TSTP Solution File: SEU742^2 by Vampire---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU742^2 : 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 : n003.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 03:51:11 EDT 2024
% Result : Theorem 0.21s 0.38s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SEU742^2 : TPTP v8.2.0. Released v3.7.0.
% 0.04/0.14 % 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
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 18:04:37 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 This is a TH0_THM_EQU_NAR problem
% 0.14/0.35 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/sandbox/benchmark/theBenchmark.p
% 0.21/0.37 % (14247)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.37 % (14248)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)
% 0.21/0.37 % (14249)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)
% 0.21/0.37 % (14251)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)
% 0.21/0.37 % (14252)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)
% 0.21/0.37 % (14251)Instruction limit reached!
% 0.21/0.37 % (14251)------------------------------
% 0.21/0.37 % (14251)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (14251)Termination reason: Unknown
% 0.21/0.37 % (14251)Termination phase: Property scanning
% 0.21/0.37
% 0.21/0.37 % (14251)Memory used [KB]: 1023
% 0.21/0.37 % (14251)Time elapsed: 0.003 s
% 0.21/0.37 % (14251)Instructions burned: 3 (million)
% 0.21/0.37 % (14251)------------------------------
% 0.21/0.37 % (14251)------------------------------
% 0.21/0.37 % (14248)Instruction limit reached!
% 0.21/0.37 % (14248)------------------------------
% 0.21/0.37 % (14248)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.37 % (14248)Termination reason: Unknown
% 0.21/0.37 % (14248)Termination phase: Function definition elimination
% 0.21/0.37
% 0.21/0.37 % (14248)Memory used [KB]: 1023
% 0.21/0.37 % (14248)Time elapsed: 0.004 s
% 0.21/0.37 % (14248)Instructions burned: 4 (million)
% 0.21/0.37 % (14248)------------------------------
% 0.21/0.37 % (14248)------------------------------
% 0.21/0.37 % (14254)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)
% 0.21/0.38 % (14254)Instruction limit reached!
% 0.21/0.38 % (14254)------------------------------
% 0.21/0.38 % (14254)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (14254)Termination reason: Unknown
% 0.21/0.38 % (14254)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (14254)Memory used [KB]: 1023
% 0.21/0.38 % (14254)Time elapsed: 0.003 s
% 0.21/0.38 % (14254)Instructions burned: 5 (million)
% 0.21/0.38 % (14254)------------------------------
% 0.21/0.38 % (14254)------------------------------
% 0.21/0.38 % (14252)First to succeed.
% 0.21/0.38 % (14250)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (14250)Instruction limit reached!
% 0.21/0.38 % (14250)------------------------------
% 0.21/0.38 % (14250)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (14250)Termination reason: Unknown
% 0.21/0.38 % (14250)Termination phase: Property scanning
% 0.21/0.38
% 0.21/0.38 % (14250)Memory used [KB]: 895
% 0.21/0.38 % (14250)Time elapsed: 0.002 s
% 0.21/0.38 % (14250)Instructions burned: 3 (million)
% 0.21/0.38 % (14250)------------------------------
% 0.21/0.38 % (14250)------------------------------
% 0.21/0.38 % (14253)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (14255)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.21/0.38 % (14249)Also succeeded, but the first one will report.
% 0.21/0.38 % (14256)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.21/0.38 % (14252)Refutation found. Thanks to Tanya!
% 0.21/0.38 % SZS status Theorem for theBenchmark
% 0.21/0.38 % SZS output start Proof for theBenchmark
% 0.21/0.38 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.38 thf(func_def_1, type, powerset: $i > $i).
% 0.21/0.38 thf(func_def_2, type, binunion: $i > $i > $i).
% 0.21/0.38 thf(func_def_3, type, binintersect: $i > $i > $i).
% 0.21/0.38 thf(f153,plain,(
% 0.21/0.38 $false),
% 0.21/0.38 inference(avatar_sat_refutation,[],[f104,f128,f152])).
% 0.21/0.38 thf(f152,plain,(
% 0.21/0.38 spl18_2),
% 0.21/0.38 inference(avatar_contradiction_clause,[],[f151])).
% 0.21/0.38 thf(f151,plain,(
% 0.21/0.38 $false | spl18_2),
% 0.21/0.38 inference(subsumption_resolution,[],[f150,f52])).
% 0.21/0.38 thf(f52,plain,(
% 0.21/0.38 ((in @ sK1 @ (powerset @ sK0)) = $true)),
% 0.21/0.38 inference(cnf_transformation,[],[f27])).
% 0.21/0.38 thf(f27,plain,(
% 0.21/0.38 (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (((in @ sK1 @ (powerset @ sK0)) = $true) & (($true = (in @ sK2 @ (powerset @ sK0))) & (($true = (in @ sK3 @ (powerset @ sK0))) & (((in @ sK4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3))) != $true) & ($true = (in @ sK4 @ sK0)) & ((in @ sK4 @ (binintersect @ sK1 @ sK2)) = $true))))) & (binintersectI = $true)),
% 0.21/0.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f16,f26,f25,f24,f23])).
% 0.21/0.38 thf(f23,plain,(
% 0.21/0.38 ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ X0)) = $true) & ? [X4] : (($true != (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) & ((in @ X4 @ X0) = $true) & ((in @ X4 @ (binintersect @ X1 @ X2)) = $true))))) => (((in @ sK1 @ (powerset @ sK0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ sK0)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ sK0)) = $true) & ? [X4] : (($true != (in @ X4 @ (binintersect @ (binunion @ sK1 @ X3) @ (binunion @ X2 @ X3)))) & ($true = (in @ X4 @ sK0)) & ($true = (in @ X4 @ (binintersect @ sK1 @ X2)))))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f24,plain,(
% 0.21/0.38 ? [X2] : (((in @ X2 @ (powerset @ sK0)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ sK0)) = $true) & ? [X4] : (($true != (in @ X4 @ (binintersect @ (binunion @ sK1 @ X3) @ (binunion @ X2 @ X3)))) & ($true = (in @ X4 @ sK0)) & ($true = (in @ X4 @ (binintersect @ sK1 @ X2)))))) => (($true = (in @ sK2 @ (powerset @ sK0))) & ? [X3] : (((in @ X3 @ (powerset @ sK0)) = $true) & ? [X4] : (((in @ X4 @ (binintersect @ (binunion @ sK1 @ X3) @ (binunion @ sK2 @ X3))) != $true) & ($true = (in @ X4 @ sK0)) & ($true = (in @ X4 @ (binintersect @ sK1 @ sK2))))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f25,plain,(
% 0.21/0.38 ? [X3] : (((in @ X3 @ (powerset @ sK0)) = $true) & ? [X4] : (((in @ X4 @ (binintersect @ (binunion @ sK1 @ X3) @ (binunion @ sK2 @ X3))) != $true) & ($true = (in @ X4 @ sK0)) & ($true = (in @ X4 @ (binintersect @ sK1 @ sK2))))) => (($true = (in @ sK3 @ (powerset @ sK0))) & ? [X4] : (((in @ X4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3))) != $true) & ($true = (in @ X4 @ sK0)) & ($true = (in @ X4 @ (binintersect @ sK1 @ sK2)))))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f26,plain,(
% 0.21/0.38 ? [X4] : (((in @ X4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3))) != $true) & ($true = (in @ X4 @ sK0)) & ($true = (in @ X4 @ (binintersect @ sK1 @ sK2)))) => (((in @ sK4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3))) != $true) & ($true = (in @ sK4 @ sK0)) & ((in @ sK4 @ (binintersect @ sK1 @ sK2)) = $true))),
% 0.21/0.38 introduced(choice_axiom,[])).
% 0.21/0.38 thf(f16,plain,(
% 0.21/0.38 (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (((in @ X3 @ (powerset @ X0)) = $true) & ? [X4] : (($true != (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) & ((in @ X4 @ X0) = $true) & ((in @ X4 @ (binintersect @ X1 @ X2)) = $true))))) & (binintersectI = $true)),
% 0.21/0.38 inference(flattening,[],[f15])).
% 0.21/0.38 thf(f15,plain,(
% 0.21/0.38 ((? [X0,X1] : (? [X2] : (? [X3] : (? [X4] : ((($true != (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) & ((in @ X4 @ (binintersect @ X1 @ X2)) = $true)) & ((in @ X4 @ X0) = $true)) & ((in @ X3 @ (powerset @ X0)) = $true)) & ((in @ X2 @ (powerset @ X0)) = $true)) & ((in @ X1 @ (powerset @ X0)) = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binintersectI = $true)),
% 0.21/0.38 inference(ennf_transformation,[],[f10])).
% 0.21/0.38 thf(f10,plain,(
% 0.21/0.38 ~((binintersectI = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ! [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3] : (((in @ X3 @ (powerset @ X0)) = $true) => ! [X4] : (((in @ X4 @ X0) = $true) => (((in @ X4 @ (binintersect @ X1 @ X2)) = $true) => ($true = (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))))))))),
% 0.21/0.38 inference(fool_elimination,[],[f9])).
% 0.21/0.38 thf(f9,plain,(
% 0.21/0.38 ~(binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))))))))))),
% 0.21/0.38 inference(rectify,[],[f5])).
% 0.21/0.38 thf(f5,negated_conjecture,(
% 0.21/0.38 ~(binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0,X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X5] : ((in @ X5 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binintersect @ (binunion @ X3 @ X5) @ (binunion @ X4 @ X5)))))))))))),
% 0.21/0.38 inference(negated_conjecture,[],[f4])).
% 0.21/0.38 thf(f4,conjecture,(
% 0.21/0.38 binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0,X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X5] : ((in @ X5 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binintersect @ (binunion @ X3 @ X5) @ (binunion @ X4 @ X5))))))))))),
% 0.21/0.38 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions)).
% 0.21/0.38 thf(f150,plain,(
% 0.21/0.38 ((in @ sK1 @ (powerset @ sK0)) != $true) | spl18_2),
% 0.21/0.38 inference(subsumption_resolution,[],[f149,f48])).
% 0.21/0.38 thf(f48,plain,(
% 0.21/0.38 ($true = (in @ sK4 @ sK0))),
% 0.21/0.38 inference(cnf_transformation,[],[f27])).
% 0.21/0.38 thf(f149,plain,(
% 0.21/0.38 ($true != (in @ sK4 @ sK0)) | ((in @ sK1 @ (powerset @ sK0)) != $true) | spl18_2),
% 0.21/0.38 inference(subsumption_resolution,[],[f148,f51])).
% 0.21/0.38 thf(f51,plain,(
% 0.21/0.38 ($true = (in @ sK2 @ (powerset @ sK0)))),
% 0.21/0.38 inference(cnf_transformation,[],[f27])).
% 0.21/0.38 thf(f148,plain,(
% 0.21/0.38 ($true != (in @ sK2 @ (powerset @ sK0))) | ((in @ sK1 @ (powerset @ sK0)) != $true) | ($true != (in @ sK4 @ sK0)) | spl18_2),
% 0.21/0.38 inference(trivial_inequality_removal,[],[f147])).
% 0.21/0.38 thf(f147,plain,(
% 0.21/0.38 ($true != $true) | ((in @ sK1 @ (powerset @ sK0)) != $true) | ($true != (in @ sK4 @ sK0)) | ($true != (in @ sK2 @ (powerset @ sK0))) | spl18_2),
% 0.21/0.38 inference(superposition,[],[f136,f50])).
% 0.21/0.38 thf(f50,plain,(
% 0.21/0.38 ($true = (in @ sK3 @ (powerset @ sK0)))),
% 0.21/0.38 inference(cnf_transformation,[],[f27])).
% 0.21/0.38 thf(f136,plain,(
% 0.21/0.38 ( ! [X0 : $i] : (($true != (in @ sK3 @ (powerset @ X0))) | ((in @ sK4 @ X0) != $true) | ((in @ sK1 @ (powerset @ X0)) != $true) | ((in @ sK2 @ (powerset @ X0)) != $true)) ) | spl18_2),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f133])).
% 0.21/0.39 thf(f133,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK1 @ (powerset @ X0)) != $true) | ((in @ sK4 @ X0) != $true) | ($true != (in @ sK3 @ (powerset @ X0))) | ($true != $true)) ) | spl18_2),
% 0.21/0.39 inference(superposition,[],[f131,f47])).
% 0.21/0.39 thf(f47,plain,(
% 0.21/0.39 ((in @ sK4 @ (binintersect @ sK1 @ sK2)) = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f27])).
% 0.21/0.39 thf(f131,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (((in @ sK4 @ (binintersect @ X0 @ sK2)) != $true) | ((in @ sK2 @ (powerset @ X1)) != $true) | ((in @ sK3 @ (powerset @ X1)) != $true) | ((in @ sK4 @ X1) != $true) | ($true != (in @ X0 @ (powerset @ X1)))) ) | spl18_2),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f129])).
% 0.21/0.39 thf(f129,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ sK4 @ X1) != $true) | ((in @ sK2 @ (powerset @ X1)) != $true) | ($true != $true) | ((in @ sK3 @ (powerset @ X1)) != $true) | ((in @ sK4 @ (binintersect @ X0 @ sK2)) != $true)) ) | spl18_2),
% 0.21/0.39 inference(superposition,[],[f103,f93])).
% 0.21/0.39 thf(f93,plain,(
% 0.21/0.39 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ X9 @ (binunion @ X7 @ X8)) = $true) | ($true != (in @ X9 @ (binintersect @ X6 @ X7))) | ((in @ X7 @ (powerset @ X5)) != $true) | ($true != (in @ X8 @ (powerset @ X5))) | ((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X9 @ X5) != $true)) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f83])).
% 0.21/0.39 thf(f83,plain,(
% 0.21/0.39 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ X9 @ X5) != $true) | ((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X7 @ (powerset @ X5)) != $true) | ($true != (in @ X9 @ (binintersect @ X6 @ X7))) | ($true != (in @ X8 @ (powerset @ X5))) | ($true != $true) | ((in @ X9 @ (binunion @ X7 @ X8)) = $true)) )),
% 0.21/0.39 inference(definition_unfolding,[],[f59,f54])).
% 0.21/0.39 thf(f54,plain,(
% 0.21/0.39 (inIntersectImpInUnion2 = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f27])).
% 0.21/0.39 thf(f59,plain,(
% 0.21/0.39 ( ! [X8 : $i,X6 : $i,X9 : $i,X7 : $i,X5 : $i] : (((in @ X6 @ (powerset @ X5)) != $true) | ((in @ X7 @ (powerset @ X5)) != $true) | ((in @ X9 @ X5) != $true) | ($true != (in @ X9 @ (binintersect @ X6 @ X7))) | ((in @ X9 @ (binunion @ X7 @ X8)) = $true) | ($true != (in @ X8 @ (powerset @ X5))) | (inIntersectImpInUnion2 != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f38])).
% 0.21/0.39 thf(f38,plain,(
% 0.21/0.39 ((inIntersectImpInUnion2 = $true) | (($true = (in @ sK9 @ (powerset @ sK8))) & (($true = (in @ sK10 @ (powerset @ sK8))) & ((((in @ sK12 @ sK8) = $true) & ((in @ sK12 @ (binintersect @ sK9 @ sK10)) = $true) & ((in @ sK12 @ (binunion @ sK10 @ sK11)) != $true)) & ((in @ sK11 @ (powerset @ sK8)) = $true))))) & (! [X5,X6] : (((in @ X6 @ (powerset @ X5)) != $true) | ! [X7] : (((in @ X7 @ (powerset @ X5)) != $true) | ! [X8] : (! [X9] : (((in @ X9 @ X5) != $true) | ($true != (in @ X9 @ (binintersect @ X6 @ X7))) | ((in @ X9 @ (binunion @ X7 @ X8)) = $true)) | ($true != (in @ X8 @ (powerset @ X5)))))) | (inIntersectImpInUnion2 != $true))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f33,f37,f36,f35,f34])).
% 0.21/0.39 thf(f34,plain,(
% 0.21/0.39 ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ X0) = $true) & ((in @ X4 @ (binintersect @ X1 @ X2)) = $true) & ((in @ X4 @ (binunion @ X2 @ X3)) != $true)) & ((in @ X3 @ (powerset @ X0)) = $true)))) => (($true = (in @ sK9 @ (powerset @ sK8))) & ? [X2] : (((in @ X2 @ (powerset @ sK8)) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ sK8) = $true) & ((in @ X4 @ (binintersect @ sK9 @ X2)) = $true) & ((in @ X4 @ (binunion @ X2 @ X3)) != $true)) & ((in @ X3 @ (powerset @ sK8)) = $true))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f35,plain,(
% 0.21/0.39 ? [X2] : (((in @ X2 @ (powerset @ sK8)) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ sK8) = $true) & ((in @ X4 @ (binintersect @ sK9 @ X2)) = $true) & ((in @ X4 @ (binunion @ X2 @ X3)) != $true)) & ((in @ X3 @ (powerset @ sK8)) = $true))) => (($true = (in @ sK10 @ (powerset @ sK8))) & ? [X3] : (? [X4] : (((in @ X4 @ sK8) = $true) & ($true = (in @ X4 @ (binintersect @ sK9 @ sK10))) & ((in @ X4 @ (binunion @ sK10 @ X3)) != $true)) & ((in @ X3 @ (powerset @ sK8)) = $true)))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f36,plain,(
% 0.21/0.39 ? [X3] : (? [X4] : (((in @ X4 @ sK8) = $true) & ($true = (in @ X4 @ (binintersect @ sK9 @ sK10))) & ((in @ X4 @ (binunion @ sK10 @ X3)) != $true)) & ((in @ X3 @ (powerset @ sK8)) = $true)) => (? [X4] : (((in @ X4 @ sK8) = $true) & ($true = (in @ X4 @ (binintersect @ sK9 @ sK10))) & ((in @ X4 @ (binunion @ sK10 @ sK11)) != $true)) & ((in @ sK11 @ (powerset @ sK8)) = $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f37,plain,(
% 0.21/0.39 ? [X4] : (((in @ X4 @ sK8) = $true) & ($true = (in @ X4 @ (binintersect @ sK9 @ sK10))) & ((in @ X4 @ (binunion @ sK10 @ sK11)) != $true)) => (((in @ sK12 @ sK8) = $true) & ((in @ sK12 @ (binintersect @ sK9 @ sK10)) = $true) & ((in @ sK12 @ (binunion @ sK10 @ sK11)) != $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f33,plain,(
% 0.21/0.39 ((inIntersectImpInUnion2 = $true) | ? [X0,X1] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ X0) = $true) & ((in @ X4 @ (binintersect @ X1 @ X2)) = $true) & ((in @ X4 @ (binunion @ X2 @ X3)) != $true)) & ((in @ X3 @ (powerset @ X0)) = $true))))) & (! [X5,X6] : (((in @ X6 @ (powerset @ X5)) != $true) | ! [X7] : (((in @ X7 @ (powerset @ X5)) != $true) | ! [X8] : (! [X9] : (((in @ X9 @ X5) != $true) | ($true != (in @ X9 @ (binintersect @ X6 @ X7))) | ((in @ X9 @ (binunion @ X7 @ X8)) = $true)) | ($true != (in @ X8 @ (powerset @ X5)))))) | (inIntersectImpInUnion2 != $true))),
% 0.21/0.39 inference(rectify,[],[f32])).
% 0.21/0.39 thf(f32,plain,(
% 0.21/0.39 ((inIntersectImpInUnion2 = $true) | ? [X1,X0] : (($true = (in @ X0 @ (powerset @ X1))) & ? [X2] : (((in @ X2 @ (powerset @ X1)) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ X1) = $true) & ((in @ X4 @ (binintersect @ X0 @ X2)) = $true) & ((in @ X4 @ (binunion @ X2 @ X3)) != $true)) & ($true = (in @ X3 @ (powerset @ X1))))))) & (! [X1,X0] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2] : (((in @ X2 @ (powerset @ X1)) != $true) | ! [X3] : (! [X4] : (((in @ X4 @ X1) != $true) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X4 @ (binunion @ X2 @ X3)) = $true)) | ($true != (in @ X3 @ (powerset @ X1)))))) | (inIntersectImpInUnion2 != $true))),
% 0.21/0.39 inference(nnf_transformation,[],[f18])).
% 0.21/0.39 thf(f18,plain,(
% 0.21/0.39 (inIntersectImpInUnion2 = $true) <=> ! [X1,X0] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2] : (((in @ X2 @ (powerset @ X1)) != $true) | ! [X3] : (! [X4] : (((in @ X4 @ X1) != $true) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true) | ((in @ X4 @ (binunion @ X2 @ X3)) = $true)) | ($true != (in @ X3 @ (powerset @ X1))))))),
% 0.21/0.39 inference(flattening,[],[f17])).
% 0.21/0.39 thf(f17,plain,(
% 0.21/0.39 ! [X1,X0] : (! [X2] : (! [X3] : (! [X4] : ((((in @ X4 @ (binunion @ X2 @ X3)) = $true) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true)) | ((in @ X4 @ X1) != $true)) | ($true != (in @ X3 @ (powerset @ X1)))) | ((in @ X2 @ (powerset @ X1)) != $true)) | ($true != (in @ X0 @ (powerset @ X1)))) <=> (inIntersectImpInUnion2 = $true)),
% 0.21/0.39 inference(ennf_transformation,[],[f12])).
% 0.21/0.39 thf(f12,plain,(
% 0.21/0.39 ! [X1,X0] : (($true = (in @ X0 @ (powerset @ X1))) => ! [X2] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3] : (($true = (in @ X3 @ (powerset @ X1))) => ! [X4] : (((in @ X4 @ X1) = $true) => (((in @ X4 @ (binintersect @ X0 @ X2)) = $true) => ((in @ X4 @ (binunion @ X2 @ X3)) = $true)))))) <=> (inIntersectImpInUnion2 = $true)),
% 0.21/0.39 inference(fool_elimination,[],[f11])).
% 0.21/0.39 thf(f11,plain,(
% 0.21/0.39 (! [X0,X1] : ((in @ X0 @ (powerset @ X1)) => ! [X2] : ((in @ X2 @ (powerset @ X1)) => ! [X3] : ((in @ X3 @ (powerset @ X1)) => ! [X4] : ((in @ X4 @ X1) => ((in @ X4 @ (binintersect @ X0 @ X2)) => (in @ X4 @ (binunion @ X2 @ X3))))))) = inIntersectImpInUnion2)),
% 0.21/0.39 inference(rectify,[],[f3])).
% 0.21/0.39 thf(f3,axiom,(
% 0.21/0.39 (! [X3,X0] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X5] : ((in @ X5 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binunion @ X4 @ X5))))))) = inIntersectImpInUnion2)),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2)).
% 0.21/0.39 thf(f103,plain,(
% 0.21/0.39 ((in @ sK4 @ (binunion @ sK2 @ sK3)) != $true) | spl18_2),
% 0.21/0.39 inference(avatar_component_clause,[],[f101])).
% 0.21/0.39 thf(f101,plain,(
% 0.21/0.39 spl18_2 <=> ((in @ sK4 @ (binunion @ sK2 @ sK3)) = $true)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl18_2])])).
% 0.21/0.39 thf(f128,plain,(
% 0.21/0.39 spl18_1),
% 0.21/0.39 inference(avatar_contradiction_clause,[],[f127])).
% 0.21/0.39 thf(f127,plain,(
% 0.21/0.39 $false | spl18_1),
% 0.21/0.39 inference(subsumption_resolution,[],[f126,f51])).
% 0.21/0.39 thf(f126,plain,(
% 0.21/0.39 ($true != (in @ sK2 @ (powerset @ sK0))) | spl18_1),
% 0.21/0.39 inference(subsumption_resolution,[],[f125,f48])).
% 0.21/0.39 thf(f125,plain,(
% 0.21/0.39 ($true != (in @ sK4 @ sK0)) | ($true != (in @ sK2 @ (powerset @ sK0))) | spl18_1),
% 0.21/0.39 inference(subsumption_resolution,[],[f124,f52])).
% 0.21/0.39 thf(f124,plain,(
% 0.21/0.39 ((in @ sK1 @ (powerset @ sK0)) != $true) | ($true != (in @ sK4 @ sK0)) | ($true != (in @ sK2 @ (powerset @ sK0))) | spl18_1),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f123])).
% 0.21/0.39 thf(f123,plain,(
% 0.21/0.39 ((in @ sK1 @ (powerset @ sK0)) != $true) | ($true != $true) | ($true != (in @ sK2 @ (powerset @ sK0))) | ($true != (in @ sK4 @ sK0)) | spl18_1),
% 0.21/0.39 inference(superposition,[],[f111,f50])).
% 0.21/0.39 thf(f111,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != (in @ sK3 @ (powerset @ X0))) | ((in @ sK4 @ X0) != $true) | ((in @ sK2 @ (powerset @ X0)) != $true) | ((in @ sK1 @ (powerset @ X0)) != $true)) ) | spl18_1),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f109])).
% 0.21/0.39 thf(f109,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((in @ sK1 @ (powerset @ X0)) != $true) | ($true != $true) | ($true != (in @ sK3 @ (powerset @ X0))) | ((in @ sK4 @ X0) != $true) | ((in @ sK2 @ (powerset @ X0)) != $true)) ) | spl18_1),
% 0.21/0.39 inference(superposition,[],[f106,f47])).
% 0.21/0.39 thf(f106,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (((in @ sK4 @ (binintersect @ sK1 @ X0)) != $true) | ((in @ sK4 @ X1) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ sK3 @ (powerset @ X1)) != $true) | ((in @ sK1 @ (powerset @ X1)) != $true)) ) | spl18_1),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f105])).
% 0.21/0.39 thf(f105,plain,(
% 0.21/0.39 ( ! [X0 : $i,X1 : $i] : (((in @ sK4 @ (binintersect @ sK1 @ X0)) != $true) | ($true != $true) | ((in @ sK3 @ (powerset @ X1)) != $true) | ((in @ sK1 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ sK4 @ X1) != $true)) ) | spl18_1),
% 0.21/0.39 inference(superposition,[],[f99,f92])).
% 0.21/0.39 thf(f92,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ (binunion @ X0 @ X3)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ((in @ X4 @ X1) != $true) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true) | ($true != (in @ X3 @ (powerset @ X1)))) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f84])).
% 0.21/0.39 thf(f84,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((in @ X4 @ (binunion @ X0 @ X3)) = $true) | ((in @ X2 @ (powerset @ X1)) != $true) | ($true != (in @ X0 @ (powerset @ X1))) | ($true != (in @ X3 @ (powerset @ X1))) | ((in @ X4 @ X1) != $true) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true) | ($true != $true)) )),
% 0.21/0.39 inference(definition_unfolding,[],[f72,f53])).
% 0.21/0.39 thf(f53,plain,(
% 0.21/0.39 (inIntersectImpInUnion = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f27])).
% 0.21/0.39 thf(f72,plain,(
% 0.21/0.39 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true != (in @ X0 @ (powerset @ X1))) | ((in @ X2 @ (powerset @ X1)) != $true) | ((in @ X4 @ X1) != $true) | ((in @ X4 @ (binunion @ X0 @ X3)) = $true) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true) | ($true != (in @ X3 @ (powerset @ X1))) | (inIntersectImpInUnion != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f45])).
% 0.21/0.39 thf(f45,plain,(
% 0.21/0.39 (! [X0,X1] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2] : (((in @ X2 @ (powerset @ X1)) != $true) | ! [X3] : (! [X4] : (((in @ X4 @ X1) != $true) | ((in @ X4 @ (binunion @ X0 @ X3)) = $true) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true)) | ($true != (in @ X3 @ (powerset @ X1)))))) | (inIntersectImpInUnion != $true)) & ((inIntersectImpInUnion = $true) | (($true = (in @ sK13 @ (powerset @ sK14))) & (((in @ sK15 @ (powerset @ sK14)) = $true) & ((((in @ sK17 @ sK14) = $true) & ((in @ sK17 @ (binunion @ sK13 @ sK16)) != $true) & ((in @ sK17 @ (binintersect @ sK13 @ sK15)) = $true)) & ((in @ sK16 @ (powerset @ sK14)) = $true)))))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14,sK15,sK16,sK17])],[f40,f44,f43,f42,f41])).
% 0.21/0.39 thf(f41,plain,(
% 0.21/0.39 ? [X5,X6] : (((in @ X5 @ (powerset @ X6)) = $true) & ? [X7] : (((in @ X7 @ (powerset @ X6)) = $true) & ? [X8] : (? [X9] : (($true = (in @ X9 @ X6)) & ((in @ X9 @ (binunion @ X5 @ X8)) != $true) & ((in @ X9 @ (binintersect @ X5 @ X7)) = $true)) & ((in @ X8 @ (powerset @ X6)) = $true)))) => (($true = (in @ sK13 @ (powerset @ sK14))) & ? [X7] : (((in @ X7 @ (powerset @ sK14)) = $true) & ? [X8] : (? [X9] : (($true = (in @ X9 @ sK14)) & ($true != (in @ X9 @ (binunion @ sK13 @ X8))) & ($true = (in @ X9 @ (binintersect @ sK13 @ X7)))) & ((in @ X8 @ (powerset @ sK14)) = $true))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f42,plain,(
% 0.21/0.39 ? [X7] : (((in @ X7 @ (powerset @ sK14)) = $true) & ? [X8] : (? [X9] : (($true = (in @ X9 @ sK14)) & ($true != (in @ X9 @ (binunion @ sK13 @ X8))) & ($true = (in @ X9 @ (binintersect @ sK13 @ X7)))) & ((in @ X8 @ (powerset @ sK14)) = $true))) => (((in @ sK15 @ (powerset @ sK14)) = $true) & ? [X8] : (? [X9] : (($true = (in @ X9 @ sK14)) & ($true != (in @ X9 @ (binunion @ sK13 @ X8))) & ($true = (in @ X9 @ (binintersect @ sK13 @ sK15)))) & ((in @ X8 @ (powerset @ sK14)) = $true)))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f43,plain,(
% 0.21/0.39 ? [X8] : (? [X9] : (($true = (in @ X9 @ sK14)) & ($true != (in @ X9 @ (binunion @ sK13 @ X8))) & ($true = (in @ X9 @ (binintersect @ sK13 @ sK15)))) & ((in @ X8 @ (powerset @ sK14)) = $true)) => (? [X9] : (($true = (in @ X9 @ sK14)) & ((in @ X9 @ (binunion @ sK13 @ sK16)) != $true) & ($true = (in @ X9 @ (binintersect @ sK13 @ sK15)))) & ((in @ sK16 @ (powerset @ sK14)) = $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f44,plain,(
% 0.21/0.39 ? [X9] : (($true = (in @ X9 @ sK14)) & ((in @ X9 @ (binunion @ sK13 @ sK16)) != $true) & ($true = (in @ X9 @ (binintersect @ sK13 @ sK15)))) => (((in @ sK17 @ sK14) = $true) & ((in @ sK17 @ (binunion @ sK13 @ sK16)) != $true) & ((in @ sK17 @ (binintersect @ sK13 @ sK15)) = $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f40,plain,(
% 0.21/0.39 (! [X0,X1] : (($true != (in @ X0 @ (powerset @ X1))) | ! [X2] : (((in @ X2 @ (powerset @ X1)) != $true) | ! [X3] : (! [X4] : (((in @ X4 @ X1) != $true) | ((in @ X4 @ (binunion @ X0 @ X3)) = $true) | ((in @ X4 @ (binintersect @ X0 @ X2)) != $true)) | ($true != (in @ X3 @ (powerset @ X1)))))) | (inIntersectImpInUnion != $true)) & ((inIntersectImpInUnion = $true) | ? [X5,X6] : (((in @ X5 @ (powerset @ X6)) = $true) & ? [X7] : (((in @ X7 @ (powerset @ X6)) = $true) & ? [X8] : (? [X9] : (($true = (in @ X9 @ X6)) & ((in @ X9 @ (binunion @ X5 @ X8)) != $true) & ((in @ X9 @ (binintersect @ X5 @ X7)) = $true)) & ((in @ X8 @ (powerset @ X6)) = $true)))))),
% 0.21/0.39 inference(rectify,[],[f39])).
% 0.21/0.39 thf(f39,plain,(
% 0.21/0.39 (! [X1,X0] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3] : (! [X4] : (((in @ X4 @ X0) != $true) | ($true = (in @ X4 @ (binunion @ X1 @ X3))) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true)) | ((in @ X3 @ (powerset @ X0)) != $true)))) | (inIntersectImpInUnion != $true)) & ((inIntersectImpInUnion = $true) | ? [X1,X0] : (((in @ X1 @ (powerset @ X0)) = $true) & ? [X2] : (((in @ X2 @ (powerset @ X0)) = $true) & ? [X3] : (? [X4] : (((in @ X4 @ X0) = $true) & ($true != (in @ X4 @ (binunion @ X1 @ X3))) & ((in @ X4 @ (binintersect @ X1 @ X2)) = $true)) & ((in @ X3 @ (powerset @ X0)) = $true)))))),
% 0.21/0.39 inference(nnf_transformation,[],[f22])).
% 0.21/0.39 thf(f22,plain,(
% 0.21/0.39 ! [X1,X0] : (((in @ X1 @ (powerset @ X0)) != $true) | ! [X2] : (((in @ X2 @ (powerset @ X0)) != $true) | ! [X3] : (! [X4] : (((in @ X4 @ X0) != $true) | ($true = (in @ X4 @ (binunion @ X1 @ X3))) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true)) | ((in @ X3 @ (powerset @ X0)) != $true)))) <=> (inIntersectImpInUnion = $true)),
% 0.21/0.39 inference(flattening,[],[f21])).
% 0.21/0.39 thf(f21,plain,(
% 0.21/0.39 (inIntersectImpInUnion = $true) <=> ! [X1,X0] : (! [X2] : (! [X3] : (! [X4] : ((($true = (in @ X4 @ (binunion @ X1 @ X3))) | ((in @ X4 @ (binintersect @ X1 @ X2)) != $true)) | ((in @ X4 @ X0) != $true)) | ((in @ X3 @ (powerset @ X0)) != $true)) | ((in @ X2 @ (powerset @ X0)) != $true)) | ((in @ X1 @ (powerset @ X0)) != $true))),
% 0.21/0.39 inference(ennf_transformation,[],[f8])).
% 0.21/0.39 thf(f8,plain,(
% 0.21/0.39 (inIntersectImpInUnion = $true) <=> ! [X1,X0] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2] : (((in @ X2 @ (powerset @ X0)) = $true) => ! [X3] : (((in @ X3 @ (powerset @ X0)) = $true) => ! [X4] : (((in @ X4 @ X0) = $true) => (((in @ X4 @ (binintersect @ X1 @ X2)) = $true) => ($true = (in @ X4 @ (binunion @ X1 @ X3))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f7])).
% 0.21/0.39 thf(f7,plain,(
% 0.21/0.39 (! [X0,X1] : ((in @ X1 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ (powerset @ X0)) => ! [X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binunion @ X1 @ X3))))))) = inIntersectImpInUnion)),
% 0.21/0.39 inference(rectify,[],[f2])).
% 0.21/0.39 thf(f2,axiom,(
% 0.21/0.39 (! [X0,X3] : ((in @ X3 @ (powerset @ X0)) => ! [X4] : ((in @ X4 @ (powerset @ X0)) => ! [X5] : ((in @ X5 @ (powerset @ X0)) => ! [X2] : ((in @ X2 @ X0) => ((in @ X2 @ (binintersect @ X3 @ X4)) => (in @ X2 @ (binunion @ X3 @ X5))))))) = inIntersectImpInUnion)),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion)).
% 0.21/0.39 thf(f99,plain,(
% 0.21/0.39 ((in @ sK4 @ (binunion @ sK1 @ sK3)) != $true) | spl18_1),
% 0.21/0.39 inference(avatar_component_clause,[],[f97])).
% 0.21/0.39 thf(f97,plain,(
% 0.21/0.39 spl18_1 <=> ((in @ sK4 @ (binunion @ sK1 @ sK3)) = $true)),
% 0.21/0.39 introduced(avatar_definition,[new_symbols(naming,[spl18_1])])).
% 0.21/0.39 thf(f104,plain,(
% 0.21/0.39 ~spl18_1 | ~spl18_2),
% 0.21/0.39 inference(avatar_split_clause,[],[f95,f101,f97])).
% 0.21/0.39 thf(f95,plain,(
% 0.21/0.39 ((in @ sK4 @ (binunion @ sK2 @ sK3)) != $true) | ((in @ sK4 @ (binunion @ sK1 @ sK3)) != $true)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f94])).
% 0.21/0.39 thf(f94,plain,(
% 0.21/0.39 ($true != $true) | ((in @ sK4 @ (binunion @ sK1 @ sK3)) != $true) | ((in @ sK4 @ (binunion @ sK2 @ sK3)) != $true)),
% 0.21/0.39 inference(superposition,[],[f49,f91])).
% 0.21/0.39 thf(f91,plain,(
% 0.21/0.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X4 @ X3)) = $true) | ($true != (in @ X5 @ X4)) | ((in @ X5 @ X3) != $true)) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f76])).
% 0.21/0.39 thf(f76,plain,(
% 0.21/0.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) != $true) | ($true != (in @ X5 @ X4)) | ($true != $true) | ((in @ X5 @ (binintersect @ X4 @ X3)) = $true)) )),
% 0.21/0.39 inference(definition_unfolding,[],[f55,f46])).
% 0.21/0.39 thf(f46,plain,(
% 0.21/0.39 (binintersectI = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f27])).
% 0.21/0.39 thf(f55,plain,(
% 0.21/0.39 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ (binintersect @ X4 @ X3)) = $true) | ($true != (in @ X5 @ X4)) | ((in @ X5 @ X3) != $true) | (binintersectI != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f31])).
% 0.21/0.39 thf(f31,plain,(
% 0.21/0.39 ((binintersectI = $true) | (((in @ sK7 @ (binintersect @ sK6 @ sK5)) != $true) & ($true = (in @ sK7 @ sK6)) & ((in @ sK7 @ sK5) = $true))) & (! [X3,X4,X5] : (((in @ X5 @ (binintersect @ X4 @ X3)) = $true) | ($true != (in @ X5 @ X4)) | ((in @ X5 @ X3) != $true)) | (binintersectI != $true))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f29,f30])).
% 0.21/0.39 thf(f30,plain,(
% 0.21/0.39 ? [X0,X1,X2] : (($true != (in @ X2 @ (binintersect @ X1 @ X0))) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) = $true)) => (((in @ sK7 @ (binintersect @ sK6 @ sK5)) != $true) & ($true = (in @ sK7 @ sK6)) & ((in @ sK7 @ sK5) = $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f29,plain,(
% 0.21/0.39 ((binintersectI = $true) | ? [X0,X1,X2] : (($true != (in @ X2 @ (binintersect @ X1 @ X0))) & ((in @ X2 @ X1) = $true) & ((in @ X2 @ X0) = $true))) & (! [X3,X4,X5] : (((in @ X5 @ (binintersect @ X4 @ X3)) = $true) | ($true != (in @ X5 @ X4)) | ((in @ X5 @ X3) != $true)) | (binintersectI != $true))),
% 0.21/0.39 inference(rectify,[],[f28])).
% 0.21/0.39 thf(f28,plain,(
% 0.21/0.39 ((binintersectI = $true) | ? [X0,X2,X1] : (((in @ X1 @ (binintersect @ X2 @ X0)) != $true) & ((in @ X1 @ X2) = $true) & ((in @ X1 @ X0) = $true))) & (! [X0,X2,X1] : (((in @ X1 @ (binintersect @ X2 @ X0)) = $true) | ((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) != $true)) | (binintersectI != $true))),
% 0.21/0.39 inference(nnf_transformation,[],[f20])).
% 0.21/0.39 thf(f20,plain,(
% 0.21/0.39 (binintersectI = $true) <=> ! [X0,X2,X1] : (((in @ X1 @ (binintersect @ X2 @ X0)) = $true) | ((in @ X1 @ X2) != $true) | ((in @ X1 @ X0) != $true))),
% 0.21/0.39 inference(flattening,[],[f19])).
% 0.21/0.39 thf(f19,plain,(
% 0.21/0.39 (binintersectI = $true) <=> ! [X1,X0,X2] : ((((in @ X1 @ (binintersect @ X2 @ X0)) = $true) | ((in @ X1 @ X0) != $true)) | ((in @ X1 @ X2) != $true))),
% 0.21/0.39 inference(ennf_transformation,[],[f14])).
% 0.21/0.39 thf(f14,plain,(
% 0.21/0.39 (binintersectI = $true) <=> ! [X1,X0,X2] : (((in @ X1 @ X2) = $true) => (((in @ X1 @ X0) = $true) => ((in @ X1 @ (binintersect @ X2 @ X0)) = $true)))),
% 0.21/0.39 inference(fool_elimination,[],[f13])).
% 0.21/0.39 thf(f13,plain,(
% 0.21/0.39 (! [X0,X1,X2] : ((in @ X1 @ X2) => ((in @ X1 @ X0) => (in @ X1 @ (binintersect @ X2 @ X0)))) = binintersectI)),
% 0.21/0.39 inference(rectify,[],[f1])).
% 0.21/0.39 thf(f1,axiom,(
% 0.21/0.39 (! [X1,X2,X0] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))) = binintersectI)),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI)).
% 0.21/0.39 thf(f49,plain,(
% 0.21/0.39 ((in @ sK4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3))) != $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f27])).
% 0.21/0.39 % SZS output end Proof for theBenchmark
% 0.21/0.39 % (14252)------------------------------
% 0.21/0.39 % (14252)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (14252)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (14252)Memory used [KB]: 5628
% 0.21/0.39 % (14252)Time elapsed: 0.017 s
% 0.21/0.39 % (14252)Instructions burned: 15 (million)
% 0.21/0.39 % (14252)------------------------------
% 0.21/0.39 % (14252)------------------------------
% 0.21/0.39 % (14246)Success in time 0.024 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------