Leo-III---1.8.0.THM-Ref.s

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SEU603^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n003.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 08:28:43 AM UTC 2026

% Result   : Theorem 13.41s 5.28s
% Output   : Refutation 15.31s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SEU603^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.08  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22  % Computer : n003.cluster.edu
% 0.10/0.22  % Model    : x86_64 x86_64
% 0.10/0.22  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22  % Memory   : 8046.5625MB
% 0.10/0.22  % OS       : Linux 6.8.0-71-generic
% 0.10/0.22  % CPULimit : 300
% 0.10/0.22  % WCLimit  : 300
% 0.10/0.22  % DateTime : Tue Sep 29 13:58:43 UTC 2026
% 0.10/0.23  % CPUTime  : 
% 0.10/0.23  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.02/0.86  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.15/1.22  % [INFO] 	 Parsing done (360ms). 
% 2.15/1.24  % [INFO] 	 Running in sequential loop mode. 
% 2.97/1.63  % [INFO] 	 eprover registered as external prover. 
% 2.97/1.64  % [INFO] 	 Scanning for conjecture ... 
% 4.05/2.05  % [INFO] 	 Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ... 
% 4.47/2.14  % [INFO] 	 Axiom selection finished. Selected 0 axioms (removed 0 axioms). 
% 4.47/2.15  % [INFO] 	 Problem is higher-order (TPTP THF). 
% 4.47/2.15  % [INFO] 	 Type checking passed. 
% 4.47/2.16  % [CONFIG] 	 Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>.  Searching for refutation ... 
% 13.41/5.27  % [INFO] 	 Killing All external provers ... 
% 13.41/5.27  % Time passed: 4907ms (effective reasoning time: 4024ms)
% 13.41/5.27  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.41/5.27  % Axioms used in derivation (0): 
% 13.41/5.27  % No. of inferences in proof: 15
% 13.41/5.28  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4907 ms resp. 4024 ms w/o parsing
% 15.31/5.61  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.31/5.61  thf(in_decl, type, in: ($i > ($i > $o))).
% 15.31/5.61  thf(exu_decl, type, exu: (($i > $o) > $o)).
% 15.31/5.61  thf(setextAx_decl, type, setextAx: $o).
% 15.31/5.61  thf(emptyset_decl, type, emptyset: $i).
% 15.31/5.61  thf(emptysetAx_decl, type, emptysetAx: $o).
% 15.31/5.61  thf(setadjoin_decl, type, setadjoin: ($i > ($i > $i))).
% 15.31/5.61  thf(setadjoinAx_decl, type, setadjoinAx: $o).
% 15.31/5.61  thf(powerset_decl, type, powerset: ($i > $i)).
% 15.31/5.61  thf(powersetAx_decl, type, powersetAx: $o).
% 15.31/5.61  thf(setunion_decl, type, setunion: ($i > $i)).
% 15.31/5.61  thf(setunionAx_decl, type, setunionAx: $o).
% 15.31/5.61  thf(omega_decl, type, omega: $i).
% 15.31/5.61  thf(omega0Ax_decl, type, omega0Ax: $o).
% 15.31/5.61  thf(omegaSAx_decl, type, omegaSAx: $o).
% 15.31/5.61  thf(omegaIndAx_decl, type, omegaIndAx: $o).
% 15.31/5.61  thf(replAx_decl, type, replAx: $o).
% 15.31/5.61  thf(foundationAx_decl, type, foundationAx: $o).
% 15.31/5.61  thf(wellorderingAx_decl, type, wellorderingAx: $o).
% 15.31/5.61  thf(descr_decl, type, descr: (($i > $o) > $i)).
% 15.31/5.61  thf(descrp_decl, type, descrp: $o).
% 15.31/5.61  thf(dsetconstr_decl, type, dsetconstr: ($i > (($i > $o) > $i))).
% 15.31/5.61  thf(dsetconstrI_decl, type, dsetconstrI: $o).
% 15.31/5.61  thf(dsetconstrEL_decl, type, dsetconstrEL: $o).
% 15.31/5.61  thf(dsetconstrER_decl, type, dsetconstrER: $o).
% 15.31/5.61  thf(exuE1_decl, type, exuE1: $o).
% 15.31/5.61  thf(prop2set_decl, type, prop2set: ($o > $i)).
% 15.31/5.61  thf(prop2setE_decl, type, prop2setE: $o).
% 15.31/5.61  thf(emptysetE_decl, type, emptysetE: $o).
% 15.31/5.61  thf(emptysetimpfalse_decl, type, emptysetimpfalse: $o).
% 15.31/5.61  thf(notinemptyset_decl, type, notinemptyset: $o).
% 15.31/5.61  thf(exuE3e_decl, type, exuE3e: $o).
% 15.31/5.61  thf(setext_decl, type, setext: $o).
% 15.31/5.61  thf(emptyI_decl, type, emptyI: $o).
% 15.31/5.61  thf(noeltsimpempty_decl, type, noeltsimpempty: $o).
% 15.31/5.61  thf(setbeta_decl, type, setbeta: $o).
% 15.31/5.61  thf(nonempty_decl, type, nonempty: ($i > $o)).
% 15.31/5.61  thf(nonemptyE1_decl, type, nonemptyE1: $o).
% 15.31/5.61  thf(nonemptyI_decl, type, nonemptyI: $o).
% 15.31/5.61  thf(nonemptyI1_decl, type, nonemptyI1: $o).
% 15.31/5.61  thf(setadjoinIL_decl, type, setadjoinIL: $o).
% 15.31/5.61  thf(emptyinunitempty_decl, type, emptyinunitempty: $o).
% 15.31/5.61  thf(setadjoinIR_decl, type, setadjoinIR: $o).
% 15.31/5.61  thf(setadjoinE_decl, type, setadjoinE: $o).
% 15.31/5.61  thf(setadjoinOr_decl, type, setadjoinOr: $o).
% 15.31/5.61  thf(setoftrueEq_decl, type, setoftrueEq: $o).
% 15.31/5.61  thf(powersetI_decl, type, powersetI: $o).
% 15.31/5.61  thf(emptyinPowerset_decl, type, emptyinPowerset: $o).
% 15.31/5.61  thf(emptyInPowerset_decl, type, emptyInPowerset: $o).
% 15.31/5.61  thf(powersetE_decl, type, powersetE: $o).
% 15.31/5.61  thf(setunionI_decl, type, setunionI: $o).
% 15.31/5.61  thf(setunionE_decl, type, setunionE: $o).
% 15.31/5.61  thf(subPowSU_decl, type, subPowSU: $o).
% 15.31/5.61  thf(exuE2_decl, type, exuE2: $o).
% 15.31/5.61  thf(nonemptyImpWitness_decl, type, nonemptyImpWitness: $o).
% 15.31/5.61  thf(uniqinunit_decl, type, uniqinunit: $o).
% 15.31/5.61  thf(notinsingleton_decl, type, notinsingleton: $o).
% 15.31/5.61  thf(eqinunit_decl, type, eqinunit: $o).
% 15.31/5.61  thf(singletonsswitch_decl, type, singletonsswitch: $o).
% 15.31/5.61  thf(upairsetE_decl, type, upairsetE: $o).
% 15.31/5.61  thf(upairsetIL_decl, type, upairsetIL: $o).
% 15.31/5.61  thf(upairsetIR_decl, type, upairsetIR: $o).
% 15.31/5.61  thf(emptyE1_decl, type, emptyE1: $o).
% 15.31/5.61  thf(vacuousDall_decl, type, vacuousDall: $o).
% 15.31/5.61  thf(quantDeMorgan1_decl, type, quantDeMorgan1: $o).
% 15.31/5.61  thf(quantDeMorgan2_decl, type, quantDeMorgan2: $o).
% 15.31/5.61  thf(quantDeMorgan3_decl, type, quantDeMorgan3: $o).
% 15.31/5.61  thf(quantDeMorgan4_decl, type, quantDeMorgan4: $o).
% 15.31/5.61  thf(prop2setI_decl, type, prop2setI: $o).
% 15.31/5.61  thf(set2prop_decl, type, set2prop: ($i > $o)).
% 15.31/5.61  thf(prop2set2propI_decl, type, prop2set2propI: $o).
% 15.31/5.61  thf(notdexE_decl, type, notdexE: $o).
% 15.31/5.61  thf(notdallE_decl, type, notdallE: $o).
% 15.31/5.61  thf(exuI1_decl, type, exuI1: $o).
% 15.31/5.61  thf(exuI3_decl, type, exuI3: $o).
% 15.31/5.61  thf(exuI2_decl, type, exuI2: $o).
% 15.31/5.61  thf(inCongP_decl, type, inCongP: $o).
% 15.31/5.61  thf(in__Cong_decl, type, in__Cong: $o).
% 15.31/5.61  thf(exuE3u_decl, type, exuE3u: $o).
% 15.31/5.61  thf(exu__Cong_decl, type, exu__Cong: $o).
% 15.31/5.61  thf(emptyset__Cong_decl, type, emptyset__Cong: $o).
% 15.31/5.61  thf(setadjoin__Cong_decl, type, setadjoin__Cong: $o).
% 15.31/5.61  thf(powerset__Cong_decl, type, powerset__Cong: $o).
% 15.31/5.61  thf(setunion__Cong_decl, type, setunion__Cong: $o).
% 15.31/5.61  thf(omega__Cong_decl, type, omega__Cong: $o).
% 15.31/5.61  thf(exuEu_decl, type, exuEu: $o).
% 15.31/5.61  thf(descr__Cong_decl, type, descr__Cong: $o).
% 15.31/5.61  thf(dsetconstr__Cong_decl, type, dsetconstr__Cong: $o).
% 15.31/5.61  thf(subset_decl, type, subset: ($i > ($i > $o))).
% 15.31/5.61  thf(subsetI1_decl, type, subsetI1: $o).
% 15.31/5.61  thf(eqimpsubset2_decl, type, eqimpsubset2: $o).
% 15.31/5.61  thf(eqimpsubset1_decl, type, eqimpsubset1: $o).
% 15.31/5.61  thf(subsetI2_decl, type, subsetI2: $o).
% 15.31/5.61  thf(emptysetsubset_decl, type, emptysetsubset: $o).
% 15.31/5.61  thf(subsetE_decl, type, subsetE: $o).
% 15.31/5.61  thf(subsetE2_decl, type, subsetE2: $o).
% 15.31/5.61  thf(notsubsetI_decl, type, notsubsetI: $o).
% 15.31/5.61  thf(notequalI1_decl, type, notequalI1: $o).
% 15.31/5.61  thf(notequalI2_decl, type, notequalI2: $o).
% 15.31/5.61  thf(subsetRefl_decl, type, subsetRefl: $o).
% 15.31/5.61  thf(subsetTrans_decl, type, subsetTrans: $o).
% 15.31/5.61  thf(setadjoinSub_decl, type, setadjoinSub: $o).
% 15.31/5.61  thf(setadjoinSub2_decl, type, setadjoinSub2: $o).
% 15.31/5.61  thf(subset2powerset_decl, type, subset2powerset: $o).
% 15.31/5.61  thf(setextsub_decl, type, setextsub: $o).
% 15.31/5.61  thf(subsetemptysetimpeq_decl, type, subsetemptysetimpeq: $o).
% 15.31/5.61  thf(powersetI1_decl, type, powersetI1: $o).
% 15.31/5.61  thf(powersetE1_decl, type, powersetE1: $o).
% 15.31/5.61  thf(inPowerset_decl, type, inPowerset: $o).
% 15.31/5.61  thf(powersetsubset_decl, type, powersetsubset: $o).
% 15.31/5.61  thf(sepInPowerset_decl, type, sepInPowerset: $o).
% 15.31/5.61  thf(sepSubset_decl, type, sepSubset: $o).
% 15.31/5.61  thf(binunion_decl, type, binunion: ($i > ($i > $i))).
% 15.31/5.61  thf(binunionIL_decl, type, binunionIL: $o).
% 15.31/5.61  thf(upairset2IR_decl, type, upairset2IR: $o).
% 15.31/5.61  thf(binunionIR_decl, type, binunionIR: $o).
% 15.31/5.61  thf(binunionEcases_decl, type, binunionEcases: $o).
% 15.31/5.61  thf(binunionE_decl, type, binunionE: $o).
% 15.31/5.61  thf(binunionLsub_decl, type, binunionLsub: $o).
% 15.31/5.61  thf(binunionRsub_decl, type, binunionRsub: $o).
% 15.31/5.61  thf(binintersect_decl, type, binintersect: ($i > ($i > $i))).
% 15.31/5.61  thf(binintersectI_decl, type, binintersectI: $o).
% 15.31/5.61  thf(binintersectSubset5_decl, type, binintersectSubset5: $o).
% 15.31/5.61  thf(binintersectEL_decl, type, binintersectEL: $o).
% 15.31/5.61  thf(binintersectLsub_decl, type, binintersectLsub: $o).
% 15.31/5.61  thf(binintersectSubset2_decl, type, binintersectSubset2: $o).
% 15.31/5.61  thf(binintersectSubset3_decl, type, binintersectSubset3: $o).
% 15.31/5.61  thf(binintersectER_decl, type, binintersectER: $o).
% 15.31/5.61  thf(disjointsetsI1_decl, type, disjointsetsI1: $o).
% 15.31/5.61  thf(binintersectRsub_decl, type, binintersectRsub: $o).
% 15.31/5.61  thf(binintersectSubset4_decl, type, binintersectSubset4: $o).
% 15.31/5.61  thf(binintersectSubset1_decl, type, binintersectSubset1: $o).
% 15.31/5.61  thf(bs114d_decl, type, bs114d: $o).
% 15.31/5.61  thf(setminus_decl, type, setminus: ($i > ($i > $i))).
% 15.31/5.61  thf(setminusI_decl, type, setminusI: $o).
% 15.31/5.61  thf(setminusEL_decl, type, setminusEL: $o).
% 15.31/5.61  thf(sk1_decl, type, sk1: ($i > ($i > $i))).
% 15.31/5.61  thf(sk2_decl, type, sk2: ($i > $i)).
% 15.31/5.61  thf(sk3_decl, type, sk3: ($i > (($i > ($i > $o)) > $i))).
% 15.31/5.61  thf(sk4_decl, type, sk4: ($i > ($i > (($i > ($i > $o)) > $i)))).
% 15.31/5.61  thf(sk5_decl, type, sk5: ($i > (($i > ($i > $o)) > $i))).
% 15.31/5.61  thf(sk6_decl, type, sk6: ($i > $i)).
% 15.31/5.61  thf(sk7_decl, type, sk7: ($i > $i)).
% 15.31/5.61  thf(sk8_decl, type, sk8: ($i > ($i > ($i > $i)))).
% 15.31/5.61  thf(sk9_decl, type, sk9: ($i > ($i > $o))).
% 15.31/5.61  thf(sk10_decl, type, sk10: ($i > ($i > $i))).
% 15.31/5.61  thf(sk11_decl, type, sk11: ($i > ($i > $i))).
% 15.31/5.61  thf(sk12_decl, type, sk12: ($i > ($i > $i))).
% 15.31/5.61  thf(sk13_decl, type, sk13: ($i > (($i > $o) > $i))).
% 15.31/5.61  thf(sk14_decl, type, sk14: ($i > (($i > $o) > $i))).
% 15.31/5.61  thf(sk15_decl, type, sk15: (($i > $o) > $i)).
% 15.31/5.61  thf(sk16_decl, type, sk16: ($i > ($i > $i))).
% 15.31/5.61  thf(sk17_decl, type, sk17: ($i > ($i > $i))).
% 15.31/5.61  thf(sk18_decl, type, sk18: ($i > $i)).
% 15.31/5.61  thf(sk19_decl, type, sk19: ($i > $i)).
% 15.31/5.61  thf(sk20_decl, type, sk20: ($i > $i)).
% 15.31/5.61  thf(sk21_decl, type, sk21: ($i > ($i > $i))).
% 15.31/5.61  thf(sk22_decl, type, sk22: ($o > ($i > ($i > $i)))).
% 15.31/5.61  thf(sk23_decl, type, sk23: ($i > (($i > $o) > $i))).
% 15.31/5.61  thf(sk24_decl, type, sk24: (($i > $o) > $i)).
% 15.31/5.61  thf(sk25_decl, type, sk25: ($i > $i)).
% 15.31/5.61  thf(sk26_decl, type, sk26: (($i > $o) > ($i > $i))).
% 15.31/5.61  thf(sk27_decl, type, sk27: (($i > $o) > ($i > $i))).
% 15.31/5.61  thf(sk28_decl, type, sk28: (($i > $o) > ($i > $i))).
% 15.31/5.61  thf(sk29_decl, type, sk29: (($i > $o) > ($i > $i))).
% 15.31/5.61  thf(sk30_decl, type, sk30: (($i > $o) > ($i > $i))).
% 15.31/5.61  thf(sk31_decl, type, sk31: (($i > $o) > ($i > $i))).
% 15.31/5.61  thf(sk32_decl, type, sk32: (($i > $o) > $i)).
% 15.31/5.61  thf(sk33_decl, type, sk33: (($i > $o) > $i)).
% 15.31/5.61  thf(sk34_decl, type, sk34: (($i > $o) > $i)).
% 15.31/5.61  thf(sk35_decl, type, sk35: ($i > (($i > $o) > $i))).
% 15.31/5.61  thf(sk36_decl, type, sk36: (($i > $o) > $i)).
% 15.31/5.61  thf(sk37_decl, type, sk37: ($i > (($i > $o) > $i))).
% 15.31/5.61  thf(sk38_decl, type, sk38: (($i > $o) > (($i > $o) > $i))).
% 15.31/5.61  thf(sk39_decl, type, sk39: (($i > $o) > (($i > $o) > $i))).
% 15.31/5.61  thf(sk40_decl, type, sk40: ($i > (($i > $o) > $i))).
% 15.31/5.61  thf(sk41_decl, type, sk41: (($i > $o) > (($i > $o) > $o))).
% 15.31/5.61  thf(sk42_decl, type, sk42: (($i > $o) > (($i > $o) > $i))).
% 15.31/5.61  thf(sk43_decl, type, sk43: (($i > $o) > (($i > $o) > $i))).
% 15.31/5.61  thf(sk44_decl, type, sk44: ($i > (($i > $o) > (($i > $o) > $i)))).
% 15.31/5.61  thf(sk45_decl, type, sk45: ($i > (($i > $o) > (($i > $o) > $i)))).
% 15.31/5.61  thf(sk46_decl, type, sk46: (($i > $o) > (($i > $o) > ($i > ($i > $i))))).
% 15.31/5.61  thf(sk47_decl, type, sk47: (($i > $o) > (($i > $o) > ($i > ($i > $i))))).
% 15.31/5.61  thf(sk48_decl, type, sk48: ($i > ($i > $i))).
% 15.31/5.61  thf(sk49_decl, type, sk49: ($i > ($i > $i))).
% 15.31/5.61  thf(sk50_decl, type, sk50: ($i > ($i > $i))).
% 15.31/5.61  thf(sk51_decl, type, sk51: $i).
% 15.31/5.61  thf(sk52_decl, type, sk52: $i).
% 15.31/5.61  thf(sk53_decl, type, sk53: $i).
% 15.31/5.61  thf(exu_def, definition, exu = (^ [A:($i > $o)]: ? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) ).
% 15.31/5.61  thf(setextAx_def, definition, setextAx = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) ).
% 15.31/5.61  thf(emptysetAx_def, definition, emptysetAx = (! [A:$i]: ~ (in @ A @ emptyset)) ).
% 15.31/5.61  thf(setadjoinAx_def, definition, setadjoinAx = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))) ).
% 15.31/5.61  thf(powersetAx_def, definition, powersetAx = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) ).
% 15.31/5.61  thf(setunionAx_def, definition, setunionAx = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))) ).
% 15.31/5.61  thf(omega0Ax_def, definition, omega0Ax = (in @ emptyset @ omega) ).
% 15.31/5.61  thf(omegaSAx_def, definition, omegaSAx = (! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))) ).
% 15.31/5.61  thf(omegaIndAx_def, definition, omegaIndAx = (! [A:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))) ).
% 15.31/5.61  thf(replAx_def, definition, replAx = (! [A:($i > ($i > $o)),B:$i]: ((! [C:$i]: ((in @ C @ B) => (exu @ (A @ C)))) => (? [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ B) & (A @ E @ D))))))) ).
% 15.31/5.61  thf(foundationAx_def, definition, foundationAx = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))) ).
% 15.31/5.61  thf(wellorderingAx_def, definition, wellorderingAx = (! [A:$i]: ? [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i,E:$i]: ((in @ D @ B) & (in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F)))))))) ).
% 15.31/5.61  thf(descrp_def, definition, descrp = (! [A:($i > $o)]: ((exu @ (A)) => (A @ (descr @ (A))))) ).
% 15.31/5.61  thf(dsetconstrI_def, definition, dsetconstrI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))) ).
% 15.31/5.61  thf(dsetconstrEL_def, definition, dsetconstrEL = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))) ).
% 15.31/5.61  thf(dsetconstrER_def, definition, dsetconstrER = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))) ).
% 15.31/5.61  thf(exuE1_def, definition, exuE1 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))) ).
% 15.31/5.61  thf(prop2setE_def, definition, prop2setE = (! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))) ).
% 15.31/5.61  thf(emptysetE_def, definition, emptysetE = (! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))) ).
% 15.31/5.61  thf(emptysetimpfalse_def, definition, emptysetimpfalse = (! [A:$i]: ((in @ A @ emptyset) => (($false)))) ).
% 15.31/5.61  thf(notinemptyset_def, definition, notinemptyset = (! [A:$i]: ~ (in @ A @ emptyset)) ).
% 15.31/5.61  thf(exuE3e_def, definition, exuE3e = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: (A @ B)))) ).
% 15.31/5.61  thf(setext_def, definition, setext = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))) ).
% 15.31/5.61  thf(emptyI_def, definition, emptyI = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) ).
% 15.31/5.61  thf(noeltsimpempty_def, definition, noeltsimpempty = (! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) ).
% 15.31/5.61  thf(setbeta_def, definition, setbeta = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))) ).
% 15.31/5.61  thf(nonempty_def, definition, nonempty = (^ [A:$i]: (A != emptyset)) ).
% 15.31/5.61  thf(nonemptyE1_def, definition, nonemptyE1 = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: (in @ B @ A)))) ).
% 15.31/5.61  thf(nonemptyI_def, definition, nonemptyI = (! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (nonempty @ (dsetconstr @ A @ (B)))))) ).
% 15.31/5.61  thf(nonemptyI1_def, definition, nonemptyI1 = (! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (nonempty @ A))) ).
% 15.31/5.61  thf(setadjoinIL_def, definition, setadjoinIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))) ).
% 15.31/5.61  thf(emptyinunitempty_def, definition, emptyinunitempty = (in @ emptyset @ (setadjoin @ emptyset @ emptyset)) ).
% 15.31/5.61  thf(setadjoinIR_def, definition, setadjoinIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))) ).
% 15.31/5.61  thf(setadjoinE_def, definition, setadjoinE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) ).
% 15.31/5.61  thf(setadjoinOr_def, definition, setadjoinOr = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))) ).
% 15.31/5.61  thf(setoftrueEq_def, definition, setoftrueEq = (! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: (($true)))) = A)) ).
% 15.31/5.61  thf(powersetI_def, definition, powersetI = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))) ).
% 15.31/5.61  thf(emptyinPowerset_def, definition, emptyinPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))) ).
% 15.31/5.61  thf(emptyInPowerset_def, definition, emptyInPowerset = (! [A:$i]: (in @ emptyset @ (powerset @ A))) ).
% 15.31/5.61  thf(powersetE_def, definition, powersetE = (! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))) ).
% 15.31/5.61  thf(setunionI_def, definition, setunionI = (! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))) ).
% 15.31/5.61  thf(setunionE_def, definition, setunionE = (! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))) ).
% 15.31/5.61  thf(subPowSU_def, definition, subPowSU = (! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))) ).
% 15.31/5.61  thf(exuE2_def, definition, exuE2 = (! [A:($i > $o)]: ((exu @ (A)) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))) ).
% 15.31/5.61  thf(nonemptyImpWitness_def, definition, nonemptyImpWitness = (! [A:$i]: ((nonempty @ A) => (? [B:$i]: ((in @ B @ A) & (($true)))))) ).
% 15.31/5.61  thf(uniqinunit_def, definition, uniqinunit = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))) ).
% 15.31/5.61  thf(notinsingleton_def, definition, notinsingleton = (! [A:$i,B:$i]: ((A != B) => (~ (in @ B @ (setadjoin @ A @ emptyset))))) ).
% 15.31/5.61  thf(eqinunit_def, definition, eqinunit = (! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))) ).
% 15.31/5.61  thf(singletonsswitch_def, definition, singletonsswitch = (! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))) ).
% 15.31/5.61  thf(upairsetE_def, definition, upairsetE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) ).
% 15.31/5.61  thf(upairsetIL_def, definition, upairsetIL = (! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) ).
% 15.31/5.61  thf(upairsetIR_def, definition, upairsetIR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) ).
% 15.31/5.61  thf(emptyE1_def, definition, emptyE1 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (((dsetconstr @ A @ (B)) = emptyset) => (($false))))) ).
% 15.31/5.61  thf(vacuousDall_def, definition, vacuousDall = (! [A:($i > $o),B:$i]: ((in @ B @ emptyset) => (A @ B))) ).
% 15.31/5.61  thf(quantDeMorgan1_def, definition, quantDeMorgan1 = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))) ).
% 15.31/5.61  thf(quantDeMorgan2_def, definition, quantDeMorgan2 = (! [A:$i,B:($i > $o)]: ((! [C:$i]: ((in @ C @ A) => (~ (B @ C)))) => (~ (? [C:$i]: ((in @ C @ A) & (B @ C)))))) ).
% 15.31/5.61  thf(quantDeMorgan3_def, definition, quantDeMorgan3 = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) ).
% 15.31/5.61  thf(quantDeMorgan4_def, definition, quantDeMorgan4 = (! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & ~ (B @ C))) => (~ (! [C:$i]: ((in @ C @ A) => (B @ C)))))) ).
% 15.31/5.61  thf(prop2setI_def, definition, prop2setI = (! [A:$o]: ((A) => (in @ emptyset @ (prop2set @ A)))) ).
% 15.31/5.61  thf(prop2set2propI_def, definition, prop2set2propI = (! [A:$o]: ((A) => (set2prop @ (prop2set @ A)))) ).
% 15.31/5.61  thf(notdexE_def, definition, notdexE = (! [A:$i,B:($i > $o)]: ((~ (? [C:$i]: ((in @ C @ A) & (B @ C)))) => (! [C:$i]: ((in @ C @ A) => (~ (B @ C)))))) ).
% 15.31/5.61  thf(notdallE_def, definition, notdallE = (! [A:$i,B:($i > $o)]: ((~ (! [C:$i]: ((in @ C @ A) => (B @ C)))) => (? [C:$i]: ((in @ C @ A) & ~ (B @ C))))) ).
% 15.31/5.61  thf(exuI1_def, definition, exuI1 = (! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (exu @ (A)))) ).
% 15.31/5.61  thf(exuI3_def, definition, exuI3 = (! [A:($i > $o)]: ((? [B:$i]: (A @ B)) => ((! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))) => (exu @ (A))))) ).
% 15.31/5.61  thf(exuI2_def, definition, exuI2 = (! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (exu @ (A)))) ).
% 15.31/5.61  thf(inCongP_def, definition, inCongP = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))) ).
% 15.31/5.61  thf(in__Cong_def, definition, in__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))) ).
% 15.31/5.61  thf(exuE3u_def, definition, exuE3u = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))) ).
% 15.31/5.61  thf(exu__Cong_def, definition, exu__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) = (exu @ (B))))) ).
% 15.31/5.61  thf(emptyset__Cong_def, definition, emptyset__Cong = (emptyset = emptyset) ).
% 15.31/5.61  thf(setadjoin__Cong_def, definition, setadjoin__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))) ).
% 15.31/5.61  thf(powerset__Cong_def, definition, powerset__Cong = (! [A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))) ).
% 15.31/5.61  thf(setunion__Cong_def, definition, setunion__Cong = (! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))) ).
% 15.31/5.61  thf(omega__Cong_def, definition, omega__Cong = (omega = omega) ).
% 15.31/5.61  thf(exuEu_def, definition, exuEu = (! [A:($i > $o)]: ((exu @ (A)) => (! [B:$i,C:$i]: ((A @ B) => ((A @ C) => (B = C)))))) ).
% 15.31/5.61  thf(descr__Cong_def, definition, descr__Cong = (! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((exu @ (A)) => ((exu @ (B)) => ((descr @ (A)) = (descr @ (B))))))) ).
% 15.31/5.61  thf(dsetconstr__Cong_def, definition, dsetconstr__Cong = (! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))) ).
% 15.31/5.61  thf(subsetI1_def, definition, subsetI1 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) ).
% 15.31/5.61  thf(eqimpsubset2_def, definition, eqimpsubset2 = (! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))) ).
% 15.31/5.61  thf(eqimpsubset1_def, definition, eqimpsubset1 = (! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))) ).
% 15.31/5.61  thf(subsetI2_def, definition, subsetI2 = (! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) ).
% 15.31/5.61  thf(emptysetsubset_def, definition, emptysetsubset = (! [A:$i]: (subset @ emptyset @ A)) ).
% 15.31/5.61  thf(subsetE_def, definition, subsetE = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((in @ C @ A) => (in @ C @ B)))) ).
% 15.31/5.61  thf(subsetE2_def, definition, subsetE2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((~ (in @ C @ B)) => (~ (in @ C @ A))))) ).
% 15.31/5.61  thf(notsubsetI_def, definition, notsubsetI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))) ).
% 15.31/5.61  thf(notequalI1_def, definition, notequalI1 = (! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (A != B))) ).
% 15.31/5.61  thf(notequalI2_def, definition, notequalI2 = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (A != B)))) ).
% 15.31/5.61  thf(subsetRefl_def, definition, subsetRefl = (! [A:$i]: (subset @ A @ A)) ).
% 15.31/5.61  thf(subsetTrans_def, definition, subsetTrans = (! [A:$i,B:$i,C:$i]: ((subset @ A @ B) => ((subset @ B @ C) => (subset @ A @ C)))) ).
% 15.31/5.61  thf(setadjoinSub_def, definition, setadjoinSub = (! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))) ).
% 15.31/5.61  thf(setadjoinSub2_def, definition, setadjoinSub2 = (! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))) ).
% 15.31/5.61  thf(subset2powerset_def, definition, subset2powerset = (! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))) ).
% 15.31/5.61  thf(setextsub_def, definition, setextsub = (! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))) ).
% 15.31/5.61  thf(subsetemptysetimpeq_def, definition, subsetemptysetimpeq = (! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))) ).
% 15.31/5.61  thf(powersetI1_def, definition, powersetI1 = (! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))) ).
% 15.31/5.61  thf(powersetE1_def, definition, powersetE1 = (! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))) ).
% 15.31/5.61  thf(inPowerset_def, definition, inPowerset = (! [A:$i]: (in @ A @ (powerset @ A))) ).
% 15.31/5.61  thf(powersetsubset_def, definition, powersetsubset = (! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))) ).
% 15.31/5.61  thf(sepInPowerset_def, definition, sepInPowerset = (! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))) ).
% 15.31/5.61  thf(sepSubset_def, definition, sepSubset = (! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)) ).
% 15.31/5.61  thf(binunionIL_def, definition, binunionIL = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B)))) ).
% 15.31/5.61  thf(upairset2IR_def, definition, upairset2IR = (! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) ).
% 15.31/5.61  thf(binunionIR_def, definition, binunionIR = (! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))) ).
% 15.31/5.61  thf(binunionEcases_def, definition, binunionEcases = (! [A:$i,B:$i,C:$i,D:$o]: ((in @ C @ (binunion @ A @ B)) => (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D))))) ).
% 15.31/5.61  thf(binunionE_def, definition, binunionE = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))) ).
% 15.31/5.61  thf(binunionLsub_def, definition, binunionLsub = (! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))) ).
% 15.31/5.61  thf(binunionRsub_def, definition, binunionRsub = (! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))) ).
% 15.31/5.61  thf(binintersectI_def, definition, binintersectI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))) ).
% 15.31/5.61  thf(binintersectSubset5_def, definition, binintersectSubset5 = (! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))) ).
% 15.31/5.61  thf(binintersectEL_def, definition, binintersectEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))) ).
% 15.31/5.61  thf(binintersectLsub_def, definition, binintersectLsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)) ).
% 15.31/5.61  thf(binintersectSubset2_def, definition, binintersectSubset2 = (! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))) ).
% 15.31/5.61  thf(binintersectSubset3_def, definition, binintersectSubset3 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))) ).
% 15.31/5.61  thf(binintersectER_def, definition, binintersectER = (! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))) ).
% 15.31/5.61  thf(disjointsetsI1_def, definition, disjointsetsI1 = (! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))) ).
% 15.31/5.61  thf(binintersectRsub_def, definition, binintersectRsub = (! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)) ).
% 15.31/5.61  thf(binintersectSubset4_def, definition, binintersectSubset4 = (! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))) ).
% 15.31/5.61  thf(binintersectSubset1_def, definition, binintersectSubset1 = (! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ B))) ).
% 15.31/5.61  thf(bs114d_def, definition, bs114d = (! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C)))) ).
% 15.31/5.61  thf(setminus_def, definition, setminus = (^ [A:$i,B:$i]: (dsetconstr @ A @ (^ [C:$i]: ~ (in @ C @ B)))) ).
% 15.31/5.61  thf(setminusI_def, definition, setminusI = (! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (setminus @ A @ B))))) ).
% 15.31/5.61  thf(setminusEL_def, definition, setminusEL = (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (in @ C @ A))) ).
% 15.31/5.61  thf(sk1_def, definition, sk1 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) = (in @ C @ A)))) ).
% 15.31/5.61  thf(sk2_def, definition, sk2 = (^ [A:$i]: (@+ [B:$i]: ~ (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A)))) ).
% 15.31/5.61  thf(sk3_def, definition, sk3 = (^ [A:$i,B:($i > ($i > $o))]: (@+ [C:$i]: ~ ((in @ C @ A) => (? [D:$i]: ((B @ C @ D) & ! [E:$i]: ((B @ C @ E) => (D = E))))))) ).
% 15.31/5.61  thf(sk4_def, definition, sk4 = (^ [A:$i,B:$i,C:($i > ($i > $o))]: (@+ [D:$i]: ~ ((C @ (sk3 @ B @ C) @ D) => (A = D)))) ).
% 15.31/5.61  thf(sk5_def, definition, sk5 = (^ [A:$i,B:($i > ($i > $o))]: (@+ [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ A) & (B @ E @ D)))))) ).
% 15.31/5.61  thf(sk6_def, definition, sk6 = (^ [A:$i]: (@+ [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A)))))) ).
% 15.31/5.61  thf(sk7_def, definition, sk7 = (^ [A:$i]: (@+ [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i]: ((in @ D @ B) & ? [E:$i]: ((in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F)))))))))) ).
% 15.31/5.61  thf(sk8_def, definition, sk8 = (^ [A:$i,B:$i,C:$i]: (@+ [D:$i]: ~ ((in @ D @ (sk7 @ C)) => ((in @ B @ D) = (in @ A @ D))))) ).
% 15.31/5.61  thf(sk10_def, definition, sk10 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ A) => (in @ C @ B)))) ).
% 15.31/5.61  thf(sk11_def, definition, sk11 = (^ [A:$i,B:$i]: (@+ [C:$i]: ((in @ C @ (sk7 @ B)) & ? [D:$i]: ((in @ D @ A) & ~ (? [E:$i]: ((in @ E @ C) & (in @ E @ A))) & ! [E:$i]: ((in @ E @ (sk7 @ B)) => (! [F:$i]: ((in @ F @ E) => (in @ F @ C)) | (in @ D @ E))))))) ).
% 15.31/5.61  thf(sk12_def, definition, sk12 = (^ [A:$i,B:$i]: (@+ [C:$i]: ((in @ C @ A) & ~ (? [D:$i]: ((in @ D @ (sk11 @ A @ B)) & (in @ D @ A))) & ! [D:$i]: ((in @ D @ (sk7 @ B)) => (! [E:$i]: ((in @ E @ D) => (in @ E @ (sk11 @ A @ B))) | (in @ C @ D)))))) ).
% 15.31/5.61  thf(sk13_def, definition, sk13 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 15.31/5.61  thf(sk14_def, definition, sk14 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 15.31/5.61  thf(sk15_def, definition, sk15 = ((@+) @ $i) ).
% 15.31/5.61  thf(sk16_def, definition, sk16 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (in @ C @ A)))) ).
% 15.31/5.61  thf(sk17_def, definition, sk17 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ A) => (in @ C @ B)))) ).
% 15.31/5.61  thf(sk18_def, definition, sk18 = (^ [A:$i]: (@+ [B:$i]: (in @ B @ A))) ).
% 15.31/5.61  thf(sk19_def, definition, sk19 = (^ [A:$i]: (@+ [B:$i]: (in @ B @ A))) ).
% 15.31/5.61  thf(sk20_def, definition, sk20 = (^ [A:$i]: (@+ [B:$i]: (in @ B @ A))) ).
% 15.31/5.61  thf(sk21_def, definition, sk21 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ A) => (in @ C @ B)))) ).
% 15.31/5.61  thf(sk22_def, definition, sk22 = (^ [A:$o,B:$i,C:$i]: (@+ [D:$i]: ~ ((in @ B @ D) => ((in @ D @ C) => (A))))) ).
% 15.31/5.61  thf(sk23_def, definition, sk23 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 15.31/5.61  thf(sk24_def, definition, sk24 = (^ [A:($i > $o)]: (@+ [B:$i]: ! [C:$i]: ((A @ C) = (C = B)))) ).
% 15.31/5.61  thf(sk25_def, definition, sk25 = (^ [A:$i]: (@+ [B:$i]: (in @ B @ A))) ).
% 15.31/5.61  thf(sk26_def, definition, sk26 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & ~ (A @ C)))) ).
% 15.31/5.61  thf(sk27_def, definition, sk27 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (~ (A @ C))))) ).
% 15.31/5.61  thf(sk28_def, definition, sk28 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & (A @ C)))) ).
% 15.31/5.61  thf(sk29_def, definition, sk29 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (A @ C)))) ).
% 15.31/5.61  thf(sk30_def, definition, sk30 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & (A @ C)))) ).
% 15.31/5.61  thf(sk31_def, definition, sk31 = (^ [A:($i > $o),B:$i]: (@+ [C:$i]: ((in @ C @ B) & ~ (A @ C)))) ).
% 15.31/5.61  thf(sk32_def, definition, sk32 = (^ [A:($i > $o)]: (@+ [B:$i]: ~ ((A @ B) => (! [C:$i]: ((A @ C) => (B = C)))))) ).
% 15.31/5.61  thf(sk33_def, definition, sk33 = (^ [A:($i > $o)]: (@+ [B:$i]: ~ ((A @ B) => ((sk32 @ A) = B)))) ).
% 15.31/5.61  thf(sk34_def, definition, sk34 = (^ [A:($i > $o)]: (@+ [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C))))) ).
% 15.31/5.61  thf(sk35_def, definition, sk35 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) = (C = A)))) ).
% 15.31/5.61  thf(sk36_def, definition, sk36 = (^ [A:($i > $o)]: (@+ [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C))))) ).
% 15.31/5.61  thf(sk37_def, definition, sk37 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 15.31/5.61  thf(sk38_def, definition, sk38 = (^ [A:($i > $o),B:($i > $o)]: (@+ [C:$i]: ~ (! [D:$i]: ((C = D) => ((B @ C) = (A @ D)))))) ).
% 15.31/5.61  thf(sk39_def, definition, sk39 = (^ [A:($i > $o),B:($i > $o)]: (@+ [C:$i]: ~ (((sk38 @ A @ B) = C) => ((B @ (sk38 @ A @ B)) = (A @ C))))) ).
% 15.31/5.61  thf(sk40_def, definition, sk40 = (^ [A:$i,B:($i > $o)]: (@+ [C:$i]: ~ ((B @ C) => (A = C)))) ).
% 15.31/5.61  thf(sk42_def, definition, sk42 = (^ [A:($i > $o),B:($i > $o)]: (@+ [C:$i]: ~ (! [D:$i]: ((C = D) => ((B @ C) = (A @ D)))))) ).
% 15.31/5.61  thf(sk43_def, definition, sk43 = (^ [A:($i > $o),B:($i > $o)]: (@+ [C:$i]: ~ (((sk42 @ A @ B) = C) => ((B @ (sk42 @ A @ B)) = (A @ C))))) ).
% 15.31/5.61  thf(sk44_def, definition, sk44 = (^ [A:$i,B:($i > $o),C:($i > $o)]: (@+ [D:$i]: ~ ((C @ D) => (A = D)))) ).
% 15.31/5.61  thf(sk45_def, definition, sk45 = (^ [A:$i,B:($i > $o),C:($i > $o)]: (@+ [D:$i]: ~ ((B @ D) => (A = D)))) ).
% 15.31/5.61  thf(sk46_def, definition, sk46 = (^ [A:($i > $o),B:($i > $o),C:$i,D:$i]: (@+ [E:$i]: ~ ((in @ E @ D) => (! [F:$i]: ((in @ F @ C) => ((E = F) => ((B @ E) = (A @ F)))))))) ).
% 15.31/5.61  thf(sk47_def, definition, sk47 = (^ [A:($i > $o),B:($i > $o),C:$i,D:$i]: (@+ [E:$i]: ~ ((in @ E @ C) => (((sk46 @ A @ B @ C @ D) = E) => ((B @ (sk46 @ A @ B @ C @ D)) = (A @ E)))))) ).
% 15.31/5.61  thf(sk48_def, definition, sk48 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (in @ C @ A)))) ).
% 15.31/5.61  thf(sk49_def, definition, sk49 = (^ [A:$i,B:$i]: (@+ [C:$i]: ~ ((in @ C @ B) => (in @ C @ A)))) ).
% 15.31/5.61  thf(sk50_def, definition, sk50 = (^ [A:$i,B:$i]: (@+ [C:$i]: ((in @ C @ B) & (in @ C @ A)))) ).
% 15.31/5.61  thf(sk51_def, definition, sk51 = (@+ [A:$i]: ~ (! [B:$i,C:$i]: ((in @ C @ (dsetconstr @ A @ (^ [D:$i]: ~ (in @ D @ B)))) => (~ (in @ C @ B))))) ).
% 15.31/5.61  thf(sk52_def, definition, sk52 = (@+ [A:$i]: ~ (! [B:$i]: ((in @ B @ (dsetconstr @ sk51 @ (^ [C:$i]: ~ (in @ C @ A)))) => (~ (in @ B @ A))))) ).
% 15.31/5.61  thf(sk53_def, definition, sk53 = (@+ [A:$i]: ~ ((in @ A @ (dsetconstr @ sk51 @ (^ [B:$i]: ~ (in @ B @ sk52)))) => (~ (in @ A @ sk52)))) ).
% 15.31/5.61  thf(1,conjecture,(((setextAx) => ((emptysetAx) => ((setadjoinAx) => ((powersetAx) => ((setunionAx) => ((omega0Ax) => ((omegaSAx) => ((omegaIndAx) => ((replAx) => ((foundationAx) => ((wellorderingAx) => ((descrp) => ((dsetconstrI) => ((dsetconstrEL) => ((dsetconstrER) => ((exuE1) => ((prop2setE) => ((emptysetE) => ((emptysetimpfalse) => ((notinemptyset) => ((exuE3e) => ((setext) => ((emptyI) => ((noeltsimpempty) => ((setbeta) => ((nonemptyE1) => ((nonemptyI) => ((nonemptyI1) => ((setadjoinIL) => ((emptyinunitempty) => ((setadjoinIR) => ((setadjoinE) => ((setadjoinOr) => ((setoftrueEq) => ((powersetI) => ((emptyinPowerset) => ((emptyInPowerset) => ((powersetE) => ((setunionI) => ((setunionE) => ((subPowSU) => ((exuE2) => ((nonemptyImpWitness) => ((uniqinunit) => ((notinsingleton) => ((eqinunit) => ((singletonsswitch) => ((upairsetE) => ((upairsetIL) => ((upairsetIR) => ((emptyE1) => ((vacuousDall) => ((quantDeMorgan1) => ((quantDeMorgan2) => ((quantDeMorgan3) => ((quantDeMorgan4) => ((prop2setI) => ((prop2set2propI) => ((notdexE) => ((notdallE) => ((exuI1) => ((exuI3) => ((exuI2) => ((inCongP) => ((in__Cong) => ((exuE3u) => ((exu__Cong) => ((emptyset__Cong) => ((setadjoin__Cong) => ((powerset__Cong) => ((setunion__Cong) => ((omega__Cong) => ((exuEu) => ((descr__Cong) => ((dsetconstr__Cong) => ((subsetI1) => ((eqimpsubset2) => ((eqimpsubset1) => ((subsetI2) => ((emptysetsubset) => ((subsetE) => ((subsetE2) => ((notsubsetI) => ((notequalI1) => ((notequalI2) => ((subsetRefl) => ((subsetTrans) => ((setadjoinSub) => ((setadjoinSub2) => ((subset2powerset) => ((setextsub) => ((subsetemptysetimpeq) => ((powersetI1) => ((powersetE1) => ((inPowerset) => ((powersetsubset) => ((sepInPowerset) => ((sepSubset) => ((binunionIL) => ((upairset2IR) => ((binunionIR) => ((binunionEcases) => ((binunionE) => ((binunionLsub) => ((binunionRsub) => ((binintersectI) => ((binintersectSubset5) => ((binintersectEL) => ((binintersectLsub) => ((binintersectSubset2) => ((binintersectSubset3) => ((binintersectER) => ((disjointsetsI1) => ((binintersectRsub) => ((binintersectSubset4) => ((binintersectSubset1) => ((bs114d) => ((setminusI) => ((setminusEL) => (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER)).
% 15.31/5.61  thf(2,negated_conjecture,((~ ((setextAx) => ((emptysetAx) => ((setadjoinAx) => ((powersetAx) => ((setunionAx) => ((omega0Ax) => ((omegaSAx) => ((omegaIndAx) => ((replAx) => ((foundationAx) => ((wellorderingAx) => ((descrp) => ((dsetconstrI) => ((dsetconstrEL) => ((dsetconstrER) => ((exuE1) => ((prop2setE) => ((emptysetE) => ((emptysetimpfalse) => ((notinemptyset) => ((exuE3e) => ((setext) => ((emptyI) => ((noeltsimpempty) => ((setbeta) => ((nonemptyE1) => ((nonemptyI) => ((nonemptyI1) => ((setadjoinIL) => ((emptyinunitempty) => ((setadjoinIR) => ((setadjoinE) => ((setadjoinOr) => ((setoftrueEq) => ((powersetI) => ((emptyinPowerset) => ((emptyInPowerset) => ((powersetE) => ((setunionI) => ((setunionE) => ((subPowSU) => ((exuE2) => ((nonemptyImpWitness) => ((uniqinunit) => ((notinsingleton) => ((eqinunit) => ((singletonsswitch) => ((upairsetE) => ((upairsetIL) => ((upairsetIR) => ((emptyE1) => ((vacuousDall) => ((quantDeMorgan1) => ((quantDeMorgan2) => ((quantDeMorgan3) => ((quantDeMorgan4) => ((prop2setI) => ((prop2set2propI) => ((notdexE) => ((notdallE) => ((exuI1) => ((exuI3) => ((exuI2) => ((inCongP) => ((in__Cong) => ((exuE3u) => ((exu__Cong) => ((emptyset__Cong) => ((setadjoin__Cong) => ((powerset__Cong) => ((setunion__Cong) => ((omega__Cong) => ((exuEu) => ((descr__Cong) => ((dsetconstr__Cong) => ((subsetI1) => ((eqimpsubset2) => ((eqimpsubset1) => ((subsetI2) => ((emptysetsubset) => ((subsetE) => ((subsetE2) => ((notsubsetI) => ((notequalI1) => ((notequalI2) => ((subsetRefl) => ((subsetTrans) => ((setadjoinSub) => ((setadjoinSub2) => ((subset2powerset) => ((setextsub) => ((subsetemptysetimpeq) => ((powersetI1) => ((powersetE1) => ((inPowerset) => ((powersetsubset) => ((sepInPowerset) => ((sepSubset) => ((binunionIL) => ((upairset2IR) => ((binunionIR) => ((binunionEcases) => ((binunionE) => ((binunionLsub) => ((binunionRsub) => ((binintersectI) => ((binintersectSubset5) => ((binintersectEL) => ((binintersectLsub) => ((binintersectSubset2) => ((binintersectSubset3) => ((binintersectER) => ((disjointsetsI1) => ((binintersectRsub) => ((binintersectSubset4) => ((binintersectSubset1) => ((bs114d) => ((setminusI) => ((setminusEL) => (! [A:$i,B:$i,C:$i]: ((in @ C @ (setminus @ A @ B)) => (~ (in @ C @ B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(neg_conjecture,[status(cth)],[1])).
% 15.31/5.61  thf(3,plain,((~ ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) = (in @ C @ B))) => (A = B))) => ((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) = ((C = A) | (in @ C @ B)))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) = (! [C:$i]: ((in @ C @ B) => (in @ C @ A))))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) = (? [C:$i]: ((in @ B @ C) & (in @ C @ A))))) => ((in @ emptyset @ omega) => ((! [A:$i]: ((in @ A @ omega) => (in @ (setadjoin @ A @ A) @ omega))) => ((! [A:$i]: (((in @ emptyset @ A) & ! [B:$i]: (((in @ B @ omega) & (in @ B @ A)) => (in @ (setadjoin @ B @ B) @ A))) => (! [B:$i]: ((in @ B @ omega) => (in @ B @ A))))) => ((! [A:($i > ($i > $o)),B:$i]: ((! [C:$i]: ((in @ C @ B) => (? [D:$i]: ((A @ C @ D) & ! [E:$i]: ((A @ C @ E) => (D = E)))))) => (? [C:$i]: ! [D:$i]: ((in @ D @ C) = (? [E:$i]: ((in @ E @ B) & (A @ E @ D))))))) => ((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (? [B:$i]: ((in @ B @ A) & ~ (? [C:$i]: ((in @ C @ B) & (in @ C @ A))))))) => ((! [A:$i]: ? [B:$i]: (! [C:$i]: ((in @ C @ B) => (! [D:$i]: ((in @ D @ C) => (in @ D @ A)))) & ! [C:$i,D:$i]: (((in @ C @ A) & (in @ D @ A)) => ((! [E:$i]: ((in @ E @ B) => ((in @ C @ E) = (in @ D @ E)))) => (C = D))) & ! [C:$i,D:$i]: (((in @ C @ B) & (in @ D @ B)) => (! [E:$i]: ((in @ E @ C) => (in @ E @ D)) | ! [E:$i]: ((in @ E @ D) => (in @ E @ C)))) & ! [C:$i]: ((! [D:$i]: ((in @ D @ C) => (in @ D @ A)) & ? [D:$i]: (in @ D @ C)) => (? [D:$i,E:$i]: ((in @ D @ B) & (in @ E @ C) & ~ (? [F:$i]: ((in @ F @ D) & (in @ F @ C))) & ! [F:$i]: ((in @ F @ B) => (! [G:$i]: ((in @ G @ F) => (in @ G @ D)) | (in @ E @ F)))))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (A @ (descr @ (A))))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (in @ C @ (dsetconstr @ A @ (B)))))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (in @ C @ A))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ (dsetconstr @ A @ (B))) => (B @ C))) => ((! [A:$o,B:$i]: ((in @ B @ (prop2set @ A)) => (A))) => ((! [A:$i]: ((in @ A @ emptyset) => (! [B:$o]: (B)))) => ((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:$i]: ~ (in @ A @ emptyset)) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: (A @ B)))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (A = B)))) => ((! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) => ((! [A:$i]: ((! [B:$i]: ~ (in @ B @ A)) => (A = emptyset))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((in @ C @ (dsetconstr @ A @ (B))) = (B @ C)))) => ((! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => ((! [A:$i,B:($i > $o),C:$i]: ((in @ C @ A) => ((B @ C) => (~ ((dsetconstr @ A @ (B)) = emptyset))))) => ((! [A:$i]: ((? [B:$i]: (in @ B @ A)) => (~ (A = emptyset)))) => ((! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ B))) => ((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (setadjoin @ A @ B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => (! [D:$o]: (((C = A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ B)) => ((C = A) | (in @ C @ B)))) => ((! [A:$i]: ((dsetconstr @ A @ (^ [B:$i]: (($true)))) = A)) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ B) => (in @ C @ A))) => (in @ B @ (powerset @ A)))) => ((! [A:$i]: (in @ emptyset @ (powerset @ A))) => ((! [A:$i]: (in @ emptyset @ (powerset @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ B @ (powerset @ A)) => ((in @ C @ B) => (in @ C @ A)))) => ((! [A:$i,B:$i,C:$i]: ((in @ B @ C) => ((in @ C @ A) => (in @ B @ (setunion @ A))))) => ((! [A:$i,B:$i]: ((in @ B @ (setunion @ A)) => (! [C:$o]: ((! [D:$i]: ((in @ B @ D) => ((in @ D @ A) => (C)))) => (C))))) => ((! [A:$i,B:$i]: ((in @ B @ A) => (in @ B @ (powerset @ (setunion @ A))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))))) => ((! [A:$i]: ((~ (A = emptyset)) => (? [B:$i]: (in @ B @ A)))) => ((! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (A = B))) => ((! [A:$i,B:$i]: ((~ (A = B)) => (~ (in @ B @ (setadjoin @ A @ emptyset))))) => ((! [A:$i,B:$i]: ((A = B) => (in @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i]: ((in @ A @ (setadjoin @ B @ emptyset)) => (in @ B @ (setadjoin @ A @ emptyset)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (setadjoin @ A @ (setadjoin @ B @ emptyset))) => ((C = A) | (C = B)))) => ((! [A:$i,B:$i]: (in @ A @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:($i > $o)]: ((? [C:$i]: ((in @ C @ A) & (B @ C))) => (~ ((dsetconstr @ A @ (B)) = emptyset)))) => ((! 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[A:$i,B:$i,C:$i]: ((in @ C @ (dsetconstr @ A @ (^ [D:$i]: ~ (in @ D @ B)))) => (in @ C @ A))) => (! [A:$i,B:$i,C:$i]: ((in @ C @ (dsetconstr @ A @ (^ [D:$i]: ~ (in @ D @ B)))) => (~ (in @ C @ B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(defexp_and_simp_and_etaexpand,[status(thm)],[2])).
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[C:$i]: ((A @ C) => (B = C))))))) => ((! [A:($i > $o)]: ((? [B:$i]: ! [C:$i]: ((A @ C) = (C = B))) => (? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) => (in @ D @ B)))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((in @ C @ A) = (in @ D @ B)))))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i]: ((A @ B) => (! [C:$i]: ((A @ C) => (B = C))))))) => ((! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((? [C:$i]: ((A @ C) & ! [D:$i]: ((A @ D) => (C = D)))) = (? [C:$i]: ((B @ C) & ! [D:$i]: ((B @ D) => (C = D))))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:$i,D:$i]: ((C = D) => ((setadjoin @ A @ C) = (setadjoin @ B @ D)))))) => ((! [A:$i,B:$i]: ((A = B) => ((powerset @ A) = (powerset @ B)))) => ((! [A:$i,B:$i]: ((A = B) => ((setunion @ A) = (setunion @ B)))) => ((! [A:($i > $o)]: ((? [B:$i]: ((A @ B) & ! [C:$i]: ((A @ C) => (B = C)))) => (! [B:$i]: ((A @ B) => (! [C:$i]: ((A @ C) => (B = C))))))) => ((! [A:($i > $o),B:($i > $o)]: ((! [C:$i,D:$i]: ((C = D) => ((A @ C) = (B @ D)))) => ((? [C:$i]: ((A @ C) & ! [D:$i]: ((A @ D) => (C = D)))) => ((? [C:$i]: ((B @ C) & ! [D:$i]: ((B @ D) => (C = D)))) => ((descr @ (A)) = (descr @ (B))))))) => ((! [A:$i,B:$i]: ((A = B) => (! [C:($i > $o),D:($i > $o)]: ((! [E:$i]: ((in @ E @ A) => (! [F:$i]: ((in @ F @ B) => ((E = F) => ((C @ E) = (D @ F))))))) => ((dsetconstr @ A @ (C)) = (dsetconstr @ B @ (D))))))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) => ((! [A:$i,B:$i]: ((A = B) => (subset @ B @ A))) => ((! [A:$i,B:$i]: ((A = B) => (subset @ A @ B))) => ((! [A:$i,B:$i]: ((! [C:$i]: ((in @ C @ A) => (in @ C @ B))) => (subset @ A @ B))) => ((! [A:$i]: (subset @ emptyset @ A)) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (! [C:$i]: ((in @ C @ A) => (in @ C @ B))))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (! [C:$i]: ((~ (in @ C @ B)) => (~ (in @ C @ A)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (subset @ A @ B))))) => ((! [A:$i,B:$i]: ((~ (subset @ A @ B)) => (~ (A = B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (~ (A = B))))) => ((! [A:$i]: (subset @ A @ A)) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (! [C:$i]: ((subset @ B @ C) => (subset @ A @ C))))) => ((! [A:$i,B:$i]: (subset @ B @ (setadjoin @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((subset @ A @ C) => (subset @ A @ (setadjoin @ B @ C)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (in @ A @ (powerset @ B)))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((subset @ B @ A) => (A = B)))) => ((! [A:$i]: ((subset @ A @ emptyset) => (A = emptyset))) => ((! [A:$i,B:$i]: ((subset @ B @ A) => (in @ B @ (powerset @ A)))) => ((! [A:$i,B:$i]: ((in @ B @ (powerset @ A)) => (subset @ B @ A))) => ((! [A:$i]: (in @ A @ (powerset @ A))) => ((! [A:$i,B:$i]: ((subset @ A @ B) => (subset @ (powerset @ A) @ (powerset @ B)))) => ((! [A:$i,B:($i > $o)]: (in @ (dsetconstr @ A @ (B)) @ (powerset @ A))) => ((! [A:$i,B:($i > $o)]: (subset @ (dsetconstr @ A @ (B)) @ A)) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => (in @ C @ (binunion @ A @ B)))) => ((! [A:$i,B:$i]: (in @ B @ (setadjoin @ A @ (setadjoin @ B @ emptyset)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ B) => (in @ C @ (binunion @ A @ B)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => (! [D:$o]: (((in @ C @ A) => (D)) => (((in @ C @ B) => (D)) => (D)))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binunion @ A @ B)) => ((in @ C @ A) | (in @ C @ B)))) => ((! [A:$i,B:$i]: (subset @ A @ (binunion @ A @ B))) => ((! [A:$i,B:$i]: (subset @ B @ (binunion @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((in @ C @ B) => (in @ C @ (binintersect @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((subset @ C @ A) => ((subset @ C @ B) => (subset @ C @ (binintersect @ A @ B))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ A))) => ((! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ A)) => ((! [A:$i,B:$i]: ((subset @ A @ B) => ((binintersect @ A @ B) = A))) => ((! [A:$i,B:$i]: (((binintersect @ A @ B) = B) => (subset @ B @ A))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (binintersect @ A @ B)) => (in @ C @ B))) => ((! [A:$i,B:$i]: ((~ (? [C:$i]: ((in @ C @ A) & (in @ C @ B)))) => ((binintersect @ A @ B) = emptyset))) => ((! [A:$i,B:$i]: (subset @ (binintersect @ A @ B) @ B)) => ((! [A:$i,B:$i]: ((subset @ B @ A) => ((binintersect @ A @ B) = B))) => ((! [A:$i,B:$i]: (((binintersect @ A @ B) = A) => (subset @ A @ B))) => ((! [A:$i,B:$i,C:$i]: ((binintersect @ A @ (binunion @ B @ C)) = (binunion @ (binintersect @ A @ B) @ (binintersect @ A @ C)))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ A) => ((~ (in @ C @ B)) => (in @ C @ (dsetconstr @ A @ (^ [D:$i]: ~ (in @ D @ B))))))) => ((! [A:$i,B:$i,C:$i]: ((in @ C @ (dsetconstr @ A @ (^ [D:$i]: ~ (in @ D @ B)))) => (in @ C @ A))) => (! [A:$i,B:$i,C:$i]: ((in @ C @ (dsetconstr @ A @ (^ [D:$i]: ~ (in @ D @ B)))) => (~ (in @ C @ B))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),inference(miniscope,[status(thm)],[3])).
% 15.31/5.61  thf(5,plain,(! [ZZZZZZZZZZT:$i,ZZZZZZZZZZS:$i,ZZZZZZZZZZR:$i,ZZZZZZZZZZQ:$i,ZZZZZZZZZZP:$i,ZZZZZZZZZZO:$i,ZZZZZZZZZZN:$i,ZZZZZZZZZZM:$i,ZZZZZZZZZZL:$i,ZZZZZZZZZZK:$i,ZZZZZZZZZZJ:$i,ZZZZZZZZZZI:$i,ZZZZZZZZZZH:$i,ZZZZZZZZZZG:$i,ZZZZZZZZZZF:$i,ZZZZZZZZZZE:$i,ZZZZZZZZZZD:$i,ZZZZZZZZZZC:$i,ZZZZZZZZZZB:$i,ZZZZZZZZZZA:$i,ZZZZZZZZZZ:$i,ZZZZZZZZZY:$i,ZZZZZZZZZX:$i,ZZZZZZZZZW:$i,ZZZZZZZZZV:$i,ZZZZZZZZZU:$i,ZZZZZZZZZT:$i,ZZZZZZZZZS:$i,ZZZZZZZZZR:$i,ZZZZZZZZZQ:$i,ZZZZZZZZZP:$i,ZZZZZZZZZO:$i,ZZZZZZZZZN:$i,ZZZZZZZZZM:$i,ZZZZZZZZZL:$i,ZZZZZZZZZK:$i,ZZZZZZZZZJ:$i,ZZZZZZZZZI:$i,ZZZZZZZZZH:$i,ZZZZZZZZZG:$i,ZZZZZZZZZF:$i,ZZZZZZZZZE:$i,ZZZZZZZZZD:$o,ZZZZZZZZZC:$i,ZZZZZZZZZB:$i,ZZZZZZZZZA:$i,ZZZZZZZZZ:$i,ZZZZZZZZY:$i,ZZZZZZZZX:$i,ZZZZZZZZW:$i,ZZZZZZZZV:$i,ZZZZZZZZU:$i,ZZZZZZZZT:$i,ZZZZZZZZS:$i,ZZZZZZZZR:($i > $o),ZZZZZZZZQ:$i,ZZZZZZZZP:($i > $o),ZZZZZZZZO:$i,ZZZZZZZZN:$i,ZZZZZZZZM:$i,ZZZZZZZZL:$i,ZZZZZZZZK:$i,ZZZZZZZZJ:$i,ZZZZZZZZI:$i,ZZZZZZZZH:$i,ZZZZZZZZG:$i,ZZZZZZZZF:$i,ZZZZZZZZE:$i,ZZZZZZZZD:$i,ZZZZZZZZC:$i,ZZZZZZZZB:$i,ZZZZZZZZA:$i,ZZZZZZZZ:$i,ZZZZZZZY:$i,ZZZZZZZX:$i,ZZZZZZZW:$i,ZZZZZZZV:$i,ZZZZZZZU:$i,ZZZZZZZT:$i,ZZZZZZZS:$i,ZZZZZZZR:$i,ZZZZZZZQ:$i,ZZZZZZZP:$i,ZZZZZZZO:$i,ZZZZZZZN:$i,ZZZZZZZM:$i,ZZZZZZZL:$i,ZZZZZZZK:$i,ZZZZZZZJ:$i,ZZZZZZZI:$i,ZZZZZZZH:$i,ZZZZZZZG:$i,ZZZZZZZF:$i,ZZZZZZZE:$i,ZZZZZZZD:$i,ZZZZZZZC:$i,ZZZZZZZB:$i,ZZZZZZZA:$i,ZZZZZZZ:$i,ZZZZZZY:$i,ZZZZZZX:$i,ZZZZZZW:$i,ZZZZZZV:($i > $o),ZZZZZZU:($i > $o),ZZZZZZT:$i,ZZZZZZS:$i,ZZZZZZR:$i,ZZZZZZQ:$i,ZZZZZZP:($i > $o),ZZZZZZO:($i > $o),ZZZZZZN:$i,ZZZZZZM:$i,ZZZZZZL:$i,ZZZZZZK:($i > $o),ZZZZZZJ:$i,ZZZZZZI:$i,ZZZZZZH:$i,ZZZZZZG:$i,ZZZZZZF:$i,ZZZZZZE:$i,ZZZZZZD:$i,ZZZZZZC:$i,ZZZZZZB:($i > $o),ZZZZZZA:($i > $o),ZZZZZZ:$i,ZZZZZY:$i,ZZZZZX:$i,ZZZZZW:($i > $o),ZZZZZV:$i,ZZZZZU:$i,ZZZZZT:$i,ZZZZZS:$i,ZZZZZR:$i,ZZZZZQ:$i,ZZZZZP:$i,ZZZZZO:$i,ZZZZZN:$i,ZZZZZM:$i,ZZZZZL:($i > $o),ZZZZZK:$i,ZZZZZJ:$i,ZZZZZI:($i > $o),ZZZZZH:$i,ZZZZZG:($i > $o),ZZZZZF:$i,ZZZZZE:$i,ZZZZZD:($i > $o),ZZZZZC:$i,ZZZZZB:$o,ZZZZZA:$o,ZZZZZ:$i,ZZZZY:($i > $o),ZZZZX:$i,ZZZZW:$i,ZZZZV:($i > $o),ZZZZU:$i,ZZZZT:$i,ZZZZS:($i > $o),ZZZZR:$i,ZZZZQ:$i,ZZZZP:($i > $o),ZZZZO:$i,ZZZZN:$i,ZZZZM:($i > $o),ZZZZL:$i,ZZZZK:($i > $o),ZZZZJ:$i,ZZZZI:$i,ZZZZH:$i,ZZZZG:$i,ZZZZF:$i,ZZZZE:$i,ZZZZD:$i,ZZZZC:$i,ZZZZB:$i,ZZZZA:$i,ZZZZ:$i,ZZZY:$i,ZZZX:$i,ZZZW:$i,ZZZV:$i,ZZZU:$i,ZZZT:$i,ZZZS:$i,ZZZR:$i,ZZZQ:($i > $o),ZZZP:$i,ZZZO:$i,ZZZN:$o,ZZZM:$i,ZZZL:$i,ZZZK:$i,ZZZJ:$i,ZZZI:$i,ZZZH:$i,ZZZG:$i,ZZZF:$i,ZZZE:$i,ZZZD:$i,ZZZC:$i,ZZZB:$i,ZZZA:$i,ZZZ:$i,ZZY:$i,ZZX:$i,ZZW:$o,ZZV:$i,ZZU:$i,ZZT:$i,ZZS:$i,ZZR:$i,ZZQ:$i,ZZP:$i,ZZO:$i,ZZN:$i,ZZM:$i,ZZL:$i,ZZK:($i > $o),ZZJ:$i,ZZI:$i,ZZH:$i,ZZG:($i > $o),ZZF:$i,ZZE:$i,ZZD:$i,ZZC:$i,ZZB:$i,ZZA:$i,ZZ:($i > $o),ZY:$i,ZX:$i,ZW:$o,ZV:$i,ZU:$i,ZT:$o,ZS:$i,ZR:($i > $o),ZQ:$i,ZP:$i,ZO:($i > $o),ZN:$i,ZM:$i,ZL:($i > $o),ZK:$i,ZJ:$i,ZI:($i > $o),ZH:$i,ZG:$i,ZF:$i,ZE:$i,ZD:$i,ZC:$i,ZB:$i,ZA:$i,Z:$i,Y:$i,X:$i,W:$i,V:$i,U:$i,T:$i,S:$i,R:$i,Q:$i,P:$i,O:$i,N:($i > ($i > $o)),M:$i,L:$i,K:$i,J:$i,I:$i,H:$i,G:$i,F:$i,E:$i,D:$i,C:$i,B:$i,A:$i] : (((~ ((in @ (sk1 @ B @ A) @ A) = (in @ (sk1 @ B @ A) @ B)) | (A = B)) & ~ (in @ C @ emptyset) & ((in @ F @ (setadjoin @ D @ E)) = ((F = D) | (in @ F @ E))) & ((in @ H @ (powerset @ G)) = (! [ZZZZZZZZZZU:$i]: ((in @ ZZZZZZZZZZU @ H) => (in @ ZZZZZZZZZZU @ G)))) & ((in @ J @ (setunion @ I)) = (? [ZZZZZZZZZZU:$i]: ((in @ J @ ZZZZZZZZZZU) & (in @ ZZZZZZZZZZU @ I)))) & (in @ emptyset @ omega) & (~ (in @ K @ omega) | (in @ (setadjoin @ K @ K) @ omega)) & (~ (in @ emptyset @ L) | (in @ (sk2 @ L) @ omega) | ~ (in @ M @ omega) | (in @ M @ L)) & (~ (in @ emptyset @ L) | (in @ (sk2 @ L) @ L) | ~ (in @ M @ omega) | (in @ M @ L)) & (~ (in @ emptyset @ L) | ~ (in @ (setadjoin @ (sk2 @ L) @ (sk2 @ L)) @ L) | ~ (in @ M @ omega) | (in @ M @ L)) & ((in @ (sk3 @ O @ (N)) @ O) | ((in @ Q @ (sk5 @ O @ (N))) = (? [ZZZZZZZZZZU:$i]: ((in @ ZZZZZZZZZZU @ O) & (N @ ZZZZZZZZZZU @ Q))))) & (~ (N @ (sk3 @ O @ (N)) @ P) | (N @ (sk3 @ O @ (N)) @ (sk4 @ P @ O @ (N))) | ((in @ Q @ (sk5 @ O @ (N))) = (? [ZZZZZZZZZZU:$i]: ((in @ ZZZZZZZZZZU @ O) & (N @ ZZZZZZZZZZU @ Q))))) & (~ (N @ (sk3 @ O @ (N)) @ P) | ~ (P = (sk4 @ P @ O @ (N))) | ((in @ Q @ (sk5 @ O @ (N))) = (? [ZZZZZZZZZZU:$i]: ((in @ ZZZZZZZZZZU @ O) & (N @ ZZZZZZZZZZU @ Q))))) & (~ (in @ S @ R) | (in @ (sk6 @ R) @ R)) & (~ (in @ S @ R) | ~ (in @ T @ (sk6 @ R)) | ~ (in @ T @ R)) & (~ (in @ V @ (sk7 @ U)) | ~ (in @ W @ V) | (in @ W @ U)) & (~ (in @ X @ U) | ~ (in @ Y @ U) | (in @ (sk8 @ Y @ X @ U) @ (sk7 @ U)) | (X = Y)) & (~ (in @ X @ U) | ~ (in @ Y @ U) | ~ ((in @ X @ (sk8 @ Y @ X @ U)) = (in @ Y @ (sk8 @ Y @ X @ U))) | (X = Y)) & (~ (in @ Z @ (sk7 @ U)) | ~ (in @ ZA @ (sk7 @ U)) | ~ (in @ ZB @ Z) | (in @ ZB @ ZA) | ~ (in @ ZC @ ZA) | (in @ ZC @ Z)) & ((in @ (sk10 @ ZD @ U) @ ZD) | ~ (in @ ZE @ ZD) | (sk9 @ U @ ZD)) & (~ (in @ (sk10 @ ZD @ U) @ U) | ~ (in @ ZE @ ZD) | (sk9 @ U @ ZD)) & (~ (sk9 @ U @ ZD) | (in @ (sk11 @ ZD @ U) @ (sk7 @ U))) & (~ (sk9 @ U @ ZD) | (in @ (sk12 @ ZD @ U) @ ZD)) & (~ (sk9 @ U @ ZD) | ~ (in @ ZF @ (sk11 @ ZD @ U)) | ~ (in @ ZF @ ZD)) & (~ (sk9 @ U @ ZD) | ~ (in @ ZG @ (sk7 @ U)) | ~ (in @ ZH @ ZG) | (in @ ZH @ (sk11 @ ZD @ U)) | (in @ (sk12 @ ZD @ U) @ ZG)) & (~ (ZI @ ZJ) | (ZI @ (sk13 @ ZJ @ (ZI))) | (ZI @ (descr @ (ZI)))) & (~ (ZI @ ZJ) | ~ (ZJ = (sk13 @ ZJ @ (ZI))) | (ZI @ (descr @ (ZI)))) & (~ (in @ ZM @ ZK) | ~ (ZL @ ZM) | (in @ ZM @ (dsetconstr @ ZK @ (ZL)))) & (~ (in @ ZP @ (dsetconstr @ ZN @ (ZO))) | (in @ ZP @ ZN)) & (~ (in @ ZS @ (dsetconstr @ ZQ @ (ZR))) | (ZR @ ZS)) & (~ (in @ ZU @ (prop2set @ ZT)) | (ZT)) & (~ (in @ ZV @ emptyset) | (ZW)) & ~ (in @ ZX @ emptyset) & ~ (in @ ZY @ emptyset) & (~ (ZZ @ ZZA) | (ZZ @ (sk14 @ ZZA @ (ZZ))) | (ZZ @ (sk15 @ (ZZ)))) & (~ (ZZ @ ZZA) | ~ (ZZA = (sk14 @ ZZA @ (ZZ))) | (ZZ @ (sk15 @ (ZZ)))) & ((in @ (sk16 @ ZZC @ ZZB) @ ZZB) | (in @ (sk17 @ ZZC @ ZZB) @ ZZC) | (ZZB = ZZC)) & ((in @ (sk16 @ ZZC @ ZZB) @ ZZB) | ~ (in @ (sk17 @ ZZC @ ZZB) @ ZZB) | (ZZB = ZZC)) & (~ (in @ (sk16 @ ZZC @ ZZB) @ ZZC) | (in @ (sk17 @ ZZC @ ZZB) @ ZZC) | (ZZB = ZZC)) & (~ (in @ (sk16 @ ZZC @ ZZB) @ ZZC) | ~ (in @ (sk17 @ ZZC @ ZZB) @ ZZB) | (ZZB = ZZC)) & ((in @ (sk18 @ ZZD) @ ZZD) | (ZZD = emptyset)) & ((in @ (sk19 @ ZZE) @ ZZE) | (ZZE = emptyset)) & (~ (in @ ZZH @ ZZF) | ((in @ ZZH @ (dsetconstr @ ZZF @ (ZZG))) = (ZZG @ ZZH))) & ((ZZI = emptyset) | (in @ (sk20 @ ZZI) @ ZZI)) & (~ (in @ ZZL @ ZZJ) | ~ (ZZK @ ZZL) | ~ ((dsetconstr @ ZZJ @ (ZZK)) = emptyset)) & (~ (in @ ZZN @ ZZM) | ~ (ZZM = emptyset)) & (in @ ZZO @ (setadjoin @ ZZO @ ZZP)) & (in @ emptyset @ (setadjoin @ emptyset @ emptyset)) & (~ (in @ ZZS @ ZZR) | (in @ ZZS @ (setadjoin @ ZZQ @ ZZR))) & (~ (in @ ZZV @ (setadjoin @ ZZT @ ZZU)) | (ZZV = ZZT) | (in @ ZZV @ ZZU) | (ZZW)) & (~ (in @ ZZV @ (setadjoin @ ZZT @ ZZU)) | (ZZV = ZZT) | ~ (ZZW) | (ZZW)) & (~ (in @ ZZV @ (setadjoin @ ZZT @ ZZU)) | ~ (ZZW) | (in @ ZZV @ ZZU) | (ZZW)) & (~ (in @ ZZV @ (setadjoin @ ZZT @ ZZU)) | ~ (ZZW) | ~ (ZZW) | (ZZW)) & (~ (in @ ZZZ @ (setadjoin @ ZZX @ ZZY)) | (ZZZ = ZZX) | (in @ ZZZ @ ZZY)) & ((dsetconstr @ ZZZA @ (^ [ZZZZZZZZZZU:$i]: (($true)))) = ZZZA) & ((in @ (sk21 @ ZZZC @ ZZZB) @ ZZZC) | (in @ ZZZC @ (powerset @ ZZZB))) & (~ (in @ (sk21 @ ZZZC @ ZZZB) @ ZZZB) | (in @ ZZZC @ (powerset @ ZZZB))) & (in @ emptyset @ (powerset @ ZZZD)) & (in @ emptyset @ (powerset @ ZZZE)) & (~ (in @ ZZZG @ (powerset @ ZZZF)) | ~ (in @ ZZZH @ ZZZG) | (in @ ZZZH @ ZZZF)) & (~ (in @ ZZZJ @ ZZZK) | ~ (in @ ZZZK @ ZZZI) | (in @ ZZZJ @ (setunion @ ZZZI))) & (~ (in @ ZZZM @ (setunion @ ZZZL)) | (in @ ZZZM @ (sk22 @ ZZZN @ ZZZM @ ZZZL)) | (ZZZN)) & (~ (in @ ZZZM @ (setunion @ ZZZL)) | (in @ (sk22 @ ZZZN @ ZZZM @ ZZZL) @ ZZZL) | (ZZZN)) & (~ (in @ ZZZM @ (setunion @ ZZZL)) | ~ (ZZZN) | (ZZZN)) & (~ (in @ ZZZP @ ZZZO) | (in @ ZZZP @ (powerset @ (setunion @ ZZZO)))) & (~ (ZZZQ @ ZZZR) | (ZZZQ @ (sk23 @ ZZZR @ (ZZZQ))) | ((ZZZQ @ ZZZS) = (ZZZS = (sk24 @ (ZZZQ))))) & (~ (ZZZQ @ ZZZR) | ~ (ZZZR = (sk23 @ ZZZR @ (ZZZQ))) | ((ZZZQ @ ZZZS) = (ZZZS = (sk24 @ (ZZZQ))))) & ((ZZZT = emptyset) | (in @ (sk25 @ ZZZT) @ ZZZT)) & (~ (in @ ZZZU @ (setadjoin @ ZZZV @ emptyset)) | (ZZZU = ZZZV)) & ((ZZZW = ZZZX) | ~ (in @ ZZZX @ (setadjoin @ ZZZW @ emptyset))) & (~ (ZZZY = ZZZZ) | (in @ ZZZY @ (setadjoin @ ZZZZ @ emptyset))) & (~ (in @ ZZZZA @ (setadjoin @ ZZZZB @ emptyset)) | (in @ ZZZZB @ (setadjoin @ ZZZZA @ emptyset))) & (~ (in @ ZZZZE @ (setadjoin @ ZZZZC @ (setadjoin @ ZZZZD @ emptyset))) | (ZZZZE = ZZZZC) | (ZZZZE = ZZZZD)) & (in @ ZZZZF @ (setadjoin @ ZZZZF @ (setadjoin @ ZZZZG @ emptyset))) & (in @ ZZZZI @ (setadjoin @ ZZZZH @ (setadjoin @ ZZZZI @ emptyset))) & (~ (in @ ZZZZL @ ZZZZJ) | ~ (ZZZZK @ ZZZZL) | ~ ((dsetconstr @ ZZZZJ @ (ZZZZK)) = emptyset)) & (~ (in @ ZZZZN @ emptyset) | (ZZZZM @ ZZZZN)) & (~ (in @ ZZZZQ @ ZZZZO) | (ZZZZP @ ZZZZQ) | (in @ (sk26 @ (ZZZZP) @ ZZZZO) @ ZZZZO)) & (~ (in @ ZZZZQ @ ZZZZO) | (ZZZZP @ ZZZZQ) | ~ (ZZZZP @ (sk26 @ (ZZZZP) @ ZZZZO))) & ((in @ (sk27 @ (ZZZZS) @ ZZZZR) @ ZZZZR) | ~ (in @ ZZZZT @ ZZZZR) | ~ (ZZZZS @ ZZZZT)) & ((ZZZZS @ (sk27 @ (ZZZZS) @ ZZZZR)) | ~ (in @ ZZZZT @ ZZZZR) | ~ (ZZZZS @ ZZZZT)) & ((in @ (sk28 @ (ZZZZV) @ ZZZZU) @ ZZZZU) | ~ (in @ ZZZZW @ ZZZZU) | ~ (ZZZZV @ ZZZZW)) & ((ZZZZV @ (sk28 @ (ZZZZV) @ ZZZZU)) | ~ (in @ ZZZZW @ ZZZZU) | ~ (ZZZZV @ ZZZZW)) & (~ (in @ ZZZZZ @ ZZZZX) | (ZZZZY @ ZZZZZ) | (in @ (sk29 @ (ZZZZY) @ ZZZZX) @ ZZZZX)) & (~ (in @ ZZZZZ @ ZZZZX) | (ZZZZY @ ZZZZZ) | ~ (ZZZZY @ (sk29 @ (ZZZZY) @ ZZZZX))) & (~ (ZZZZZA) | (in @ emptyset @ (prop2set @ ZZZZZA))) & (~ (ZZZZZB) | (set2prop @ (prop2set @ ZZZZZB))) & ((in @ (sk30 @ (ZZZZZD) @ ZZZZZC) @ ZZZZZC) | ~ (in @ ZZZZZE @ ZZZZZC) | ~ (ZZZZZD @ ZZZZZE)) & ((ZZZZZD @ (sk30 @ (ZZZZZD) @ ZZZZZC)) | ~ (in @ ZZZZZE @ ZZZZZC) | ~ (ZZZZZD @ ZZZZZE)) & (~ (in @ ZZZZZH @ ZZZZZF) | (ZZZZZG @ ZZZZZH) | (in @ (sk31 @ (ZZZZZG) @ ZZZZZF) @ ZZZZZF)) & (~ (in @ ZZZZZH @ ZZZZZF) | (ZZZZZG @ ZZZZZH) | ~ (ZZZZZG @ (sk31 @ (ZZZZZG) @ ZZZZZF))) & (~ (ZZZZZI @ ZZZZZJ) | (ZZZZZI @ (sk32 @ (ZZZZZI))) | (ZZZZZI @ (sk34 @ (ZZZZZI)))) & (~ (ZZZZZI @ ZZZZZJ) | (ZZZZZI @ (sk32 @ (ZZZZZI))) | ~ (ZZZZZI @ ZZZZZK) | ((sk34 @ (ZZZZZI)) = ZZZZZK)) & (~ (ZZZZZI @ ZZZZZJ) | (ZZZZZI @ (sk33 @ (ZZZZZI))) | (ZZZZZI @ (sk34 @ (ZZZZZI)))) & (~ (ZZZZZI @ ZZZZZJ) | (ZZZZZI @ (sk33 @ (ZZZZZI))) | ~ (ZZZZZI @ ZZZZZK) | ((sk34 @ (ZZZZZI)) = ZZZZZK)) & (~ (ZZZZZI @ ZZZZZJ) | ~ ((sk32 @ (ZZZZZI)) = (sk33 @ (ZZZZZI))) | (ZZZZZI @ (sk34 @ (ZZZZZI)))) & (~ (ZZZZZI @ ZZZZZJ) | ~ ((sk32 @ (ZZZZZI)) = (sk33 @ (ZZZZZI))) | ~ (ZZZZZI @ ZZZZZK) | ((sk34 @ (ZZZZZI)) = ZZZZZK)) & (~ ((ZZZZZL @ (sk35 @ ZZZZZM @ (ZZZZZL))) = ((sk35 @ ZZZZZM @ (ZZZZZL)) = ZZZZZM)) | (ZZZZZL @ (sk36 @ (ZZZZZL)))) & (~ ((ZZZZZL @ (sk35 @ ZZZZZM @ (ZZZZZL))) = ((sk35 @ ZZZZZM @ (ZZZZZL)) = ZZZZZM)) | ~ (ZZZZZL @ ZZZZZN) | ((sk36 @ (ZZZZZL)) = ZZZZZN)) & (~ (ZZZZZO = ZZZZZP) | ~ (ZZZZZQ = ZZZZZR) | ~ (in @ ZZZZZQ @ ZZZZZO) | (in @ ZZZZZR @ ZZZZZP)) & (~ (ZZZZZS = ZZZZZT) | ~ (ZZZZZU = ZZZZZV) | ((in @ ZZZZZU @ ZZZZZS) = (in @ ZZZZZV @ ZZZZZT))) & (~ (ZZZZZW @ ZZZZZX) | (ZZZZZW @ (sk37 @ ZZZZZX @ (ZZZZZW))) | ~ (ZZZZZW @ ZZZZZY) | ~ (ZZZZZW @ ZZZZZZ) | (ZZZZZY = ZZZZZZ)) & (~ (ZZZZZW @ ZZZZZX) | ~ (ZZZZZX = (sk37 @ ZZZZZX @ (ZZZZZW))) | ~ (ZZZZZW @ ZZZZZY) | ~ (ZZZZZW @ ZZZZZZ) | (ZZZZZY = ZZZZZZ)) & (((sk38 @ (ZZZZZZB) @ (ZZZZZZA)) = (sk39 @ (ZZZZZZB) @ (ZZZZZZA))) | ((? [ZZZZZZZZZZU:$i]: ((ZZZZZZA @ ZZZZZZZZZZU) & ! [ZZZZZZZZZZV:$i]: ((ZZZZZZA @ ZZZZZZZZZZV) => (ZZZZZZZZZZU = ZZZZZZZZZZV)))) = (? [ZZZZZZZZZZU:$i]: ((ZZZZZZB @ ZZZZZZZZZZU) & ! [ZZZZZZZZZZV:$i]: ((ZZZZZZB @ ZZZZZZZZZZV) => (ZZZZZZZZZZU = ZZZZZZZZZZV)))))) & (~ ((ZZZZZZA @ (sk38 @ (ZZZZZZB) @ (ZZZZZZA))) = (ZZZZZZB @ (sk39 @ (ZZZZZZB) @ (ZZZZZZA)))) | ((? [ZZZZZZZZZZU:$i]: ((ZZZZZZA @ ZZZZZZZZZZU) & ! [ZZZZZZZZZZV:$i]: ((ZZZZZZA @ ZZZZZZZZZZV) => (ZZZZZZZZZZU = ZZZZZZZZZZV)))) = (? [ZZZZZZZZZZU:$i]: ((ZZZZZZB @ ZZZZZZZZZZU) & ! [ZZZZZZZZZZV:$i]: ((ZZZZZZB @ ZZZZZZZZZZV) => (ZZZZZZZZZZU = ZZZZZZZZZZV)))))) & (~ (ZZZZZZC = ZZZZZZD) | ~ (ZZZZZZE = ZZZZZZF) | ((setadjoin @ ZZZZZZC @ ZZZZZZE) = (setadjoin @ ZZZZZZD @ ZZZZZZF))) & (~ (ZZZZZZG = ZZZZZZH) | ((powerset @ ZZZZZZG) = (powerset @ ZZZZZZH))) & (~ (ZZZZZZI = ZZZZZZJ) | ((setunion @ ZZZZZZI) = (setunion @ ZZZZZZJ))) & (~ (ZZZZZZK @ ZZZZZZL) | (ZZZZZZK @ (sk40 @ ZZZZZZL @ (ZZZZZZK))) | ~ (ZZZZZZK @ ZZZZZZM) | ~ (ZZZZZZK @ ZZZZZZN) | (ZZZZZZM = ZZZZZZN)) & (~ (ZZZZZZK @ ZZZZZZL) | ~ (ZZZZZZL = (sk40 @ ZZZZZZL @ (ZZZZZZK))) | ~ (ZZZZZZK @ ZZZZZZM) | ~ (ZZZZZZK @ ZZZZZZN) | (ZZZZZZM = ZZZZZZN)) & (((sk42 @ (ZZZZZZP) @ (ZZZZZZO)) = (sk43 @ (ZZZZZZP) @ (ZZZZZZO))) | (sk41 @ ZZZZZZO @ ZZZZZZP)) & (~ ((ZZZZZZO @ (sk42 @ (ZZZZZZP) @ (ZZZZZZO))) = (ZZZZZZP @ (sk43 @ (ZZZZZZP) @ (ZZZZZZO)))) | (sk41 @ ZZZZZZO @ ZZZZZZP)) & (~ (sk41 @ ZZZZZZO @ ZZZZZZP) | ~ (ZZZZZZO @ ZZZZZZQ) | (ZZZZZZO @ (sk44 @ ZZZZZZQ @ (ZZZZZZP) @ (ZZZZZZO))) | ~ (ZZZZZZP @ ZZZZZZR) | (ZZZZZZP @ (sk45 @ ZZZZZZR @ (ZZZZZZP) @ (ZZZZZZO))) | ((descr @ (ZZZZZZO)) = (descr @ (ZZZZZZP)))) & (~ (sk41 @ ZZZZZZO @ ZZZZZZP) | ~ (ZZZZZZO @ ZZZZZZQ) | (ZZZZZZO @ (sk44 @ ZZZZZZQ @ (ZZZZZZP) @ (ZZZZZZO))) | ~ (ZZZZZZP @ ZZZZZZR) | ~ (ZZZZZZR = (sk45 @ ZZZZZZR @ (ZZZZZZP) @ (ZZZZZZO))) | ((descr @ (ZZZZZZO)) = (descr @ (ZZZZZZP)))) & (~ (sk41 @ ZZZZZZO @ ZZZZZZP) | ~ (ZZZZZZO @ ZZZZZZQ) | ~ (ZZZZZZQ = (sk44 @ ZZZZZZQ @ (ZZZZZZP) @ (ZZZZZZO))) | ~ (ZZZZZZP @ ZZZZZZR) | (ZZZZZZP @ (sk45 @ ZZZZZZR @ (ZZZZZZP) @ (ZZZZZZO))) | ((descr @ (ZZZZZZO)) = (descr @ (ZZZZZZP)))) & (~ (sk41 @ ZZZZZZO @ ZZZZZZP) | ~ (ZZZZZZO @ ZZZZZZQ) | ~ (ZZZZZZQ = (sk44 @ ZZZZZZQ @ (ZZZZZZP) @ (ZZZZZZO))) | ~ (ZZZZZZP @ ZZZZZZR) | ~ (ZZZZZZR = (sk45 @ ZZZZZZR @ (ZZZZZZP) @ (ZZZZZZO))) | ((descr @ (ZZZZZZO)) = (descr @ (ZZZZZZP)))) & (~ (ZZZZZZS = ZZZZZZT) | (in @ (sk46 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS) @ ZZZZZZS) | ((dsetconstr @ ZZZZZZS @ (ZZZZZZU)) = (dsetconstr @ ZZZZZZT @ (ZZZZZZV)))) & (~ (ZZZZZZS = ZZZZZZT) | (in @ (sk47 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS) @ ZZZZZZT) | ((dsetconstr @ ZZZZZZS @ (ZZZZZZU)) = (dsetconstr @ ZZZZZZT @ (ZZZZZZV)))) & (~ (ZZZZZZS = ZZZZZZT) | ((sk46 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS) = (sk47 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS)) | ((dsetconstr @ ZZZZZZS @ (ZZZZZZU)) = (dsetconstr @ ZZZZZZT @ (ZZZZZZV)))) & (~ (ZZZZZZS = ZZZZZZT) | ~ ((ZZZZZZU @ (sk46 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS)) = (ZZZZZZV @ (sk47 @ (ZZZZZZV) @ (ZZZZZZU) @ ZZZZZZT @ ZZZZZZS))) | ((dsetconstr @ ZZZZZZS @ (ZZZZZZU)) = (dsetconstr @ ZZZZZZT @ (ZZZZZZV)))) & ((in @ (sk48 @ ZZZZZZX @ ZZZZZZW) @ ZZZZZZW) | (subset @ ZZZZZZW @ ZZZZZZX)) & (~ (in @ (sk48 @ ZZZZZZX @ ZZZZZZW) @ ZZZZZZX) | (subset @ ZZZZZZW @ ZZZZZZX)) & (~ (ZZZZZZY = ZZZZZZZ) | (subset @ ZZZZZZZ @ ZZZZZZY)) & (~ (ZZZZZZZA = ZZZZZZZB) | (subset @ ZZZZZZZA @ ZZZZZZZB)) & ((in @ (sk49 @ ZZZZZZZD @ ZZZZZZZC) @ ZZZZZZZC) | (subset @ ZZZZZZZC @ ZZZZZZZD)) & (~ (in @ (sk49 @ ZZZZZZZD @ ZZZZZZZC) @ ZZZZZZZD) | (subset @ ZZZZZZZC @ ZZZZZZZD)) & (subset @ emptyset @ ZZZZZZZE) & (~ (subset @ ZZZZZZZF @ ZZZZZZZG) | ~ (in @ ZZZZZZZH @ ZZZZZZZF) | (in @ ZZZZZZZH @ ZZZZZZZG)) & (~ (subset @ ZZZZZZZI @ ZZZZZZZJ) | (in @ ZZZZZZZK @ ZZZZZZZJ) | ~ (in @ ZZZZZZZK @ ZZZZZZZI)) & (~ (in @ ZZZZZZZN @ ZZZZZZZL) | (in @ ZZZZZZZN @ ZZZZZZZM) | ~ (subset @ ZZZZZZZL @ ZZZZZZZM)) & ((subset @ ZZZZZZZO @ ZZZZZZZP) | ~ (ZZZZZZZO = ZZZZZZZP)) & (~ (in @ ZZZZZZZS @ ZZZZZZZQ) | (in @ ZZZZZZZS @ ZZZZZZZR) | ~ (ZZZZZZZQ = ZZZZZZZR)) & (subset @ ZZZZZZZT @ ZZZZZZZT) & (~ (subset @ ZZZZZZZU @ ZZZZZZZV) | ~ (subset @ ZZZZZZZV @ ZZZZZZZW) | (subset @ ZZZZZZZU @ ZZZZZZZW)) & (subset @ ZZZZZZZY @ (setadjoin @ ZZZZZZZX @ ZZZZZZZY)) & (~ (subset @ ZZZZZZZZ @ ZZZZZZZZB) | (subset @ ZZZZZZZZ @ (setadjoin @ ZZZZZZZZA @ ZZZZZZZZB))) & (~ (subset @ ZZZZZZZZC @ ZZZZZZZZD) | (in @ ZZZZZZZZC @ (powerset @ ZZZZZZZZD))) & (~ (subset @ ZZZZZZZZE @ ZZZZZZZZF) | ~ (subset @ ZZZZZZZZF @ ZZZZZZZZE) | (ZZZZZZZZE = ZZZZZZZZF)) & (~ (subset @ ZZZZZZZZG @ emptyset) | (ZZZZZZZZG = emptyset)) & (~ (subset @ ZZZZZZZZI @ ZZZZZZZZH) | (in @ ZZZZZZZZI @ (powerset @ ZZZZZZZZH))) & (~ (in @ ZZZZZZZZK @ (powerset @ ZZZZZZZZJ)) | (subset @ ZZZZZZZZK @ ZZZZZZZZJ)) & (in @ ZZZZZZZZL @ (powerset @ ZZZZZZZZL)) & (~ (subset @ ZZZZZZZZM @ ZZZZZZZZN) | (subset @ (powerset @ ZZZZZZZZM) @ (powerset @ ZZZZZZZZN))) & (in @ (dsetconstr @ ZZZZZZZZO @ (ZZZZZZZZP)) @ (powerset @ ZZZZZZZZO)) & (subset @ (dsetconstr @ ZZZZZZZZQ @ (ZZZZZZZZR)) @ ZZZZZZZZQ) & (~ (in @ ZZZZZZZZU @ ZZZZZZZZS) | (in @ ZZZZZZZZU @ (binunion @ ZZZZZZZZS @ ZZZZZZZZT))) & (in @ ZZZZZZZZW @ (setadjoin @ ZZZZZZZZV @ (setadjoin @ ZZZZZZZZW @ emptyset))) & (~ (in @ ZZZZZZZZZ @ ZZZZZZZZY) | (in @ ZZZZZZZZZ @ (binunion @ ZZZZZZZZX @ ZZZZZZZZY))) & (~ (in @ ZZZZZZZZZC @ (binunion @ ZZZZZZZZZA @ ZZZZZZZZZB)) | (in @ ZZZZZZZZZC @ ZZZZZZZZZA) | (in @ ZZZZZZZZZC @ ZZZZZZZZZB) | (ZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZC @ (binunion @ ZZZZZZZZZA @ ZZZZZZZZZB)) | (in @ ZZZZZZZZZC @ ZZZZZZZZZA) | ~ (ZZZZZZZZZD) | (ZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZC @ (binunion @ ZZZZZZZZZA @ ZZZZZZZZZB)) | ~ (ZZZZZZZZZD) | (in @ ZZZZZZZZZC @ ZZZZZZZZZB) | (ZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZC @ (binunion @ ZZZZZZZZZA @ ZZZZZZZZZB)) | ~ (ZZZZZZZZZD) | ~ (ZZZZZZZZZD) | (ZZZZZZZZZD)) & (~ (in @ ZZZZZZZZZG @ (binunion @ ZZZZZZZZZE @ ZZZZZZZZZF)) | (in @ ZZZZZZZZZG @ ZZZZZZZZZE) | (in @ ZZZZZZZZZG @ ZZZZZZZZZF)) & (subset @ ZZZZZZZZZH @ (binunion @ ZZZZZZZZZH @ ZZZZZZZZZI)) & (subset @ ZZZZZZZZZK @ (binunion @ ZZZZZZZZZJ @ ZZZZZZZZZK)) & (~ (in @ ZZZZZZZZZN @ ZZZZZZZZZL) | ~ (in @ ZZZZZZZZZN @ ZZZZZZZZZM) | (in @ ZZZZZZZZZN @ (binintersect @ ZZZZZZZZZL @ ZZZZZZZZZM))) & (~ (subset @ ZZZZZZZZZQ @ ZZZZZZZZZO) | ~ (subset @ ZZZZZZZZZQ @ ZZZZZZZZZP) | (subset @ ZZZZZZZZZQ @ (binintersect @ ZZZZZZZZZO @ ZZZZZZZZZP))) & (~ (in @ ZZZZZZZZZT @ (binintersect @ ZZZZZZZZZR @ ZZZZZZZZZS)) | (in @ ZZZZZZZZZT @ ZZZZZZZZZR)) & (subset @ (binintersect @ ZZZZZZZZZU @ ZZZZZZZZZV) @ ZZZZZZZZZU) & (~ (subset @ ZZZZZZZZZW @ ZZZZZZZZZX) | ((binintersect @ ZZZZZZZZZW @ ZZZZZZZZZX) = ZZZZZZZZZW)) & (~ ((binintersect @ ZZZZZZZZZY @ ZZZZZZZZZZ) = ZZZZZZZZZZ) | (subset @ ZZZZZZZZZZ @ ZZZZZZZZZY)) & (~ (in @ ZZZZZZZZZZC @ (binintersect @ ZZZZZZZZZZA @ ZZZZZZZZZZB)) | (in @ ZZZZZZZZZZC @ ZZZZZZZZZZB)) & ((in @ (sk50 @ ZZZZZZZZZZE @ ZZZZZZZZZZD) @ ZZZZZZZZZZD) | ((binintersect @ ZZZZZZZZZZD @ ZZZZZZZZZZE) = emptyset)) & ((in @ (sk50 @ ZZZZZZZZZZE @ ZZZZZZZZZZD) @ ZZZZZZZZZZE) | ((binintersect @ ZZZZZZZZZZD @ ZZZZZZZZZZE) = emptyset)) & (subset @ (binintersect @ ZZZZZZZZZZF @ ZZZZZZZZZZG) @ ZZZZZZZZZZG) & (~ (subset @ ZZZZZZZZZZI @ ZZZZZZZZZZH) | ((binintersect @ ZZZZZZZZZZH @ ZZZZZZZZZZI) = ZZZZZZZZZZI)) & (~ ((binintersect @ ZZZZZZZZZZJ @ ZZZZZZZZZZK) = ZZZZZZZZZZJ) | (subset @ ZZZZZZZZZZJ @ ZZZZZZZZZZK)) & ((binintersect @ ZZZZZZZZZZL @ (binunion @ ZZZZZZZZZZM @ ZZZZZZZZZZN)) = (binunion @ (binintersect @ ZZZZZZZZZZL @ ZZZZZZZZZZM) @ (binintersect @ ZZZZZZZZZZL @ ZZZZZZZZZZN))) & (~ (in @ ZZZZZZZZZZQ @ ZZZZZZZZZZO) | (in @ ZZZZZZZZZZQ @ ZZZZZZZZZZP) | (in @ ZZZZZZZZZZQ @ (dsetconstr @ ZZZZZZZZZZO @ (^ [ZZZZZZZZZZU:$i]: ~ (in @ ZZZZZZZZZZU @ ZZZZZZZZZZP))))) & (~ (in @ ZZZZZZZZZZT @ (dsetconstr @ ZZZZZZZZZZR @ (^ [ZZZZZZZZZZU:$i]: ~ (in @ ZZZZZZZZZZU @ ZZZZZZZZZZS)))) | (in @ ZZZZZZZZZZT @ ZZZZZZZZZZR)) & (in @ sk53 @ (dsetconstr @ sk51 @ (^ [ZZZZZZZZZZU:$i]: ~ (in @ ZZZZZZZZZZU @ sk52)))) & (in @ sk53 @ sk52)))),inference(cnf,[status(esa)],[4])).
% 15.31/5.61  thf(105,plain,((in @ sk53 @ (dsetconstr @ sk51 @ (^ [A:$i]: ~ (in @ A @ sk52))))),inference(cnfConj,[status(thm)],[5])).
% 15.31/5.61  thf(101,plain,(! [C:$i,B:($i > $o),A:$i] : ((~ (in @ C @ (dsetconstr @ A @ (B)))) | (B @ C))),inference(cnfConj,[status(thm)],[5])).
% 15.31/5.61  thf(203,plain,(! [C:$i,B:($i > $o),A:$i] : ((~ (in @ C @ (dsetconstr @ A @ (B)))) | (B @ C))),inference(simp,[status(thm)],[101])).
% 15.31/5.61  thf(659,plain,(! [C:$i,B:($i > $o),A:$i] : (~ (($true)) | (B @ C) | ((in @ sk53 @ (dsetconstr @ sk51 @ (^ [D:$i]: ~ (in @ D @ sk52)))) != (in @ C @ (dsetconstr @ A @ (B)))))),inference(paramod_ordered,[status(thm)],[105,203])).
% 15.31/5.61  thf(660,plain,(! [C:$i,B:($i > $o),A:$i] : ((B @ C) | ((in @ sk53 @ (dsetconstr @ sk51 @ (^ [D:$i]: ~ (in @ D @ sk52)))) != (in @ C @ (dsetconstr @ A @ (B)))))),inference(simp,[status(thm)],[659])).
% 15.31/5.61  thf(661,plain,((~ (in @ sk53 @ sk52))),inference(pattern_uni,[status(thm)],[660:[bind(A, $thf(sk51)),bind(B, $thf(^ [D:$i]: ~ (in @ D @ sk52))),bind(C, $thf(sk53))]])).
% 15.31/5.61  thf(706,plain,((~ (in @ sk53 @ sk52))),inference(cnf,[status(esa)],[661])).
% 15.31/5.61  thf(27,plain,((in @ sk53 @ sk52)),inference(cnfConj,[status(thm)],[5])).
% 15.31/5.61  thf(731,plain,(~ (($true))),inference(rewrite,[status(thm)],[706,27])).
% 15.31/5.61  thf(732,plain,(($false)),inference(simp,[status(thm)],[731])).
% 15.31/5.61  % SZS output end Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.31/5.61  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------