sK2)) | (sP0 != $true) | ($true != (in @ sK5 @ sK1)) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3)))),
% 0.13/0.36 inference(subsumption_resolution,[],[f68,f39])).
% 0.13/0.36 thf(f39,plain,(
% 0.13/0.36 ($true = (in @ sK4 @ sK1))),
% 0.13/0.36 inference(cnf_transformation,[],[f25])).
% 0.13/0.36 thf(f68,plain,(
% 0.13/0.36 ($true != (in @ sK4 @ sK1)) | ($true != (in @ sK5 @ sK1)) | ($true != (breln1 @ sK1 @ sK2)) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3))) | (sP0 != $true)),
% 0.13/0.36 inference(subsumption_resolution,[],[f67,f40])).
% 0.13/0.36 thf(f40,plain,(
% 0.13/0.36 ($true = (breln1 @ sK1 @ sK3))),
% 0.13/0.36 inference(cnf_transformation,[],[f25])).
% 0.13/0.36 thf(f67,plain,(
% 0.13/0.36 ($true != (breln1 @ sK1 @ sK3)) | (sP0 != $true) | ($true != (in @ sK4 @ sK1)) | ($true != (in @ sK5 @ sK1)) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3))) | ($true != (breln1 @ sK1 @ sK2))),
% 0.13/0.36 inference(trivial_inequality_removal,[],[f66])).
% 0.13/0.36 thf(f66,plain,(
% 0.13/0.36 ($true != (breln1 @ sK1 @ sK2)) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3))) | ($true != $true) | ($true != (in @ sK5 @ sK1)) | ($true != (in @ sK4 @ sK1)) | ($true != (breln1 @ sK1 @ sK3)) | (sP0 != $true)),
% 0.13/0.36 inference(duplicate_literal_removal,[],[f65])).
% 0.13/0.36 thf(f65,plain,(
% 0.13/0.36 ($true != (breln1 @ sK1 @ sK3)) | (sP0 != $true) | ($true != (in @ sK4 @ sK1)) | ($true != $true) | ($true != (breln1 @ sK1 @ sK2)) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3))) | ($true != (in @ sK5 @ sK1)) | ($true != (breln1 @ sK1 @ sK3)) | ($true != (in @ sK5 @ sK1)) | ($true != (breln1 @ sK1 @ sK2)) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ sK1 @ sK2 @ sK3))) | ($true != (in @ sK4 @ sK1))),
% 0.13/0.36 inference(superposition,[],[f64,f44])).
% 0.13/0.36 thf(f44,plain,(
% 0.13/0.36 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = (in @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6) @ X7)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X7 @ X6 @ X8))) | ($true != (breln1 @ X7 @ X8)) | ($true != (in @ X9 @ X7)) | ((in @ X10 @ X7) != $true) | (sP0 != $true) | ((breln1 @ X7 @ X6) != $true)) )),
% 0.13/0.36 inference(cnf_transformation,[],[f33])).
% 0.13/0.36 thf(f33,plain,(
% 0.13/0.36 ((sP0 = $true) | (((((in @ sK10 @ sK8) = $true) & (($true = (in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9))) & ! [X5] : (($true != (in @ (kpair @ sK10 @ X5) @ sK7)) | ($true != (in @ X5 @ sK8)) | ((in @ (kpair @ X5 @ sK11) @ sK9) != $true)) & ($true = (in @ sK11 @ sK8)))) & ((breln1 @ sK8 @ sK9) = $true)) & ((breln1 @ sK8 @ sK7) = $true))) & (! [X6,X7] : (! [X8] : (! [X9] : (($true != (in @ X9 @ X7)) | ! [X10] : (($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X7 @ X6 @ X8))) | (($true = (in @ (kpair @ X9 @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X6)) & ($true = (in @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6) @ X7)) & ($true = (in @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8))) | ((in @ X10 @ X7) != $true))) | ($true != (breln1 @ X7 @ X8))) | ((breln1 @ X7 @ X6) != $true)) | (sP0 != $true))),
% 0.13/0.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12])],[f27,f32,f31,f30,f29,f28])).
% 0.13/0.36 thf(f28,plain,(
% 0.13/0.36 ? [X0,X1] : (? [X2] : (? [X3] : (($true = (in @ X3 @ X1)) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) & ! [X5] : (((in @ (kpair @ X3 @ X5) @ X0) != $true) | ((in @ X5 @ X1) != $true) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ($true = (in @ X4 @ X1)))) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true)) => (? [X2] : (? [X3] : (($true = (in @ X3 @ sK8)) & ? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK8 @ sK7 @ X2))) & ! [X5] : (((in @ (kpair @ X3 @ X5) @ sK7) != $true) | ($true != (in @ X5 @ sK8)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ($true = (in @ X4 @ sK8)))) & ($true = (breln1 @ sK8 @ X2))) & ((breln1 @ sK8 @ sK7) = $true))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f29,plain,(
% 0.13/0.36 ? [X2] : (? [X3] : (($true = (in @ X3 @ sK8)) & ? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK8 @ sK7 @ X2))) & ! [X5] : (((in @ (kpair @ X3 @ X5) @ sK7) != $true) | ($true != (in @ X5 @ sK8)) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ($true = (in @ X4 @ sK8)))) & ($true = (breln1 @ sK8 @ X2))) => (? [X3] : (($true = (in @ X3 @ sK8)) & ? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK8 @ sK7 @ sK9))) & ! [X5] : (((in @ (kpair @ X3 @ X5) @ sK7) != $true) | ($true != (in @ X5 @ sK8)) | ($true != (in @ (kpair @ X5 @ X4) @ sK9))) & ($true = (in @ X4 @ sK8)))) & ((breln1 @ sK8 @ sK9) = $true))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f30,plain,(
% 0.13/0.36 ? [X3] : (($true = (in @ X3 @ sK8)) & ? [X4] : (($true = (in @ (kpair @ X3 @ X4) @ (breln1compset @ sK8 @ sK7 @ sK9))) & ! [X5] : (((in @ (kpair @ X3 @ X5) @ sK7) != $true) | ($true != (in @ X5 @ sK8)) | ($true != (in @ (kpair @ X5 @ X4) @ sK9))) & ($true = (in @ X4 @ sK8)))) => (((in @ sK10 @ sK8) = $true) & ? [X4] : (($true = (in @ (kpair @ sK10 @ X4) @ (breln1compset @ sK8 @ sK7 @ sK9))) & ! [X5] : (($true != (in @ (kpair @ sK10 @ X5) @ sK7)) | ($true != (in @ X5 @ sK8)) | ($true != (in @ (kpair @ X5 @ X4) @ sK9))) & ($true = (in @ X4 @ sK8))))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f31,plain,(
% 0.13/0.36 ? [X4] : (($true = (in @ (kpair @ sK10 @ X4) @ (breln1compset @ sK8 @ sK7 @ sK9))) & ! [X5] : (($true != (in @ (kpair @ sK10 @ X5) @ sK7)) | ($true != (in @ X5 @ sK8)) | ($true != (in @ (kpair @ X5 @ X4) @ sK9))) & ($true = (in @ X4 @ sK8))) => (($true = (in @ (kpair @ sK10 @ sK11) @ (breln1compset @ sK8 @ sK7 @ sK9))) & ! [X5] : (($true != (in @ (kpair @ sK10 @ X5) @ sK7)) | ($true != (in @ X5 @ sK8)) | ((in @ (kpair @ X5 @ sK11) @ sK9) != $true)) & ($true = (in @ sK11 @ sK8)))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f32,plain,(
% 0.13/0.36 ! [X6,X7,X8,X9,X10] : (? [X11] : (((in @ (kpair @ X9 @ X11) @ X6) = $true) & ((in @ X11 @ X7) = $true) & ($true = (in @ (kpair @ X11 @ X10) @ X8))) => (($true = (in @ (kpair @ X9 @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X6)) & ($true = (in @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6) @ X7)) & ($true = (in @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8))))),
% 0.13/0.36 introduced(choice_axiom,[])).
% 0.13/0.36 thf(f27,plain,(
% 0.13/0.36 ((sP0 = $true) | ? [X0,X1] : (? [X2] : (? [X3] : (($true = (in @ X3 @ X1)) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) & ! [X5] : (((in @ (kpair @ X3 @ X5) @ X0) != $true) | ((in @ X5 @ X1) != $true) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ($true = (in @ X4 @ X1)))) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true))) & (! [X6,X7] : (! [X8] : (! [X9] : (($true != (in @ X9 @ X7)) | ! [X10] : (($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X7 @ X6 @ X8))) | ? [X11] : (((in @ (kpair @ X9 @ X11) @ X6) = $true) & ((in @ X11 @ X7) = $true) & ($true = (in @ (kpair @ X11 @ X10) @ X8))) | ((in @ X10 @ X7) != $true))) | ($true != (breln1 @ X7 @ X8))) | ((breln1 @ X7 @ X6) != $true)) | (sP0 != $true))),
% 0.13/0.36 inference(rectify,[],[f26])).
% 0.13/0.36 thf(f26,plain,(
% 0.13/0.36 ((sP0 = $true) | ? [X0,X1] : (? [X2] : (? [X3] : (($true = (in @ X3 @ X1)) & ? [X4] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) = $true) & ! [X5] : (((in @ (kpair @ X3 @ X5) @ X0) != $true) | ((in @ X5 @ X1) != $true) | ((in @ (kpair @ X5 @ X4) @ X2) != $true)) & ($true = (in @ X4 @ X1)))) & ((breln1 @ X1 @ X2) = $true)) & ((breln1 @ X1 @ X0) = $true))) & (! [X0,X1] : (! [X2] : (! [X3] : (($true != (in @ X3 @ X1)) | ! [X4] : (((in @ (kpair @ X3 @ X4) @ (breln1compset @ X1 @ X0 @ X2)) != $true) | ? [X5] : (((in @ (kpair @ X3 @ X5) @ X0) = $true) & ((in @ X5 @ X1) = $true) & ((in @ (kpair @ X5 @ X4) @ X2) = $true)) | ($true != (in @ X4 @ X1)))) | ((breln1 @ X1 @ X2) != $true)) | ((breln1 @ X1 @ X0) != $true)) | (sP0 != $true))),
% 0.13/0.36 inference(nnf_transformation,[],[f18])).
% 0.13/0.36 thf(f64,plain,(
% 0.13/0.36 ( ! [X0 : $i] : (($true != (in @ (sK12 @ sK5 @ sK4 @ sK3 @ X0 @ sK2) @ sK1)) | ((in @ sK4 @ X0) != $true) | ((in @ sK5 @ X0) != $true) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ X0 @ sK2 @ sK3))) | ((breln1 @ X0 @ sK2) != $true) | ($true != (breln1 @ X0 @ sK3))) )),
% 0.13/0.36 inference(subsumption_resolution,[],[f63,f56])).
% 0.13/0.36 thf(f63,plain,(
% 0.13/0.36 ( ! [X0 : $i] : (((in @ sK5 @ X0) != $true) | ($true != (breln1 @ X0 @ sK3)) | ((breln1 @ X0 @ sK2) != $true) | ((in @ sK4 @ X0) != $true) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ X0 @ sK2 @ sK3))) | ($true != (in @ (sK12 @ sK5 @ sK4 @ sK3 @ X0 @ sK2) @ sK1)) | (sP0 != $true)) )),
% 0.13/0.36 inference(trivial_inequality_removal,[],[f62])).
% 0.13/0.36 thf(f62,plain,(
% 0.13/0.36 ( ! [X0 : $i] : (((in @ sK4 @ X0) != $true) | ((in @ sK5 @ X0) != $true) | (sP0 != $true) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ X0 @ sK2 @ sK3))) | ($true != (breln1 @ X0 @ sK3)) | ($true != (in @ (sK12 @ sK5 @ sK4 @ sK3 @ X0 @ sK2) @ sK1)) | ((breln1 @ X0 @ sK2) != $true) | ($true != $true)) )),
% 0.13/0.36 inference(duplicate_literal_removal,[],[f61])).
% 0.13/0.36 thf(f61,plain,(
% 0.13/0.36 ( ! [X0 : $i] : (((in @ sK4 @ X0) != $true) | ((in @ sK4 @ X0) != $true) | ($true != (breln1 @ X0 @ sK3)) | ((breln1 @ X0 @ sK2) != $true) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ X0 @ sK2 @ sK3))) | ((in @ sK5 @ X0) != $true) | (sP0 != $true) | ($true != $true) | ((breln1 @ X0 @ sK2) != $true) | ($true != (in @ (sK12 @ sK5 @ sK4 @ sK3 @ X0 @ sK2) @ sK1)) | ($true != (breln1 @ X0 @ sK3)) | ((in @ sK5 @ X0) != $true) | ($true != (in @ (kpair @ sK4 @ sK5) @ (breln1compset @ X0 @ sK2 @ sK3)))) )),
% 0.13/0.36 inference(superposition,[],[f60,f45])).
% 0.13/0.36 thf(f45,plain,(
% 0.13/0.36 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = (in @ (kpair @ X9 @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6)) @ X6)) | (sP0 != $true) | ($true != (breln1 @ X7 @ X8)) | ($true != (in @ X9 @ X7)) | ((breln1 @ X7 @ X6) != $true) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X7 @ X6 @ X8))) | ((in @ X10 @ X7) != $true)) )),
% 0.13/0.36 inference(cnf_transformation,[],[f33])).
% 0.13/0.36 thf(f60,plain,(
% 0.13/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ sK4 @ (sK12 @ sK5 @ X0 @ sK3 @ X1 @ X2)) @ sK2)) | ($true != (in @ X0 @ X1)) | ((breln1 @ X1 @ X2) != $true) | ($true != (in @ (kpair @ X0 @ sK5) @ (breln1compset @ X1 @ X2 @ sK3))) | ($true != (in @ sK5 @ X1)) | ((breln1 @ X1 @ sK3) != $true) | ((in @ (sK12 @ sK5 @ X0 @ sK3 @ X1 @ X2) @ sK1) != $true)) )),
% 0.13/0.36 inference(subsumption_resolution,[],[f59,f56])).
% 0.13/0.36 thf(f59,plain,(
% 0.13/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X0 @ sK5) @ (breln1compset @ X1 @ X2 @ sK3))) | ((breln1 @ X1 @ sK3) != $true) | ((breln1 @ X1 @ X2) != $true) | ($true != (in @ sK5 @ X1)) | (sP0 != $true) | ((in @ (sK12 @ sK5 @ X0 @ sK3 @ X1 @ X2) @ sK1) != $true) | ($true != (in @ (kpair @ sK4 @ (sK12 @ sK5 @ X0 @ sK3 @ X1 @ X2)) @ sK2)) | ($true != (in @ X0 @ X1))) )),
% 0.13/0.36 inference(trivial_inequality_removal,[],[f58])).
% 0.13/0.36 thf(f58,plain,(
% 0.13/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X1)) | ((breln1 @ X1 @ X2) != $true) | (sP0 != $true) | ($true != (in @ (kpair @ X0 @ sK5) @ (breln1compset @ X1 @ X2 @ sK3))) | ($true != (in @ (kpair @ sK4 @ (sK12 @ sK5 @ X0 @ sK3 @ X1 @ X2)) @ sK2)) | ((breln1 @ X1 @ sK3) != $true) | ((in @ (sK12 @ sK5 @ X0 @ sK3 @ X1 @ X2) @ sK1) != $true) | ($true != (in @ sK5 @ X1)) | ($true != $true)) )),
% 0.13/0.36 inference(superposition,[],[f57,f43])).
% 0.13/0.36 thf(f43,plain,(
% 0.13/0.36 ( ! [X10 : $i,X8 : $i,X6 : $i,X9 : $i,X7 : $i] : (($true = (in @ (kpair @ (sK12 @ X10 @ X9 @ X8 @ X7 @ X6) @ X10) @ X8)) | ($true != (in @ (kpair @ X9 @ X10) @ (breln1compset @ X7 @ X6 @ X8))) | ((in @ X10 @ X7) != $true) | ($true != (in @ X9 @ X7)) | ((breln1 @ X7 @ X6) != $true) | ($true != (breln1 @ X7 @ X8)) | (sP0 != $true)) )),
% 0.13/0.36 inference(cnf_transformation,[],[f33])).
% 0.13/0.36 thf(f57,plain,(
% 0.13/0.36 ( ! [X6 : $i] : (($true != (in @ (kpair @ X6 @ sK5) @ sK3)) | ((in @ (kpair @ sK4 @ X6) @ sK2) != $true) | ((in @ X6 @ sK1) != $true)) )),
% 0.13/0.36 inference(subsumption_resolution,[],[f38,f37])).
% 0.13/0.36 thf(f37,plain,(
% 0.13/0.36 ($true != sK6)),
% 0.13/0.36 inference(cnf_transformation,[],[f25])).
% 0.13/0.36 thf(f38,plain,(
% 0.13/0.36 ( ! [X6 : $i] : (((in @ X6 @ sK1) != $true) | ($true != (in @ (kpair @ X6 @ sK5) @ sK3)) | ((in @ (kpair @ sK4 @ X6) @ sK2) != $true) | ($true = sK6)) )),
% 0.13/0.36 inference(cnf_transformation,[],[f25])).
% 0.13/0.36 % SZS output end Proof for theBenchmark
% 0.13/0.36 % (26693)------------------------------
% 0.13/0.36 % (26693)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.36 % (26693)Termination reason: Refutation
% 0.13/0.36
% 0.13/0.36 % (26693)Memory used [KB]: 5628
% 0.13/0.36 % (26693)Time elapsed: 0.012 s
% 0.13/0.36 % (26693)Instructions burned: 12 (million)
% 0.13/0.36 % (26693)------------------------------
% 0.13/0.36 % (26693)------------------------------
% 0.13/0.36 % (26687)Success in time 0.021 s
% 0.13/0.37 % Vampire---4.8 exiting
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