%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU742^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:33:13 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU742^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:22:07 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.30 % (1360646)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (1360652)% WARNING: option uhcvi not known.
% 0.20/0.30 % (1360656)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1612443757:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (1360654)dis+10_1_sil=32000:sp=arity:random_seed=1399393579:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (1360651)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3900314178_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (1360652)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2737938539:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (1360653)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=134865669:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (1360655)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=947156739:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (1360652)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (1360655)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (1360652)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.30 % (1360657)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=870480292:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % (1360664)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2892666722:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (1360656)Instruction limit reached!
% 0.20/0.30 % (1360656)------------------------------
% 0.20/0.30 % (1360656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1360656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1360656)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1360656)Termination reason: Instruction limit
% 0.20/0.30 % (1360656)Termination phase: Saturation
% 0.20/0.30 % (1360656)Time elapsed: 0.032 s
% 0.20/0.30 % (1360656)Peak memory usage: 12 MB
% 0.20/0.30 % (1360656)Instructions burned: 135 (million)
% 0.20/0.30 % (1360654) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1360646-1360654"...
% 0.20/0.30 % (1360654)...printing done.
% 0.20/0.30 % (1360667)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3160767706:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (1360657) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1360646-1360657"...
% 0.20/0.30 % (1360654)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% 0.20/0.30 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.30 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.30 thf(func_def_1, type, powerset: ($i > $i)).
% 0.20/0.30 thf(func_def_2, type, binunion: ($i > $i > $i)).
% 0.20/0.30 thf(func_def_3, type, binintersect: ($i > $i > $i)).
% 0.20/0.30 thf(func_def_4, type, binintersectI: $o).
% 0.20/0.30 thf(func_def_6, type, inIntersectImpInUnion: $o).
% 0.20/0.30 thf(func_def_7, type, inIntersectImpInUnion2: $o).
% 0.20/0.30 thf(func_def_8, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.30 thf(func_def_9, type, vIMP: ($o > $o > $o)).
% 0.20/0.30 thf(func_def_10, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_11, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_12, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_13, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.30 thf(func_def_14, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_15, type, db4: !>[X0: $tType]:(X0)).
% 0.20/0.30 thf(func_def_23, type, vNOT: ($o > $o)).
% 0.20/0.30 thf(f1,axiom,(
% 0.20/0.30 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI)).
% 0.20/0.30 thf(f2,axiom,(
% 0.20/0.30 (inIntersectImpInUnion = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binunion @ X1 @ X3))))))))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion)).
% 0.20/0.30 thf(f3,axiom,(
% 0.20/0.30 (inIntersectImpInUnion2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binunion @ X2 @ X3))))))))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInUnion2)).
% 0.20/0.30 thf(f4,conjecture,(
% 0.20/0.30 binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3))))))))))),
% 0.20/0.30 file('/export/starexec/sandbox/benchmark/theBenchmark.p',inIntersectImpInIntersectUnions)).
% 0.20/0.30 thf(f5,negated_conjecture,(
% 0.20/0.30 ~(binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))))))))))),
% 0.20/0.30 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.30 thf(f6,plain,(
% 0.20/0.30 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 0.20/0.30 inference(rectify,[],[f1])).
% 0.20/0.30 thf(f7,plain,(
% 0.20/0.30 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))))))),
% 0.20/0.30 inference(fool_elimination,[],[f6])).
% 0.20/0.30 thf(f8,plain,(
% 0.20/0.30 (inIntersectImpInUnion = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binunion @ X1 @ X3))))))))),
% 0.20/0.30 inference(rectify,[],[f2])).
% 0.20/0.30 thf(f9,plain,(
% 0.20/0.30 (inIntersectImpInUnion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y4 @ (binintersect @ Y0 @ Y2)) => (in @ Y4 @ (binunion @ Y0 @ Y3)))))))))))))))))))),
% 0.20/0.30 inference(fool_elimination,[],[f8])).
% 0.20/0.30 thf(f10,plain,(
% 0.20/0.30 (inIntersectImpInUnion2 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binunion @ X2 @ X3))))))))),
% 0.20/0.30 inference(rectify,[],[f3])).
% 0.20/0.30 thf(f11,plain,(
% 0.20/0.30 (inIntersectImpInUnion2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y4 @ (binintersect @ Y0 @ Y2)) => (in @ Y4 @ (binunion @ Y2 @ Y3)))))))))))))))))))),
% 0.20/0.30 inference(fool_elimination,[],[f10])).
% 0.20/0.30 thf(f12,plain,(
% 0.20/0.30 ~(binintersectI => (inIntersectImpInUnion => (inIntersectImpInUnion2 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X0)) => ! [X4 : $i] : ((in @ X4 @ X0) => ((in @ X4 @ (binintersect @ X1 @ X2)) => (in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))))))))))),
% 0.20/0.30 inference(rectify,[],[f5])).
% 0.20/0.30 thf(f13,plain,(
% 0.20/0.30 ~((binintersectI = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => ! [X3 : $i] : ((((in @ X3 @ (powerset @ X0))) = $true) => ! [X4 : $i] : ((((in @ X4 @ X0)) = $true) => ((((in @ X4 @ (binintersect @ X1 @ X2))) = $true) => (((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) = $true)))))))))),
% 0.20/0.30 inference(fool_elimination,[],[f12])).
% 0.20/0.30 thf(f14,plain,(
% 0.20/0.30 ((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true) & (((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)),
% 0.20/0.30 inference(ennf_transformation,[],[f13])).
% 0.20/0.30 thf(f15,plain,(
% 0.20/0.30 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : ((((in @ X4 @ (binintersect @ (binunion @ X1 @ X3) @ (binunion @ X2 @ X3)))) != $true) & (((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 = $true)),
% 0.20/0.30 inference(flattening,[],[f14])).
% 0.20/0.30 thf(f16,plain,(
% 0.20/0.30 ((((($true != ((in @ sK4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3))))) & ($true = ((in @ sK4 @ (binintersect @ sK1 @ sK2)))) & ($true = ((in @ sK4 @ sK0)))) & ($true = ((in @ sK3 @ (powerset @ sK0))))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (inIntersectImpInUnion2 = $true) & (inIntersectImpInUnion = $true) & (binintersectI = $true)),
% 0.20/0.30 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f15])).
% 0.20/0.30 thf(f17,plain,(
% 0.20/0.30 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f7])).
% 0.20/0.30 thf(f18,plain,(
% 0.20/0.30 (inIntersectImpInUnion = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y4 @ (binintersect @ Y0 @ Y2)) => (in @ Y4 @ (binunion @ Y0 @ Y3)))))))))))))))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f9])).
% 0.20/0.30 thf(f19,plain,(
% 0.20/0.30 (inIntersectImpInUnion2 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y4 @ (binintersect @ Y0 @ Y2)) => (in @ Y4 @ (binunion @ Y2 @ Y3)))))))))))))))))))),
% 0.20/0.30 inference(cnf_transformation,[],[f11])).
% 0.20/0.30 thf(f20,plain,(
% 0.20/0.30 (binintersectI = $true)),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f21,plain,(
% 0.20/0.30 (inIntersectImpInUnion = $true)),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f22,plain,(
% 0.20/0.30 (inIntersectImpInUnion2 = $true)),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f23,plain,(
% 0.20/0.30 ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f24,plain,(
% 0.20/0.30 ($true = ((in @ sK2 @ (powerset @ sK0))))),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f25,plain,(
% 0.20/0.30 ($true = ((in @ sK3 @ (powerset @ sK0))))),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f26,plain,(
% 0.20/0.30 ($true = ((in @ sK4 @ sK0)))),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f27,plain,(
% 0.20/0.30 ($true = ((in @ sK4 @ (binintersect @ sK1 @ sK2))))),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f28,plain,(
% 0.20/0.30 ($true != ((in @ sK4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3)))))),
% 0.20/0.30 inference(cnf_transformation,[],[f16])).
% 0.20/0.30 thf(f30,definition,(
% 0.20/0.30 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.30 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.30 thf(f31,plain,(
% 0.20/0.30 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))))) = $true)),
% 0.20/0.30 inference(definition_unfolding,[],[f17,f20])).
% 0.20/0.30 thf(f32,plain,(
% 0.20/0.30 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y4 @ (binintersect @ Y0 @ Y2)) => (in @ Y4 @ (binunion @ Y0 @ Y3)))))))))))))))))) = $true)),
% 0.20/0.30 inference(definition_unfolding,[],[f18,f21])).
% 0.20/0.30 thf(f33,plain,(
% 0.20/0.30 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y4 @ (binintersect @ Y0 @ Y2)) => (in @ Y4 @ (binunion @ Y2 @ Y3)))))))))))))))))) = $true)),
% 0.20/0.30 inference(definition_unfolding,[],[f19,f22])).
% 0.20/0.30 thf(f34,plain,(
% 0.20/0.30 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y4 @ (binintersect @ Y0 @ Y2)) => (in @ Y4 @ (binunion @ Y2 @ Y3)))))))))))))))) @ X1)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f33])).
% 0.20/0.30 thf(f35,plain,(
% 0.20/0.30 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (binintersect @ X1 @ Y1)) => (in @ Y3 @ (binunion @ Y1 @ Y2)))))))))))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f34])).
% 0.20/0.30 thf(f36,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (binintersect @ X1 @ Y1)) => (in @ Y3 @ (binunion @ Y1 @ Y2)))))))))))))) @ X2)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f35])).
% 0.20/0.30 thf(f37,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ Y2 @ (binintersect @ X1 @ Y0)) => (in @ Y2 @ (binunion @ Y0 @ Y1)))))))))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f36])).
% 0.20/0.30 thf(f38,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ Y2 @ (binintersect @ X1 @ Y0)) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))))))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f37])).
% 0.20/0.30 thf(f39,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ Y2 @ (binintersect @ X1 @ Y0)) => (in @ Y2 @ (binunion @ Y0 @ Y1))))))))))) @ X3)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f38])).
% 0.20/0.30 thf(f40,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (binintersect @ X1 @ X3)) => (in @ Y1 @ (binunion @ X3 @ Y0))))))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f39])).
% 0.20/0.30 thf(f41,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (binintersect @ X1 @ X3)) => (in @ Y1 @ (binunion @ X3 @ Y0)))))))))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f40])).
% 0.20/0.30 thf(f42,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (binintersect @ X1 @ X3)) => (in @ Y1 @ (binunion @ X3 @ Y0)))))))) @ X4)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f41])).
% 0.20/0.30 thf(f43,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((in @ X4 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (binintersect @ X1 @ X3)) => (in @ Y0 @ (binunion @ X3 @ X4)))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f42])).
% 0.20/0.30 thf(f44,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (binintersect @ X1 @ X3)) => (in @ Y0 @ (binunion @ X3 @ X4))))))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f43])).
% 0.20/0.30 thf(f45,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (binintersect @ X1 @ X3)) => (in @ Y0 @ (binunion @ X3 @ X4))))) @ X5)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f44])).
% 0.20/0.30 thf(f46,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = (((in @ X5 @ X2) => ((in @ X5 @ (binintersect @ X1 @ X3)) => (in @ X5 @ (binunion @ X3 @ X4))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f45])).
% 0.20/0.30 thf(f47,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($false = ((in @ X5 @ X2))) | ($true = (((in @ X5 @ (binintersect @ X1 @ X3)) => (in @ X5 @ (binunion @ X3 @ X4)))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f46])).
% 0.20/0.30 thf(f48,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ X5 @ (binintersect @ X1 @ X3)))) | ($true = ((in @ X5 @ (binunion @ X3 @ X4))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f47])).
% 0.20/0.30 thf(f49,plain,(
% 0.20/0.30 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ (powerset @ Y1)) => (!! @ $i @ (^[Y4 : $i]: ((in @ Y4 @ Y1) => ((in @ Y4 @ (binintersect @ Y0 @ Y2)) => (in @ Y4 @ (binunion @ Y0 @ Y3)))))))))))))))) @ X1)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f32])).
% 0.20/0.30 thf(f50,plain,(
% 0.20/0.30 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (binintersect @ X1 @ Y1)) => (in @ Y3 @ (binunion @ X1 @ Y2)))))))))))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f49])).
% 0.20/0.30 thf(f51,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y0)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y0) => ((in @ Y3 @ (binintersect @ X1 @ Y1)) => (in @ Y3 @ (binunion @ X1 @ Y2)))))))))))))) @ X2)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f50])).
% 0.20/0.30 thf(f52,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ Y2 @ (binintersect @ X1 @ Y0)) => (in @ Y2 @ (binunion @ X1 @ Y1)))))))))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f51])).
% 0.20/0.30 thf(f53,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ Y2 @ (binintersect @ X1 @ Y0)) => (in @ Y2 @ (binunion @ X1 @ Y1))))))))))))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f52])).
% 0.20/0.30 thf(f54,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ X2)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ X2) => ((in @ Y2 @ (binintersect @ X1 @ Y0)) => (in @ Y2 @ (binunion @ X1 @ Y1))))))))))) @ X3)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f53])).
% 0.20/0.30 thf(f55,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (binintersect @ X1 @ X3)) => (in @ Y1 @ (binunion @ X1 @ Y0))))))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f54])).
% 0.20/0.30 thf(f56,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (binintersect @ X1 @ X3)) => (in @ Y1 @ (binunion @ X1 @ Y0)))))))))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f55])).
% 0.20/0.30 thf(f57,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (binintersect @ X1 @ X3)) => (in @ Y1 @ (binunion @ X1 @ Y0)))))))) @ X4)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f56])).
% 0.20/0.30 thf(f58,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((in @ X4 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (binintersect @ X1 @ X3)) => (in @ Y0 @ (binunion @ X1 @ X4)))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f57])).
% 0.20/0.30 thf(f59,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (binintersect @ X1 @ X3)) => (in @ Y0 @ (binunion @ X1 @ X4))))))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f58])).
% 0.20/0.30 thf(f60,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (binintersect @ X1 @ X3)) => (in @ Y0 @ (binunion @ X1 @ X4))))) @ X5)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f59])).
% 0.20/0.30 thf(f61,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($true = (((in @ X5 @ X2) => ((in @ X5 @ (binintersect @ X1 @ X3)) => (in @ X5 @ (binunion @ X1 @ X4))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f60])).
% 0.20/0.30 thf(f62,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($false = ((in @ X5 @ X2))) | ($true = (((in @ X5 @ (binintersect @ X1 @ X3)) => (in @ X5 @ (binunion @ X1 @ X4)))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f61])).
% 0.20/0.30 thf(f63,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i,X5 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ (powerset @ X2)))) | ($false = ((in @ X5 @ X2))) | ($false = ((in @ X5 @ (binintersect @ X1 @ X3)))) | ($true = ((in @ X5 @ (binunion @ X1 @ X4))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f62])).
% 0.20/0.30 thf(f64,plain,(
% 0.20/0.30 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))) @ X1)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f31])).
% 0.20/0.30 thf(f65,plain,(
% 0.20/0.30 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ X1 @ Y0) => (in @ X1 @ (binintersect @ Y1 @ Y0))))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f64])).
% 0.20/0.30 thf(f66,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ X1 @ Y0) => (in @ X1 @ (binintersect @ Y1 @ Y0))))))) @ X2)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f65])).
% 0.20/0.30 thf(f67,plain,(
% 0.20/0.30 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ Y0 @ X2))))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f66])).
% 0.20/0.30 thf(f68,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ Y0 @ X2))))) @ X3)))) )),
% 0.20/0.30 inference(pi_proxy_clausification,[],[f67])).
% 0.20/0.30 thf(f69,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ X3 @ X2))))))) )),
% 0.20/0.30 inference(beta-eta_normalization,[],[f68])).
% 0.20/0.30 thf(f70,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((in @ X1 @ X2) => (in @ X1 @ (binintersect @ X3 @ X2)))))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f69])).
% 0.20/0.30 thf(f71,plain,(
% 0.20/0.30 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ (binintersect @ X3 @ X2)))) | ($false = ((in @ X1 @ X2))) | ($false = ((in @ X1 @ X3)))) )),
% 0.20/0.30 inference(imp_proxy_clausification,[],[f70])).
% 0.20/0.30 thf(f75,definition,(
% 0.20/0.30 spl5_1 <=> ($false = ((in @ sK4 @ (binunion @ sK1 @ sK3))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition])).
% 0.20/0.30 thf(f77,plain,(
% 0.20/0.30 ($false = ((in @ sK4 @ (binunion @ sK1 @ sK3)))) | ~spl5_1),
% 0.20/0.30 inference(avatar_component_clause,[],[f75])).
% 0.20/0.30 thf(f79,definition,(
% 0.20/0.30 spl5_2 <=> ($false = ((in @ sK4 @ (binunion @ sK2 @ sK3))))),
% 0.20/0.30 introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition])).
% 0.20/0.30 thf(f81,plain,(
% 0.20/0.30 ($false = ((in @ sK4 @ (binunion @ sK2 @ sK3)))) | ~spl5_2),
% 0.20/0.30 inference(avatar_component_clause,[],[f79])).
% 0.20/0.30 thf(f85,plain,(
% 0.20/0.30 ($true != $true) | (((in @ sK4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3)))) = $false)),
% 0.20/0.30 inference(constrained_superposition,[],[f28,f30])).
% 0.20/0.30 thf(f89,plain,(
% 0.20/0.30 (((in @ sK4 @ (binintersect @ (binunion @ sK1 @ sK3) @ (binunion @ sK2 @ sK3)))) = $false)),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f85])).
% 0.20/0.30 thf(f94,plain,(
% 0.20/0.30 ($true = $false) | ($false = ((in @ sK4 @ (binunion @ sK2 @ sK3)))) | ($false = ((in @ sK4 @ (binunion @ sK1 @ sK3))))),
% 0.20/0.30 inference(constrained_superposition,[],[f89,f71])).
% 0.20/0.30 thf(f100,plain,(
% 0.20/0.30 ($false = ((in @ sK4 @ (binunion @ sK2 @ sK3)))) | ($false = ((in @ sK4 @ (binunion @ sK1 @ sK3))))),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f94])).
% 0.20/0.30 thf(f113,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ sK1 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) = $false) | ($false = ((in @ sK4 @ X0))) | ($true = ((in @ sK4 @ (binunion @ sK2 @ X1))))) )),
% 0.20/0.30 inference(constrained_superposition,[],[f27,f48])).
% 0.20/0.30 thf(f132,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ sK4 @ (binunion @ sK2 @ X1)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) = $false) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK1 @ (powerset @ X0))))) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f113])).
% 0.20/0.30 thf(f148,plain,(
% 0.20/0.30 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK1 @ (powerset @ X0))))) ) | ~spl5_2),
% 0.20/0.30 inference(constrained_superposition,[],[f81,f132])).
% 0.20/0.30 thf(f153,plain,(
% 0.20/0.30 ( ! [X0 : $i] : (($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK1 @ (powerset @ X0))))) ) | ~spl5_2),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f148])).
% 0.20/0.30 thf(f181,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ sK1 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) = $false) | ($false = ((in @ sK4 @ X0))) | ($true = ((in @ sK4 @ (binunion @ sK1 @ X1))))) )),
% 0.20/0.30 inference(constrained_superposition,[],[f27,f63])).
% 0.20/0.30 thf(f202,plain,(
% 0.20/0.30 ( ! [X0 : $i,X1 : $i] : (($true = ((in @ sK4 @ (binunion @ sK1 @ X1)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | (((in @ X1 @ (powerset @ X0))) = $false) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK1 @ (powerset @ X0))))) )),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f181])).
% 0.20/0.30 thf(f302,plain,(
% 0.20/0.30 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK4 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_2),
% 0.20/0.30 inference(constrained_superposition,[],[f25,f153])).
% 0.20/0.30 thf(f303,plain,(
% 0.20/0.30 (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK4 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_2),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f302])).
% 0.20/0.30 thf(f306,plain,(
% 0.20/0.30 ($true = $false) | (((in @ sK4 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_2),
% 0.20/0.30 inference(forward_demodulation,[],[f303,f24])).
% 0.20/0.30 thf(f307,plain,(
% 0.20/0.30 (((in @ sK4 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_2),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f306])).
% 0.20/0.30 thf(f310,plain,(
% 0.20/0.30 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_2),
% 0.20/0.30 inference(forward_demodulation,[],[f307,f26])).
% 0.20/0.30 thf(f311,plain,(
% 0.20/0.30 (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_2),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f310])).
% 0.20/0.30 thf(f378,plain,(
% 0.20/0.30 ($true = $false) | ~spl5_2),
% 0.20/0.30 inference(constrained_superposition,[],[f311,f23])).
% 0.20/0.30 thf(f384,plain,(
% 0.20/0.30 $false | ~spl5_2),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f378])).
% 0.20/0.30 thf(f385,plain,(
% 0.20/0.30 ~spl5_2),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f384])).
% 0.20/0.30 thf(f387,plain,(
% 0.20/0.30 spl5_1 | spl5_2),
% 0.20/0.30 inference(avatar_split_clause,[],[f100,f79,f75])).
% 0.20/0.30 thf(f390,plain,(
% 0.20/0.30 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK1 @ (powerset @ X0))))) ) | ~spl5_1),
% 0.20/0.30 inference(constrained_superposition,[],[f202,f77])).
% 0.20/0.30 thf(f391,plain,(
% 0.20/0.30 ( ! [X0 : $i] : (($false = ((in @ sK3 @ (powerset @ X0)))) | ($false = ((in @ sK2 @ (powerset @ X0)))) | ($false = ((in @ sK4 @ X0))) | ($false = ((in @ sK1 @ (powerset @ X0))))) ) | ~spl5_1),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f390])).
% 0.20/0.30 thf(f461,plain,(
% 0.20/0.30 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK4 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_1),
% 0.20/0.30 inference(constrained_superposition,[],[f25,f391])).
% 0.20/0.30 thf(f462,plain,(
% 0.20/0.30 (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK4 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_1),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f461])).
% 0.20/0.30 thf(f465,plain,(
% 0.20/0.30 ($true = $false) | (((in @ sK4 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_1),
% 0.20/0.30 inference(forward_demodulation,[],[f462,f24])).
% 0.20/0.30 thf(f466,plain,(
% 0.20/0.30 (((in @ sK4 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_1),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f465])).
% 0.20/0.30 thf(f469,plain,(
% 0.20/0.30 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_1),
% 0.20/0.30 inference(forward_demodulation,[],[f466,f26])).
% 0.20/0.30 thf(f470,plain,(
% 0.20/0.30 (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl5_1),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f469])).
% 0.20/0.30 thf(f473,plain,(
% 0.20/0.30 ($true = $false) | ~spl5_1),
% 0.20/0.30 inference(constrained_superposition,[],[f470,f23])).
% 0.20/0.30 thf(f479,plain,(
% 0.20/0.30 $false | ~spl5_1),
% 0.20/0.30 inference(trivial_inequality_removal,[],[f473])).
% 0.20/0.30 thf(f480,plain,(
% 0.20/0.30 ~spl5_1),
% 0.20/0.30 inference(avatar_contradiction_clause,[],[f479])).
% 0.20/0.30 cnf(s11, plain, ~spl5_2, inference(sat_conversion,[],[f385])).
% 0.20/0.30 cnf(s13, plain, spl5_1 | spl5_2, inference(sat_conversion,[],[f387])).
% 0.20/0.30 cnf(s15, plain, ~spl5_1, inference(sat_conversion,[],[f480])).
% 0.20/0.30 cnf(s16, plain, spl5_2, inference(rat,[],[s13,s15])).
% 0.20/0.30 cnf(s17, plain, $false, inference(rat,[],[s11,s16])).
% 0.20/0.30 thf(f481,plain,(
% 0.20/0.30 $false),
% 0.20/0.30 inference(avatar_sat_refutation,[],[s17])).
% 0.20/0.30 % SZS output end Proof for theBenchmark
% 0.20/0.30 % (1360654)------------------------------
% 0.20/0.30 % (1360654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1360654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1360654)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1360654)Termination reason: Refutation
% 0.20/0.30 % (1360654)Time elapsed: 0.040 s
% 0.20/0.30 % (1360654)Peak memory usage: 12 MB
% 0.20/0.30 % (1360654)Instructions burned: 87 (million)
% 0.20/0.30 % (1360646)Success in time 0.075 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------