TSTP Solution File: SEU780^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU780^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:30:10 EDT 2024
% Result : Theorem 1.21s 0.65s
% Output : CNFRefutation 1.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU780^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n005.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:19:38 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.22/0.49 Running higher-order theorem proving
% 0.22/0.50 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.21/0.65 # Version: 3.1.0-ho
% 1.21/0.65 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.21/0.65 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.65 # Starting ehoh_best5 with 300s (1) cores
% 1.21/0.65 # Starting almost_fo_3_lam with 300s (1) cores
% 1.21/0.65 # Starting new_bool_5 with 300s (1) cores
% 1.21/0.65 # Starting pre_casc_3 with 300s (1) cores
% 1.21/0.65 # Starting ho_unfolding_8 with 300s (1) cores
% 1.21/0.65 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.21/0.65 # Starting new_bool_3 with 300s (1) cores
% 1.21/0.65 # Starting new_ho_5 with 300s (1) cores
% 1.21/0.65 # pre_casc_3 with pid 10049 completed with status 0
% 1.21/0.65 # Result found by pre_casc_3
% 1.21/0.65 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.21/0.65 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.65 # Starting ehoh_best5 with 300s (1) cores
% 1.21/0.65 # Starting almost_fo_3_lam with 300s (1) cores
% 1.21/0.65 # Starting new_bool_5 with 300s (1) cores
% 1.21/0.65 # Starting pre_casc_3 with 300s (1) cores
% 1.21/0.65 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 1.21/0.65 # Search class: HGHSM-FSLM33-MHFMMFBN
% 1.21/0.65 # partial match(2): HGHSM-FSLM32-MHFMMSBN
% 1.21/0.65 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.21/0.65 # Starting ho_unfolding_8 with 61s (1) cores
% 1.21/0.65 # ho_unfolding_8 with pid 10071 completed with status 0
% 1.21/0.65 # Result found by ho_unfolding_8
% 1.21/0.65 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.21/0.65 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.21/0.65 # Starting ehoh_best5 with 300s (1) cores
% 1.21/0.65 # Starting almost_fo_3_lam with 300s (1) cores
% 1.21/0.65 # Starting new_bool_5 with 300s (1) cores
% 1.21/0.65 # Starting pre_casc_3 with 300s (1) cores
% 1.21/0.65 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 1.21/0.65 # Search class: HGHSM-FSLM33-MHFMMFBN
% 1.21/0.65 # partial match(2): HGHSM-FSLM32-MHFMMSBN
% 1.21/0.65 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.21/0.65 # Starting ho_unfolding_8 with 61s (1) cores
% 1.21/0.65 # Preprocessing time : 0.033 s
% 1.21/0.65 # Presaturation interreduction done
% 1.21/0.65
% 1.21/0.65 # Proof found!
% 1.21/0.65 # SZS status Theorem
% 1.21/0.65 # SZS output start CNFRefutation
% 1.21/0.65 thf(decl_22, type, in: $i > $i > $o).
% 1.21/0.65 thf(decl_24, type, setextAx: $o).
% 1.21/0.65 thf(decl_25, type, emptyset: $i).
% 1.21/0.65 thf(decl_26, type, emptysetAx: $o).
% 1.21/0.65 thf(decl_27, type, setadjoin: $i > $i > $i).
% 1.21/0.65 thf(decl_28, type, setadjoinAx: $o).
% 1.21/0.65 thf(decl_30, type, powersetAx: $o).
% 1.21/0.65 thf(decl_31, type, setunion: $i > $i).
% 1.21/0.65 thf(decl_32, type, setunionAx: $o).
% 1.21/0.65 thf(decl_34, type, omega0Ax: $o).
% 1.21/0.65 thf(decl_35, type, omegaSAx: $o).
% 1.21/0.65 thf(decl_36, type, omegaIndAx: $o).
% 1.21/0.65 thf(decl_37, type, replAx: $o).
% 1.21/0.65 thf(decl_38, type, foundationAx: $o).
% 1.21/0.65 thf(decl_39, type, wellorderingAx: $o).
% 1.21/0.65 thf(decl_41, type, descrp: $o).
% 1.21/0.65 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
% 1.21/0.65 thf(decl_43, type, dsetconstrI: $o).
% 1.21/0.65 thf(decl_44, type, dsetconstrEL: $o).
% 1.21/0.65 thf(decl_45, type, dsetconstrER: $o).
% 1.21/0.65 thf(decl_46, type, exuE1: $o).
% 1.21/0.65 thf(decl_48, type, prop2setE: $o).
% 1.21/0.65 thf(decl_49, type, emptysetE: $o).
% 1.21/0.65 thf(decl_50, type, emptysetimpfalse: $o).
% 1.21/0.65 thf(decl_51, type, notinemptyset: $o).
% 1.21/0.65 thf(decl_52, type, exuE3e: $o).
% 1.21/0.65 thf(decl_53, type, setext: $o).
% 1.21/0.65 thf(decl_54, type, emptyI: $o).
% 1.21/0.65 thf(decl_55, type, noeltsimpempty: $o).
% 1.21/0.65 thf(decl_56, type, setbeta: $o).
% 1.21/0.65 thf(decl_58, type, nonemptyE1: $o).
% 1.21/0.65 thf(decl_59, type, nonemptyI: $o).
% 1.21/0.65 thf(decl_60, type, nonemptyI1: $o).
% 1.21/0.65 thf(decl_61, type, setadjoinIL: $o).
% 1.21/0.65 thf(decl_62, type, emptyinunitempty: $o).
% 1.21/0.65 thf(decl_63, type, setadjoinIR: $o).
% 1.21/0.65 thf(decl_64, type, setadjoinE: $o).
% 1.21/0.65 thf(decl_65, type, setadjoinOr: $o).
% 1.21/0.65 thf(decl_66, type, setoftrueEq: $o).
% 1.21/0.65 thf(decl_67, type, powersetI: $o).
% 1.21/0.65 thf(decl_68, type, emptyinPowerset: $o).
% 1.21/0.65 thf(decl_69, type, emptyInPowerset: $o).
% 1.21/0.65 thf(decl_70, type, powersetE: $o).
% 1.21/0.65 thf(decl_71, type, setunionI: $o).
% 1.21/0.65 thf(decl_72, type, setunionE: $o).
% 1.21/0.65 thf(decl_73, type, subPowSU: $o).
% 1.21/0.65 thf(decl_74, type, exuE2: $o).
% 1.21/0.65 thf(decl_75, type, nonemptyImpWitness: $o).
% 1.21/0.65 thf(decl_76, type, uniqinunit: $o).
% 1.21/0.65 thf(decl_77, type, notinsingleton: $o).
% 1.21/0.65 thf(decl_78, type, eqinunit: $o).
% 1.21/0.65 thf(decl_79, type, singletonsswitch: $o).
% 1.21/0.65 thf(decl_80, type, upairsetE: $o).
% 1.21/0.65 thf(decl_81, type, upairsetIL: $o).
% 1.21/0.65 thf(decl_82, type, upairsetIR: $o).
% 1.21/0.65 thf(decl_83, type, emptyE1: $o).
% 1.21/0.65 thf(decl_84, type, vacuousDall: $o).
% 1.21/0.65 thf(decl_85, type, quantDeMorgan1: $o).
% 1.21/0.65 thf(decl_86, type, quantDeMorgan2: $o).
% 1.21/0.65 thf(decl_87, type, quantDeMorgan3: $o).
% 1.21/0.65 thf(decl_88, type, quantDeMorgan4: $o).
% 1.21/0.65 thf(decl_89, type, prop2setI: $o).
% 1.21/0.65 thf(decl_91, type, prop2set2propI: $o).
% 1.21/0.65 thf(decl_92, type, notdexE: $o).
% 1.21/0.65 thf(decl_93, type, notdallE: $o).
% 1.21/0.65 thf(decl_94, type, exuI1: $o).
% 1.21/0.65 thf(decl_95, type, exuI3: $o).
% 1.21/0.65 thf(decl_96, type, exuI2: $o).
% 1.21/0.65 thf(decl_97, type, inCongP: $o).
% 1.21/0.65 thf(decl_98, type, in__Cong: $o).
% 1.21/0.65 thf(decl_99, type, exuE3u: $o).
% 1.21/0.65 thf(decl_100, type, exu__Cong: $o).
% 1.21/0.65 thf(decl_101, type, emptyset__Cong: $o).
% 1.21/0.65 thf(decl_102, type, setadjoin__Cong: $o).
% 1.21/0.65 thf(decl_103, type, powerset__Cong: $o).
% 1.21/0.65 thf(decl_104, type, setunion__Cong: $o).
% 1.21/0.65 thf(decl_105, type, omega__Cong: $o).
% 1.21/0.65 thf(decl_106, type, exuEu: $o).
% 1.21/0.65 thf(decl_107, type, descr__Cong: $o).
% 1.21/0.65 thf(decl_108, type, dsetconstr__Cong: $o).
% 1.21/0.65 thf(decl_109, type, subset: $i > $i > $o).
% 1.21/0.65 thf(decl_112, type, subsetI1: $o).
% 1.21/0.65 thf(decl_113, type, eqimpsubset2: $o).
% 1.21/0.65 thf(decl_114, type, eqimpsubset1: $o).
% 1.21/0.65 thf(decl_115, type, subsetI2: $o).
% 1.21/0.65 thf(decl_116, type, emptysetsubset: $o).
% 1.21/0.65 thf(decl_117, type, subsetE: $o).
% 1.21/0.65 thf(decl_118, type, subsetE2: $o).
% 1.21/0.65 thf(decl_119, type, notsubsetI: $o).
% 1.21/0.65 thf(decl_120, type, notequalI1: $o).
% 1.21/0.65 thf(decl_121, type, notequalI2: $o).
% 1.21/0.65 thf(decl_122, type, subsetRefl: $o).
% 1.21/0.65 thf(decl_123, type, subsetTrans: $o).
% 1.21/0.65 thf(decl_124, type, setadjoinSub: $o).
% 1.21/0.65 thf(decl_125, type, setadjoinSub2: $o).
% 1.21/0.65 thf(decl_126, type, subset2powerset: $o).
% 1.21/0.65 thf(decl_127, type, setextsub: $o).
% 1.21/0.65 thf(decl_128, type, subsetemptysetimpeq: $o).
% 1.21/0.65 thf(decl_129, type, powersetI1: $o).
% 1.21/0.65 thf(decl_130, type, powersetE1: $o).
% 1.21/0.65 thf(decl_131, type, inPowerset: $o).
% 1.21/0.65 thf(decl_132, type, powersetsubset: $o).
% 1.21/0.65 thf(decl_133, type, sepInPowerset: $o).
% 1.21/0.65 thf(decl_134, type, sepSubset: $o).
% 1.21/0.65 thf(decl_136, type, binunionIL: $o).
% 1.21/0.65 thf(decl_137, type, upairset2IR: $o).
% 1.21/0.65 thf(decl_138, type, binunionIR: $o).
% 1.21/0.65 thf(decl_139, type, binunionEcases: $o).
% 1.21/0.65 thf(decl_140, type, binunionE: $o).
% 1.21/0.65 thf(decl_141, type, binunionLsub: $o).
% 1.21/0.65 thf(decl_142, type, binunionRsub: $o).
% 1.21/0.65 thf(decl_144, type, binintersectI: $o).
% 1.21/0.65 thf(decl_145, type, binintersectSubset5: $o).
% 1.21/0.65 thf(decl_146, type, binintersectEL: $o).
% 1.21/0.65 thf(decl_147, type, binintersectLsub: $o).
% 1.21/0.65 thf(decl_148, type, binintersectSubset2: $o).
% 1.21/0.65 thf(decl_149, type, binintersectSubset3: $o).
% 1.21/0.65 thf(decl_150, type, binintersectER: $o).
% 1.21/0.65 thf(decl_151, type, disjointsetsI1: $o).
% 1.21/0.65 thf(decl_152, type, binintersectRsub: $o).
% 1.21/0.65 thf(decl_153, type, binintersectSubset4: $o).
% 1.21/0.65 thf(decl_154, type, binintersectSubset1: $o).
% 1.21/0.65 thf(decl_155, type, bs114d: $o).
% 1.21/0.65 thf(decl_158, type, setminusI: $o).
% 1.21/0.65 thf(decl_159, type, setminusEL: $o).
% 1.21/0.65 thf(decl_160, type, setminusER: $o).
% 1.21/0.65 thf(decl_161, type, setminusSubset2: $o).
% 1.21/0.65 thf(decl_162, type, setminusERneg: $o).
% 1.21/0.65 thf(decl_163, type, setminusELneg: $o).
% 1.21/0.65 thf(decl_164, type, setminusILneg: $o).
% 1.21/0.65 thf(decl_165, type, setminusIRneg: $o).
% 1.21/0.65 thf(decl_166, type, setminusLsub: $o).
% 1.21/0.65 thf(decl_167, type, setminusSubset1: $o).
% 1.21/0.65 thf(decl_169, type, symdiffE: $o).
% 1.21/0.65 thf(decl_170, type, symdiffI1: $o).
% 1.21/0.65 thf(decl_171, type, symdiffI2: $o).
% 1.21/0.65 thf(decl_172, type, symdiffIneg1: $o).
% 1.21/0.65 thf(decl_173, type, symdiffIneg2: $o).
% 1.21/0.65 thf(decl_174, type, iskpair: $i > $o).
% 1.21/0.65 thf(decl_175, type, secondinupair: $o).
% 1.21/0.65 thf(decl_176, type, setukpairIL: $o).
% 1.21/0.65 thf(decl_177, type, setukpairIR: $o).
% 1.21/0.65 thf(decl_178, type, kpairiskpair: $o).
% 1.21/0.65 thf(decl_179, type, kpair: $i > $i > $i).
% 1.21/0.65 thf(decl_180, type, kpairp: $o).
% 1.21/0.65 thf(decl_181, type, cartprod: $i > $i > $i).
% 1.21/0.65 thf(decl_182, type, singletonsubset: $o).
% 1.21/0.65 thf(decl_183, type, singletoninpowerset: $o).
% 1.21/0.65 thf(decl_184, type, singletoninpowunion: $o).
% 1.21/0.65 thf(decl_185, type, upairset2E: $o).
% 1.21/0.65 thf(decl_186, type, upairsubunion: $o).
% 1.21/0.65 thf(decl_187, type, upairinpowunion: $o).
% 1.21/0.65 thf(decl_188, type, ubforcartprodlem1: $o).
% 1.21/0.65 thf(decl_189, type, ubforcartprodlem2: $o).
% 1.21/0.65 thf(decl_190, type, ubforcartprodlem3: $o).
% 1.21/0.65 thf(decl_191, type, cartprodpairin: $o).
% 1.21/0.65 thf(decl_192, type, cartprodmempair1: $o).
% 1.21/0.65 thf(decl_193, type, cartprodmempair: $o).
% 1.21/0.65 thf(decl_194, type, setunionE2: $o).
% 1.21/0.65 thf(decl_195, type, setunionsingleton1: $o).
% 1.21/0.65 thf(decl_196, type, setunionsingleton2: $o).
% 1.21/0.65 thf(decl_197, type, setunionsingleton: $o).
% 1.21/0.65 thf(decl_198, type, singleton: $i > $o).
% 1.21/0.65 thf(decl_199, type, singletonprop: $o).
% 1.21/0.65 thf(decl_201, type, ex1E1: $o).
% 1.21/0.65 thf(decl_202, type, ex1I: $o).
% 1.21/0.65 thf(decl_203, type, ex1I2: $o).
% 1.21/0.65 thf(decl_204, type, singletonsuniq: $o).
% 1.21/0.65 thf(decl_209, type, setukpairinjL1: $o).
% 1.21/0.65 thf(decl_210, type, kfstsingleton: $o).
% 1.21/0.65 thf(decl_211, type, theprop: $o).
% 1.21/0.65 thf(decl_212, type, kfst: $i > $i).
% 1.21/0.65 thf(decl_213, type, kfstpairEq: $o).
% 1.21/0.65 thf(decl_214, type, cartprodfstin: $o).
% 1.21/0.65 thf(decl_215, type, setukpairinjL2: $o).
% 1.21/0.65 thf(decl_216, type, setukpairinjL: $o).
% 1.21/0.65 thf(decl_217, type, setukpairinjR11: $o).
% 1.21/0.65 thf(decl_218, type, setukpairinjR12: $o).
% 1.21/0.65 thf(decl_219, type, setukpairinjR1: $o).
% 1.21/0.65 thf(decl_220, type, upairequniteq: $o).
% 1.21/0.65 thf(decl_221, type, setukpairinjR2: $o).
% 1.21/0.65 thf(decl_222, type, setukpairinjR: $o).
% 1.21/0.65 thf(decl_223, type, ksndsingleton: $o).
% 1.21/0.65 thf(decl_224, type, ksnd: $i > $i).
% 1.21/0.65 thf(decl_225, type, ksndpairEq: $o).
% 1.21/0.65 thf(decl_226, type, kpairsurjEq: $o).
% 1.21/0.65 thf(decl_227, type, cartprodsndin: $o).
% 1.21/0.65 thf(decl_228, type, cartprodpairmemEL: $o).
% 1.21/0.65 thf(decl_229, type, cartprodpairmemER: $o).
% 1.21/0.65 thf(decl_230, type, cartprodmempaircEq: $o).
% 1.21/0.65 thf(decl_231, type, cartprodfstpairEq: $o).
% 1.21/0.65 thf(decl_232, type, cartprodsndpairEq: $o).
% 1.21/0.65 thf(decl_233, type, cartprodpairsurjEq: $o).
% 1.21/0.65 thf(decl_234, type, breln: $i > $i > $i > $o).
% 1.21/0.65 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.21/0.65 thf(decl_236, type, dpsetconstrI: $o).
% 1.21/0.65 thf(decl_237, type, dpsetconstrSub: $o).
% 1.21/0.65 thf(decl_238, type, setOfPairsIsBReln: $o).
% 1.21/0.65 thf(decl_239, type, dpsetconstrERa: $o).
% 1.21/0.65 thf(decl_240, type, dpsetconstrEL1: $o).
% 1.21/0.65 thf(decl_241, type, dpsetconstrEL2: $o).
% 1.21/0.65 thf(decl_242, type, dpsetconstrER: $o).
% 1.21/0.65 thf(decl_243, type, func: $i > $i > $i > $o).
% 1.21/0.65 thf(decl_245, type, funcImageSingleton: $o).
% 1.21/0.65 thf(decl_246, type, apProp: $o).
% 1.21/0.65 thf(decl_248, type, app: $o).
% 1.21/0.65 thf(decl_249, type, infuncsetfunc: $o).
% 1.21/0.65 thf(decl_250, type, ap2p: $o).
% 1.21/0.65 thf(decl_251, type, funcinfuncset: $o).
% 1.21/0.65 thf(decl_252, type, lamProp: $o).
% 1.21/0.65 thf(decl_254, type, lamp: $o).
% 1.21/0.65 thf(decl_255, type, lam2p: $o).
% 1.21/0.65 thf(decl_256, type, brelnall1: $o).
% 1.21/0.65 thf(decl_257, type, brelnall2: $o).
% 1.21/0.65 thf(decl_258, type, ex1E2: $o).
% 1.21/0.65 thf(decl_259, type, funcGraphProp1: $o).
% 1.21/0.65 thf(decl_260, type, funcGraphProp3: $o).
% 1.21/0.65 thf(decl_261, type, funcGraphProp2: $o).
% 1.21/0.65 thf(decl_262, type, funcextLem: $o).
% 1.21/0.65 thf(decl_263, type, funcGraphProp4: $o).
% 1.21/0.65 thf(decl_264, type, subbreln: $o).
% 1.21/0.65 thf(decl_265, type, eqbreln: $o).
% 1.21/0.65 thf(decl_266, type, funcext: $o).
% 1.21/0.65 thf(decl_267, type, funcext2: $o).
% 1.21/0.65 thf(decl_268, type, ap2apEq1: $o).
% 1.21/0.65 thf(decl_269, type, ap2apEq2: $o).
% 1.21/0.65 thf(decl_270, type, beta1: $o).
% 1.21/0.65 thf(decl_271, type, eta1: $o).
% 1.21/0.65 thf(decl_272, type, lam2lamEq: $o).
% 1.21/0.65 thf(decl_273, type, beta2: $o).
% 1.21/0.65 thf(decl_274, type, eta2: $o).
% 1.21/0.65 thf(decl_275, type, iffalseProp1: $o).
% 1.21/0.65 thf(decl_276, type, iffalseProp2: $o).
% 1.21/0.65 thf(decl_277, type, iftrueProp1: $o).
% 1.21/0.65 thf(decl_278, type, iftrueProp2: $o).
% 1.21/0.65 thf(decl_279, type, ifSingleton: $o).
% 1.21/0.65 thf(decl_281, type, ifp: $o).
% 1.21/0.65 thf(decl_282, type, theeq: $o).
% 1.21/0.65 thf(decl_283, type, iftrue: $o).
% 1.21/0.65 thf(decl_284, type, iffalse: $o).
% 1.21/0.65 thf(decl_285, type, iftrueorfalse: $o).
% 1.21/0.65 thf(decl_286, type, binintersectT_lem: $o).
% 1.21/0.65 thf(decl_287, type, binunionT_lem: $o).
% 1.21/0.65 thf(decl_288, type, powersetT_lem: $o).
% 1.21/0.65 thf(decl_289, type, setminusT_lem: $o).
% 1.21/0.65 thf(decl_290, type, complementT_lem: $o).
% 1.21/0.65 thf(decl_291, type, setextT: $o).
% 1.21/0.65 thf(decl_292, type, subsetTI: $o).
% 1.21/0.65 thf(decl_293, type, powersetTI1: $o).
% 1.21/0.65 thf(decl_294, type, powersetTE1: $o).
% 1.21/0.65 thf(decl_295, type, complementTI1: $o).
% 1.21/0.65 thf(decl_296, type, complementTE1: $o).
% 1.21/0.65 thf(decl_297, type, binintersectTELcontra: $o).
% 1.21/0.65 thf(decl_298, type, binintersectTERcontra: $o).
% 1.21/0.65 thf(decl_299, type, contrasubsetT: $o).
% 1.21/0.65 thf(decl_300, type, contrasubsetT1: $o).
% 1.21/0.65 thf(decl_301, type, contrasubsetT2: $o).
% 1.21/0.65 thf(decl_302, type, contrasubsetT3: $o).
% 1.21/0.65 thf(decl_303, type, doubleComplementI1: $o).
% 1.21/0.65 thf(decl_304, type, doubleComplementE1: $o).
% 1.21/0.65 thf(decl_305, type, doubleComplementSub1: $o).
% 1.21/0.65 thf(decl_306, type, doubleComplementSub2: $o).
% 1.21/0.65 thf(decl_307, type, doubleComplementEq: $o).
% 1.21/0.65 thf(decl_308, type, complementTnotintersectT: $o).
% 1.21/0.65 thf(decl_309, type, complementImpComplementIntersect: $o).
% 1.21/0.65 thf(decl_310, type, complementSubsetComplementIntersect: $o).
% 1.21/0.65 thf(decl_311, type, complementInPowersetComplementIntersect: $o).
% 1.21/0.65 thf(decl_312, type, contraSubsetComplement: $o).
% 1.21/0.65 thf(decl_313, type, complementTcontraSubset: $o).
% 1.21/0.65 thf(decl_314, type, binunionTILcontra: $o).
% 1.21/0.65 thf(decl_315, type, binunionTIRcontra: $o).
% 1.21/0.65 thf(decl_316, type, inIntersectImpInUnion: $o).
% 1.21/0.65 thf(decl_317, type, inIntersectImpInUnion2: $o).
% 1.21/0.65 thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
% 1.21/0.65 thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
% 1.21/0.65 thf(decl_320, type, inComplementUnionImpNotIn1: $o).
% 1.21/0.65 thf(decl_321, type, inComplementUnionImpInComplement1: $o).
% 1.21/0.65 thf(decl_322, type, binunionTE: $o).
% 1.21/0.65 thf(decl_323, type, binunionTEcontra: $o).
% 1.21/0.65 thf(decl_324, type, demorgan2a1: $o).
% 1.21/0.65 thf(decl_325, type, complementUnionInPowersetComplement: $o).
% 1.21/0.65 thf(decl_326, type, demorgan2a2: $o).
% 1.21/0.65 thf(decl_327, type, demorgan1a: $o).
% 1.21/0.65 thf(decl_328, type, demorgan1b: $o).
% 1.21/0.65 thf(decl_329, type, demorgan1: $o).
% 1.21/0.65 thf(decl_330, type, demorgan2a: $o).
% 1.21/0.65 thf(decl_331, type, demorgan2b2: $o).
% 1.21/0.65 thf(decl_332, type, demorgan2b: $o).
% 1.21/0.65 thf(decl_333, type, demorgan2: $o).
% 1.21/0.65 thf(decl_334, type, woz13rule0: $o).
% 1.21/0.65 thf(decl_335, type, woz13rule1: $o).
% 1.21/0.65 thf(decl_336, type, woz13rule2: $o).
% 1.21/0.65 thf(decl_337, type, woz13rule3: $o).
% 1.21/0.65 thf(decl_338, type, woz13rule4: $o).
% 1.21/0.65 thf(decl_339, type, woz1_1: $o).
% 1.21/0.65 thf(decl_340, type, woz1_2: $o).
% 1.21/0.65 thf(decl_341, type, woz1_3: $o).
% 1.21/0.65 thf(decl_342, type, woz1_4: $o).
% 1.21/0.65 thf(decl_343, type, woz1_5: $o).
% 1.21/0.65 thf(decl_344, type, breln1: $i > $i > $o).
% 1.21/0.65 thf(decl_345, type, breln1all2: $o).
% 1.21/0.65 thf(decl_346, type, breln1Set: $i > $i).
% 1.21/0.65 thf(decl_347, type, breln1SetBreln1: $o).
% 1.21/0.65 thf(decl_353, type, reflwellordering: $i > $i > $o).
% 1.21/0.65 thf(decl_354, type, choice2fnsingleton: $o).
% 1.21/0.65 thf(decl_355, type, setOfPairsIsBReln1: $o).
% 1.21/0.65 thf(decl_356, type, breln1all1: $o).
% 1.21/0.65 thf(decl_357, type, subbreln1: $o).
% 1.21/0.65 thf(decl_358, type, eqbreln1: $o).
% 1.21/0.65 thf(decl_360, type, breln1invprop: $o).
% 1.21/0.65 thf(decl_361, type, breln1invI: $o).
% 1.21/0.65 thf(decl_362, type, breln1invE: $o).
% 1.21/0.65 thf(decl_363, type, breln1compset: $i > $i > $i > $i).
% 1.21/0.65 thf(decl_364, type, breln1compprop: $o).
% 1.21/0.65 thf(decl_365, type, breln1compI: $o).
% 1.21/0.65 thf(decl_366, type, esk1_3: $i > $i > $i > $i).
% 1.21/0.65 thf(decl_367, type, esk2_3: $i > $i > $i > $i).
% 1.21/0.65 thf(decl_368, type, esk3_2: $i > ($i > $o) > $i).
% 1.21/0.65 thf(decl_369, type, esk4_2: $i > ($i > $o) > $i).
% 1.21/0.65 thf(decl_370, type, esk5_3: $i > $i > ($i > $i) > $i).
% 1.21/0.65 thf(decl_371, type, esk6_4: $i > $i > $i > ($i > $o) > $i).
% 1.21/0.65 thf(decl_372, type, esk7_4: $i > $i > $i > ($i > $o) > $i).
% 1.21/0.65 thf(decl_373, type, esk8_4: $i > $i > $i > ($i > $o) > $i).
% 1.21/0.65 thf(decl_374, type, esk9_4: $i > $i > $i > ($i > $o) > $i).
% 1.21/0.65 thf(decl_375, type, esk10_4: $i > $i > $i > $i > $i).
% 1.21/0.65 thf(decl_376, type, esk11_4: $i > $i > $i > $i > $i).
% 1.21/0.65 thf(decl_377, type, esk12_4: $i > $i > $i > $i > $i).
% 1.21/0.65 thf(decl_378, type, esk13_4: $i > $i > $i > $i > $i).
% 1.21/0.65 thf(decl_379, type, esk14_4: $i > $i > $i > $i > $i).
% 1.21/0.65 thf(decl_380, type, esk15_4: $i > $i > $i > $i > $i).
% 1.21/0.65 thf(decl_381, type, esk16_3: $i > $i > ($i > $i > $o) > $i).
% 1.21/0.65 thf(decl_382, type, esk17_0: $i).
% 1.21/0.65 thf(decl_383, type, esk18_0: $i).
% 1.21/0.65 thf(decl_384, type, esk19_0: $i).
% 1.21/0.65 thf(decl_385, type, esk20_0: $i).
% 1.21/0.65 thf(decl_386, type, esk21_0: $i).
% 1.21/0.65 thf(decl_393, type, epred7_3: $i > $i > $i > $i > $i > $o).
% 1.21/0.65 thf(decl_394, type, esk22_5: $i > $i > $i > $i > $i > $i).
% 1.21/0.65 thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1)).
% 1.21/0.65 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln)).
% 1.21/0.65 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setOfPairsIsBReln1)).
% 1.21/0.65 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setOfPairsIsBReln)).
% 1.21/0.65 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compprop)).
% 1.21/0.65 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonprop)).
% 1.21/0.65 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndsingleton)).
% 1.21/0.65 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstsingleton)).
% 1.21/0.65 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:(((X52 @ X2 @ X3)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', choice2fnsingleton)).
% 1.21/0.65 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ifSingleton)).
% 1.21/0.65 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', funcImageSingleton)).
% 1.21/0.65 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqbreln)).
% 1.21/0.65 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subbreln)).
% 1.21/0.65 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', brelnall2)).
% 1.21/0.65 thf(brelnall1, axiom, ((brelnall1)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', brelnall1)).
% 1.21/0.65 thf(lamProp, axiom, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:(((X30 @ X2)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', lamProp)).
% 1.21/0.65 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrER)).
% 1.21/0.65 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL2)).
% 1.21/0.65 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrEL1)).
% 1.21/0.65 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrERa)).
% 1.21/0.65 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrSub)).
% 1.21/0.65 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrI)).
% 1.21/0.65 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compI)).
% 1.21/0.65 thf(breln1compE, 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)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>((dpsetconstrEL1)=>((dpsetconstrEL2)=>((dpsetconstrER)=>((funcImageSingleton)=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>((lamProp)=>((lamp)=>((lam2p)=>((brelnall1)=>((brelnall2)=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>((subbreln)=>((eqbreln)=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>((ifSingleton)=>((ifp)=>((theeq)=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>((choice2fnsingleton)=>((setOfPairsIsBReln1)=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>((breln1compprop)=>((breln1compI)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compE)).
% 1.21/0.65 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theprop)).
% 1.21/0.65 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndpairEq)).
% 1.21/0.65 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndpairEq)).
% 1.21/0.65 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstpairEq)).
% 1.21/0.65 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstpairEq)).
% 1.21/0.65 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairsurjEq)).
% 1.21/0.65 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)).
% 1.21/0.65 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairiskpair)).
% 1.21/0.65 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairsurjEq)).
% 1.21/0.65 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemER)).
% 1.21/0.65 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemEL)).
% 1.21/0.65 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theeq)).
% 1.21/0.65 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndin)).
% 1.21/0.65 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstin)).
% 1.21/0.65 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)).
% 1.21/0.65 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)).
% 1.21/0.65 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairin)).
% 1.21/0.65 thf(breln1compset, axiom, ((breln1compset)=(^[X4:$i, X33:$i, X35:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:(?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', breln1compset)).
% 1.21/0.65 thf(c_0_42, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
% 1.21/0.65 thf(c_0_43, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 1.21/0.65 thf(c_0_44, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_42, c_0_43])).
% 1.21/0.65 thf(c_0_45, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
% 1.21/0.65 thf(c_0_46, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 1.21/0.65 thf(c_0_47, axiom, ((breln1compprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>((subset @ (breln1compset @ X4 @ X33 @ X35) @ (cartprod @ X4 @ X4))))))))), inference(apply_def,[status(thm)],[breln1compprop, c_0_44])).
% 1.21/0.65 thf(c_0_48, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.21/0.65 thf(c_0_49, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.21/0.65 thf(c_0_50, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.21/0.65 thf(c_0_51, plain, ((choice2fnsingleton)<=>![X4:$i, X5:$i, X52:$i > $i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>?[X3:$i]:(((in @ X3 @ X5)&(X52 @ X2 @ X3)))))=>![X33:$i]:(((in @ X33 @ (breln1Set @ X5))=>((reflwellordering @ X5 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 8 */:$i]:(((X52 @ X2 @ Z0)&![X14:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
% 1.21/0.65 thf(c_0_52, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 1.21/0.65 thf(c_0_53, plain, ((funcImageSingleton)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(singleton @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29)))))))))), inference(fof_simplification,[status(thm)],[funcImageSingleton])).
% 1.21/0.65 thf(c_0_54, axiom, ((eqbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_43])).
% 1.21/0.65 thf(c_0_55, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_43])).
% 1.21/0.65 thf(c_0_56, axiom, ((brelnall2)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall2, c_0_43])).
% 1.21/0.65 thf(c_0_57, axiom, ((brelnall1)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[brelnall1, c_0_43])).
% 1.21/0.65 thf(c_0_58, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_45, c_0_44])).
% 1.21/0.65 thf(c_0_59, plain, ((lamProp)<=>![X4:$i, X5:$i, X30:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X30 @ X2) @ X5)))=>(func @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:(((X30 @ Z0)=(Z1))))))))), inference(fof_simplification,[status(thm)],[lamProp])).
% 1.21/0.65 thf(c_0_60, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 1.21/0.65 thf(c_0_61, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 1.21/0.65 thf(c_0_62, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 1.21/0.65 thf(c_0_63, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X25:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 1.21/0.65 thf(c_0_64, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_46, c_0_43])).
% 1.21/0.65 thf(c_0_65, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 1.21/0.65 thf(c_0_66, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X22:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X22 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 1.21/0.65 thf(c_0_67, axiom, ((breln1compI)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35)))))))))))))))), inference(apply_def,[status(thm)],[breln1compI, c_0_44])).
% 1.21/0.65 thf(c_0_68, 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)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>(![X205:$i, X206:$i]:((iskpair @ (setadjoin @ (setadjoin @ X205 @ emptyset) @ (setadjoin @ (setadjoin @ X205 @ (setadjoin @ X206 @ emptyset)) @ emptyset))))=>(![X207:$i, X208:$i]:((iskpair @ (kpair @ X207 @ X208)))=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(![X209:$i, X210:$i, X211:$i]:(((in @ X211 @ X209)=>![X212:$i]:(((in @ X212 @ X210)=>(in @ (kpair @ X211 @ X212) @ (cartprod @ X209 @ X210))))))=>(![X213:$i, X214:$i, X215:$i]:(((in @ X215 @ (cartprod @ X213 @ X214))=>?[X216:$i]:(((in @ X216 @ X213)&?[X217:$i]:(((in @ X217 @ X214)&((X215)=(kpair @ X216 @ X217))))))))=>(![X218:$i, X219:$i, X220:$i]:(((in @ X220 @ (cartprod @ X218 @ X219))=>(iskpair @ X220)))=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(![X221:$i, X222:$i > $o]:((![X223:$i]:(((in @ X223 @ X221)=>![X224:$i]:(((in @ X224 @ X221)=>((X222 @ X223)=>((X222 @ X224)=>((X223)=(X224))))))))=>(?[X225:$i]:(((in @ X225 @ X221)&(X222 @ X225)))=>(singleton @ (dsetconstr @ X221 @ X222)))))=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>(![X226:$i]:(((iskpair @ X226)=>(singleton @ (dsetconstr @ (setunion @ X226) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X226)))))))=>(![X227:$i]:(((singleton @ X227)=>(in @ (setunion @ X227) @ X227)))=>(![X228:$i, X229:$i]:(((kfst @ (kpair @ X228 @ X229))=(X228)))=>(![X230:$i, X231:$i, X232:$i]:(((in @ X232 @ (cartprod @ X230 @ X231))=>(in @ (kfst @ X232) @ X230)))=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>(![X233:$i]:(((iskpair @ X233)=>(singleton @ (dsetconstr @ (setunion @ X233) @ (^[Z0/* 3 */:$i]:(((X233)=(kpair @ (kfst @ X233) @ Z0))))))))=>(![X234:$i, X235:$i]:(((ksnd @ (kpair @ X234 @ X235))=(X235)))=>(![X236:$i]:(((iskpair @ X236)=>((kpair @ (kfst @ X236) @ (ksnd @ X236))=(X236))))=>(![X237:$i, X238:$i, X239:$i]:(((in @ X239 @ (cartprod @ X237 @ X238))=>(in @ (ksnd @ X239) @ X238)))=>(![X240:$i, X241:$i, X242:$i, X243:$i]:(((in @ (kpair @ X242 @ X243) @ (cartprod @ X240 @ X241))=>(in @ X242 @ X240)))=>(![X244:$i, X245:$i, X246:$i, X247:$i]:(((in @ (kpair @ X246 @ X247) @ (cartprod @ X244 @ X245))=>(in @ X247 @ X245)))=>((cartprodmempaircEq)=>(![X248:$i, X249:$i, X250:$i]:(((in @ X250 @ X248)=>![X251:$i]:(((in @ X251 @ X249)=>((kfst @ (kpair @ X250 @ X251))=(X250))))))=>(![X252:$i, X253:$i, X254:$i]:(((in @ X254 @ X252)=>![X255:$i]:(((in @ X255 @ X253)=>((ksnd @ (kpair @ X254 @ X255))=(X255))))))=>(![X256:$i, X257:$i, X258:$i]:(((in @ X258 @ (cartprod @ X256 @ X257))=>((kpair @ (kfst @ X258) @ (ksnd @ X258))=(X258))))=>(![X259:$i, X260:$i, X261:$i > $i > $o, X262:$i]:(((in @ X262 @ X259)=>![X263:$i]:(((in @ X263 @ X260)=>((X261 @ X262 @ X263)=>(in @ (kpair @ X262 @ X263) @ (dpsetconstr @ X259 @ X260 @ X261)))))))=>(![X264:$i, X265:$i, X266:$i > $i > $o]:((subset @ (dpsetconstr @ X264 @ X265 @ X266) @ (cartprod @ X264 @ X265)))=>(![X267:$i, X268:$i, X269:$i > $i > $o]:((subset @ (dpsetconstr @ X267 @ X268 @ X269) @ (cartprod @ X267 @ X268)))=>(![X270:$i, X271:$i, X272:$i > $i > $o, X273:$i]:(((in @ X273 @ X270)=>![X274:$i]:(((in @ X274 @ X271)=>((in @ (kpair @ X273 @ X274) @ (dpsetconstr @ X270 @ X271 @ X272))=>(X272 @ X273 @ X274))))))=>(![X275:$i, X276:$i, X277:$i > $i > $o, X278:$i, X279:$i]:(((in @ (kpair @ X278 @ X279) @ (dpsetconstr @ X275 @ X276 @ X277))=>(in @ X278 @ X275)))=>(![X280:$i, X281:$i, X282:$i > $i > $o, X283:$i, X284:$i]:(((in @ (kpair @ X283 @ X284) @ (dpsetconstr @ X280 @ X281 @ X282))=>(in @ X284 @ X281)))=>(![X285:$i, X286:$i, X287:$i > $i > $o, X288:$i, X289:$i]:(((in @ (kpair @ X288 @ X289) @ (dpsetconstr @ X285 @ X286 @ X287))=>(X287 @ X288 @ X289)))=>(![X290:$i, X291:$i, X292:$i]:(((func @ X290 @ X291 @ X292)=>![X293:$i]:(((in @ X293 @ X290)=>(singleton @ (dsetconstr @ X291 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X293 @ Z0) @ X292)))))))))=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>(![X294:$i, X295:$i, X296:$i > $i]:((![X297:$i]:(((in @ X297 @ X294)=>(in @ (X296 @ X297) @ X295)))=>(func @ X294 @ X295 @ (dpsetconstr @ X294 @ X295 @ (^[Z0/* 3 */:$i]:($eq @ (X296 @ Z0)))))))=>((lamp)=>((lam2p)=>(![X298:$i, X299:$i, X300:$i]:(((subset @ X300 @ (cartprod @ X298 @ X299))=>![X301:$i > $o]:((![X302:$i]:(((in @ X302 @ X298)=>![X303:$i]:(((in @ X303 @ X299)=>((in @ (kpair @ X302 @ X303) @ X300)=>(X301 @ (kpair @ X302 @ X303)))))))=>![X304:$i]:(((in @ X304 @ X300)=>(X301 @ X304)))))))=>(![X305:$i, X306:$i, X307:$i]:(((subset @ X307 @ (cartprod @ X305 @ X306))=>![X308:$i > $o]:((![X309:$i]:(((in @ X309 @ X305)=>![X310:$i]:(((in @ X310 @ X306)=>((in @ (kpair @ X309 @ X310) @ X307)=>(X308 @ (kpair @ X309 @ X310)))))))=>![X311:$i]:(((in @ X311 @ X307)=>(X308 @ X311)))))))=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(![X312:$i, X313:$i, X314:$i]:(((subset @ X314 @ (cartprod @ X312 @ X313))=>![X315:$i]:(((subset @ X315 @ (cartprod @ X312 @ X313))=>(![X316:$i]:(((in @ X316 @ X312)=>![X317:$i]:(((in @ X317 @ X313)=>((in @ (kpair @ X316 @ X317) @ X314)=>(in @ (kpair @ X316 @ X317) @ X315))))))=>(subset @ X314 @ X315))))))=>(![X318:$i, X319:$i, X320:$i]:(((subset @ X320 @ (cartprod @ X318 @ X319))=>![X321:$i]:(((subset @ X321 @ (cartprod @ X318 @ X319))=>(![X322:$i]:(((in @ X322 @ X318)=>![X323:$i]:(((in @ X323 @ X319)=>((in @ (kpair @ X322 @ X323) @ X320)=>(in @ (kpair @ X322 @ X323) @ X321))))))=>(![X324:$i]:(((in @ X324 @ X318)=>![X325:$i]:(((in @ X325 @ X319)=>((in @ (kpair @ X324 @ X325) @ X321)=>(in @ (kpair @ X324 @ X325) @ X320))))))=>((X320)=(X321))))))))=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>(![X326:$i, X327:$o, X328:$i]:(((in @ X328 @ X326)=>![X329:$i]:(((in @ X329 @ X326)=>(singleton @ (dsetconstr @ X326 @ (^[Z0/* 9 */:$i]:((((X327)&((Z0)=(X328)))|(~((X327))&((Z0)=(X329))))))))))))=>((ifp)=>(![X330:$i]:(((singleton @ X330)=>![X331:$i]:(((in @ X331 @ X330)=>((setunion @ X330)=(X331))))))=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>((breln1all2)=>((breln1SetBreln1)=>(![X332:$i, X333:$i, X334:$i > $i > $o]:((![X335:$i]:(((in @ X335 @ X332)=>?[X336:$i]:(((in @ X336 @ X333)&(X334 @ X335 @ X336)))))=>![X337:$i]:(((in @ X337 @ (breln1Set @ X333))=>((reflwellordering @ X333 @ X337)=>![X338:$i]:(((in @ X338 @ X332)=>(singleton @ (dsetconstr @ X333 @ (^[Z0/* 8 */:$i]:((X334 @ X338 @ Z0&![X339:$i]:(((in @ X339 @ X333)=>(X334 @ X338 @ X339=>(in @ (kpair @ Z0 @ X339) @ X337))))))))))))))))=>(![X340:$i, X341:$i > $i > $o]:((subset @ (dpsetconstr @ X340 @ X340 @ X341) @ (cartprod @ X340 @ X340)))=>((breln1all1)=>((subbreln1)=>((eqbreln1)=>((breln1invprop)=>((breln1invI)=>((breln1invE)=>(![X342:$i, X343:$i]:(((subset @ X343 @ (cartprod @ X342 @ X342))=>![X344:$i]:(((subset @ X344 @ (cartprod @ X342 @ X342))=>(subset @ (breln1compset @ X342 @ X343 @ X344) @ (cartprod @ X342 @ X342))))))=>(![X345:$i, X346:$i]:(((subset @ X346 @ (cartprod @ X345 @ X345))=>![X347:$i]:(((subset @ X347 @ (cartprod @ X345 @ X345))=>![X348:$i]:(((in @ X348 @ X345)=>![X349:$i]:(((in @ X349 @ X345)=>![X350:$i]:(((in @ X350 @ X345)=>((in @ (kpair @ X348 @ X350) @ X346)=>((in @ (kpair @ X350 @ X349) @ X347)=>(in @ (kpair @ X348 @ X349) @ (breln1compset @ X345 @ X346 @ X347))))))))))))))=>![X4:$i, X33:$i]:(((subset @ X33 @ (cartprod @ X4 @ X4))=>![X35:$i]:(((subset @ X35 @ (cartprod @ X4 @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))=>?[X14:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1compE]), c_0_47]), theprop]), c_0_48]), cartprodsndpairEq]), ksndpairEq]), cartprodfstpairEq]), kfstpairEq]), kpairsurjEq]), c_0_49]), c_0_50]), kpairp]), kpairiskpair]), cartprodpairsurjEq]), cartprodpairmemER]), cartprodpairmemEL]), c_0_51]), theeq]), c_0_52]), c_0_53]), cartprodsndin]), cartprodfstin]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), c_0_54]), c_0_55]), c_0_56]), c_0_57]), c_0_58]), c_0_59]), c_0_60]), c_0_61]), c_0_62]), c_0_63]), c_0_64]), c_0_65]), c_0_66]), c_0_44]), c_0_67])])).
% 1.21/0.65 thf(c_0_69, negated_conjecture, ![X354:$i, X355:$i, X356:$i, X357:$i, X358:$i, X359:$i, X360:$i, X361:$i, X362:$i, X363:$i, X364:$i, X367:$i, X368:$i, X369:$i, X370:$i, X371:$i > $o, X374:$i, X375:$i, X376:$i, X377:$i, X378:$i, X379:$i, X380:$i, X381:$i, X382:$i, X383:$i, X384:$i, X385:$i, X386:$i, X387:$i, X388:$i, X389:$i, X390:$i, X391:$i, X392:$i, X393:$i, X394:$i, X395:$i, X396:$i, X397:$i, X398:$i, X399:$i, X400:$i, X401:$i, X402:$i, X403:$i, X404:$i, X405:$i, X406:$i, X407:$i, X408:$i, X409:$i, X410:$i > $i > $o, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i > $i > $o, X416:$i, X417:$i, X418:$i > $i > $o, X419:$i, X420:$i, X421:$i > $i > $o, X422:$i, X423:$i, X424:$i, X425:$i, X426:$i > $i > $o, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i > $i > $o, X432:$i, X433:$i, X434:$i, X435:$i, X436:$i > $i > $o, X437:$i, X438:$i, X439:$i, X440:$i, X441:$i, X442:$i, X443:$i, X444:$i, X445:$i > $i, X447:$i, X448:$i, X449:$i, X450:$i > $o, X453:$i, X454:$i, X455:$i, X456:$i, X457:$i > $o, X460:$i, X461:$i, X462:$i, X463:$i, X464:$i, X467:$i, X468:$i, X469:$i, X470:$i, X475:$i, X476:$o, X477:$i, X478:$i, X479:$i, X480:$i, X481:$i, X482:$i, X483:$i > $i > $o, X485:$i, X486:$i, X487:$i, X488:$i, X489:$i > $i > $o, X490:$i, X491:$i, X492:$i, X493:$i, X494:$i, X495:$i, X496:$i, X497:$i, X498:$i, X504:$i]:(((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)&((setminusER)&((setminusSubset2)&((setminusERneg)&((setminusELneg)&((setminusILneg)&((setminusIRneg)&((setminusLsub)&((setminusSubset1)&((symdiffE)&((symdiffI1)&((symdiffI2)&((symdiffIneg1)&((symdiffIneg2)&((secondinupair)&((setukpairIL)&((setukpairIR)&((iskpair 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@ X467 @ X468 @ X469 @ X470) @ X468)|~(subset @ X470 @ (cartprod @ X467 @ X468))|~(subset @ X469 @ (cartprod @ X467 @ X468))))))&((((in @ (esk14_4 @ X467 @ X468 @ X469 @ X470) @ X467)|((X469)=(X470))|(in @ (kpair @ (esk12_4 @ X467 @ X468 @ X469 @ X470) @ (esk13_4 @ X467 @ X468 @ X469 @ X470)) @ X469)|~(subset @ X470 @ (cartprod @ X467 @ X468))|~(subset @ X469 @ (cartprod @ X467 @ X468)))&(((in @ (esk15_4 @ X467 @ X468 @ X469 @ X470) @ X468)|((X469)=(X470))|(in @ (kpair @ (esk12_4 @ X467 @ X468 @ X469 @ X470) @ (esk13_4 @ X467 @ X468 @ X469 @ X470)) @ X469)|~(subset @ X470 @ (cartprod @ X467 @ X468))|~(subset @ X469 @ (cartprod @ X467 @ X468)))&(((in @ (kpair @ (esk14_4 @ X467 @ X468 @ X469 @ X470) @ (esk15_4 @ X467 @ X468 @ X469 @ X470)) @ X470)|((X469)=(X470))|(in @ (kpair @ (esk12_4 @ X467 @ X468 @ X469 @ X470) @ (esk13_4 @ X467 @ X468 @ X469 @ X470)) @ X469)|~(subset @ X470 @ (cartprod @ X467 @ X468))|~(subset @ X469 @ (cartprod @ X467 @ X468)))&(~(in @ (kpair @ (esk14_4 @ X467 @ 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X468 @ X469 @ X470)) @ X470)|~(subset @ X470 @ (cartprod @ X467 @ X468))|~(subset @ X469 @ (cartprod @ X467 @ X468)))&(~(in @ (kpair @ (esk14_4 @ X467 @ X468 @ X469 @ X470) @ (esk15_4 @ X467 @ X468 @ X469 @ X470)) @ X469)|((X469)=(X470))|~(in @ (kpair @ (esk12_4 @ X467 @ X468 @ X469 @ X470) @ (esk13_4 @ X467 @ X468 @ X469 @ X470)) @ X470)|~(subset @ X470 @ (cartprod @ X467 @ X468))|~(subset @ X469 @ (cartprod @ X467 @ X468)))))))))&((funcext)&((funcext2)&((ap2apEq1)&((ap2apEq2)&((beta1)&((eta1)&((lam2lamEq)&((beta2)&((eta2)&((iffalseProp1)&((iffalseProp2)&((iftrueProp1)&((iftrueProp2)&((~(in @ X477 @ X475)|(~(in @ X478 @ X475)|(singleton @ (dsetconstr @ X475 @ (^[Z0/* 9 */:$i]:((((X476)&((Z0)=(X477)))|(~((X476))&((Z0)=(X478))))))))))&((ifp)&((~(singleton @ X479)|(~(in @ X480 @ X479)|((setunion @ X479)=(X480))))&((iftrue)&((iffalse)&((iftrueorfalse)&((binintersectT_lem)&((binunionT_lem)&((powersetT_lem)&((setminusT_lem)&((complementT_lem)&((setextT)&((subsetTI)&((powersetTI1)&((powersetTE1)&((complementTI1)&((complementTE1)&((binintersectTELcontra)&((binintersectTERcontra)&((contrasubsetT)&((contrasubsetT1)&((contrasubsetT2)&((contrasubsetT3)&((doubleComplementI1)&((doubleComplementE1)&((doubleComplementSub1)&((doubleComplementSub2)&((doubleComplementEq)&((complementTnotintersectT)&((complementImpComplementIntersect)&((complementSubsetComplementIntersect)&((complementInPowersetComplementIntersect)&((contraSubsetComplement)&((complementTcontraSubset)&((binunionTILcontra)&((binunionTIRcontra)&((inIntersectImpInUnion)&((inIntersectImpInUnion2)&((inIntersectImpInIntersectUnions)&((intersectInPowersetIntersectUnions)&((inComplementUnionImpNotIn1)&((inComplementUnionImpInComplement1)&((binunionTE)&((binunionTEcontra)&((demorgan2a1)&((complementUnionInPowersetComplement)&((demorgan2a2)&((demorgan1a)&((demorgan1b)&((demorgan1)&((demorgan2a)&((demorgan2b2)&((demorgan2b)&((demorgan2)&((woz13rule0)&((woz13rule1)&((woz13rule2)&((woz13rule3)&((woz13rule4)&((woz1_1)&((woz1_2)&((woz1_3)&((woz1_4)&((woz1_5)&((breln1all2)&((breln1SetBreln1)&((((in @ (esk16_3 @ X481 @ X482 @ X483) @ X481)|(~(in @ X486 @ (breln1Set @ X482))|(~(reflwellordering @ X482 @ X486)|(~(in @ X487 @ X481)|(singleton @ (dsetconstr @ X482 @ (^[Z0/* 8 */:$i]:((X483 @ X487 @ Z0&![X339:$i]:(((in @ X339 @ X482)=>(X483 @ X487 @ X339=>(in @ (kpair @ Z0 @ X339) @ X486)))))))))))))&(~(in @ X485 @ X482)|~(X483 @ (esk16_3 @ X481 @ X482 @ X483) @ X485)|(~(in @ X486 @ (breln1Set @ X482))|(~(reflwellordering @ X482 @ X486)|(~(in @ X487 @ X481)|(singleton @ (dsetconstr @ X482 @ (^[Z0/* 8 */:$i]:((X483 @ X487 @ Z0&![X339:$i]:(((in @ X339 @ X482)=>(X483 @ X487 @ X339=>(in @ (kpair @ Z0 @ X339) @ X486))))))))))))))&((subset @ (dpsetconstr @ X488 @ X488 @ X489) @ (cartprod @ X488 @ X488))&((breln1all1)&((subbreln1)&((eqbreln1)&((breln1invprop)&((breln1invI)&((breln1invE)&((~(subset @ X491 @ (cartprod @ X490 @ X490))|(~(subset @ X492 @ (cartprod @ X490 @ X490))|(subset @ (breln1compset @ X490 @ X491 @ X492) @ (cartprod @ X490 @ X490))))&((~(subset @ X494 @ (cartprod @ X493 @ X493))|(~(subset @ X495 @ (cartprod @ X493 @ X493))|(~(in @ X496 @ X493)|(~(in @ X497 @ X493)|(~(in @ X498 @ X493)|(~(in @ (kpair @ X496 @ X498) @ X494)|(~(in @ (kpair @ X498 @ X497) @ X495)|(in @ (kpair @ X496 @ X497) @ (breln1compset @ X493 @ X494 @ X495)))))))))&((subset @ esk18_0 @ (cartprod @ esk17_0 @ esk17_0))&((subset @ esk19_0 @ (cartprod @ esk17_0 @ esk17_0))&((in @ esk20_0 @ esk17_0)&((in @ esk21_0 @ esk17_0)&((in @ (kpair @ esk20_0 @ esk21_0) @ (breln1compset @ esk17_0 @ esk18_0 @ esk19_0))&(~(in @ X504 @ esk17_0)|~(in @ (kpair @ esk20_0 @ X504) @ esk18_0)|~(in @ (kpair @ X504 @ esk21_0) @ esk19_0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_68])])])])])])).
% 1.21/0.65 thf(c_0_70, plain, ![X521:$i, X522:$i, X523:$i, X524:$i, X525:$i, X527:$i]:((((((in @ (esk22_5 @ X521 @ X522 @ X523 @ X524 @ X525) @ X523)|~(epred7_3 @ X525 @ X524 @ X523 @ X522 @ X521))&((in @ (kpair @ X522 @ (esk22_5 @ X521 @ X522 @ X523 @ X524 @ X525)) @ X524)|~(epred7_3 @ X525 @ X524 @ X523 @ X522 @ X521)))&((in @ (kpair @ (esk22_5 @ X521 @ X522 @ X523 @ X524 @ X525) @ X521) @ X525)|~(epred7_3 @ X525 @ X524 @ X523 @ X522 @ X521)))&(~(in @ X527 @ X523)|~(in @ (kpair @ X522 @ X527) @ X524)|~(in @ (kpair @ X527 @ X521) @ X525)|(epred7_3 @ X525 @ X524 @ X523 @ X522 @ X521)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])).
% 1.21/0.65 thf(c_0_71, plain, ![X351:$i, X352:$i, X353:$i]:(((breln1compset @ X351 @ X352 @ X353)=(dpsetconstr @ X351 @ X351 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X14:$i]:((((in @ X14 @ X351)&(in @ (kpair @ Z0 @ X14) @ X352))&(in @ (kpair @ X14 @ Z1) @ X353)))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[breln1compset])])).
% 1.21/0.65 thf(c_0_72, negated_conjecture, ![X2:$i]:((~((in @ X2 @ esk17_0))|~((in @ (kpair @ esk20_0 @ X2) @ esk18_0))|~((in @ (kpair @ X2 @ esk21_0) @ esk19_0)))), inference(split_conjunct,[status(thm)],[c_0_69])).
% 1.21/0.65 thf(c_0_73, plain, ![X7:$i, X5:$i, X4:$i, X3:$i, X2:$i]:(((in @ (kpair @ (esk22_5 @ X2 @ X3 @ X4 @ X5 @ X7) @ X2) @ X7)|~((epred7_3 @ X7 @ X5 @ X4 @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_70])).
% 1.21/0.65 thf(c_0_74, plain, ![X505:$i, X506:$i, X507:$i]:(((breln1compset @ X505 @ X506 @ X507)=(dpsetconstr @ X505 @ X505 @ (^[Z0/* 19 */:$i, Z1:$i]:(?[X14:$i]:((((in @ X14 @ X505)&(in @ (kpair @ Z0 @ X14) @ X506))&(in @ (kpair @ X14 @ Z1) @ X507)))))))), inference(variable_rename,[status(thm)],[c_0_71])).
% 1.21/0.65 thf(c_0_75, plain, ![X520:$i, X519:$i, X2:$i, X3:$i, X4:$i]:(((epred7_3 @ X4 @ X3 @ X2 @ X519 @ X520)<=>?[X518:$i]:((((in @ X518 @ X2)&(in @ (kpair @ X519 @ X518) @ X3))&(in @ (kpair @ X518 @ X520) @ X4))))), introduced(definition)).
% 1.21/0.65 thf(c_0_76, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:((~((in @ (kpair @ esk20_0 @ (esk22_5 @ esk21_0 @ X2 @ X3 @ X4 @ esk19_0)) @ esk18_0))|~((in @ (esk22_5 @ esk21_0 @ X2 @ X3 @ X4 @ esk19_0) @ esk17_0))|~((epred7_3 @ esk19_0 @ X4 @ X3 @ X2 @ esk21_0)))), inference(spm,[status(thm)],[c_0_72, c_0_73])).
% 1.21/0.65 thf(c_0_77, plain, ![X2:$i, X7:$i, X5:$i, X4:$i, X3:$i]:(((in @ (kpair @ X2 @ (esk22_5 @ X3 @ X2 @ X4 @ X5 @ X7)) @ X5)|~((epred7_3 @ X7 @ X5 @ X4 @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_70])).
% 1.21/0.65 thf(c_0_78, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i, X6:$i > $i > $o]:(((X6 @ X2 @ X3)|~((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ X6))))), inference(split_conjunct,[status(thm)],[c_0_69])).
% 1.21/0.65 thf(c_0_79, plain, ![X4:$i, X3:$i, X2:$i]:(((breln1compset @ X2 @ X3 @ X4)=(dpsetconstr @ X2 @ X2 @ (epred7_3 @ X4 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_74]), c_0_75])).
% 1.21/0.65 thf(c_0_80, plain, ![X2:$i]:((~((in @ (esk22_5 @ esk21_0 @ esk20_0 @ X2 @ esk18_0 @ esk19_0) @ esk17_0))|~((epred7_3 @ esk19_0 @ esk18_0 @ X2 @ esk20_0 @ esk21_0)))), inference(spm,[status(thm)],[c_0_76, c_0_77])).
% 1.21/0.65 thf(c_0_81, plain, ![X7:$i, X5:$i, X4:$i, X3:$i, X2:$i]:(((in @ (esk22_5 @ X2 @ X3 @ X4 @ X5 @ X7) @ X4)|~((epred7_3 @ X7 @ X5 @ X4 @ X3 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_70])).
% 1.21/0.65 thf(c_0_82, negated_conjecture, ![X7:$i, X5:$i, X4:$i, X3:$i, X2:$i]:(((epred7_3 @ X2 @ X3 @ X4 @ X5 @ X7)|~((in @ (kpair @ X5 @ X7) @ (breln1compset @ X4 @ X3 @ X2))))), inference(spm,[status(thm)],[c_0_78, c_0_79])).
% 1.21/0.65 thf(c_0_83, negated_conjecture, (in @ (kpair @ esk20_0 @ esk21_0) @ (breln1compset @ esk17_0 @ esk18_0 @ esk19_0)), inference(split_conjunct,[status(thm)],[c_0_69])).
% 1.21/0.65 thf(c_0_84, plain, ~((epred7_3 @ esk19_0 @ esk18_0 @ esk17_0 @ esk20_0 @ esk21_0)), inference(spm,[status(thm)],[c_0_80, c_0_81])).
% 1.21/0.65 thf(c_0_85, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_83]), c_0_84]), ['proof']).
% 1.21/0.65 # SZS output end CNFRefutation
% 1.21/0.65 # Parsed axioms : 646
% 1.21/0.65 # Removed by relevancy pruning/SinE : 604
% 1.21/0.65 # Initial clauses : 357
% 1.21/0.65 # Removed in clause preprocessing : 1
% 1.21/0.65 # Initial clauses in saturation : 356
% 1.21/0.65 # Processed clauses : 755
% 1.21/0.65 # ...of these trivial : 4
% 1.21/0.65 # ...subsumed : 7
% 1.21/0.65 # ...remaining for further processing : 744
% 1.21/0.65 # Other redundant clauses eliminated : 7
% 1.21/0.65 # Clauses deleted for lack of memory : 0
% 1.21/0.65 # Backward-subsumed : 0
% 1.21/0.65 # Backward-rewritten : 0
% 1.21/0.65 # Generated clauses : 766
% 1.21/0.65 # ...of the previous two non-redundant : 700
% 1.21/0.65 # ...aggressively subsumed : 0
% 1.21/0.65 # Contextual simplify-reflections : 0
% 1.21/0.65 # Paramodulations : 754
% 1.21/0.65 # Factorizations : 0
% 1.21/0.65 # NegExts : 0
% 1.21/0.65 # Equation resolutions : 7
% 1.21/0.65 # Disequality decompositions : 0
% 1.21/0.65 # Total rewrite steps : 142
% 1.21/0.65 # ...of those cached : 94
% 1.21/0.65 # Propositional unsat checks : 0
% 1.21/0.65 # Propositional check models : 0
% 1.21/0.65 # Propositional check unsatisfiable : 0
% 1.21/0.65 # Propositional clauses : 0
% 1.21/0.65 # Propositional clauses after purity: 0
% 1.21/0.65 # Propositional unsat core size : 0
% 1.21/0.65 # Propositional preprocessing time : 0.000
% 1.21/0.65 # Propositional encoding time : 0.000
% 1.21/0.65 # Propositional solver time : 0.000
% 1.21/0.65 # Success case prop preproc time : 0.000
% 1.21/0.65 # Success case prop encoding time : 0.000
% 1.21/0.65 # Success case prop solver time : 0.000
% 1.21/0.65 # Current number of processed clauses : 390
% 1.21/0.65 # Positive orientable unit clauses : 275
% 1.21/0.65 # Positive unorientable unit clauses: 0
% 1.21/0.65 # Negative unit clauses : 1
% 1.21/0.65 # Non-unit-clauses : 114
% 1.21/0.65 # Current number of unprocessed clauses: 642
% 1.21/0.65 # ...number of literals in the above : 3025
% 1.21/0.65 # Current number of archived formulas : 0
% 1.21/0.65 # Current number of archived clauses : 352
% 1.21/0.65 # Clause-clause subsumption calls (NU) : 4196
% 1.21/0.65 # Rec. Clause-clause subsumption calls : 1323
% 1.21/0.65 # Non-unit clause-clause subsumptions : 7
% 1.21/0.65 # Unit Clause-clause subsumption calls : 2016
% 1.21/0.65 # Rewrite failures with RHS unbound : 0
% 1.21/0.65 # BW rewrite match attempts : 14
% 1.21/0.65 # BW rewrite match successes : 0
% 1.21/0.65 # Condensation attempts : 0
% 1.21/0.65 # Condensation successes : 0
% 1.21/0.65 # Termbank termtop insertions : 44136
% 1.21/0.65 # Search garbage collected termcells : 11265
% 1.21/0.65
% 1.21/0.65 # -------------------------------------------------
% 1.21/0.65 # User time : 0.113 s
% 1.21/0.65 # System time : 0.012 s
% 1.21/0.65 # Total time : 0.125 s
% 1.21/0.65 # Maximum resident set size: 5296 pages
% 1.21/0.65
% 1.21/0.65 # -------------------------------------------------
% 1.21/0.65 # User time : 0.131 s
% 1.21/0.65 # System time : 0.016 s
% 1.21/0.65 # Total time : 0.147 s
% 1.21/0.65 # Maximum resident set size: 2484 pages
% 1.21/0.65 % E---3.1 exiting
% 1.21/0.66 % E exiting
%------------------------------------------------------------------------------