%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU751^2 : 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 : n019.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 08:33:15 AM UTC 2026
% Result : Theorem 0.20s 0.31s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU751^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.20 % Computer : n019.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:21:33 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.23 Running first-order model finding
% 0.10/0.23 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
% 0.20/0.31 % (847487)Will run a generic schedule for satisfiability detection.
% 0.20/0.31 % (847497)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=246925446:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.31 % (847493)% WARNING: option uhcvi not known.
% 0.20/0.31 % (847498)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1142711960:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.31 % (847492)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4042942323_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.31 % (847493)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2165400978:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.31 % (847495)dis+10_1_sil=32000:sp=arity:random_seed=1210827089:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.31 % (847494)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2102545493:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.31 % (847496)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2401402250:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.31 % (847493)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % (847496)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.31 % Exception at run slice level
% 0.20/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.31 % (847493)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.31 % (847495) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-847487-847495"...
% 0.20/0.31 % (847506)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3996840220:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.31 % (847496) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-847487-847496"...
% 0.20/0.31 % Exception at run slice level
% 0.20/0.31 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.31 % (847497)Instruction limit reached!
% 0.20/0.31 % (847497)------------------------------
% 0.20/0.31 % (847497)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.31 % (847497)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.31 % (847497)CaDiCaL version: 2.1.3
% 0.20/0.31 % (847497)Termination reason: Instruction limit
% 0.20/0.31 % (847497)Termination phase: Saturation
% 0.20/0.31 % (847497)Time elapsed: 0.035 s
% 0.20/0.31 % (847497)Peak memory usage: 12 MB
% 0.20/0.31 % (847497)Instructions burned: 135 (million)
% 0.20/0.31 % (847495)...printing done.
% 0.20/0.31 % (847495)Refutation found. Thanks to Tanya!
% 0.20/0.31 % SZS status Theorem for theBenchmark
% 0.20/0.31 % SZS output start Proof for theBenchmark
% 0.20/0.31 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.31 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.20/0.31 thf(func_def_1, type, powerset: ($i > $i)).
% 0.20/0.31 thf(func_def_2, type, binunion: ($i > $i > $i)).
% 0.20/0.31 thf(func_def_3, type, binintersect: ($i > $i > $i)).
% 0.20/0.31 thf(func_def_4, type, binintersectI: $o).
% 0.20/0.31 thf(func_def_6, type, setminus: ($i > $i > $i)).
% 0.20/0.31 thf(func_def_7, type, setminusER: $o).
% 0.20/0.31 thf(func_def_8, type, complementT_lem: $o).
% 0.20/0.31 thf(func_def_9, type, complementTE1: $o).
% 0.20/0.31 thf(func_def_10, type, binunionTILcontra: $o).
% 0.20/0.31 thf(func_def_11, type, binunionTIRcontra: $o).
% 0.20/0.31 thf(func_def_12, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.31 thf(func_def_13, type, vIMP: ($o > $o > $o)).
% 0.20/0.31 thf(func_def_14, type, db2: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_15, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_16, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(func_def_17, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.31 thf(func_def_18, type, vNOT: ($o > $o)).
% 0.20/0.31 thf(func_def_19, type, db3: !>[X0: $tType]:(X0)).
% 0.20/0.31 thf(f1,axiom,(
% 0.20/0.31 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectI)).
% 0.20/0.31 thf(f2,axiom,(
% 0.20/0.31 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER)).
% 0.20/0.31 thf(f3,axiom,(
% 0.20/0.31 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem)).
% 0.20/0.31 thf(f4,axiom,(
% 0.20/0.31 (complementTE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X1)))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementTE1)).
% 0.20/0.31 thf(f5,axiom,(
% 0.20/0.31 (binunionTILcontra = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ (binunion @ X1 @ X2)) => ~(in @ X3 @ X1))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTILcontra)).
% 0.20/0.31 thf(f6,axiom,(
% 0.20/0.31 (binunionTIRcontra = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ (binunion @ X1 @ X2)) => ~(in @ X3 @ X2))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionTIRcontra)).
% 0.20/0.31 thf(f7,conjecture,(
% 0.20/0.31 binintersectI => (setminusER => (complementT_lem => (complementTE1 => (binunionTILcontra => (binunionTIRcontra => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2))))))))))))),
% 0.20/0.31 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan1a)).
% 0.20/0.31 thf(f8,negated_conjecture,(
% 0.20/0.31 ~(binintersectI => (setminusER => (complementT_lem => (complementTE1 => (binunionTILcontra => (binunionTIRcontra => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))))))))),
% 0.20/0.31 inference(negated_conjecture,[status(cth)],[f7])).
% 0.20/0.31 thf(f9,plain,(
% 0.20/0.31 (binintersectI = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ (binintersect @ X0 @ X1)))))),
% 0.20/0.31 inference(rectify,[],[f1])).
% 0.20/0.31 thf(f10,plain,(
% 0.20/0.31 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f9])).
% 0.20/0.31 thf(f11,plain,(
% 0.20/0.31 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X0 @ X1)) => ~(in @ X2 @ X1)))),
% 0.20/0.31 inference(rectify,[],[f2])).
% 0.20/0.31 thf(f12,plain,(
% 0.20/0.31 (setminusER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1)))))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f11])).
% 0.20/0.31 thf(f13,plain,(
% 0.20/0.31 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.20/0.31 inference(rectify,[],[f3])).
% 0.20/0.31 thf(f14,plain,(
% 0.20/0.31 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f13])).
% 0.20/0.31 thf(f15,plain,(
% 0.20/0.31 (complementTE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ X0) => (~(in @ X2 @ (setminus @ X0 @ X1)) => (in @ X2 @ X1)))))),
% 0.20/0.31 inference(rectify,[],[f4])).
% 0.20/0.31 thf(f16,plain,(
% 0.20/0.31 (complementTE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0))))))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f15])).
% 0.20/0.31 thf(f17,plain,(
% 0.20/0.31 (binunionTILcontra = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ (binunion @ X1 @ X2)) => ~(in @ X3 @ X1))))))),
% 0.20/0.31 inference(rectify,[],[f5])).
% 0.20/0.31 thf(f18,plain,(
% 0.20/0.31 (binunionTILcontra = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0))))))))))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f17])).
% 0.20/0.31 thf(f19,plain,(
% 0.20/0.31 (binunionTIRcontra = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => (~(in @ X3 @ (binunion @ X1 @ X2)) => ~(in @ X3 @ X2))))))),
% 0.20/0.31 inference(rectify,[],[f6])).
% 0.20/0.31 thf(f20,plain,(
% 0.20/0.31 (binunionTIRcontra = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y2))))))))))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f19])).
% 0.20/0.31 thf(f21,plain,(
% 0.20/0.31 ~(binintersectI => (setminusER => (complementT_lem => (complementTE1 => (binunionTILcontra => (binunionTIRcontra => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2))) => (in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))))))))))))),
% 0.20/0.31 inference(rectify,[],[f8])).
% 0.20/0.31 thf(f22,plain,(
% 0.20/0.31 ~((binintersectI = $true) => ((setminusER = $true) => ((complementT_lem = $true) => ((complementTE1 = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => ! [X3 : $i] : ((((in @ X3 @ X0)) = $true) => ((((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) => (((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) = $true)))))))))))),
% 0.20/0.31 inference(fool_elimination,[],[f21])).
% 0.20/0.31 thf(f23,plain,(
% 0.20/0.31 (((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) & (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true)) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTE1 = $true)) & (complementT_lem = $true)) & (setminusER = $true)) & (binintersectI = $true)),
% 0.20/0.31 inference(ennf_transformation,[],[f22])).
% 0.20/0.31 thf(f24,plain,(
% 0.20/0.31 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : ((((in @ X3 @ (binunion @ (setminus @ X0 @ X1) @ (setminus @ X0 @ X2)))) != $true) & (((in @ X3 @ (setminus @ X0 @ (binintersect @ X1 @ X2)))) = $true) & (((in @ X3 @ X0)) = $true)) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTE1 = $true) & (complementT_lem = $true) & (setminusER = $true) & (binintersectI = $true)),
% 0.20/0.31 inference(flattening,[],[f23])).
% 0.20/0.31 thf(f25,plain,(
% 0.20/0.31 (((($true != ((in @ sK3 @ (binunion @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ sK2))))) & ($true = ((in @ sK3 @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2))))) & ($true = ((in @ sK3 @ sK0)))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (binunionTIRcontra = $true) & (binunionTILcontra = $true) & (complementTE1 = $true) & (complementT_lem = $true) & (setminusER = $true) & (binintersectI = $true)),
% 0.20/0.31 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f24])).
% 0.20/0.31 thf(f26,plain,(
% 0.20/0.31 (binintersectI = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f10])).
% 0.20/0.31 thf(f27,plain,(
% 0.20/0.31 (setminusER = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1)))))))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f12])).
% 0.20/0.31 thf(f28,plain,(
% 0.20/0.31 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f14])).
% 0.20/0.31 thf(f29,plain,(
% 0.20/0.31 (complementTE1 = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0))))))))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f16])).
% 0.20/0.31 thf(f30,plain,(
% 0.20/0.31 (binunionTILcontra = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0))))))))))))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f18])).
% 0.20/0.31 thf(f31,plain,(
% 0.20/0.31 (binunionTIRcontra = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y2))))))))))))))))),
% 0.20/0.31 inference(cnf_transformation,[],[f20])).
% 0.20/0.31 thf(f32,plain,(
% 0.20/0.31 (binintersectI = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f33,plain,(
% 0.20/0.31 (setminusER = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f34,plain,(
% 0.20/0.31 (complementT_lem = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f35,plain,(
% 0.20/0.31 (complementTE1 = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f36,plain,(
% 0.20/0.31 (binunionTILcontra = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f37,plain,(
% 0.20/0.31 (binunionTIRcontra = $true)),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f38,plain,(
% 0.20/0.31 ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f39,plain,(
% 0.20/0.31 ($true = ((in @ sK2 @ (powerset @ sK0))))),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f40,plain,(
% 0.20/0.31 ($true = ((in @ sK3 @ sK0)))),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f41,plain,(
% 0.20/0.31 ($true = ((in @ sK3 @ (setminus @ sK0 @ (binintersect @ sK1 @ sK2)))))),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f42,plain,(
% 0.20/0.31 ($true != ((in @ sK3 @ (binunion @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ sK2)))))),
% 0.20/0.31 inference(cnf_transformation,[],[f25])).
% 0.20/0.31 thf(f44,definition,(
% 0.20/0.31 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.20/0.31 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.20/0.31 thf(f45,plain,(
% 0.20/0.31 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))))) = $true)),
% 0.20/0.31 inference(definition_unfolding,[],[f26,f32])).
% 0.20/0.31 thf(f46,plain,(
% 0.20/0.31 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1)))))))))) = $true)),
% 0.20/0.31 inference(definition_unfolding,[],[f27,f33])).
% 0.20/0.31 thf(f47,plain,(
% 0.20/0.31 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))) = $true)),
% 0.20/0.31 inference(definition_unfolding,[],[f28,f34])).
% 0.20/0.31 thf(f48,plain,(
% 0.20/0.31 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0))))))))))) = $true)),
% 0.20/0.31 inference(definition_unfolding,[],[f29,f35])).
% 0.20/0.31 thf(f49,plain,(
% 0.20/0.31 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0))))))))))))))) = $true)),
% 0.20/0.31 inference(definition_unfolding,[],[f30,f36])).
% 0.20/0.31 thf(f50,plain,(
% 0.20/0.31 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y2))))))))))))))) = $true)),
% 0.20/0.31 inference(definition_unfolding,[],[f31,f37])).
% 0.20/0.31 thf(f51,plain,(
% 0.20/0.31 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y2))))))))))))) @ X1)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f50])).
% 0.20/0.31 thf(f52,plain,(
% 0.20/0.31 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ (binunion @ X1 @ Y1))) => (~ (in @ Y2 @ Y1))))))))))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f51])).
% 0.20/0.31 thf(f53,plain,(
% 0.20/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ (binunion @ X1 @ Y1))) => (~ (in @ Y2 @ Y1))))))))))) @ X2)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f52])).
% 0.20/0.31 thf(f54,plain,(
% 0.20/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ Y0))))))))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f53])).
% 0.20/0.31 thf(f55,plain,(
% 0.20/0.31 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ Y0)))))))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f54])).
% 0.20/0.31 thf(f56,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ Y0)))))))) @ X3)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f55])).
% 0.20/0.31 thf(f57,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X3)))))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f56])).
% 0.20/0.31 thf(f58,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X3))))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f57])).
% 0.20/0.31 thf(f59,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X3))))) @ X4)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f58])).
% 0.20/0.31 thf(f60,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((in @ X4 @ X2) => ((~ (in @ X4 @ (binunion @ X1 @ X3))) => (~ (in @ X4 @ X3))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f59])).
% 0.20/0.31 thf(f61,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($true = (((~ (in @ X4 @ (binunion @ X1 @ X3))) => (~ (in @ X4 @ X3)))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f60])).
% 0.20/0.31 thf(f62,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((~ (in @ X4 @ (binunion @ X1 @ X3))))) | ($true = ((~ (in @ X4 @ X3))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f61])).
% 0.20/0.31 thf(f63,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($true = ((in @ X4 @ (binunion @ X1 @ X3)))) | ($true = ((~ (in @ X4 @ X3))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f62])).
% 0.20/0.31 thf(f64,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ X4 @ (binunion @ X1 @ X3)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X4 @ X3)))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f63])).
% 0.20/0.31 thf(f65,plain,(
% 0.20/0.31 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (!! @ $i @ (^[Y3 : $i]: ((in @ Y3 @ Y1) => ((~ (in @ Y3 @ (binunion @ Y0 @ Y2))) => (~ (in @ Y3 @ Y0))))))))))))) @ X1)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f49])).
% 0.20/0.31 thf(f66,plain,(
% 0.20/0.31 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ (binunion @ X1 @ Y1))) => (~ (in @ Y2 @ X1))))))))))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f65])).
% 0.20/0.31 thf(f67,plain,(
% 0.20/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((~ (in @ Y2 @ (binunion @ X1 @ Y1))) => (~ (in @ Y2 @ X1))))))))))) @ X2)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f66])).
% 0.20/0.31 thf(f68,plain,(
% 0.20/0.31 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ X1))))))))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f67])).
% 0.20/0.31 thf(f69,plain,(
% 0.20/0.31 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ X1)))))))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f68])).
% 0.20/0.31 thf(f70,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((~ (in @ Y1 @ (binunion @ X1 @ Y0))) => (~ (in @ Y1 @ X1)))))))) @ X3)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f69])).
% 0.20/0.31 thf(f71,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X1)))))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f70])).
% 0.20/0.31 thf(f72,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X1))))))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f71])).
% 0.20/0.31 thf(f73,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (binunion @ X1 @ X3))) => (~ (in @ Y0 @ X1))))) @ X4)))) )),
% 0.20/0.31 inference(pi_proxy_clausification,[],[f72])).
% 0.20/0.31 thf(f74,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((in @ X4 @ X2) => ((~ (in @ X4 @ (binunion @ X1 @ X3))) => (~ (in @ X4 @ X1))))))) )),
% 0.20/0.31 inference(beta-eta_normalization,[],[f73])).
% 0.20/0.31 thf(f75,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($true = (((~ (in @ X4 @ (binunion @ X1 @ X3))) => (~ (in @ X4 @ X1)))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f74])).
% 0.20/0.31 thf(f76,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((~ (in @ X4 @ (binunion @ X1 @ X3))))) | ($true = ((~ (in @ X4 @ X1))))) )),
% 0.20/0.31 inference(imp_proxy_clausification,[],[f75])).
% 0.20/0.31 thf(f77,plain,(
% 0.20/0.31 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($true = ((in @ X4 @ (binunion @ X1 @ X3)))) | ($true = ((~ (in @ X4 @ X1))))) )),
% 0.20/0.31 inference(not_proxy_clausification,[],[f76])).
% 0.20/0.32 thf(f78,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($true = ((in @ X4 @ (binunion @ X1 @ X3)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($false = ((in @ X4 @ X1)))) )),
% 0.20/0.32 inference(not_proxy_clausification,[],[f77])).
% 0.20/0.32 thf(f79,plain,(
% 0.20/0.32 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => ((~ (in @ Y2 @ (setminus @ Y1 @ Y0))) => (in @ Y2 @ Y0))))))))) @ X1)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f48])).
% 0.20/0.32 thf(f80,plain,(
% 0.20/0.32 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ (setminus @ Y0 @ X1))) => (in @ Y1 @ X1))))))))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f79])).
% 0.20/0.32 thf(f81,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => ((~ (in @ Y1 @ (setminus @ Y0 @ X1))) => (in @ Y1 @ X1))))))) @ X2)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f80])).
% 0.20/0.32 thf(f82,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (setminus @ X2 @ X1))) => (in @ Y0 @ X1))))))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f81])).
% 0.20/0.32 thf(f83,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (setminus @ X2 @ X1))) => (in @ Y0 @ X1)))))))) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f82])).
% 0.20/0.32 thf(f84,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((~ (in @ Y0 @ (setminus @ X2 @ X1))) => (in @ Y0 @ X1)))) @ X3)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f83])).
% 0.20/0.32 thf(f85,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | ($true = (((in @ X3 @ X2) => ((~ (in @ X3 @ (setminus @ X2 @ X1))) => (in @ X3 @ X1)))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f84])).
% 0.20/0.32 thf(f86,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | (((in @ X3 @ X2)) = $false) | ($true = (((~ (in @ X3 @ (setminus @ X2 @ X1))) => (in @ X3 @ X1))))) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f85])).
% 0.20/0.32 thf(f87,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (powerset @ X2)))) | (((in @ X3 @ X2)) = $false) | ($false = ((~ (in @ X3 @ (setminus @ X2 @ X1))))) | (((in @ X3 @ X1)) = $true)) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f86])).
% 0.20/0.32 thf(f88,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ (setminus @ X2 @ X1)))) | (((in @ X3 @ X2)) = $false) | ($false = ((in @ X1 @ (powerset @ X2)))) | (((in @ X3 @ X1)) = $true)) )),
% 0.20/0.32 inference(not_proxy_clausification,[],[f87])).
% 0.20/0.32 thf(f89,plain,(
% 0.20/0.32 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))) @ X1)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f47])).
% 0.20/0.32 thf(f90,plain,(
% 0.20/0.32 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ X1) @ (powerset @ Y0)))))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f89])).
% 0.20/0.32 thf(f91,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ X1) @ (powerset @ Y0)))) @ X2)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f90])).
% 0.20/0.32 thf(f92,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (in @ (setminus @ X2 @ X1) @ (powerset @ X2)))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f91])).
% 0.20/0.32 thf(f93,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (setminus @ X2 @ X1) @ (powerset @ X2)))) | ($false = ((in @ X1 @ (powerset @ X2))))) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f92])).
% 0.20/0.32 thf(f94,plain,(
% 0.20/0.32 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setminus @ Y2 @ Y1)) => (~ (in @ Y0 @ Y1)))))))) @ X1)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f46])).
% 0.20/0.32 thf(f95,plain,(
% 0.20/0.32 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setminus @ Y1 @ Y0)) => (~ (in @ X1 @ Y0)))))))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f94])).
% 0.20/0.32 thf(f96,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setminus @ Y1 @ Y0)) => (~ (in @ X1 @ Y0)))))) @ X2)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f95])).
% 0.20/0.32 thf(f97,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setminus @ Y0 @ X2)) => (~ (in @ X1 @ X2)))))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f96])).
% 0.20/0.32 thf(f98,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (setminus @ Y0 @ X2)) => (~ (in @ X1 @ X2)))) @ X3)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f97])).
% 0.20/0.32 thf(f99,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ (setminus @ X3 @ X2)) => (~ (in @ X1 @ X2)))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f98])).
% 0.20/0.32 thf(f100,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setminus @ X3 @ X2)))) | ($true = ((~ (in @ X1 @ X2))))) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f99])).
% 0.20/0.32 thf(f101,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ (setminus @ X3 @ X2)))) | ($false = ((in @ X1 @ X2)))) )),
% 0.20/0.32 inference(not_proxy_clausification,[],[f100])).
% 0.20/0.32 thf(f102,plain,(
% 0.20/0.32 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ Y2) => ((in @ Y0 @ Y1) => (in @ Y0 @ (binintersect @ Y2 @ Y1))))))))) @ X1)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f45])).
% 0.20/0.32 thf(f103,plain,(
% 0.20/0.32 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ X1 @ Y0) => (in @ X1 @ (binintersect @ Y1 @ Y0))))))))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f102])).
% 0.20/0.32 thf(f104,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ Y1) => ((in @ X1 @ Y0) => (in @ X1 @ (binintersect @ Y1 @ Y0))))))) @ X2)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f103])).
% 0.20/0.32 thf(f105,plain,(
% 0.20/0.32 ( ! [X2 : $i,X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ Y0 @ X2))))))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f104])).
% 0.20/0.32 thf(f106,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ Y0) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ Y0 @ X2))))) @ X3)))) )),
% 0.20/0.32 inference(pi_proxy_clausification,[],[f105])).
% 0.20/0.32 thf(f107,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (((in @ X1 @ X3) => ((in @ X1 @ X2) => (in @ X1 @ (binintersect @ X3 @ X2))))))) )),
% 0.20/0.32 inference(beta-eta_normalization,[],[f106])).
% 0.20/0.32 thf(f108,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ X1 @ X3))) | ($true = (((in @ X1 @ X2) => (in @ X1 @ (binintersect @ X3 @ X2)))))) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f107])).
% 0.20/0.32 thf(f109,plain,(
% 0.20/0.32 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X1 @ (binintersect @ X3 @ X2)))) | ($false = ((in @ X1 @ X2))) | ($false = ((in @ X1 @ X3)))) )),
% 0.20/0.32 inference(imp_proxy_clausification,[],[f108])).
% 0.20/0.32 thf(f111,plain,(
% 0.20/0.32 ($true = $false) | ($false = ((in @ sK3 @ (binintersect @ sK1 @ sK2))))),
% 0.20/0.32 inference(constrained_superposition,[],[f41,f101])).
% 0.20/0.32 thf(f112,plain,(
% 0.20/0.32 ($false = ((in @ sK3 @ (binintersect @ sK1 @ sK2))))),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f111])).
% 0.20/0.32 thf(f114,plain,(
% 0.20/0.32 ($true = $false) | ($false = ((in @ sK3 @ sK2))) | ($false = ((in @ sK3 @ sK1)))),
% 0.20/0.32 inference(constrained_superposition,[],[f109,f112])).
% 0.20/0.32 thf(f117,plain,(
% 0.20/0.32 ($false = ((in @ sK3 @ sK2))) | ($false = ((in @ sK3 @ sK1)))),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f114])).
% 0.20/0.32 thf(f119,definition,(
% 0.20/0.32 spl4_1 <=> ($false = ((in @ sK3 @ sK1)))),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.20/0.32 thf(f121,plain,(
% 0.20/0.32 ($false = ((in @ sK3 @ sK1))) | ~spl4_1),
% 0.20/0.32 inference(avatar_component_clause,[],[f119])).
% 0.20/0.32 thf(f123,definition,(
% 0.20/0.32 spl4_2 <=> ($false = ((in @ sK3 @ sK2)))),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.20/0.32 thf(f125,plain,(
% 0.20/0.32 ($false = ((in @ sK3 @ sK2))) | ~spl4_2),
% 0.20/0.32 inference(avatar_component_clause,[],[f123])).
% 0.20/0.32 thf(f127,plain,(
% 0.20/0.32 spl4_1 | spl4_2),
% 0.20/0.32 inference(avatar_split_clause,[],[f117,f123,f119])).
% 0.20/0.32 thf(f132,plain,(
% 0.20/0.32 ($true != $true) | (((in @ sK3 @ (binunion @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ sK2)))) = $false)),
% 0.20/0.32 inference(constrained_superposition,[],[f42,f44])).
% 0.20/0.32 thf(f134,plain,(
% 0.20/0.32 (((in @ sK3 @ (binunion @ (setminus @ sK0 @ sK1) @ (setminus @ sK0 @ sK2)))) = $false)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f132])).
% 0.20/0.32 thf(f151,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ (setminus @ sK0 @ sK2) @ (powerset @ X0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))) | ($false = ((in @ sK3 @ X0))) | ($false = ((in @ sK3 @ (setminus @ sK0 @ sK2))))) )),
% 0.20/0.32 inference(constrained_superposition,[],[f64,f134])).
% 0.20/0.32 thf(f189,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($false = ((in @ (setminus @ sK0 @ sK2) @ (powerset @ X0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))) | ($false = ((in @ sK3 @ X0))) | ($false = ((in @ sK3 @ (setminus @ sK0 @ sK2))))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f151])).
% 0.20/0.32 thf(f192,definition,(
% 0.20/0.32 spl4_3 <=> ($false = ((in @ sK3 @ (setminus @ sK0 @ sK2))))),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition])).
% 0.20/0.32 thf(f194,plain,(
% 0.20/0.32 ($false = ((in @ sK3 @ (setminus @ sK0 @ sK2)))) | ~spl4_3),
% 0.20/0.32 inference(avatar_component_clause,[],[f192])).
% 0.20/0.32 thf(f196,definition,(
% 0.20/0.32 spl4_4 <=> ! [X0 : $i] : (($false = ((in @ (setminus @ sK0 @ sK2) @ (powerset @ X0)))) | ($false = ((in @ sK3 @ X0))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))))),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition])).
% 0.20/0.32 thf(f197,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($false = ((in @ (setminus @ sK0 @ sK2) @ (powerset @ X0)))) | ($false = ((in @ sK3 @ X0))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0))))) ) | ~spl4_4),
% 0.20/0.32 inference(avatar_component_clause,[],[f196])).
% 0.20/0.32 thf(f200,plain,(
% 0.20/0.32 spl4_3 | spl4_4),
% 0.20/0.32 inference(avatar_split_clause,[],[f189,f196,f192])).
% 0.20/0.32 thf(f201,plain,(
% 0.20/0.32 ($true = $false) | (((in @ sK3 @ sK0)) = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK3 @ sK2))) | ~spl4_3),
% 0.20/0.32 inference(constrained_superposition,[],[f194,f88])).
% 0.20/0.32 thf(f206,plain,(
% 0.20/0.32 (((in @ sK3 @ sK0)) = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK3 @ sK2))) | ~spl4_3),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f201])).
% 0.20/0.32 thf(f209,plain,(
% 0.20/0.32 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK3 @ sK2))) | ~spl4_3),
% 0.20/0.32 inference(forward_demodulation,[],[f206,f40])).
% 0.20/0.32 thf(f210,plain,(
% 0.20/0.32 (((in @ sK2 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK3 @ sK2))) | ~spl4_3),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f209])).
% 0.20/0.32 thf(f213,plain,(
% 0.20/0.32 ($true = $false) | ($true = ((in @ sK3 @ sK2))) | ~spl4_3),
% 0.20/0.32 inference(forward_demodulation,[],[f210,f39])).
% 0.20/0.32 thf(f214,plain,(
% 0.20/0.32 ($true = ((in @ sK3 @ sK2))) | ~spl4_3),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f213])).
% 0.20/0.32 thf(f218,plain,(
% 0.20/0.32 ($true = $false) | (~spl4_2 | ~spl4_3)),
% 0.20/0.32 inference(forward_demodulation,[],[f214,f125])).
% 0.20/0.32 thf(f219,plain,(
% 0.20/0.32 $false | (~spl4_2 | ~spl4_3)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f218])).
% 0.20/0.32 thf(f220,plain,(
% 0.20/0.32 ~spl4_2 | ~spl4_3),
% 0.20/0.32 inference(avatar_contradiction_clause,[],[f219])).
% 0.20/0.32 thf(f223,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($true = $false) | ($false = ((in @ (setminus @ sK0 @ sK2) @ (powerset @ X0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))) | ($false = ((in @ sK3 @ X0))) | ($false = ((in @ sK3 @ (setminus @ sK0 @ sK1))))) )),
% 0.20/0.32 inference(constrained_superposition,[],[f78,f134])).
% 0.20/0.32 thf(f267,plain,(
% 0.20/0.32 ( ! [X0 : $i] : (($false = ((in @ (setminus @ sK0 @ sK2) @ (powerset @ X0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ X0)))) | ($false = ((in @ sK3 @ X0))) | ($false = ((in @ sK3 @ (setminus @ sK0 @ sK1))))) )),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f223])).
% 0.20/0.32 thf(f271,definition,(
% 0.20/0.32 spl4_5 <=> ($false = ((in @ sK3 @ (setminus @ sK0 @ sK1))))),
% 0.20/0.32 introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition])).
% 0.20/0.32 thf(f273,plain,(
% 0.20/0.32 ($false = ((in @ sK3 @ (setminus @ sK0 @ sK1)))) | ~spl4_5),
% 0.20/0.32 inference(avatar_component_clause,[],[f271])).
% 0.20/0.32 thf(f276,plain,(
% 0.20/0.32 spl4_5 | spl4_4),
% 0.20/0.32 inference(avatar_split_clause,[],[f267,f196,f271])).
% 0.20/0.32 thf(f320,plain,(
% 0.20/0.32 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK3 @ sK0)) = $false) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ~spl4_4),
% 0.20/0.32 inference(constrained_superposition,[],[f93,f197])).
% 0.20/0.32 thf(f321,plain,(
% 0.20/0.32 (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK3 @ sK0)) = $false) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ~spl4_4),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f320])).
% 0.20/0.32 thf(f324,plain,(
% 0.20/0.32 ($true = $false) | (((in @ sK3 @ sK0)) = $false) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ~spl4_4),
% 0.20/0.32 inference(forward_demodulation,[],[f321,f39])).
% 0.20/0.32 thf(f325,plain,(
% 0.20/0.32 (((in @ sK3 @ sK0)) = $false) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ~spl4_4),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f324])).
% 0.20/0.32 thf(f328,plain,(
% 0.20/0.32 ($true = $false) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ~spl4_4),
% 0.20/0.32 inference(forward_demodulation,[],[f325,f40])).
% 0.20/0.32 thf(f329,plain,(
% 0.20/0.32 ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ~spl4_4),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f328])).
% 0.20/0.32 thf(f334,plain,(
% 0.20/0.32 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_4),
% 0.20/0.32 inference(constrained_superposition,[],[f93,f329])).
% 0.20/0.32 thf(f335,plain,(
% 0.20/0.32 (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_4),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f334])).
% 0.20/0.32 thf(f371,plain,(
% 0.20/0.32 ($true = $false) | ~spl4_4),
% 0.20/0.32 inference(constrained_superposition,[],[f335,f38])).
% 0.20/0.32 thf(f377,plain,(
% 0.20/0.32 $false | ~spl4_4),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f371])).
% 0.20/0.32 thf(f378,plain,(
% 0.20/0.32 ~spl4_4),
% 0.20/0.32 inference(avatar_contradiction_clause,[],[f377])).
% 0.20/0.32 thf(f416,plain,(
% 0.20/0.32 ($true = $false) | (((in @ sK3 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK3 @ sK1))) | ~spl4_5),
% 0.20/0.32 inference(constrained_superposition,[],[f273,f88])).
% 0.20/0.32 thf(f421,plain,(
% 0.20/0.32 (((in @ sK3 @ sK0)) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK3 @ sK1))) | ~spl4_5),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f416])).
% 0.20/0.32 thf(f424,plain,(
% 0.20/0.32 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK3 @ sK1))) | ~spl4_5),
% 0.20/0.32 inference(forward_demodulation,[],[f421,f40])).
% 0.20/0.32 thf(f425,plain,(
% 0.20/0.32 (((in @ sK1 @ (powerset @ sK0))) = $false) | ($true = ((in @ sK3 @ sK1))) | ~spl4_5),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f424])).
% 0.20/0.32 thf(f428,plain,(
% 0.20/0.32 ($true = $false) | ($true = ((in @ sK3 @ sK1))) | ~spl4_5),
% 0.20/0.32 inference(forward_demodulation,[],[f425,f38])).
% 0.20/0.32 thf(f429,plain,(
% 0.20/0.32 ($true = ((in @ sK3 @ sK1))) | ~spl4_5),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f428])).
% 0.20/0.32 thf(f433,plain,(
% 0.20/0.32 ($true = $false) | (~spl4_1 | ~spl4_5)),
% 0.20/0.32 inference(forward_demodulation,[],[f429,f121])).
% 0.20/0.32 thf(f434,plain,(
% 0.20/0.32 $false | (~spl4_1 | ~spl4_5)),
% 0.20/0.32 inference(trivial_inequality_removal,[],[f433])).
% 0.20/0.32 thf(f435,plain,(
% 0.20/0.32 ~spl4_1 | ~spl4_5),
% 0.20/0.32 inference(avatar_contradiction_clause,[],[f434])).
% 0.20/0.32 cnf(s2, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f127])).
% 0.20/0.32 cnf(s5, plain, spl4_3 | spl4_4, inference(sat_conversion,[],[f200])).
% 0.20/0.32 cnf(s7, plain, ~spl4_2 | ~spl4_3, inference(sat_conversion,[],[f220])).
% 0.20/0.32 cnf(s10, plain, spl4_4 | spl4_5, inference(sat_conversion,[],[f276])).
% 0.20/0.32 cnf(s12, plain, ~spl4_4, inference(sat_conversion,[],[f378])).
% 0.20/0.32 cnf(s17, plain, ~spl4_1 | ~spl4_5, inference(sat_conversion,[],[f435])).
% 0.20/0.32 cnf(s18, plain, spl4_5, inference(rat,[],[s10,s12])).
% 0.20/0.32 cnf(s19, plain, ~spl4_1, inference(rat,[],[s17,s18])).
% 0.20/0.32 cnf(s20, plain, spl4_3, inference(rat,[],[s5,s12])).
% 0.20/0.32 cnf(s21, plain, ~spl4_2, inference(rat,[],[s7,s20])).
% 0.20/0.32 cnf(s22, plain, $false, inference(rat,[],[s2,s21,s19])).
% 0.20/0.32 thf(f436,plain,(
% 0.20/0.32 $false),
% 0.20/0.32 inference(avatar_sat_refutation,[],[s22])).
% 0.20/0.32 % SZS output end Proof for theBenchmark
% 0.20/0.32 % (847495)------------------------------
% 0.20/0.32 % (847495)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (847495)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (847495)CaDiCaL version: 2.1.3
% 0.20/0.32 % (847495)Termination reason: Refutation
% 0.20/0.32 % (847495)Time elapsed: 0.026 s
% 0.20/0.32 % (847495)Peak memory usage: 13 MB
% 0.20/0.32 % (847495)Instructions burned: 51 (million)
% 0.20/0.32 % (847487)Success in time 0.074 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------