TSTP Solution File: SEU805^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU805^2 : 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 : n010.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 03:51:41 EDT 2024
% Result : Theorem 0.12s 0.38s
% Output : Refutation 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU805^2 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.15 % 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
% 0.12/0.35 % Computer : n010.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun May 19 18:16:08 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.35 This is a TH0_THM_EQU_NAR problem
% 0.12/0.35 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
% 0.12/0.37 % (8119)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)
% 0.12/0.37 % (8120)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.12/0.37 % (8122)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)
% 0.12/0.37 % (8120)Instruction limit reached!
% 0.12/0.37 % (8120)------------------------------
% 0.12/0.37 % (8120)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (8120)Termination reason: Unknown
% 0.12/0.37 % (8120)Termination phase: Preprocessing 1
% 0.12/0.37
% 0.12/0.37 % (8120)Memory used [KB]: 895
% 0.12/0.37 % (8120)Time elapsed: 0.003 s
% 0.12/0.37 % (8120)Instructions burned: 2 (million)
% 0.12/0.37 % (8117)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.12/0.37 % (8120)------------------------------
% 0.12/0.37 % (8120)------------------------------
% 0.12/0.37 % (8123)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.12/0.37 % (8118)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)
% 0.12/0.37 % (8118)Instruction limit reached!
% 0.12/0.37 % (8118)------------------------------
% 0.12/0.37 % (8118)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.37 % (8118)Termination reason: Unknown
% 0.12/0.37 % (8118)Termination phase: Saturation
% 0.12/0.37
% 0.12/0.37 % (8118)Memory used [KB]: 5500
% 0.12/0.37 % (8118)Time elapsed: 0.004 s
% 0.12/0.37 % (8118)Instructions burned: 5 (million)
% 0.12/0.37 % (8118)------------------------------
% 0.12/0.37 % (8118)------------------------------
% 0.12/0.37 % (8124)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)
% 0.12/0.37 % (8122)First to succeed.
% 0.12/0.37 % (8121)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)
% 0.12/0.37 % (8124)Instruction limit reached!
% 0.12/0.37 % (8124)------------------------------
% 0.12/0.37 % (8124)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38 % (8124)Termination reason: Unknown
% 0.12/0.38 % (8124)Termination phase: Saturation
% 0.12/0.38
% 0.12/0.38 % (8124)Memory used [KB]: 895
% 0.12/0.38 % (8124)Time elapsed: 0.003 s
% 0.12/0.38 % (8124)Instructions burned: 3 (million)
% 0.12/0.38 % (8124)------------------------------
% 0.12/0.38 % (8124)------------------------------
% 0.12/0.38 % (8121)Instruction limit reached!
% 0.12/0.38 % (8121)------------------------------
% 0.12/0.38 % (8121)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38 % (8121)Termination reason: Unknown
% 0.12/0.38 % (8121)Termination phase: Property scanning
% 0.12/0.38
% 0.12/0.38 % (8121)Memory used [KB]: 895
% 0.12/0.38 % (8121)Time elapsed: 0.003 s
% 0.12/0.38 % (8121)Instructions burned: 2 (million)
% 0.12/0.38 % (8121)------------------------------
% 0.12/0.38 % (8121)------------------------------
% 0.12/0.38 % (8123)Also succeeded, but the first one will report.
% 0.12/0.38 % (8122)Refutation found. Thanks to Tanya!
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38 % SZS output start Proof for theBenchmark
% 0.12/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.12/0.38 thf(func_def_4, type, nonempty: $i > $o).
% 0.12/0.38 thf(func_def_6, type, binintersect: $i > $i > $i).
% 0.12/0.38 thf(func_def_14, type, sK0: $i > $i > $i).
% 0.12/0.38 thf(func_def_18, type, sK4: $i > $i).
% 0.12/0.38 thf(func_def_21, type, sK7: $i > $i).
% 0.12/0.38 thf(func_def_23, type, sK9: $i > $i).
% 0.12/0.38 thf(f117,plain,(
% 0.12/0.38 $false),
% 0.12/0.38 inference(avatar_sat_refutation,[],[f88,f106,f116])).
% 0.12/0.38 thf(f116,plain,(
% 0.12/0.38 ~spl10_2),
% 0.12/0.38 inference(avatar_contradiction_clause,[],[f115])).
% 0.12/0.38 thf(f115,plain,(
% 0.12/0.38 $false | ~spl10_2),
% 0.12/0.38 inference(subsumption_resolution,[],[f111,f49])).
% 0.12/0.38 thf(f49,plain,(
% 0.12/0.38 ($true = (nonempty @ sK3))),
% 0.12/0.38 inference(cnf_transformation,[],[f29])).
% 0.12/0.38 thf(f29,plain,(
% 0.12/0.38 (! [X1] : ((emptyset != (binintersect @ X1 @ sK3)) | ($true != (in @ X1 @ sK3))) & ($true = (nonempty @ sK3))) & (disjointsetsI1 = $true) & (foundationAx = $true) & (nonemptyE1 = $true)),
% 0.12/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f20,f28])).
% 0.12/0.38 thf(f28,plain,(
% 0.12/0.38 ? [X0] : (! [X1] : ((emptyset != (binintersect @ X1 @ X0)) | ((in @ X1 @ X0) != $true)) & ((nonempty @ X0) = $true)) => (! [X1] : ((emptyset != (binintersect @ X1 @ sK3)) | ($true != (in @ X1 @ sK3))) & ($true = (nonempty @ sK3)))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f20,plain,(
% 0.12/0.38 ? [X0] : (! [X1] : ((emptyset != (binintersect @ X1 @ X0)) | ((in @ X1 @ X0) != $true)) & ((nonempty @ X0) = $true)) & (disjointsetsI1 = $true) & (foundationAx = $true) & (nonemptyE1 = $true)),
% 0.12/0.38 inference(flattening,[],[f19])).
% 0.12/0.38 thf(f19,plain,(
% 0.12/0.38 ((? [X0] : (! [X1] : ((emptyset != (binintersect @ X1 @ X0)) | ((in @ X1 @ X0) != $true)) & ((nonempty @ X0) = $true)) & (disjointsetsI1 = $true)) & (nonemptyE1 = $true)) & (foundationAx = $true)),
% 0.12/0.38 inference(ennf_transformation,[],[f15])).
% 0.12/0.38 thf(f15,plain,(
% 0.12/0.38 ~((foundationAx = $true) => ((nonemptyE1 = $true) => ((disjointsetsI1 = $true) => ! [X0] : (((nonempty @ X0) = $true) => ? [X1] : ((emptyset = (binintersect @ X1 @ X0)) & ((in @ X1 @ X0) = $true))))))),
% 0.12/0.38 inference(fool_elimination,[],[f14])).
% 0.12/0.38 thf(f14,plain,(
% 0.12/0.38 ~(foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0] : ((nonempty @ X0) => ? [X1] : ((emptyset = (binintersect @ X1 @ X0)) & (in @ X1 @ X0))))))),
% 0.12/0.38 inference(rectify,[],[f6])).
% 0.12/0.38 thf(f6,negated_conjecture,(
% 0.12/0.38 ~(foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0] : ((nonempty @ X0) => ? [X3] : ((emptyset = (binintersect @ X3 @ X0)) & (in @ X3 @ X0))))))),
% 0.12/0.38 inference(negated_conjecture,[],[f5])).
% 0.12/0.38 thf(f5,conjecture,(
% 0.12/0.38 foundationAx => (nonemptyE1 => (disjointsetsI1 => ! [X0] : ((nonempty @ X0) => ? [X3] : ((emptyset = (binintersect @ X3 @ X0)) & (in @ X3 @ X0)))))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundation2)).
% 0.12/0.38 thf(f111,plain,(
% 0.12/0.38 ($true != (nonempty @ sK3)) | ~spl10_2),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f107])).
% 0.12/0.38 thf(f107,plain,(
% 0.12/0.38 ($true != (nonempty @ sK3)) | ($true != $true) | ~spl10_2),
% 0.12/0.38 inference(superposition,[],[f87,f75])).
% 0.12/0.38 thf(f75,plain,(
% 0.12/0.38 ( ! [X2 : $i] : (($true = (in @ (sK9 @ X2) @ X2)) | ((nonempty @ X2) != $true)) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f70])).
% 0.12/0.38 thf(f70,plain,(
% 0.12/0.38 ( ! [X2 : $i] : (($true != $true) | ($true = (in @ (sK9 @ X2) @ X2)) | ((nonempty @ X2) != $true)) )),
% 0.12/0.38 inference(definition_unfolding,[],[f56,f46])).
% 0.12/0.38 thf(f46,plain,(
% 0.12/0.38 (nonemptyE1 = $true)),
% 0.12/0.38 inference(cnf_transformation,[],[f29])).
% 0.12/0.38 thf(f56,plain,(
% 0.12/0.38 ( ! [X2 : $i] : (($true = (in @ (sK9 @ X2) @ X2)) | ((nonempty @ X2) != $true) | (nonemptyE1 != $true)) )),
% 0.12/0.38 inference(cnf_transformation,[],[f41])).
% 0.12/0.38 thf(f41,plain,(
% 0.12/0.38 ((nonemptyE1 = $true) | (! [X1] : ((in @ X1 @ sK8) != $true) & ($true = (nonempty @ sK8)))) & (! [X2] : (($true = (in @ (sK9 @ X2) @ X2)) | ((nonempty @ X2) != $true)) | (nonemptyE1 != $true))),
% 0.12/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f38,f40,f39])).
% 0.12/0.38 thf(f39,plain,(
% 0.12/0.38 ? [X0] : (! [X1] : ((in @ X1 @ X0) != $true) & ((nonempty @ X0) = $true)) => (! [X1] : ((in @ X1 @ sK8) != $true) & ($true = (nonempty @ sK8)))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f40,plain,(
% 0.12/0.38 ! [X2] : (? [X3] : ($true = (in @ X3 @ X2)) => ($true = (in @ (sK9 @ X2) @ X2)))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f38,plain,(
% 0.12/0.38 ((nonemptyE1 = $true) | ? [X0] : (! [X1] : ((in @ X1 @ X0) != $true) & ((nonempty @ X0) = $true))) & (! [X2] : (? [X3] : ($true = (in @ X3 @ X2)) | ((nonempty @ X2) != $true)) | (nonemptyE1 != $true))),
% 0.12/0.38 inference(rectify,[],[f37])).
% 0.12/0.38 thf(f37,plain,(
% 0.12/0.38 ((nonemptyE1 = $true) | ? [X0] : (! [X1] : ((in @ X1 @ X0) != $true) & ((nonempty @ X0) = $true))) & (! [X0] : (? [X1] : ((in @ X1 @ X0) = $true) | ((nonempty @ X0) != $true)) | (nonemptyE1 != $true))),
% 0.12/0.38 inference(nnf_transformation,[],[f18])).
% 0.12/0.38 thf(f18,plain,(
% 0.12/0.38 (nonemptyE1 = $true) <=> ! [X0] : (? [X1] : ((in @ X1 @ X0) = $true) | ((nonempty @ X0) != $true))),
% 0.12/0.38 inference(ennf_transformation,[],[f9])).
% 0.12/0.38 thf(f9,plain,(
% 0.12/0.38 ! [X0] : (((nonempty @ X0) = $true) => ? [X1] : ((in @ X1 @ X0) = $true)) <=> (nonemptyE1 = $true)),
% 0.12/0.38 inference(fool_elimination,[],[f8])).
% 0.12/0.38 thf(f8,plain,(
% 0.12/0.38 (nonemptyE1 = ! [X0] : ((nonempty @ X0) => ? [X1] : (in @ X1 @ X0)))),
% 0.12/0.38 inference(rectify,[],[f3])).
% 0.12/0.38 thf(f3,axiom,(
% 0.12/0.38 (nonemptyE1 = ! [X0] : ((nonempty @ X0) => ? [X1] : (in @ X1 @ X0)))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1)).
% 0.12/0.38 thf(f87,plain,(
% 0.12/0.38 ( ! [X0 : $i] : (((in @ X0 @ sK3) != $true)) ) | ~spl10_2),
% 0.12/0.38 inference(avatar_component_clause,[],[f86])).
% 0.12/0.38 thf(f86,plain,(
% 0.12/0.38 spl10_2 <=> ! [X0] : ((in @ X0 @ sK3) != $true)),
% 0.12/0.38 introduced(avatar_definition,[new_symbols(naming,[spl10_2])])).
% 0.12/0.38 thf(f106,plain,(
% 0.12/0.38 spl10_2 | spl10_1),
% 0.12/0.38 inference(avatar_split_clause,[],[f105,f82,f86])).
% 0.12/0.38 thf(f82,plain,(
% 0.12/0.38 spl10_1 <=> (emptyset = (binintersect @ (sK4 @ sK3) @ sK3))),
% 0.12/0.38 introduced(avatar_definition,[new_symbols(naming,[spl10_1])])).
% 0.12/0.38 thf(f105,plain,(
% 0.12/0.38 ( ! [X0 : $i] : (((in @ X0 @ sK3) != $true)) ) | spl10_1),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f104])).
% 0.12/0.38 thf(f104,plain,(
% 0.12/0.38 ( ! [X0 : $i] : (((in @ X0 @ sK3) != $true) | (emptyset != emptyset)) ) | spl10_1),
% 0.12/0.38 inference(superposition,[],[f84,f103])).
% 0.12/0.38 thf(f103,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ (sK4 @ X0) @ X0)) | ((in @ X1 @ X0) != $true)) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f102])).
% 0.12/0.38 thf(f102,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (emptyset = (binintersect @ (sK4 @ X0) @ X0)) | ((in @ X1 @ X0) != $true)) )),
% 0.12/0.38 inference(duplicate_literal_removal,[],[f101])).
% 0.12/0.38 thf(f101,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (emptyset = (binintersect @ (sK4 @ X0) @ X0)) | ((in @ X1 @ X0) != $true) | (emptyset = (binintersect @ (sK4 @ X0) @ X0))) )),
% 0.12/0.38 inference(superposition,[],[f98,f71])).
% 0.12/0.38 thf(f71,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK0 @ X1 @ X0) @ X0)) | (emptyset = (binintersect @ X1 @ X0))) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f60])).
% 0.12/0.38 thf(f60,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK0 @ X1 @ X0) @ X0)) | (emptyset = (binintersect @ X1 @ X0)) | ($true != $true)) )),
% 0.12/0.38 inference(definition_unfolding,[],[f44,f48])).
% 0.12/0.38 thf(f48,plain,(
% 0.12/0.38 (disjointsetsI1 = $true)),
% 0.12/0.38 inference(cnf_transformation,[],[f29])).
% 0.12/0.38 thf(f44,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) | ($true = (in @ (sK0 @ X1 @ X0) @ X0)) | (disjointsetsI1 != $true)) )),
% 0.12/0.38 inference(cnf_transformation,[],[f27])).
% 0.12/0.38 thf(f27,plain,(
% 0.12/0.38 (! [X0,X1] : ((emptyset = (binintersect @ X1 @ X0)) | (((in @ (sK0 @ X1 @ X0) @ X1) = $true) & ($true = (in @ (sK0 @ X1 @ X0) @ X0)))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | ((emptyset != (binintersect @ sK2 @ sK1)) & ! [X5] : (($true != (in @ X5 @ sK2)) | ($true != (in @ X5 @ sK1)))))),
% 0.12/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f26,f25])).
% 0.12/0.38 thf(f25,plain,(
% 0.12/0.38 ! [X0,X1] : (? [X2] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) = $true)) => (((in @ (sK0 @ X1 @ X0) @ X1) = $true) & ($true = (in @ (sK0 @ X1 @ X0) @ X0))))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f26,plain,(
% 0.12/0.38 ? [X3,X4] : ((emptyset != (binintersect @ X4 @ X3)) & ! [X5] : (($true != (in @ X5 @ X4)) | ($true != (in @ X5 @ X3)))) => ((emptyset != (binintersect @ sK2 @ sK1)) & ! [X5] : (($true != (in @ X5 @ sK2)) | ($true != (in @ X5 @ sK1))))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f24,plain,(
% 0.12/0.38 (! [X0,X1] : ((emptyset = (binintersect @ X1 @ X0)) | ? [X2] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) = $true))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | ? [X3,X4] : ((emptyset != (binintersect @ X4 @ X3)) & ! [X5] : (($true != (in @ X5 @ X4)) | ($true != (in @ X5 @ X3)))))),
% 0.12/0.38 inference(rectify,[],[f23])).
% 0.12/0.38 thf(f23,plain,(
% 0.12/0.38 (! [X0,X1] : ((emptyset = (binintersect @ X1 @ X0)) | ? [X2] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) = $true))) | (disjointsetsI1 != $true)) & ((disjointsetsI1 = $true) | ? [X0,X1] : ((emptyset != (binintersect @ X1 @ X0)) & ! [X2] : (($true != (in @ X2 @ X1)) | ((in @ X2 @ X0) != $true))))),
% 0.12/0.38 inference(nnf_transformation,[],[f22])).
% 0.12/0.38 thf(f22,plain,(
% 0.12/0.38 ! [X0,X1] : ((emptyset = (binintersect @ X1 @ X0)) | ? [X2] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) = $true))) <=> (disjointsetsI1 = $true)),
% 0.12/0.38 inference(ennf_transformation,[],[f17])).
% 0.12/0.38 thf(f17,plain,(
% 0.12/0.38 (disjointsetsI1 = $true) <=> ! [X0,X1] : (~? [X2] : (($true = (in @ X2 @ X1)) & ((in @ X2 @ X0) = $true)) => (emptyset = (binintersect @ X1 @ X0)))),
% 0.12/0.38 inference(fool_elimination,[],[f16])).
% 0.12/0.38 thf(f16,plain,(
% 0.12/0.38 (disjointsetsI1 = ! [X0,X1] : (~? [X2] : ((in @ X2 @ X0) & (in @ X2 @ X1)) => (emptyset = (binintersect @ X1 @ X0))))),
% 0.12/0.38 inference(rectify,[],[f4])).
% 0.12/0.38 thf(f4,axiom,(
% 0.12/0.38 (disjointsetsI1 = ! [X2,X0] : (~? [X1] : ((in @ X1 @ X2) & (in @ X1 @ X0)) => (emptyset = (binintersect @ X0 @ X2))))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1)).
% 0.12/0.38 thf(f98,plain,(
% 0.12/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK0 @ (sK4 @ X0) @ X1) @ X0)) | ((in @ X2 @ X0) != $true) | (emptyset = (binintersect @ (sK4 @ X0) @ X1))) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f95])).
% 0.12/0.38 thf(f95,plain,(
% 0.12/0.38 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK0 @ (sK4 @ X0) @ X1) @ X0)) | (emptyset = (binintersect @ (sK4 @ X0) @ X1)) | ((in @ X2 @ X0) != $true) | ($true != $true)) )),
% 0.12/0.38 inference(superposition,[],[f74,f73])).
% 0.12/0.38 thf(f73,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (((in @ (sK0 @ X1 @ X0) @ X1) = $true) | (emptyset = (binintersect @ X1 @ X0))) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f59])).
% 0.12/0.38 thf(f59,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (($true != $true) | (emptyset = (binintersect @ X1 @ X0)) | ((in @ (sK0 @ X1 @ X0) @ X1) = $true)) )),
% 0.12/0.38 inference(definition_unfolding,[],[f45,f48])).
% 0.12/0.38 thf(f45,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : ((emptyset = (binintersect @ X1 @ X0)) | ((in @ (sK0 @ X1 @ X0) @ X1) = $true) | (disjointsetsI1 != $true)) )),
% 0.12/0.38 inference(cnf_transformation,[],[f27])).
% 0.12/0.38 thf(f74,plain,(
% 0.12/0.38 ( ! [X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ (sK4 @ X0)) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X1 @ X0) != $true)) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f63])).
% 0.12/0.38 thf(f63,plain,(
% 0.12/0.38 ( ! [X3 : $i,X0 : $i,X1 : $i] : (((in @ X3 @ X0) != $true) | ($true != $true) | ((in @ X3 @ (sK4 @ X0)) != $true) | ((in @ X1 @ X0) != $true)) )),
% 0.12/0.38 inference(definition_unfolding,[],[f55,f47])).
% 0.12/0.38 thf(f47,plain,(
% 0.12/0.38 (foundationAx = $true)),
% 0.12/0.38 inference(cnf_transformation,[],[f29])).
% 0.12/0.38 thf(f55,plain,(
% 0.12/0.38 ( ! [X3 : $i,X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ((in @ X3 @ X0) != $true) | ((in @ X3 @ (sK4 @ X0)) != $true) | (foundationAx != $true)) )),
% 0.12/0.38 inference(cnf_transformation,[],[f36])).
% 0.12/0.38 thf(f36,plain,(
% 0.12/0.38 (! [X0] : (! [X1] : ((in @ X1 @ X0) != $true) | (! [X3] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ (sK4 @ X0)) != $true)) & ($true = (in @ (sK4 @ X0) @ X0)))) | (foundationAx != $true)) & ((foundationAx = $true) | (((in @ sK6 @ sK5) = $true) & ! [X6] : ((((in @ (sK7 @ X6) @ sK5) = $true) & ($true = (in @ (sK7 @ X6) @ X6))) | ((in @ X6 @ sK5) != $true))))),
% 0.12/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f31,f35,f34,f33,f32])).
% 0.12/0.38 thf(f32,plain,(
% 0.12/0.38 ! [X0] : (? [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ($true != (in @ X3 @ X2))) & ((in @ X2 @ X0) = $true)) => (! [X3] : (((in @ X3 @ X0) != $true) | ((in @ X3 @ (sK4 @ X0)) != $true)) & ($true = (in @ (sK4 @ X0) @ X0))))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f33,plain,(
% 0.12/0.38 ? [X4] : (? [X5] : ($true = (in @ X5 @ X4)) & ! [X6] : (? [X7] : (((in @ X7 @ X4) = $true) & ($true = (in @ X7 @ X6))) | ((in @ X6 @ X4) != $true))) => (? [X5] : ($true = (in @ X5 @ sK5)) & ! [X6] : (? [X7] : (($true = (in @ X7 @ sK5)) & ($true = (in @ X7 @ X6))) | ((in @ X6 @ sK5) != $true)))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f34,plain,(
% 0.12/0.38 ? [X5] : ($true = (in @ X5 @ sK5)) => ((in @ sK6 @ sK5) = $true)),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f35,plain,(
% 0.12/0.38 ! [X6] : (? [X7] : (($true = (in @ X7 @ sK5)) & ($true = (in @ X7 @ X6))) => (((in @ (sK7 @ X6) @ sK5) = $true) & ($true = (in @ (sK7 @ X6) @ X6))))),
% 0.12/0.38 introduced(choice_axiom,[])).
% 0.12/0.38 thf(f31,plain,(
% 0.12/0.38 (! [X0] : (! [X1] : ((in @ X1 @ X0) != $true) | ? [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ($true != (in @ X3 @ X2))) & ((in @ X2 @ X0) = $true))) | (foundationAx != $true)) & ((foundationAx = $true) | ? [X4] : (? [X5] : ($true = (in @ X5 @ X4)) & ! [X6] : (? [X7] : (((in @ X7 @ X4) = $true) & ($true = (in @ X7 @ X6))) | ((in @ X6 @ X4) != $true))))),
% 0.12/0.38 inference(rectify,[],[f30])).
% 0.12/0.38 thf(f30,plain,(
% 0.12/0.38 (! [X0] : (! [X1] : ((in @ X1 @ X0) != $true) | ? [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ($true != (in @ X3 @ X2))) & ((in @ X2 @ X0) = $true))) | (foundationAx != $true)) & ((foundationAx = $true) | ? [X0] : (? [X1] : ((in @ X1 @ X0) = $true) & ! [X2] : (? [X3] : (((in @ X3 @ X0) = $true) & ($true = (in @ X3 @ X2))) | ((in @ X2 @ X0) != $true))))),
% 0.12/0.38 inference(nnf_transformation,[],[f21])).
% 0.12/0.38 thf(f21,plain,(
% 0.12/0.38 ! [X0] : (! [X1] : ((in @ X1 @ X0) != $true) | ? [X2] : (! [X3] : (((in @ X3 @ X0) != $true) | ($true != (in @ X3 @ X2))) & ((in @ X2 @ X0) = $true))) <=> (foundationAx = $true)),
% 0.12/0.38 inference(ennf_transformation,[],[f11])).
% 0.12/0.38 thf(f11,plain,(
% 0.12/0.38 (foundationAx = $true) <=> ! [X0] : (? [X1] : ((in @ X1 @ X0) = $true) => ? [X2] : (~? [X3] : (((in @ X3 @ X0) = $true) & ($true = (in @ X3 @ X2))) & ((in @ X2 @ X0) = $true)))),
% 0.12/0.38 inference(fool_elimination,[],[f10])).
% 0.12/0.38 thf(f10,plain,(
% 0.12/0.38 (foundationAx = ! [X0] : (? [X1] : (in @ X1 @ X0) => ? [X2] : (~? [X3] : ((in @ X3 @ X0) & (in @ X3 @ X2)) & (in @ X2 @ X0))))),
% 0.12/0.38 inference(rectify,[],[f1])).
% 0.12/0.38 thf(f1,axiom,(
% 0.12/0.38 (foundationAx = ! [X0] : (? [X1] : (in @ X1 @ X0) => ? [X2] : (~? [X1] : ((in @ X1 @ X0) & (in @ X1 @ X2)) & (in @ X2 @ X0))))),
% 0.12/0.38 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx)).
% 0.12/0.38 thf(f84,plain,(
% 0.12/0.38 (emptyset != (binintersect @ (sK4 @ sK3) @ sK3)) | spl10_1),
% 0.12/0.38 inference(avatar_component_clause,[],[f82])).
% 0.12/0.38 thf(f88,plain,(
% 0.12/0.38 ~spl10_1 | spl10_2),
% 0.12/0.38 inference(avatar_split_clause,[],[f80,f86,f82])).
% 0.12/0.38 thf(f80,plain,(
% 0.12/0.38 ( ! [X0 : $i] : ((emptyset != (binintersect @ (sK4 @ sK3) @ sK3)) | ((in @ X0 @ sK3) != $true)) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f79])).
% 0.12/0.38 thf(f79,plain,(
% 0.12/0.38 ( ! [X0 : $i] : ((emptyset != (binintersect @ (sK4 @ sK3) @ sK3)) | ((in @ X0 @ sK3) != $true) | ($true != $true)) )),
% 0.12/0.38 inference(superposition,[],[f50,f72])).
% 0.12/0.38 thf(f72,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (sK4 @ X0) @ X0)) | ((in @ X1 @ X0) != $true)) )),
% 0.12/0.38 inference(trivial_inequality_removal,[],[f64])).
% 0.12/0.38 thf(f64,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ($true = (in @ (sK4 @ X0) @ X0)) | ($true != $true)) )),
% 0.12/0.38 inference(definition_unfolding,[],[f54,f47])).
% 0.12/0.38 thf(f54,plain,(
% 0.12/0.38 ( ! [X0 : $i,X1 : $i] : (((in @ X1 @ X0) != $true) | ($true = (in @ (sK4 @ X0) @ X0)) | (foundationAx != $true)) )),
% 0.12/0.38 inference(cnf_transformation,[],[f36])).
% 0.12/0.38 thf(f50,plain,(
% 0.12/0.38 ( ! [X1 : $i] : (($true != (in @ X1 @ sK3)) | (emptyset != (binintersect @ X1 @ sK3))) )),
% 0.12/0.38 inference(cnf_transformation,[],[f29])).
% 0.12/0.38 % SZS output end Proof for theBenchmark
% 0.12/0.38 % (8122)------------------------------
% 0.12/0.38 % (8122)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.12/0.38 % (8122)Termination reason: Refutation
% 0.12/0.38
% 0.12/0.38 % (8122)Memory used [KB]: 5628
% 0.12/0.38 % (8122)Time elapsed: 0.009 s
% 0.12/0.38 % (8122)Instructions burned: 9 (million)
% 0.12/0.38 % (8122)------------------------------
% 0.12/0.38 % (8122)------------------------------
% 0.12/0.38 % (8116)Success in time 0.022 s
% 0.12/0.38 % Vampire---4.8 exiting
%------------------------------------------------------------------------------