TSTP Solution File: SEU776^2 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU776^2 : 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/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n013.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 03:51:26 EDT 2024
% Result : Theorem 0.15s 0.40s
% Output : Refutation 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SEU776^2 : TPTP v8.2.0. Released v3.7.0.
% 0.09/0.16 % 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
% 0.15/0.37 % Computer : n013.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Sun May 19 15:29:38 EDT 2024
% 0.15/0.37 % CPUTime :
% 0.15/0.37 This is a TH0_THM_EQU_NAR problem
% 0.15/0.38 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
% 0.15/0.40 % (1238)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)
% 0.15/0.40 % (1231)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.15/0.40 % (1232)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)
% 0.15/0.40 % (1233)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)
% 0.15/0.40 % (1234)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.15/0.40 % (1235)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)
% 0.15/0.40 % (1236)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)
% 0.15/0.40 % (1238)Instruction limit reached!
% 0.15/0.40 % (1238)------------------------------
% 0.15/0.40 % (1238)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1238)Termination reason: Unknown
% 0.15/0.40 % (1238)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (1238)Memory used [KB]: 1023
% 0.15/0.40 % (1238)Time elapsed: 0.003 s
% 0.15/0.40 % (1238)Instructions burned: 3 (million)
% 0.15/0.40 % (1238)------------------------------
% 0.15/0.40 % (1238)------------------------------
% 0.15/0.40 % (1237)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.15/0.40 % (1234)Instruction limit reached!
% 0.15/0.40 % (1234)------------------------------
% 0.15/0.40 % (1234)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1234)Termination reason: Unknown
% 0.15/0.40 % (1235)Instruction limit reached!
% 0.15/0.40 % (1235)------------------------------
% 0.15/0.40 % (1235)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1235)Termination reason: Unknown
% 0.15/0.40 % (1235)Termination phase: Property scanning
% 0.15/0.40
% 0.15/0.40 % (1235)Memory used [KB]: 895
% 0.15/0.40 % (1235)Time elapsed: 0.003 s
% 0.15/0.40 % (1235)Instructions burned: 2 (million)
% 0.15/0.40 % (1235)------------------------------
% 0.15/0.40 % (1235)------------------------------
% 0.15/0.40 % (1234)Termination phase: Unused predicate definition removal
% 0.15/0.40
% 0.15/0.40 % (1234)Memory used [KB]: 895
% 0.15/0.40 % (1234)Time elapsed: 0.003 s
% 0.15/0.40 % (1234)Instructions burned: 2 (million)
% 0.15/0.40 % (1234)------------------------------
% 0.15/0.40 % (1234)------------------------------
% 0.15/0.40 % (1232)Instruction limit reached!
% 0.15/0.40 % (1232)------------------------------
% 0.15/0.40 % (1232)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1232)Termination reason: Unknown
% 0.15/0.40 % (1232)Termination phase: Saturation
% 0.15/0.40
% 0.15/0.40 % (1232)Memory used [KB]: 5500
% 0.15/0.40 % (1232)Time elapsed: 0.005 s
% 0.15/0.40 % (1232)Instructions burned: 5 (million)
% 0.15/0.40 % (1232)------------------------------
% 0.15/0.40 % (1232)------------------------------
% 0.15/0.40 % (1236)First to succeed.
% 0.15/0.40 % (1233)Also succeeded, but the first one will report.
% 0.15/0.40 % (1231)Also succeeded, but the first one will report.
% 0.15/0.40 % (1236)Refutation found. Thanks to Tanya!
% 0.15/0.40 % SZS status Theorem for theBenchmark
% 0.15/0.40 % SZS output start Proof for theBenchmark
% 0.15/0.40 thf(func_def_0, type, in: $i > $i > $o).
% 0.15/0.40 thf(func_def_1, type, subset: $i > $i > $o).
% 0.15/0.40 thf(func_def_2, type, kpair: $i > $i > $i).
% 0.15/0.40 thf(func_def_3, type, cartprod: $i > $i > $i).
% 0.15/0.40 thf(func_def_4, type, breln: $i > $i > $i > $o).
% 0.15/0.40 thf(func_def_6, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.15/0.40 thf(func_def_8, type, breln1: $i > $i > $o).
% 0.15/0.40 thf(func_def_9, type, breln1invset: $i > $i > $i).
% 0.15/0.40 thf(func_def_19, type, sK3: $i > $i > $o).
% 0.15/0.40 thf(func_def_27, type, ph10: !>[X0: $tType]:(X0)).
% 0.15/0.40 thf(f59,plain,(
% 0.15/0.40 $false),
% 0.15/0.40 inference(subsumption_resolution,[],[f58,f38])).
% 0.15/0.40 thf(f38,plain,(
% 0.15/0.40 ($true = (in @ (kpair @ sK7 @ sK8) @ sK5))),
% 0.15/0.40 inference(cnf_transformation,[],[f29])).
% 0.15/0.40 thf(f29,plain,(
% 0.15/0.40 (($true = (breln1 @ sK6 @ sK5)) & ((($true = (in @ sK8 @ sK6)) & ($true = (in @ (kpair @ sK7 @ sK8) @ sK5)) & ($true != (in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK6 @ sK5)))) & ($true = (in @ sK7 @ sK6)))) & (dpsetconstrI = $true)),
% 0.15/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8])],[f20,f28,f27,f26])).
% 0.15/0.40 thf(f26,plain,(
% 0.15/0.40 ? [X0,X1] : (((breln1 @ X1 @ X0) = $true) & ? [X2] : (? [X3] : (($true = (in @ X3 @ X1)) & ($true = (in @ (kpair @ X2 @ X3) @ X0)) & ($true != (in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0)))) & ($true = (in @ X2 @ X1)))) => (($true = (breln1 @ sK6 @ sK5)) & ? [X2] : (? [X3] : (($true = (in @ X3 @ sK6)) & ($true = (in @ (kpair @ X2 @ X3) @ sK5)) & ($true != (in @ (kpair @ X3 @ X2) @ (breln1invset @ sK6 @ sK5)))) & ($true = (in @ X2 @ sK6))))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f27,plain,(
% 0.15/0.40 ? [X2] : (? [X3] : (($true = (in @ X3 @ sK6)) & ($true = (in @ (kpair @ X2 @ X3) @ sK5)) & ($true != (in @ (kpair @ X3 @ X2) @ (breln1invset @ sK6 @ sK5)))) & ($true = (in @ X2 @ sK6))) => (? [X3] : (($true = (in @ X3 @ sK6)) & ($true = (in @ (kpair @ sK7 @ X3) @ sK5)) & ((in @ (kpair @ X3 @ sK7) @ (breln1invset @ sK6 @ sK5)) != $true)) & ($true = (in @ sK7 @ sK6)))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f28,plain,(
% 0.15/0.40 ? [X3] : (($true = (in @ X3 @ sK6)) & ($true = (in @ (kpair @ sK7 @ X3) @ sK5)) & ((in @ (kpair @ X3 @ sK7) @ (breln1invset @ sK6 @ sK5)) != $true)) => (($true = (in @ sK8 @ sK6)) & ($true = (in @ (kpair @ sK7 @ sK8) @ sK5)) & ($true != (in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK6 @ sK5))))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f20,plain,(
% 0.15/0.40 ? [X0,X1] : (((breln1 @ X1 @ X0) = $true) & ? [X2] : (? [X3] : (($true = (in @ X3 @ X1)) & ($true = (in @ (kpair @ X2 @ X3) @ X0)) & ($true != (in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0)))) & ($true = (in @ X2 @ X1)))) & (dpsetconstrI = $true)),
% 0.15/0.40 inference(flattening,[],[f19])).
% 0.15/0.40 thf(f19,plain,(
% 0.15/0.40 ? [X0,X1] : (? [X2] : (? [X3] : ((($true != (in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0))) & ($true = (in @ (kpair @ X2 @ X3) @ X0))) & ($true = (in @ X3 @ X1))) & ($true = (in @ X2 @ X1))) & ((breln1 @ X1 @ X0) = $true)) & (dpsetconstrI = $true)),
% 0.15/0.40 inference(ennf_transformation,[],[f16])).
% 0.15/0.40 thf(f16,plain,(
% 0.15/0.40 ~((dpsetconstrI = $true) => ! [X0,X1] : (((breln1 @ X1 @ X0) = $true) => ! [X2] : (($true = (in @ X2 @ X1)) => ! [X3] : (($true = (in @ X3 @ X1)) => (($true = (in @ (kpair @ X2 @ X3) @ X0)) => ($true = (in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f15])).
% 0.15/0.40 thf(f15,plain,(
% 0.15/0.40 ~(dpsetconstrI => ! [X0,X1] : ((breln1 @ X1 @ X0) => ! [X2] : ((in @ X2 @ X1) => ! [X3] : ((in @ X3 @ X1) => ((in @ (kpair @ X2 @ X3) @ X0) => (in @ (kpair @ X3 @ X2) @ (breln1invset @ X1 @ X0)))))))),
% 0.15/0.40 inference(rectify,[],[f6])).
% 0.15/0.40 thf(f6,negated_conjecture,(
% 0.15/0.40 ~(dpsetconstrI => ! [X8,X0] : ((breln1 @ X0 @ X8) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X8) => (in @ (kpair @ X5 @ X4) @ (breln1invset @ X0 @ X8)))))))),
% 0.15/0.40 inference(negated_conjecture,[],[f5])).
% 0.15/0.40 thf(f5,conjecture,(
% 0.15/0.40 dpsetconstrI => ! [X8,X0] : ((breln1 @ X0 @ X8) => ! [X4] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X0) => ((in @ (kpair @ X4 @ X5) @ X8) => (in @ (kpair @ X5 @ X4) @ (breln1invset @ X0 @ X8))))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invI)).
% 0.15/0.40 thf(f58,plain,(
% 0.15/0.40 ($true != (in @ (kpair @ sK7 @ sK8) @ sK5))),
% 0.15/0.40 inference(subsumption_resolution,[],[f57,f36])).
% 0.15/0.40 thf(f36,plain,(
% 0.15/0.40 ($true = (in @ sK7 @ sK6))),
% 0.15/0.40 inference(cnf_transformation,[],[f29])).
% 0.15/0.40 thf(f57,plain,(
% 0.15/0.40 ($true != (in @ sK7 @ sK6)) | ($true != (in @ (kpair @ sK7 @ sK8) @ sK5))),
% 0.15/0.40 inference(subsumption_resolution,[],[f56,f39])).
% 0.15/0.40 thf(f39,plain,(
% 0.15/0.40 ($true = (in @ sK8 @ sK6))),
% 0.15/0.40 inference(cnf_transformation,[],[f29])).
% 0.15/0.40 thf(f56,plain,(
% 0.15/0.40 ($true != (in @ sK8 @ sK6)) | ($true != (in @ sK7 @ sK6)) | ($true != (in @ (kpair @ sK7 @ sK8) @ sK5))),
% 0.15/0.40 inference(beta_eta_normalization,[],[f55])).
% 0.15/0.40 thf(f55,plain,(
% 0.15/0.40 ($true != (in @ sK7 @ sK6)) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK5)))) @ sK8 @ sK7)) | ($true != (in @ sK8 @ sK6))),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f54])).
% 0.15/0.40 thf(f54,plain,(
% 0.15/0.40 ($true != $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK5)))) @ sK8 @ sK7)) | ($true != (in @ sK8 @ sK6)) | ($true != (in @ sK7 @ sK6))),
% 0.15/0.40 inference(superposition,[],[f50,f53])).
% 0.15/0.40 thf(f53,plain,(
% 0.15/0.40 ( ! [X8 : $i > $i > $o,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true = (in @ (kpair @ X7 @ X9) @ (dpsetconstr @ X6 @ X5 @ X8))) | ($true != (in @ X7 @ X6)) | ($true != (X8 @ X7 @ X9)) | ((in @ X9 @ X5) != $true)) )),
% 0.15/0.40 inference(beta_eta_normalization,[],[f52])).
% 0.15/0.40 thf(f52,plain,(
% 0.15/0.40 ( ! [X8 : $i > $i > $o,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true != (in @ X7 @ X6)) | ($true != (X8 @ X7 @ X9)) | ((in @ X9 @ X5) != $true) | ($true = (in @ (kpair @ X7 @ X9) @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1)))))))) )),
% 0.15/0.40 inference(trivial_inequality_removal,[],[f47])).
% 0.15/0.40 thf(f47,plain,(
% 0.15/0.40 ( ! [X8 : $i > $i > $o,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true != (in @ X7 @ X6)) | ($true = (in @ (kpair @ X7 @ X9) @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1))))))) | ($true != $true) | ((in @ X9 @ X5) != $true) | ($true != (X8 @ X7 @ X9))) )),
% 0.15/0.40 inference(definition_unfolding,[],[f30,f35])).
% 0.15/0.40 thf(f35,plain,(
% 0.15/0.40 (dpsetconstrI = $true)),
% 0.15/0.40 inference(cnf_transformation,[],[f29])).
% 0.15/0.40 thf(f30,plain,(
% 0.15/0.40 ( ! [X8 : $i > $i > $o,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (($true = (in @ (kpair @ X7 @ X9) @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1))))))) | ((in @ X9 @ X5) != $true) | ($true != (X8 @ X7 @ X9)) | ($true != (in @ X7 @ X6)) | (dpsetconstrI != $true)) )),
% 0.15/0.40 inference(cnf_transformation,[],[f25])).
% 0.15/0.40 thf(f25,plain,(
% 0.15/0.40 ((dpsetconstrI = $true) | ((($true != (in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK1 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ Y0 @ Y1))))))) & ($true = (in @ sK4 @ sK0)) & ($true = (sK3 @ sK2 @ sK4))) & ($true = (in @ sK2 @ sK1)))) & (! [X5,X6,X7,X8 : $i > $i > $o] : (! [X9] : (($true = (in @ (kpair @ X7 @ X9) @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1))))))) | ((in @ X9 @ X5) != $true) | ($true != (X8 @ X7 @ X9))) | ($true != (in @ X7 @ X6))) | (dpsetconstrI != $true))),
% 0.15/0.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f22,f24,f23])).
% 0.15/0.40 thf(f23,plain,(
% 0.15/0.40 ? [X0,X1,X2,X3 : $i > $i > $o] : (? [X4] : (($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) & ((in @ X4 @ X0) = $true) & ($true = (X3 @ X2 @ X4))) & ($true = (in @ X2 @ X1))) => (? [X4] : (($true != (in @ (kpair @ sK2 @ X4) @ (dpsetconstr @ sK1 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ Y0 @ Y1))))))) & ($true = (in @ X4 @ sK0)) & ((sK3 @ sK2 @ X4) = $true)) & ($true = (in @ sK2 @ sK1)))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f24,plain,(
% 0.15/0.40 ? [X4] : (($true != (in @ (kpair @ sK2 @ X4) @ (dpsetconstr @ sK1 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ Y0 @ Y1))))))) & ($true = (in @ X4 @ sK0)) & ((sK3 @ sK2 @ X4) = $true)) => (($true != (in @ (kpair @ sK2 @ sK4) @ (dpsetconstr @ sK1 @ sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (sK3 @ Y0 @ Y1))))))) & ($true = (in @ sK4 @ sK0)) & ($true = (sK3 @ sK2 @ sK4)))),
% 0.15/0.40 introduced(choice_axiom,[])).
% 0.15/0.40 thf(f22,plain,(
% 0.15/0.40 ((dpsetconstrI = $true) | ? [X0,X1,X2,X3 : $i > $i > $o] : (? [X4] : (($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) & ((in @ X4 @ X0) = $true) & ($true = (X3 @ X2 @ X4))) & ($true = (in @ X2 @ X1)))) & (! [X5,X6,X7,X8 : $i > $i > $o] : (! [X9] : (($true = (in @ (kpair @ X7 @ X9) @ (dpsetconstr @ X6 @ X5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X8 @ Y0 @ Y1))))))) | ((in @ X9 @ X5) != $true) | ($true != (X8 @ X7 @ X9))) | ($true != (in @ X7 @ X6))) | (dpsetconstrI != $true))),
% 0.15/0.40 inference(rectify,[],[f21])).
% 0.15/0.40 thf(f21,plain,(
% 0.15/0.40 ((dpsetconstrI = $true) | ? [X0,X1,X2,X3 : $i > $i > $o] : (? [X4] : (($true != (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) & ((in @ X4 @ X0) = $true) & ($true = (X3 @ X2 @ X4))) & ($true = (in @ X2 @ X1)))) & (! [X0,X1,X2,X3 : $i > $i > $o] : (! [X4] : (($true = (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) | ((in @ X4 @ X0) != $true) | ($true != (X3 @ X2 @ X4))) | ($true != (in @ X2 @ X1))) | (dpsetconstrI != $true))),
% 0.15/0.40 inference(nnf_transformation,[],[f18])).
% 0.15/0.40 thf(f18,plain,(
% 0.15/0.40 (dpsetconstrI = $true) <=> ! [X0,X1,X2,X3 : $i > $i > $o] : (! [X4] : (($true = (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) | ((in @ X4 @ X0) != $true) | ($true != (X3 @ X2 @ X4))) | ($true != (in @ X2 @ X1)))),
% 0.15/0.40 inference(flattening,[],[f17])).
% 0.15/0.40 thf(f17,plain,(
% 0.15/0.40 (dpsetconstrI = $true) <=> ! [X0,X1,X2,X3 : $i > $i > $o] : (! [X4] : ((($true = (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))) | ($true != (X3 @ X2 @ X4))) | ((in @ X4 @ X0) != $true)) | ($true != (in @ X2 @ X1)))),
% 0.15/0.40 inference(ennf_transformation,[],[f14])).
% 0.15/0.40 thf(f14,plain,(
% 0.15/0.40 (dpsetconstrI = $true) <=> ! [X0,X1,X2,X3 : $i > $i > $o] : (($true = (in @ X2 @ X1)) => ! [X4] : (((in @ X4 @ X0) = $true) => (($true = (X3 @ X2 @ X4)) => ($true = (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (X3 @ Y0 @ Y1))))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f13])).
% 0.15/0.40 thf(f13,plain,(
% 0.15/0.40 (! [X0,X1,X2,X3 : $i > $i > $o] : ((in @ X2 @ X1) => ! [X4] : ((in @ X4 @ X0) => ((X3 @ X2 @ X4) => (in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X1 @ X0 @ (^[X5 : $i, X6 : $i] : (X3 @ X5 @ X6))))))) = dpsetconstrI)),
% 0.15/0.40 inference(rectify,[],[f2])).
% 0.15/0.40 thf(f2,axiom,(
% 0.15/0.40 (! [X1,X0,X4,X3 : $i > $i > $o] : ((in @ X4 @ X0) => ! [X5] : ((in @ X5 @ X1) => ((X3 @ X4 @ X5) => (in @ (kpair @ X4 @ X5) @ (dpsetconstr @ X0 @ X1 @ (^[X6 : $i, X7 : $i] : (X3 @ X6 @ X7))))))) = dpsetconstrI)),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dpsetconstrI)).
% 0.15/0.40 thf(f50,plain,(
% 0.15/0.40 ($true != (in @ (kpair @ sK8 @ sK7) @ (dpsetconstr @ sK6 @ sK6 @ (^[Y0 : $i]: ((^[Y1 : $i]: (in @ (kpair @ Y1 @ Y0) @ sK5)))))))),
% 0.15/0.40 inference(beta_eta_normalization,[],[f49])).
% 0.15/0.40 thf(f49,plain,(
% 0.15/0.40 ($true != (in @ (kpair @ sK8 @ sK7) @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))) @ sK6 @ sK5)))),
% 0.15/0.40 inference(definition_unfolding,[],[f37,f42])).
% 0.15/0.40 thf(f42,plain,(
% 0.15/0.40 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 0.15/0.40 inference(cnf_transformation,[],[f12])).
% 0.15/0.40 thf(f12,plain,(
% 0.15/0.40 (breln1invset = (^[Y0 : $i]: ((^[Y1 : $i]: (dpsetconstr @ Y0 @ Y0 @ (^[Y2 : $i]: ((^[Y3 : $i]: (in @ (kpair @ Y3 @ Y2) @ Y1)))))))))),
% 0.15/0.40 inference(fool_elimination,[],[f11])).
% 0.15/0.40 thf(f11,plain,(
% 0.15/0.40 (breln1invset = (^[X0 : $i, X1 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X2 : $i, X3 : $i] : (in @ (kpair @ X3 @ X2) @ X1)))))),
% 0.15/0.40 inference(rectify,[],[f4])).
% 0.15/0.40 thf(f4,axiom,(
% 0.15/0.40 (breln1invset = (^[X0 : $i, X8 : $i] : (dpsetconstr @ X0 @ X0 @ (^[X4 : $i, X5 : $i] : (in @ (kpair @ X5 @ X4) @ X8)))))),
% 0.15/0.40 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',breln1invset)).
% 0.15/0.40 thf(f37,plain,(
% 0.15/0.40 ($true != (in @ (kpair @ sK8 @ sK7) @ (breln1invset @ sK6 @ sK5)))),
% 0.15/0.40 inference(cnf_transformation,[],[f29])).
% 0.15/0.40 % SZS output end Proof for theBenchmark
% 0.15/0.40 % (1236)------------------------------
% 0.15/0.40 % (1236)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.15/0.40 % (1236)Termination reason: Refutation
% 0.15/0.40
% 0.15/0.40 % (1236)Memory used [KB]: 5500
% 0.15/0.40 % (1236)Time elapsed: 0.008 s
% 0.15/0.40 % (1236)Instructions burned: 4 (million)
% 0.15/0.40 % (1236)------------------------------
% 0.15/0.40 % (1236)------------------------------
% 0.15/0.40 % (1230)Success in time 0.009 s
% 0.15/0.40 % Vampire---4.8 exiting
%------------------------------------------------------------------------------