TSTP Solution File: SEU717^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU717^2 : 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 : n017.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 03:51:00 EDT 2024
% Result : Theorem 0.13s 0.39s
% Output : Refutation 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU717^2 : TPTP v8.2.0. Released v3.7.0.
% 0.11/0.14 % 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
% 0.13/0.35 % Computer : n017.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 17:44:38 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 This is a TH0_THM_EQU_NAR problem
% 0.13/0.35 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
% 0.13/0.37 % (12493)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.13/0.37 % (12495)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)
% 0.13/0.37 % (12496)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.13/0.37 % (12494)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)
% 0.13/0.37 % (12492)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)
% 0.13/0.37 % (12490)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.13/0.37 % (12497)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)
% 0.13/0.37 % (12493)Instruction limit reached!
% 0.13/0.37 % (12493)------------------------------
% 0.13/0.37 % (12493)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37 % (12493)Termination reason: Unknown
% 0.13/0.37 % (12493)Termination phase: Saturation
% 0.13/0.37 % (12494)Instruction limit reached!
% 0.13/0.37 % (12494)------------------------------
% 0.13/0.37 % (12494)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.37
% 0.13/0.37 % (12493)Memory used [KB]: 1023
% 0.13/0.37 % (12493)Time elapsed: 0.004 s
% 0.13/0.37 % (12493)Instructions burned: 3 (million)
% 0.13/0.37 % (12493)------------------------------
% 0.13/0.37 % (12493)------------------------------
% 0.13/0.37 % (12494)Termination reason: Unknown
% 0.13/0.37 % (12494)Termination phase: Function definition elimination
% 0.13/0.37 % (12491)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)
% 0.13/0.37
% 0.13/0.37 % (12494)Memory used [KB]: 895
% 0.13/0.37 % (12494)Time elapsed: 0.004 s
% 0.13/0.37 % (12494)Instructions burned: 2 (million)
% 0.13/0.38 % (12494)------------------------------
% 0.13/0.38 % (12494)------------------------------
% 0.13/0.38 % (12497)Instruction limit reached!
% 0.13/0.38 % (12497)------------------------------
% 0.13/0.38 % (12497)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (12497)Termination reason: Unknown
% 0.13/0.38 % (12497)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (12497)Memory used [KB]: 5500
% 0.13/0.38 % (12497)Time elapsed: 0.004 s
% 0.13/0.38 % (12497)Instructions burned: 4 (million)
% 0.13/0.38 % (12497)------------------------------
% 0.13/0.38 % (12497)------------------------------
% 0.13/0.38 % (12491)Instruction limit reached!
% 0.13/0.38 % (12491)------------------------------
% 0.13/0.38 % (12491)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.38 % (12491)Termination reason: Unknown
% 0.13/0.38 % (12491)Termination phase: Saturation
% 0.13/0.38
% 0.13/0.38 % (12491)Memory used [KB]: 5500
% 0.13/0.38 % (12491)Time elapsed: 0.005 s
% 0.13/0.38 % (12491)Instructions burned: 4 (million)
% 0.13/0.38 % (12491)------------------------------
% 0.13/0.38 % (12491)------------------------------
% 0.13/0.38 % (12495)First to succeed.
% 0.13/0.39 % (12496)Also succeeded, but the first one will report.
% 0.13/0.39 % (12495)Refutation found. Thanks to Tanya!
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39 % SZS output start Proof for theBenchmark
% 0.13/0.39 thf(func_def_0, type, in: $i > $i > $o).
% 0.13/0.39 thf(func_def_1, type, powerset: $i > $i).
% 0.13/0.39 thf(func_def_2, type, subset: $i > $i > $o).
% 0.13/0.39 thf(func_def_13, type, sK5: $i > $i > $i > $i).
% 0.13/0.39 thf(f134,plain,(
% 0.13/0.39 $false),
% 0.13/0.39 inference(subsumption_resolution,[],[f133,f43])).
% 0.13/0.39 thf(f43,plain,(
% 0.13/0.39 ((in @ sK8 @ (powerset @ sK6)) = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f30])).
% 0.13/0.39 thf(f30,plain,(
% 0.13/0.39 (powersetI1 = $true) & (((in @ sK7 @ (powerset @ sK6)) = $true) & (! [X3] : (((in @ X3 @ sK6) != $true) | ((in @ X3 @ sK8) = $true) | ((in @ X3 @ sK7) != $true)) & ((in @ sK8 @ (powerset @ sK6)) = $true) & ((in @ sK7 @ (powerset @ sK8)) != $true))) & (subsetTI = $true)),
% 0.13/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f27,f29,f28])).
% 0.13/0.39 thf(f28,plain,(
% 0.13/0.39 ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ X1) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true) & ((in @ X1 @ (powerset @ X2)) != $true))) => (((in @ sK7 @ (powerset @ sK6)) = $true) & ? [X2] : (! [X3] : (((in @ X3 @ sK6) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ sK7) != $true)) & ((in @ X2 @ (powerset @ sK6)) = $true) & ((in @ sK7 @ (powerset @ X2)) != $true)))),
% 0.13/0.39 introduced(choice_axiom,[])).
% 0.13/0.39 thf(f29,plain,(
% 0.13/0.39 ? [X2] : (! [X3] : (((in @ X3 @ sK6) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ sK7) != $true)) & ((in @ X2 @ (powerset @ sK6)) = $true) & ((in @ sK7 @ (powerset @ X2)) != $true)) => (! [X3] : (((in @ X3 @ sK6) != $true) | ((in @ X3 @ sK8) = $true) | ((in @ X3 @ sK7) != $true)) & ((in @ sK8 @ (powerset @ sK6)) = $true) & ((in @ sK7 @ (powerset @ sK8)) != $true))),
% 0.13/0.39 introduced(choice_axiom,[])).
% 0.13/0.39 thf(f27,plain,(
% 0.13/0.39 (powersetI1 = $true) & ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ X1) != $true)) & ((in @ X2 @ (powerset @ X0)) = $true) & ((in @ X1 @ (powerset @ X2)) != $true))) & (subsetTI = $true)),
% 0.13/0.39 inference(rectify,[],[f13])).
% 0.13/0.39 thf(f13,plain,(
% 0.13/0.39 (powersetI1 = $true) & ? [X1,X0] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true)) & ((in @ X2 @ (powerset @ X1)) = $true) & ((in @ X0 @ (powerset @ X2)) != $true))) & (subsetTI = $true)),
% 0.13/0.39 inference(flattening,[],[f12])).
% 0.13/0.39 thf(f12,plain,(
% 0.13/0.39 (? [X0,X1] : (? [X2] : ((((in @ X0 @ (powerset @ X2)) != $true) & ! [X3] : ((((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true)) | ((in @ X3 @ X1) != $true))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (subsetTI = $true)) & (powersetI1 = $true)),
% 0.13/0.39 inference(ennf_transformation,[],[f11])).
% 0.13/0.39 thf(f11,plain,(
% 0.13/0.39 ~((powersetI1 = $true) => ((subsetTI = $true) => ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X1)) = $true) => (! [X3] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ((in @ X3 @ X2) = $true))) => ((in @ X0 @ (powerset @ X2)) = $true))))))),
% 0.13/0.39 inference(fool_elimination,[],[f10])).
% 0.13/0.39 thf(f10,plain,(
% 0.13/0.39 ~(powersetI1 => (subsetTI => ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => (! [X3] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (in @ X0 @ (powerset @ X2)))))))),
% 0.13/0.39 inference(rectify,[],[f4])).
% 0.13/0.39 thf(f4,negated_conjecture,(
% 0.13/0.39 ~(powersetI1 => (subsetTI => ! [X2,X0] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => (! [X4] : ((in @ X4 @ X0) => ((in @ X4 @ X2) => (in @ X4 @ X3))) => (in @ X2 @ (powerset @ X3)))))))),
% 0.13/0.39 inference(negated_conjecture,[],[f3])).
% 0.13/0.39 thf(f3,conjecture,(
% 0.13/0.39 powersetI1 => (subsetTI => ! [X2,X0] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => (! [X4] : ((in @ X4 @ X0) => ((in @ X4 @ X2) => (in @ X4 @ X3))) => (in @ X2 @ (powerset @ X3))))))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetTI1)).
% 0.13/0.39 thf(f133,plain,(
% 0.13/0.39 ((in @ sK8 @ (powerset @ sK6)) != $true)),
% 0.13/0.39 inference(subsumption_resolution,[],[f132,f45])).
% 0.13/0.39 thf(f45,plain,(
% 0.13/0.39 ((in @ sK7 @ (powerset @ sK6)) = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f30])).
% 0.13/0.39 thf(f132,plain,(
% 0.13/0.39 ((in @ sK7 @ (powerset @ sK6)) != $true) | ((in @ sK8 @ (powerset @ sK6)) != $true)),
% 0.13/0.39 inference(subsumption_resolution,[],[f131,f62])).
% 0.13/0.39 thf(f62,plain,(
% 0.13/0.39 ((subset @ sK7 @ sK8) != $true)),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f61])).
% 0.13/0.39 thf(f61,plain,(
% 0.13/0.39 ($true != $true) | ((subset @ sK7 @ sK8) != $true)),
% 0.13/0.39 inference(superposition,[],[f42,f60])).
% 0.13/0.39 thf(f60,plain,(
% 0.13/0.39 ( ! [X2 : $i,X3 : $i] : (((in @ X2 @ (powerset @ X3)) = $true) | ((subset @ X2 @ X3) != $true)) )),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f49])).
% 0.13/0.39 thf(f49,plain,(
% 0.13/0.39 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ((subset @ X2 @ X3) != $true) | ((in @ X2 @ (powerset @ X3)) = $true)) )),
% 0.13/0.39 inference(definition_unfolding,[],[f31,f46])).
% 0.13/0.39 thf(f46,plain,(
% 0.13/0.39 (powersetI1 = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f30])).
% 0.13/0.39 thf(f31,plain,(
% 0.13/0.39 ( ! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ((in @ X2 @ (powerset @ X3)) = $true) | (powersetI1 != $true)) )),
% 0.13/0.39 inference(cnf_transformation,[],[f20])).
% 0.13/0.39 thf(f20,plain,(
% 0.13/0.39 ((powersetI1 = $true) | (((subset @ sK0 @ sK1) = $true) & ((in @ sK0 @ (powerset @ sK1)) != $true))) & (! [X2,X3] : (((subset @ X2 @ X3) != $true) | ((in @ X2 @ (powerset @ X3)) = $true)) | (powersetI1 != $true))),
% 0.13/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f18,f19])).
% 0.13/0.39 thf(f19,plain,(
% 0.13/0.39 ? [X0,X1] : (((subset @ X0 @ X1) = $true) & ((in @ X0 @ (powerset @ X1)) != $true)) => (((subset @ sK0 @ sK1) = $true) & ((in @ sK0 @ (powerset @ sK1)) != $true))),
% 0.13/0.39 introduced(choice_axiom,[])).
% 0.13/0.39 thf(f18,plain,(
% 0.13/0.39 ((powersetI1 = $true) | ? [X0,X1] : (((subset @ X0 @ X1) = $true) & ((in @ X0 @ (powerset @ X1)) != $true))) & (! [X2,X3] : (((subset @ X2 @ X3) != $true) | ((in @ X2 @ (powerset @ X3)) = $true)) | (powersetI1 != $true))),
% 0.13/0.39 inference(rectify,[],[f17])).
% 0.13/0.39 thf(f17,plain,(
% 0.13/0.39 ((powersetI1 = $true) | ? [X0,X1] : (((subset @ X0 @ X1) = $true) & ((in @ X0 @ (powerset @ X1)) != $true))) & (! [X0,X1] : (((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true)) | (powersetI1 != $true))),
% 0.13/0.39 inference(nnf_transformation,[],[f16])).
% 0.13/0.39 thf(f16,plain,(
% 0.13/0.39 (powersetI1 = $true) <=> ! [X0,X1] : (((subset @ X0 @ X1) != $true) | ((in @ X0 @ (powerset @ X1)) = $true))),
% 0.13/0.39 inference(ennf_transformation,[],[f9])).
% 0.13/0.39 thf(f9,plain,(
% 0.13/0.39 (powersetI1 = $true) <=> ! [X1,X0] : (((subset @ X0 @ X1) = $true) => ((in @ X0 @ (powerset @ X1)) = $true))),
% 0.13/0.39 inference(fool_elimination,[],[f8])).
% 0.13/0.39 thf(f8,plain,(
% 0.13/0.39 (powersetI1 = ! [X0,X1] : ((subset @ X0 @ X1) => (in @ X0 @ (powerset @ X1))))),
% 0.13/0.39 inference(rectify,[],[f1])).
% 0.13/0.39 thf(f1,axiom,(
% 0.13/0.39 (powersetI1 = ! [X1,X0] : ((subset @ X1 @ X0) => (in @ X1 @ (powerset @ X0))))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1)).
% 0.13/0.39 thf(f42,plain,(
% 0.13/0.39 ((in @ sK7 @ (powerset @ sK8)) != $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f30])).
% 0.13/0.39 thf(f131,plain,(
% 0.13/0.39 ((subset @ sK7 @ sK8) = $true) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ((in @ sK7 @ (powerset @ sK6)) != $true)),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f130])).
% 0.13/0.39 thf(f130,plain,(
% 0.13/0.39 ((in @ sK8 @ (powerset @ sK6)) != $true) | ((subset @ sK7 @ sK8) = $true) | ($true != $true) | ((in @ sK7 @ (powerset @ sK6)) != $true)),
% 0.13/0.39 inference(duplicate_literal_removal,[],[f129])).
% 0.13/0.39 thf(f129,plain,(
% 0.13/0.39 ((in @ sK8 @ (powerset @ sK6)) != $true) | ($true != $true) | ((in @ sK7 @ (powerset @ sK6)) != $true) | ((in @ sK7 @ (powerset @ sK6)) != $true) | ((in @ sK8 @ (powerset @ sK6)) != $true) | ((subset @ sK7 @ sK8) = $true)),
% 0.13/0.39 inference(superposition,[],[f114,f58])).
% 0.13/0.39 thf(f58,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK5 @ X6 @ X5 @ X4) @ X4) = $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true)) )),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f56])).
% 0.13/0.39 thf(f56,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X6) = $true) | ((in @ (sK5 @ X6 @ X5 @ X4) @ X4) = $true) | ($true != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true)) )),
% 0.13/0.39 inference(definition_unfolding,[],[f34,f41])).
% 0.13/0.39 thf(f41,plain,(
% 0.13/0.39 (subsetTI = $true)),
% 0.13/0.39 inference(cnf_transformation,[],[f30])).
% 0.13/0.39 thf(f34,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK5 @ X6 @ X5 @ X4) @ X4) = $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (subsetTI != $true)) )),
% 0.13/0.39 inference(cnf_transformation,[],[f26])).
% 0.13/0.39 thf(f26,plain,(
% 0.13/0.39 ((subsetTI = $true) | ((! [X3] : (((in @ X3 @ sK3) != $true) | ((in @ X3 @ sK4) = $true) | ((in @ X3 @ sK2) != $true)) & ((subset @ sK3 @ sK4) != $true) & ((in @ sK4 @ (powerset @ sK2)) = $true)) & ((in @ sK3 @ (powerset @ sK2)) = $true))) & (! [X4,X5] : (! [X6] : ((((in @ (sK5 @ X6 @ X5 @ X4) @ X5) = $true) & ((in @ (sK5 @ X6 @ X5 @ X4) @ X6) != $true) & ((in @ (sK5 @ X6 @ X5 @ X4) @ X4) = $true)) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true)) | ((in @ X5 @ (powerset @ X4)) != $true)) | (subsetTI != $true))),
% 0.13/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f22,f25,f24,f23])).
% 0.13/0.39 thf(f23,plain,(
% 0.13/0.39 ? [X0,X1] : (? [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true)) & ((subset @ X1 @ X2) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2] : (! [X3] : (((in @ X3 @ sK3) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ sK2) != $true)) & ((subset @ sK3 @ X2) != $true) & ((in @ X2 @ (powerset @ sK2)) = $true)) & ((in @ sK3 @ (powerset @ sK2)) = $true))),
% 0.13/0.39 introduced(choice_axiom,[])).
% 0.13/0.39 thf(f24,plain,(
% 0.13/0.39 ? [X2] : (! [X3] : (((in @ X3 @ sK3) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ sK2) != $true)) & ((subset @ sK3 @ X2) != $true) & ((in @ X2 @ (powerset @ sK2)) = $true)) => (! [X3] : (((in @ X3 @ sK3) != $true) | ((in @ X3 @ sK4) = $true) | ((in @ X3 @ sK2) != $true)) & ((subset @ sK3 @ sK4) != $true) & ((in @ sK4 @ (powerset @ sK2)) = $true))),
% 0.13/0.39 introduced(choice_axiom,[])).
% 0.13/0.39 thf(f25,plain,(
% 0.13/0.39 ! [X4,X5,X6] : (? [X7] : (((in @ X7 @ X5) = $true) & ((in @ X7 @ X6) != $true) & ((in @ X7 @ X4) = $true)) => (((in @ (sK5 @ X6 @ X5 @ X4) @ X5) = $true) & ((in @ (sK5 @ X6 @ X5 @ X4) @ X6) != $true) & ((in @ (sK5 @ X6 @ X5 @ X4) @ X4) = $true)))),
% 0.13/0.39 introduced(choice_axiom,[])).
% 0.13/0.39 thf(f22,plain,(
% 0.13/0.39 ((subsetTI = $true) | ? [X0,X1] : (? [X2] : (! [X3] : (((in @ X3 @ X1) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ X0) != $true)) & ((subset @ X1 @ X2) != $true) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true))) & (! [X4,X5] : (! [X6] : (? [X7] : (((in @ X7 @ X5) = $true) & ((in @ X7 @ X6) != $true) & ((in @ X7 @ X4) = $true)) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true)) | ((in @ X5 @ (powerset @ X4)) != $true)) | (subsetTI != $true))),
% 0.13/0.39 inference(rectify,[],[f21])).
% 0.13/0.39 thf(f21,plain,(
% 0.13/0.39 ((subsetTI = $true) | ? [X1,X0] : (? [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ X2) = $true) | ((in @ X3 @ X1) != $true)) & ((subset @ X0 @ X2) != $true) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true))) & (! [X1,X0] : (! [X2] : (? [X3] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ X1) = $true)) | ((subset @ X0 @ X2) = $true) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true)) | (subsetTI != $true))),
% 0.13/0.39 inference(nnf_transformation,[],[f15])).
% 0.13/0.39 thf(f15,plain,(
% 0.13/0.39 (subsetTI = $true) <=> ! [X1,X0] : (! [X2] : (? [X3] : (((in @ X3 @ X0) = $true) & ((in @ X3 @ X2) != $true) & ((in @ X3 @ X1) = $true)) | ((subset @ X0 @ X2) = $true) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.13/0.39 inference(flattening,[],[f14])).
% 0.13/0.39 thf(f14,plain,(
% 0.13/0.39 (subsetTI = $true) <=> ! [X0,X1] : (! [X2] : ((((subset @ X0 @ X2) = $true) | ? [X3] : ((((in @ X3 @ X2) != $true) & ((in @ X3 @ X0) = $true)) & ((in @ X3 @ X1) = $true))) | ((in @ X2 @ (powerset @ X1)) != $true)) | ((in @ X0 @ (powerset @ X1)) != $true))),
% 0.13/0.39 inference(ennf_transformation,[],[f7])).
% 0.13/0.39 thf(f7,plain,(
% 0.13/0.39 (subsetTI = $true) <=> ! [X0,X1] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X1)) = $true) => (! [X3] : (((in @ X3 @ X1) = $true) => (((in @ X3 @ X0) = $true) => ((in @ X3 @ X2) = $true))) => ((subset @ X0 @ X2) = $true))))),
% 0.13/0.39 inference(fool_elimination,[],[f6])).
% 0.13/0.39 thf(f6,plain,(
% 0.13/0.39 (subsetTI = ! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => (! [X3] : ((in @ X3 @ X1) => ((in @ X3 @ X0) => (in @ X3 @ X2))) => (subset @ X0 @ X2)))))),
% 0.13/0.39 inference(rectify,[],[f2])).
% 0.13/0.39 thf(f2,axiom,(
% 0.13/0.39 (subsetTI = ! [X2,X0] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => (! [X4] : ((in @ X4 @ X0) => ((in @ X4 @ X2) => (in @ X4 @ X3))) => (subset @ X2 @ X3)))))),
% 0.13/0.39 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTI)).
% 0.13/0.39 thf(f114,plain,(
% 0.13/0.39 ( ! [X0 : $i] : (((in @ (sK5 @ sK8 @ sK7 @ X0) @ sK6) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true)) )),
% 0.13/0.39 inference(subsumption_resolution,[],[f113,f62])).
% 0.13/0.39 thf(f113,plain,(
% 0.13/0.39 ( ! [X0 : $i] : (((in @ sK8 @ (powerset @ X0)) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ (sK5 @ sK8 @ sK7 @ X0) @ sK6) != $true) | ((subset @ sK7 @ sK8) = $true)) )),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f112])).
% 0.13/0.39 thf(f112,plain,(
% 0.13/0.39 ( ! [X0 : $i] : (((in @ (sK5 @ sK8 @ sK7 @ X0) @ sK6) != $true) | ($true != $true) | ((subset @ sK7 @ sK8) = $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((in @ sK8 @ (powerset @ X0)) != $true)) )),
% 0.13/0.39 inference(duplicate_literal_removal,[],[f108])).
% 0.13/0.39 thf(f108,plain,(
% 0.13/0.39 ( ! [X0 : $i] : (((in @ sK8 @ (powerset @ X0)) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((subset @ sK7 @ sK8) = $true) | ((in @ sK8 @ (powerset @ X0)) != $true) | ((in @ (sK5 @ sK8 @ sK7 @ X0) @ sK6) != $true) | ((in @ sK7 @ (powerset @ X0)) != $true) | ((subset @ sK7 @ sK8) = $true) | ($true != $true)) )),
% 0.13/0.39 inference(superposition,[],[f65,f59])).
% 0.13/0.39 thf(f59,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK5 @ X6 @ X5 @ X4) @ X5) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((subset @ X5 @ X6) = $true)) )),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f54])).
% 0.13/0.39 thf(f54,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (powerset @ X4)) != $true) | ((in @ (sK5 @ X6 @ X5 @ X4) @ X5) = $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ($true != $true)) )),
% 0.13/0.39 inference(definition_unfolding,[],[f36,f41])).
% 0.13/0.39 thf(f36,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK5 @ X6 @ X5 @ X4) @ X5) = $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (subsetTI != $true)) )),
% 0.13/0.39 inference(cnf_transformation,[],[f26])).
% 0.13/0.39 thf(f65,plain,(
% 0.13/0.39 ( ! [X0 : $i,X1 : $i] : (((in @ (sK5 @ sK8 @ X0 @ X1) @ sK7) != $true) | ((in @ sK8 @ (powerset @ X1)) != $true) | ((in @ (sK5 @ sK8 @ X0 @ X1) @ sK6) != $true) | ((subset @ X0 @ sK8) = $true) | ((in @ X0 @ (powerset @ X1)) != $true)) )),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f64])).
% 0.13/0.39 thf(f64,plain,(
% 0.13/0.39 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) != $true) | ((in @ (sK5 @ sK8 @ X0 @ X1) @ sK7) != $true) | ((in @ sK8 @ (powerset @ X1)) != $true) | ($true != $true) | ((in @ (sK5 @ sK8 @ X0 @ X1) @ sK6) != $true) | ((subset @ X0 @ sK8) = $true)) )),
% 0.13/0.39 inference(superposition,[],[f57,f44])).
% 0.13/0.39 thf(f44,plain,(
% 0.13/0.39 ( ! [X3 : $i] : (((in @ X3 @ sK8) = $true) | ((in @ X3 @ sK7) != $true) | ((in @ X3 @ sK6) != $true)) )),
% 0.13/0.39 inference(cnf_transformation,[],[f30])).
% 0.13/0.39 thf(f57,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK5 @ X6 @ X5 @ X4) @ X6) != $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true)) )),
% 0.13/0.39 inference(trivial_inequality_removal,[],[f55])).
% 0.13/0.39 thf(f55,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK5 @ X6 @ X5 @ X4) @ X6) != $true) | ($true != $true) | ((subset @ X5 @ X6) = $true) | ((in @ X5 @ (powerset @ X4)) != $true) | ((in @ X6 @ (powerset @ X4)) != $true)) )),
% 0.13/0.39 inference(definition_unfolding,[],[f35,f41])).
% 0.13/0.39 thf(f35,plain,(
% 0.13/0.39 ( ! [X6 : $i,X4 : $i,X5 : $i] : (((in @ (sK5 @ X6 @ X5 @ X4) @ X6) != $true) | ((subset @ X5 @ X6) = $true) | ((in @ X6 @ (powerset @ X4)) != $true) | ((in @ X5 @ (powerset @ X4)) != $true) | (subsetTI != $true)) )),
% 0.13/0.39 inference(cnf_transformation,[],[f26])).
% 0.13/0.39 % SZS output end Proof for theBenchmark
% 0.13/0.39 % (12495)------------------------------
% 0.13/0.39 % (12495)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.13/0.39 % (12495)Termination reason: Refutation
% 0.13/0.39
% 0.13/0.39 % (12495)Memory used [KB]: 5628
% 0.13/0.39 % (12495)Time elapsed: 0.017 s
% 0.13/0.39 % (12495)Instructions burned: 16 (million)
% 0.13/0.39 % (12495)------------------------------
% 0.13/0.39 % (12495)------------------------------
% 0.13/0.39 % (12489)Success in time 0.042 s
% 0.13/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------