%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU749^2 : 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 : n004.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 0.35s 0.36s
% Output : Refutation 0.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU749^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n004.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 14:20:32 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.35/0.36 % (1357668)Will run a generic schedule for satisfiability detection.
% 0.35/0.36 % (1357676)dis+10_1_sil=32000:sp=arity:random_seed=1807703535:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.35/0.36 % (1357674)% WARNING: option uhcvi not known.
% 0.35/0.36 % (1357673)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1364866401_2999 on theBenchmark for (2999ds/0Mi)
% 0.35/0.36 % (1357674)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2388757263:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.35/0.36 % (1357675)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2775572480:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.35/0.36 % (1357677)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2122037455:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.35/0.36 % (1357674)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.35/0.36 % (1357677)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.35/0.36 % (1357674)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.35/0.36 % Exception at run slice level
% 0.35/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.35/0.36 % (1357678)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1492286562:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.35/0.36 % (1357679)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1462480433:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.35/0.36 % (1357676)Instruction limit reached!
% 0.35/0.36 % (1357676)------------------------------
% 0.35/0.36 % (1357676)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.36 % (1357676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.36 % (1357676)CaDiCaL version: 2.1.3
% 0.35/0.36 % (1357676)Termination reason: Instruction limit
% 0.35/0.36 % (1357676)Termination phase: Saturation
% 0.35/0.36 % (1357676)Time elapsed: 0.027 s
% 0.35/0.36 % (1357676)Peak memory usage: 12 MB
% 0.35/0.36 % (1357676)Instructions burned: 105 (million)
% 0.35/0.36 % (1357685)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3519344693:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.35/0.36 % Exception at run slice level
% 0.35/0.36 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.35/0.36 % (1357688)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=4084638013:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.35/0.36 % (1357690)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=3926610381:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.35/0.36 % (1357690)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.35/0.36 % (1357690)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.35/0.36 % (1357677)Instruction limit reached!
% 0.35/0.36 % (1357677)------------------------------
% 0.35/0.36 % (1357677)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.36 % (1357677)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.36 % (1357677)CaDiCaL version: 2.1.3
% 0.35/0.36 % (1357677)Termination reason: Instruction limit
% 0.35/0.36 % (1357677)Termination phase: Saturation
% 0.35/0.36 % (1357677)Time elapsed: 0.057 s
% 0.35/0.36 % (1357677)Peak memory usage: 12 MB
% 0.35/0.36 % (1357677)Instructions burned: 116 (million)
% 0.35/0.36 % (1357688)Instruction limit reached!
% 0.35/0.36 % (1357688)------------------------------
% 0.35/0.36 % (1357688)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.36 % (1357688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.36 % (1357688)CaDiCaL version: 2.1.3
% 0.35/0.36 % (1357688)Termination reason: Instruction limit
% 0.35/0.36 % (1357688)Termination phase: Saturation
% 0.35/0.36 % (1357688)Time elapsed: 0.036 s
% 0.35/0.36 % (1357688)Peak memory usage: 12 MB
% 0.35/0.36 % (1357688)Instructions burned: 133 (million)
% 0.35/0.36 % (1357694)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=1841136470:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.35/0.36 % (1357693)ott-21_1_sil=16000:fs=off:random_seed=3516207514:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.35/0.36 % (1357674) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1357668-1357674"...
% 0.35/0.36 % (1357674)...printing done.
% 0.35/0.36 % (1357674)Refutation found. Thanks to Tanya!
% 0.35/0.36 % SZS status Theorem for theBenchmark
% 0.35/0.36 % SZS output start Proof for theBenchmark
% 0.35/0.36 thf(type_def_5, type, sTfun: ($tType * $tType) > $tType).
% 0.35/0.36 thf(func_def_0, type, in: ($i > $i > $o)).
% 0.35/0.36 thf(func_def_1, type, powerset: ($i > $i)).
% 0.35/0.36 thf(func_def_2, type, binunion: ($i > $i > $i)).
% 0.35/0.36 thf(func_def_3, type, setminus: ($i > $i > $i)).
% 0.35/0.36 thf(func_def_4, type, binunionT_lem: $o).
% 0.35/0.36 thf(func_def_6, type, complementT_lem: $o).
% 0.35/0.36 thf(func_def_7, type, powersetTI1: $o).
% 0.35/0.36 thf(func_def_8, type, demorgan2a1: $o).
% 0.35/0.36 thf(func_def_9, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.35/0.36 thf(func_def_10, type, vIMP: ($o > $o > $o)).
% 0.35/0.36 thf(func_def_11, type, db1: !>[X0: $tType]:(X0)).
% 0.35/0.36 thf(func_def_12, type, db0: !>[X0: $tType]:(X0)).
% 0.35/0.36 thf(func_def_13, type, db2: !>[X0: $tType]:(X0)).
% 0.35/0.36 thf(func_def_14, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.35/0.36 thf(func_def_15, type, db3: !>[X0: $tType]:(X0)).
% 0.35/0.36 thf(func_def_21, type, vNOT: ($o > $o)).
% 0.35/0.36 thf(func_def_22, type, sK3: ($i > $i > $i > $i)).
% 0.35/0.36 thf(f1,axiom,(
% 0.35/0.36 (binunionT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))))),
% 0.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionT_lem)).
% 0.35/0.36 thf(f2,axiom,(
% 0.35/0.36 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementT_lem)).
% 0.35/0.36 thf(f3,axiom,(
% 0.35/0.36 (powersetTI1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))))),
% 0.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetTI1)).
% 0.35/0.36 thf(f4,axiom,(
% 0.35/0.36 (demorgan2a1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))))),
% 0.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',demorgan2a1)).
% 0.35/0.36 thf(f5,conjecture,(
% 0.35/0.36 binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1))))))))),
% 0.35/0.36 file('/export/starexec/sandbox/benchmark/theBenchmark.p',complementUnionInPowersetComplement)).
% 0.35/0.36 thf(f6,negated_conjecture,(
% 0.35/0.36 ~(binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))))))))),
% 0.35/0.36 inference(negated_conjecture,[status(cth)],[f5])).
% 0.35/0.36 thf(f7,plain,(
% 0.35/0.36 (binunionT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (binunion @ X1 @ X2) @ (powerset @ X0)))))),
% 0.35/0.36 inference(rectify,[],[f1])).
% 0.35/0.36 thf(f8,plain,(
% 0.35/0.36 (binunionT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binunion @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 0.35/0.36 inference(fool_elimination,[],[f7])).
% 0.35/0.36 thf(f9,plain,(
% 0.35/0.36 (complementT_lem = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (in @ (setminus @ X0 @ X1) @ (powerset @ X0))))),
% 0.35/0.36 inference(rectify,[],[f2])).
% 0.35/0.36 thf(f10,plain,(
% 0.35/0.36 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 0.35/0.36 inference(fool_elimination,[],[f9])).
% 0.35/0.36 thf(f11,plain,(
% 0.35/0.36 (powersetTI1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ X1) => (in @ X3 @ X2))) => (in @ X1 @ (powerset @ X2))))))),
% 0.35/0.36 inference(rectify,[],[f3])).
% 0.35/0.36 thf(f12,plain,(
% 0.35/0.36 (powersetTI1 = ((!! @ $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 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2)))))))))))))),
% 0.35/0.36 inference(fool_elimination,[],[f11])).
% 0.35/0.36 thf(f13,plain,(
% 0.35/0.36 (demorgan2a1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((in @ X3 @ (setminus @ X0 @ (binunion @ X1 @ X2))) => (in @ X3 @ (setminus @ X0 @ X1)))))))),
% 0.35/0.36 inference(rectify,[],[f4])).
% 0.35/0.36 thf(f14,plain,(
% 0.35/0.36 (demorgan2a1 = ((!! @ $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 @ (setminus @ Y1 @ (binunion @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))))))),
% 0.35/0.36 inference(fool_elimination,[],[f13])).
% 0.35/0.36 thf(f15,plain,(
% 0.35/0.36 ~(binunionT_lem => (complementT_lem => (powersetTI1 => (demorgan2a1 => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => (in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))))))))),
% 0.35/0.36 inference(rectify,[],[f6])).
% 0.35/0.36 thf(f16,plain,(
% 0.35/0.36 ~((binunionT_lem = $true) => ((complementT_lem = $true) => ((powersetTI1 = $true) => ((demorgan2a1 = $true) => ! [X0 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X0))) = $true) => ! [X2 : $i] : ((((in @ X2 @ (powerset @ X0))) = $true) => (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true)))))))),
% 0.35/0.36 inference(fool_elimination,[],[f15])).
% 0.35/0.36 thf(f17,plain,(
% 0.35/0.36 (((? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (demorgan2a1 = $true)) & (powersetTI1 = $true)) & (complementT_lem = $true)) & (binunionT_lem = $true)),
% 0.35/0.36 inference(ennf_transformation,[],[f16])).
% 0.35/0.36 thf(f18,plain,(
% 0.35/0.36 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : ((((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) != $true) & (((in @ X2 @ (powerset @ X0))) = $true)) & (((in @ X1 @ (powerset @ X0))) = $true)) & (demorgan2a1 = $true) & (powersetTI1 = $true) & (complementT_lem = $true) & (binunionT_lem = $true)),
% 0.35/0.36 inference(flattening,[],[f17])).
% 0.35/0.36 thf(f19,plain,(
% 0.35/0.36 ((($true != ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ (setminus @ sK0 @ sK1))))) & ($true = ((in @ sK2 @ (powerset @ sK0))))) & ($true = ((in @ sK1 @ (powerset @ sK0))))) & (demorgan2a1 = $true) & (powersetTI1 = $true) & (complementT_lem = $true) & (binunionT_lem = $true)),
% 0.35/0.36 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f18])).
% 0.35/0.36 thf(f20,plain,(
% 0.35/0.36 (binunionT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binunion @ Y0 @ Y2) @ (powerset @ Y1))))))))))))),
% 0.35/0.36 inference(cnf_transformation,[],[f8])).
% 0.35/0.36 thf(f21,plain,(
% 0.35/0.36 (complementT_lem = ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))))),
% 0.35/0.36 inference(cnf_transformation,[],[f10])).
% 0.35/0.36 thf(f22,plain,(
% 0.35/0.36 (powersetTI1 = ((!! @ $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 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2)))))))))))))),
% 0.35/0.36 inference(cnf_transformation,[],[f12])).
% 0.35/0.36 thf(f23,plain,(
% 0.35/0.36 (demorgan2a1 = ((!! @ $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 @ (setminus @ Y1 @ (binunion @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))))))),
% 0.35/0.36 inference(cnf_transformation,[],[f14])).
% 0.35/0.36 thf(f24,plain,(
% 0.35/0.36 (binunionT_lem = $true)),
% 0.35/0.36 inference(cnf_transformation,[],[f19])).
% 0.35/0.36 thf(f25,plain,(
% 0.35/0.36 (complementT_lem = $true)),
% 0.35/0.36 inference(cnf_transformation,[],[f19])).
% 0.35/0.36 thf(f26,plain,(
% 0.35/0.36 (powersetTI1 = $true)),
% 0.35/0.36 inference(cnf_transformation,[],[f19])).
% 0.35/0.36 thf(f27,plain,(
% 0.35/0.36 (demorgan2a1 = $true)),
% 0.35/0.36 inference(cnf_transformation,[],[f19])).
% 0.35/0.36 thf(f28,plain,(
% 0.35/0.36 ($true = ((in @ sK1 @ (powerset @ sK0))))),
% 0.35/0.36 inference(cnf_transformation,[],[f19])).
% 0.35/0.36 thf(f29,plain,(
% 0.35/0.36 ($true = ((in @ sK2 @ (powerset @ sK0))))),
% 0.35/0.36 inference(cnf_transformation,[],[f19])).
% 0.35/0.36 thf(f30,plain,(
% 0.35/0.36 ($true != ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ (setminus @ sK0 @ sK1)))))),
% 0.35/0.36 inference(cnf_transformation,[],[f19])).
% 0.35/0.36 thf(f32,definition,(
% 0.35/0.36 ( ! [X0 : $o] : (($true = X0) | ($false = X0)) )),
% 0.35/0.36 introduced(theory,[fool_exhaustiveness_axiom])).
% 0.35/0.36 thf(f33,plain,(
% 0.35/0.36 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binunion @ Y0 @ Y2) @ (powerset @ Y1))))))))))) = $true)),
% 0.35/0.36 inference(definition_unfolding,[],[f20,f24])).
% 0.35/0.36 thf(f34,plain,(
% 0.35/0.36 (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))))) = $true)),
% 0.35/0.36 inference(definition_unfolding,[],[f21,f25])).
% 0.35/0.36 thf(f35,plain,(
% 0.35/0.36 (((!! @ $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 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2)))))))))))) = $true)),
% 0.35/0.36 inference(definition_unfolding,[],[f22,f26])).
% 0.35/0.36 thf(f36,plain,(
% 0.35/0.36 (((!! @ $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 @ (setminus @ Y1 @ (binunion @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))))) = $true)),
% 0.35/0.36 inference(definition_unfolding,[],[f23,f27])).
% 0.35/0.36 thf(f37,plain,(
% 0.35/0.36 ( ! [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 @ (setminus @ Y1 @ (binunion @ Y0 @ Y2))) => (in @ Y3 @ (setminus @ Y1 @ Y0))))))))))))) @ X1)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f36])).
% 0.35/0.36 thf(f38,plain,(
% 0.35/0.36 ( ! [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 @ (setminus @ Y0 @ (binunion @ X1 @ Y1))) => (in @ Y2 @ (setminus @ Y0 @ X1))))))))))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f37])).
% 0.35/0.36 thf(f39,plain,(
% 0.35/0.36 ( ! [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 @ (setminus @ Y0 @ (binunion @ X1 @ Y1))) => (in @ Y2 @ (setminus @ Y0 @ X1))))))))))) @ X2)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f38])).
% 0.35/0.36 thf(f40,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (setminus @ X2 @ (binunion @ X1 @ Y0))) => (in @ Y1 @ (setminus @ X2 @ X1))))))))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f39])).
% 0.35/0.36 thf(f41,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (setminus @ X2 @ (binunion @ X1 @ Y0))) => (in @ Y1 @ (setminus @ X2 @ X1)))))))))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f40])).
% 0.35/0.36 thf(f42,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ (setminus @ X2 @ (binunion @ X1 @ Y0))) => (in @ Y1 @ (setminus @ X2 @ X1)))))))) @ X3)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f41])).
% 0.35/0.36 thf(f43,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = (((in @ X3 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (in @ Y0 @ (setminus @ X2 @ X1)))))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f42])).
% 0.35/0.36 thf(f44,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (in @ Y0 @ (setminus @ X2 @ X1))))))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f43])).
% 0.35/0.36 thf(f45,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (in @ Y0 @ (setminus @ X2 @ X1))))) @ X4)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f44])).
% 0.35/0.36 thf(f46,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((in @ X4 @ X2) => ((in @ X4 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (in @ X4 @ (setminus @ X2 @ X1))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f45])).
% 0.35/0.36 thf(f47,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | ($true = (((in @ X4 @ (setminus @ X2 @ (binunion @ X1 @ X3))) => (in @ X4 @ (setminus @ X2 @ X1)))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f46])).
% 0.35/0.36 thf(f48,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $i] : (($false = ((in @ X4 @ (setminus @ X2 @ (binunion @ X1 @ X3))))) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((in @ X4 @ X2))) | (((in @ X1 @ (powerset @ X2))) = $false) | ($true = ((in @ X4 @ (setminus @ X2 @ X1))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f47])).
% 0.35/0.36 thf(f49,plain,(
% 0.35/0.36 ( ! [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 @ Y0) => (in @ Y3 @ Y2))))) => (in @ Y0 @ (powerset @ Y2)))))))))) @ X1)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f35])).
% 0.35/0.36 thf(f50,plain,(
% 0.35/0.36 ( ! [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 @ X1) => (in @ Y2 @ Y1))))) => (in @ X1 @ (powerset @ Y1)))))))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f49])).
% 0.35/0.36 thf(f51,plain,(
% 0.35/0.36 ( ! [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 @ X1) => (in @ Y2 @ Y1))))) => (in @ X1 @ (powerset @ Y1)))))))) @ X2)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f50])).
% 0.35/0.36 thf(f52,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))) => (in @ X1 @ (powerset @ Y0)))))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f51])).
% 0.35/0.36 thf(f53,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))) => (in @ X1 @ (powerset @ Y0))))))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f52])).
% 0.35/0.36 thf(f54,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => ((!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X2) => ((in @ Y1 @ X1) => (in @ Y1 @ Y0))))) => (in @ X1 @ (powerset @ Y0))))) @ X3)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f53])).
% 0.35/0.36 thf(f55,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = (((in @ X3 @ (powerset @ X2)) => ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X3))))) => (in @ X1 @ (powerset @ X3))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f54])).
% 0.35/0.36 thf(f56,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($true = (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X3))))) => (in @ X1 @ (powerset @ X3)))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f55])).
% 0.35/0.36 thf(f57,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X3))))))) | ($true = ((in @ X1 @ (powerset @ X3))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f56])).
% 0.35/0.36 thf(f58,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = (((^[Y0 : $i]: ((in @ Y0 @ X2) => ((in @ Y0 @ X1) => (in @ Y0 @ X3)))) @ (sK3 @ X3 @ X1 @ X2)))) | ($true = ((in @ X1 @ (powerset @ X3))))) )),
% 0.35/0.36 inference(sigma_proxy_clausification,[],[f57])).
% 0.35/0.36 thf(f59,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = (((in @ (sK3 @ X3 @ X1 @ X2) @ X2) => ((in @ (sK3 @ X3 @ X1 @ X2) @ X1) => (in @ (sK3 @ X3 @ X1 @ X2) @ X3))))) | ($true = ((in @ X1 @ (powerset @ X3))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f58])).
% 0.35/0.36 thf(f60,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($false = ((in @ X3 @ (powerset @ X2)))) | ($false = (((in @ (sK3 @ X3 @ X1 @ X2) @ X1) => (in @ (sK3 @ X3 @ X1 @ X2) @ X3)))) | ($true = ((in @ X1 @ (powerset @ X3))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f59])).
% 0.35/0.36 thf(f61,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X3 @ X1 @ X2) @ X2))) | ($false = ((in @ X3 @ (powerset @ X2)))) | (((in @ X1 @ (powerset @ X2))) = $false) | ($true = ((in @ X1 @ (powerset @ X3))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f59])).
% 0.35/0.36 thf(f62,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = ((in @ (sK3 @ X3 @ X1 @ X2) @ X3))) | ($false = ((in @ X3 @ (powerset @ X2)))) | (((in @ X1 @ (powerset @ X2))) = $false) | ($true = ((in @ X1 @ (powerset @ X3))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f60])).
% 0.35/0.36 thf(f63,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ (sK3 @ X3 @ X1 @ X2) @ X1))) | ($false = ((in @ X3 @ (powerset @ X2)))) | (((in @ X1 @ (powerset @ X2))) = $false) | ($true = ((in @ X1 @ (powerset @ X3))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f60])).
% 0.35/0.36 thf(f64,plain,(
% 0.35/0.36 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (in @ (setminus @ Y1 @ Y0) @ (powerset @ Y1)))))) @ X1)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f34])).
% 0.35/0.36 thf(f65,plain,(
% 0.35/0.36 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ X1) @ (powerset @ Y0)))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f64])).
% 0.35/0.36 thf(f66,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (in @ (setminus @ Y0 @ X1) @ (powerset @ Y0)))) @ X2)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f65])).
% 0.35/0.36 thf(f67,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (in @ (setminus @ X2 @ X1) @ (powerset @ X2)))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f66])).
% 0.35/0.36 thf(f68,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ (setminus @ X2 @ X1) @ (powerset @ X2)))) | (((in @ X1 @ (powerset @ X2))) = $false)) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f67])).
% 0.35/0.36 thf(f69,plain,(
% 0.35/0.36 ( ! [X1 : $i] : (($true = (((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (powerset @ Y1)) => (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (powerset @ Y1)) => (in @ (binunion @ Y0 @ Y2) @ (powerset @ Y1))))))))) @ X1)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f33])).
% 0.35/0.36 thf(f70,plain,(
% 0.35/0.36 ( ! [X1 : $i] : (($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (binunion @ X1 @ Y1) @ (powerset @ Y0))))))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f69])).
% 0.35/0.36 thf(f71,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : (($true = (((^[Y0 : $i]: ((in @ X1 @ (powerset @ Y0)) => (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (powerset @ Y0)) => (in @ (binunion @ X1 @ Y1) @ (powerset @ Y0))))))) @ X2)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f70])).
% 0.35/0.36 thf(f72,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : (($true = (((in @ X1 @ (powerset @ X2)) => (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (in @ (binunion @ X1 @ Y0) @ (powerset @ X2))))))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f71])).
% 0.35/0.36 thf(f73,plain,(
% 0.35/0.36 ( ! [X2 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = ((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (in @ (binunion @ X1 @ Y0) @ (powerset @ X2)))))))) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f72])).
% 0.35/0.36 thf(f74,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = (((^[Y0 : $i]: ((in @ Y0 @ (powerset @ X2)) => (in @ (binunion @ X1 @ Y0) @ (powerset @ X2)))) @ X3)))) )),
% 0.35/0.36 inference(pi_proxy_clausification,[],[f73])).
% 0.35/0.36 thf(f75,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (powerset @ X2))) = $false) | ($true = (((in @ X3 @ (powerset @ X2)) => (in @ (binunion @ X1 @ X3) @ (powerset @ X2)))))) )),
% 0.35/0.36 inference(beta-eta_normalization,[],[f74])).
% 0.35/0.36 thf(f76,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ (binunion @ X1 @ X3) @ (powerset @ X2)))) | ($false = ((in @ X3 @ (powerset @ X2)))) | (((in @ X1 @ (powerset @ X2))) = $false)) )),
% 0.35/0.36 inference(imp_proxy_clausification,[],[f75])).
% 0.35/0.36 thf(f79,plain,(
% 0.35/0.36 ($true != $true) | (((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ (setminus @ sK0 @ sK1)))) = $false)),
% 0.35/0.36 inference(constrained_superposition,[],[f30,f32])).
% 0.35/0.36 thf(f81,plain,(
% 0.35/0.36 (((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ (setminus @ sK0 @ sK1)))) = $false)),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f79])).
% 0.35/0.36 thf(f106,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true = $false) | ($false = ((in @ X3 @ (powerset @ X1)))) | ($false = ((in @ (sK3 @ X0 @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ X4) @ X1))) | ($false = ((in @ X2 @ (powerset @ X1)))) | ($true = ((in @ (sK3 @ X0 @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ X4) @ (setminus @ X1 @ X2)))) | ($false = ((in @ X0 @ (powerset @ X4)))) | ($false = ((in @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ (powerset @ X4)))) | ($true = ((in @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ (powerset @ X0))))) )),
% 0.35/0.36 inference(constrained_superposition,[],[f48,f63])).
% 0.35/0.36 thf(f107,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (($true = ((in @ (sK3 @ X0 @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ X4) @ (setminus @ X1 @ X2)))) | ($false = ((in @ (sK3 @ X0 @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ X4) @ X1))) | ($false = ((in @ X2 @ (powerset @ X1)))) | ($false = ((in @ X3 @ (powerset @ X1)))) | ($false = ((in @ X0 @ (powerset @ X4)))) | ($false = ((in @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ (powerset @ X4)))) | ($true = ((in @ (setminus @ X1 @ (binunion @ X2 @ X3)) @ (powerset @ X0))))) )),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f106])).
% 0.35/0.36 thf(f165,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)))) | ($false = ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | ($false = ((in @ (sK3 @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0))) | (((in @ X1 @ (powerset @ X0))) = $false) | (((in @ X2 @ (powerset @ X0))) = $false) | ($false = ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)))) | ($false = ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true)) )),
% 0.35/0.36 inference(constrained_superposition,[],[f62,f107])).
% 0.35/0.36 thf(f172,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = $false) | ($false = ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)))) | ($false = ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | ($false = ((in @ (sK3 @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0))) | (((in @ X1 @ (powerset @ X0))) = $false) | (((in @ X2 @ (powerset @ X0))) = $false)) )),
% 0.35/0.36 inference(duplicate_literal_removal,[],[f165])).
% 0.35/0.36 thf(f173,plain,(
% 0.35/0.36 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($false = ((in @ (sK3 @ (setminus @ X0 @ X1) @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ X3) @ X0))) | ($false = ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X3)))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | ($false = ((in @ (setminus @ X0 @ X1) @ (powerset @ X3)))) | (((in @ X1 @ (powerset @ X0))) = $false) | (((in @ X2 @ (powerset @ X0))) = $false)) )),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f172])).
% 0.35/0.36 thf(f250,plain,(
% 0.35/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $false) | ($false = ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | ($false = ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false) | (((in @ X2 @ (powerset @ X0))) = $false)) )),
% 0.35/0.36 inference(constrained_superposition,[],[f61,f173])).
% 0.35/0.36 thf(f257,plain,(
% 0.35/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true = $false) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $false) | ($false = ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | (((in @ X1 @ (powerset @ X0))) = $false) | (((in @ X2 @ (powerset @ X0))) = $false)) )),
% 0.35/0.36 inference(duplicate_literal_removal,[],[f250])).
% 0.35/0.36 thf(f258,plain,(
% 0.35/0.36 ( ! [X2 : $i,X0 : $i,X1 : $i] : ((((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ (setminus @ X0 @ X1)))) = $true) | ($false = ((in @ (setminus @ X0 @ (binunion @ X1 @ X2)) @ (powerset @ X0)))) | (((in @ (setminus @ X0 @ X1) @ (powerset @ X0))) = $false) | (((in @ X1 @ (powerset @ X0))) = $false) | (((in @ X2 @ (powerset @ X0))) = $false)) )),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f257])).
% 0.35/0.36 thf(f386,plain,(
% 0.35/0.36 ($true = $false) | ($false = ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | (((in @ sK1 @ (powerset @ sK0))) = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false)),
% 0.35/0.36 inference(constrained_superposition,[],[f258,f81])).
% 0.35/0.36 thf(f391,plain,(
% 0.35/0.36 ($false = ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | (((in @ sK1 @ (powerset @ sK0))) = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false)),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f386])).
% 0.35/0.36 thf(f396,plain,(
% 0.35/0.36 ($true = $false) | ($false = ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | (((in @ sK2 @ (powerset @ sK0))) = $false)),
% 0.35/0.36 inference(forward_demodulation,[],[f391,f28])).
% 0.35/0.36 thf(f397,plain,(
% 0.35/0.36 ($false = ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | (((in @ sK2 @ (powerset @ sK0))) = $false)),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f396])).
% 0.35/0.36 thf(f402,plain,(
% 0.35/0.36 ($true = $false) | ($false = ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0))))),
% 0.35/0.36 inference(forward_demodulation,[],[f397,f29])).
% 0.35/0.36 thf(f403,plain,(
% 0.35/0.36 ($false = ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ sK0)))) | ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0))))),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f402])).
% 0.35/0.36 thf(f405,definition,(
% 0.35/0.36 spl4_1 <=> ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0))))),
% 0.35/0.36 introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition])).
% 0.35/0.36 thf(f407,plain,(
% 0.35/0.36 ($false = ((in @ (setminus @ sK0 @ sK1) @ (powerset @ sK0)))) | ~spl4_1),
% 0.35/0.36 inference(avatar_component_clause,[],[f405])).
% 0.35/0.36 thf(f409,definition,(
% 0.35/0.36 spl4_2 <=> ($false = ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ sK0))))),
% 0.35/0.36 introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition])).
% 0.35/0.36 thf(f411,plain,(
% 0.35/0.36 ($false = ((in @ (setminus @ sK0 @ (binunion @ sK1 @ sK2)) @ (powerset @ sK0)))) | ~spl4_2),
% 0.35/0.36 inference(avatar_component_clause,[],[f409])).
% 0.35/0.36 thf(f414,plain,(
% 0.35/0.36 spl4_1 | spl4_2),
% 0.35/0.36 inference(avatar_split_clause,[],[f403,f409,f405])).
% 0.35/0.36 thf(f445,plain,(
% 0.35/0.36 ($true = $false) | ($false = ((in @ (binunion @ sK1 @ sK2) @ (powerset @ sK0)))) | ~spl4_2),
% 0.35/0.36 inference(constrained_superposition,[],[f68,f411])).
% 0.35/0.36 thf(f446,plain,(
% 0.35/0.36 ($false = ((in @ (binunion @ sK1 @ sK2) @ (powerset @ sK0)))) | ~spl4_2),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f445])).
% 0.35/0.36 thf(f503,plain,(
% 0.35/0.36 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_2),
% 0.35/0.36 inference(constrained_superposition,[],[f76,f446])).
% 0.35/0.36 thf(f504,plain,(
% 0.35/0.36 (((in @ sK2 @ (powerset @ sK0))) = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_2),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f503])).
% 0.35/0.36 thf(f507,plain,(
% 0.35/0.36 ($true = $false) | (((in @ sK2 @ (powerset @ sK0))) = $false) | ~spl4_2),
% 0.35/0.36 inference(forward_demodulation,[],[f504,f28])).
% 0.35/0.36 thf(f508,plain,(
% 0.35/0.36 (((in @ sK2 @ (powerset @ sK0))) = $false) | ~spl4_2),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f507])).
% 0.35/0.36 thf(f511,plain,(
% 0.35/0.36 ($true = $false) | ~spl4_2),
% 0.35/0.36 inference(constrained_superposition,[],[f508,f29])).
% 0.35/0.36 thf(f517,plain,(
% 0.35/0.36 $false | ~spl4_2),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f511])).
% 0.35/0.36 thf(f518,plain,(
% 0.35/0.36 ~spl4_2),
% 0.35/0.36 inference(avatar_contradiction_clause,[],[f517])).
% 0.35/0.36 thf(f521,plain,(
% 0.35/0.36 ($true = $false) | (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_1),
% 0.35/0.36 inference(constrained_superposition,[],[f68,f407])).
% 0.35/0.36 thf(f522,plain,(
% 0.35/0.36 (((in @ sK1 @ (powerset @ sK0))) = $false) | ~spl4_1),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f521])).
% 0.35/0.36 thf(f527,plain,(
% 0.35/0.36 ($true = $false) | ~spl4_1),
% 0.35/0.36 inference(constrained_superposition,[],[f522,f28])).
% 0.35/0.36 thf(f533,plain,(
% 0.35/0.36 $false | ~spl4_1),
% 0.35/0.36 inference(trivial_inequality_removal,[],[f527])).
% 0.35/0.36 thf(f534,plain,(
% 0.35/0.36 ~spl4_1),
% 0.35/0.36 inference(avatar_contradiction_clause,[],[f533])).
% 0.35/0.36 cnf(s3, plain, spl4_1 | spl4_2, inference(sat_conversion,[],[f414])).
% 0.35/0.36 cnf(s5, plain, ~spl4_2, inference(sat_conversion,[],[f518])).
% 0.35/0.36 cnf(s7, plain, ~spl4_1, inference(sat_conversion,[],[f534])).
% 0.35/0.36 cnf(s8, plain, $false, inference(rat,[],[s3,s5,s7])).
% 0.35/0.36 thf(f535,plain,(
% 0.35/0.36 $false),
% 0.35/0.36 inference(avatar_sat_refutation,[],[s8])).
% 0.35/0.36 % SZS output end Proof for theBenchmark
% 0.35/0.36 % (1357674)------------------------------
% 0.35/0.36 % (1357674)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.35/0.36 % (1357674)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.35/0.36 % (1357674)CaDiCaL version: 2.1.3
% 0.35/0.36 % (1357674)Termination reason: Refutation
% 0.35/0.36 % (1357674)Time elapsed: 0.107 s
% 0.35/0.36 % (1357674)Peak memory usage: 13 MB
% 0.35/0.36 % (1357674)Instructions burned: 178 (million)
% 0.35/0.36 % (1357668)Success in time 0.143 s
% 0.35/0.36 % Vampire exiting
%------------------------------------------------------------------------------