TSTP Solution File: SEU776^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU776^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n027.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 03:30:09 EDT 2024
% Result : Theorem 3.26s 0.87s
% Output : CNFRefutation 3.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU776^1 : TPTP v8.2.0. Released v3.7.0.
% 0.10/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun May 19 16:21:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Running higher-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 3.26/0.87 # Version: 3.1.0-ho
% 3.26/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 3.26/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.26/0.87 # Starting ehoh_best5 with 300s (1) cores
% 3.26/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 3.26/0.87 # Starting new_bool_5 with 300s (1) cores
% 3.26/0.87 # Starting pre_casc_3 with 300s (1) cores
% 3.26/0.87 # Starting ho_unfolding_8 with 300s (1) cores
% 3.26/0.87 # Starting new_ho_10_cnf2 with 300s (1) cores
% 3.26/0.87 # Starting new_bool_3 with 300s (1) cores
% 3.26/0.87 # Starting new_ho_5 with 300s (1) cores
% 3.26/0.87 # pre_casc_3 with pid 28647 completed with status 0
% 3.26/0.87 # Result found by pre_casc_3
% 3.26/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 3.26/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.26/0.87 # Starting ehoh_best5 with 300s (1) cores
% 3.26/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 3.26/0.87 # Starting new_bool_5 with 300s (1) cores
% 3.26/0.87 # Starting pre_casc_3 with 300s (1) cores
% 3.26/0.87 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 3.26/0.87 # Search class: HGUSM-FSLM32-MHFMMFBN
% 3.26/0.87 # partial match(2): HGHSM-FSLM32-MHFMMSBN
% 3.26/0.87 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 3.26/0.87 # Starting ho_unfolding_8 with 61s (1) cores
% 3.26/0.87 # ho_unfolding_8 with pid 28653 completed with status 0
% 3.26/0.87 # Result found by ho_unfolding_8
% 3.26/0.87 # Preprocessing class: HSLMSLSSLLLCHFA.
% 3.26/0.87 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 3.26/0.87 # Starting ehoh_best5 with 300s (1) cores
% 3.26/0.87 # Starting almost_fo_3_lam with 300s (1) cores
% 3.26/0.87 # Starting new_bool_5 with 300s (1) cores
% 3.26/0.87 # Starting pre_casc_3 with 300s (1) cores
% 3.26/0.87 # SinE strategy is GSinE(CountFormulas,hypos,10,,5,20000,3.0,true)
% 3.26/0.87 # Search class: HGUSM-FSLM32-MHFMMFBN
% 3.26/0.87 # partial match(2): HGHSM-FSLM32-MHFMMSBN
% 3.26/0.87 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 3.26/0.87 # Starting ho_unfolding_8 with 61s (1) cores
% 3.26/0.87 # Preprocessing time : 0.040 s
% 3.26/0.87 # Presaturation interreduction done
% 3.26/0.87
% 3.26/0.87 # Proof found!
% 3.26/0.87 # SZS status Theorem
% 3.26/0.87 # SZS output start CNFRefutation
% 3.26/0.87 thf(decl_22, type, in: $i > $i > $o).
% 3.26/0.87 thf(decl_24, type, setextAx: $o).
% 3.26/0.87 thf(decl_25, type, emptyset: $i).
% 3.26/0.87 thf(decl_26, type, emptysetAx: $o).
% 3.26/0.87 thf(decl_27, type, setadjoin: $i > $i > $i).
% 3.26/0.87 thf(decl_28, type, setadjoinAx: $o).
% 3.26/0.87 thf(decl_30, type, powersetAx: $o).
% 3.26/0.87 thf(decl_31, type, setunion: $i > $i).
% 3.26/0.87 thf(decl_32, type, setunionAx: $o).
% 3.26/0.87 thf(decl_34, type, omega0Ax: $o).
% 3.26/0.87 thf(decl_35, type, omegaSAx: $o).
% 3.26/0.87 thf(decl_36, type, omegaIndAx: $o).
% 3.26/0.87 thf(decl_37, type, replAx: $o).
% 3.26/0.87 thf(decl_38, type, foundationAx: $o).
% 3.26/0.87 thf(decl_39, type, wellorderingAx: $o).
% 3.26/0.87 thf(decl_41, type, descrp: $o).
% 3.26/0.87 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_43, type, dsetconstrI: $o).
% 3.26/0.87 thf(decl_44, type, dsetconstrEL: $o).
% 3.26/0.87 thf(decl_45, type, dsetconstrER: $o).
% 3.26/0.87 thf(decl_46, type, exuE1: $o).
% 3.26/0.87 thf(decl_48, type, prop2setE: $o).
% 3.26/0.87 thf(decl_49, type, emptysetE: $o).
% 3.26/0.87 thf(decl_50, type, emptysetimpfalse: $o).
% 3.26/0.87 thf(decl_51, type, notinemptyset: $o).
% 3.26/0.87 thf(decl_52, type, exuE3e: $o).
% 3.26/0.87 thf(decl_53, type, setext: $o).
% 3.26/0.87 thf(decl_54, type, emptyI: $o).
% 3.26/0.87 thf(decl_55, type, noeltsimpempty: $o).
% 3.26/0.87 thf(decl_56, type, setbeta: $o).
% 3.26/0.87 thf(decl_58, type, nonemptyE1: $o).
% 3.26/0.87 thf(decl_59, type, nonemptyI: $o).
% 3.26/0.87 thf(decl_60, type, nonemptyI1: $o).
% 3.26/0.87 thf(decl_61, type, setadjoinIL: $o).
% 3.26/0.87 thf(decl_62, type, emptyinunitempty: $o).
% 3.26/0.87 thf(decl_63, type, setadjoinIR: $o).
% 3.26/0.87 thf(decl_64, type, setadjoinE: $o).
% 3.26/0.87 thf(decl_65, type, setadjoinOr: $o).
% 3.26/0.87 thf(decl_66, type, setoftrueEq: $o).
% 3.26/0.87 thf(decl_67, type, powersetI: $o).
% 3.26/0.87 thf(decl_68, type, emptyinPowerset: $o).
% 3.26/0.87 thf(decl_69, type, emptyInPowerset: $o).
% 3.26/0.87 thf(decl_70, type, powersetE: $o).
% 3.26/0.87 thf(decl_71, type, setunionI: $o).
% 3.26/0.87 thf(decl_72, type, setunionE: $o).
% 3.26/0.87 thf(decl_73, type, subPowSU: $o).
% 3.26/0.87 thf(decl_74, type, exuE2: $o).
% 3.26/0.87 thf(decl_75, type, nonemptyImpWitness: $o).
% 3.26/0.87 thf(decl_76, type, uniqinunit: $o).
% 3.26/0.87 thf(decl_77, type, notinsingleton: $o).
% 3.26/0.87 thf(decl_78, type, eqinunit: $o).
% 3.26/0.87 thf(decl_79, type, singletonsswitch: $o).
% 3.26/0.87 thf(decl_80, type, upairsetE: $o).
% 3.26/0.87 thf(decl_81, type, upairsetIL: $o).
% 3.26/0.87 thf(decl_82, type, upairsetIR: $o).
% 3.26/0.87 thf(decl_83, type, emptyE1: $o).
% 3.26/0.87 thf(decl_84, type, vacuousDall: $o).
% 3.26/0.87 thf(decl_85, type, quantDeMorgan1: $o).
% 3.26/0.87 thf(decl_86, type, quantDeMorgan2: $o).
% 3.26/0.87 thf(decl_87, type, quantDeMorgan3: $o).
% 3.26/0.87 thf(decl_88, type, quantDeMorgan4: $o).
% 3.26/0.87 thf(decl_89, type, prop2setI: $o).
% 3.26/0.87 thf(decl_91, type, prop2set2propI: $o).
% 3.26/0.87 thf(decl_92, type, notdexE: $o).
% 3.26/0.87 thf(decl_93, type, notdallE: $o).
% 3.26/0.87 thf(decl_94, type, exuI1: $o).
% 3.26/0.87 thf(decl_95, type, exuI3: $o).
% 3.26/0.87 thf(decl_96, type, exuI2: $o).
% 3.26/0.87 thf(decl_97, type, inCongP: $o).
% 3.26/0.87 thf(decl_98, type, in__Cong: $o).
% 3.26/0.87 thf(decl_99, type, exuE3u: $o).
% 3.26/0.87 thf(decl_100, type, exu__Cong: $o).
% 3.26/0.87 thf(decl_101, type, emptyset__Cong: $o).
% 3.26/0.87 thf(decl_102, type, setadjoin__Cong: $o).
% 3.26/0.87 thf(decl_103, type, powerset__Cong: $o).
% 3.26/0.87 thf(decl_104, type, setunion__Cong: $o).
% 3.26/0.87 thf(decl_105, type, omega__Cong: $o).
% 3.26/0.87 thf(decl_106, type, exuEu: $o).
% 3.26/0.87 thf(decl_107, type, descr__Cong: $o).
% 3.26/0.87 thf(decl_108, type, dsetconstr__Cong: $o).
% 3.26/0.87 thf(decl_109, type, subset: $i > $i > $o).
% 3.26/0.87 thf(decl_112, type, subsetI1: $o).
% 3.26/0.87 thf(decl_113, type, eqimpsubset2: $o).
% 3.26/0.87 thf(decl_114, type, eqimpsubset1: $o).
% 3.26/0.87 thf(decl_115, type, subsetI2: $o).
% 3.26/0.87 thf(decl_116, type, emptysetsubset: $o).
% 3.26/0.87 thf(decl_117, type, subsetE: $o).
% 3.26/0.87 thf(decl_118, type, subsetE2: $o).
% 3.26/0.87 thf(decl_119, type, notsubsetI: $o).
% 3.26/0.87 thf(decl_120, type, notequalI1: $o).
% 3.26/0.87 thf(decl_121, type, notequalI2: $o).
% 3.26/0.87 thf(decl_122, type, subsetRefl: $o).
% 3.26/0.87 thf(decl_123, type, subsetTrans: $o).
% 3.26/0.87 thf(decl_124, type, setadjoinSub: $o).
% 3.26/0.87 thf(decl_125, type, setadjoinSub2: $o).
% 3.26/0.87 thf(decl_126, type, subset2powerset: $o).
% 3.26/0.87 thf(decl_127, type, setextsub: $o).
% 3.26/0.87 thf(decl_128, type, subsetemptysetimpeq: $o).
% 3.26/0.87 thf(decl_129, type, powersetI1: $o).
% 3.26/0.87 thf(decl_130, type, powersetE1: $o).
% 3.26/0.87 thf(decl_131, type, inPowerset: $o).
% 3.26/0.87 thf(decl_132, type, powersetsubset: $o).
% 3.26/0.87 thf(decl_133, type, sepInPowerset: $o).
% 3.26/0.87 thf(decl_134, type, sepSubset: $o).
% 3.26/0.87 thf(decl_136, type, binunionIL: $o).
% 3.26/0.87 thf(decl_137, type, upairset2IR: $o).
% 3.26/0.87 thf(decl_138, type, binunionIR: $o).
% 3.26/0.87 thf(decl_139, type, binunionEcases: $o).
% 3.26/0.87 thf(decl_140, type, binunionE: $o).
% 3.26/0.87 thf(decl_141, type, binunionLsub: $o).
% 3.26/0.87 thf(decl_142, type, binunionRsub: $o).
% 3.26/0.87 thf(decl_144, type, binintersectI: $o).
% 3.26/0.87 thf(decl_145, type, binintersectSubset5: $o).
% 3.26/0.87 thf(decl_146, type, binintersectEL: $o).
% 3.26/0.87 thf(decl_147, type, binintersectLsub: $o).
% 3.26/0.87 thf(decl_148, type, binintersectSubset2: $o).
% 3.26/0.87 thf(decl_149, type, binintersectSubset3: $o).
% 3.26/0.87 thf(decl_150, type, binintersectER: $o).
% 3.26/0.87 thf(decl_151, type, disjointsetsI1: $o).
% 3.26/0.87 thf(decl_152, type, binintersectRsub: $o).
% 3.26/0.87 thf(decl_153, type, binintersectSubset4: $o).
% 3.26/0.87 thf(decl_154, type, binintersectSubset1: $o).
% 3.26/0.87 thf(decl_155, type, bs114d: $o).
% 3.26/0.87 thf(decl_158, type, setminusI: $o).
% 3.26/0.87 thf(decl_159, type, setminusEL: $o).
% 3.26/0.87 thf(decl_160, type, setminusER: $o).
% 3.26/0.87 thf(decl_161, type, setminusSubset2: $o).
% 3.26/0.87 thf(decl_162, type, setminusERneg: $o).
% 3.26/0.87 thf(decl_163, type, setminusELneg: $o).
% 3.26/0.87 thf(decl_164, type, setminusILneg: $o).
% 3.26/0.87 thf(decl_165, type, setminusIRneg: $o).
% 3.26/0.87 thf(decl_166, type, setminusLsub: $o).
% 3.26/0.87 thf(decl_167, type, setminusSubset1: $o).
% 3.26/0.87 thf(decl_169, type, symdiffE: $o).
% 3.26/0.87 thf(decl_170, type, symdiffI1: $o).
% 3.26/0.87 thf(decl_171, type, symdiffI2: $o).
% 3.26/0.87 thf(decl_172, type, symdiffIneg1: $o).
% 3.26/0.87 thf(decl_173, type, symdiffIneg2: $o).
% 3.26/0.87 thf(decl_174, type, iskpair: $i > $o).
% 3.26/0.87 thf(decl_175, type, secondinupair: $o).
% 3.26/0.87 thf(decl_176, type, setukpairIL: $o).
% 3.26/0.87 thf(decl_177, type, setukpairIR: $o).
% 3.26/0.87 thf(decl_178, type, kpairiskpair: $o).
% 3.26/0.87 thf(decl_179, type, kpair: $i > $i > $i).
% 3.26/0.87 thf(decl_180, type, kpairp: $o).
% 3.26/0.87 thf(decl_181, type, cartprod: $i > $i > $i).
% 3.26/0.87 thf(decl_182, type, singletonsubset: $o).
% 3.26/0.87 thf(decl_183, type, singletoninpowerset: $o).
% 3.26/0.87 thf(decl_184, type, singletoninpowunion: $o).
% 3.26/0.87 thf(decl_185, type, upairset2E: $o).
% 3.26/0.87 thf(decl_186, type, upairsubunion: $o).
% 3.26/0.87 thf(decl_187, type, upairinpowunion: $o).
% 3.26/0.87 thf(decl_188, type, ubforcartprodlem1: $o).
% 3.26/0.87 thf(decl_189, type, ubforcartprodlem2: $o).
% 3.26/0.87 thf(decl_190, type, ubforcartprodlem3: $o).
% 3.26/0.87 thf(decl_191, type, cartprodpairin: $o).
% 3.26/0.87 thf(decl_192, type, cartprodmempair1: $o).
% 3.26/0.87 thf(decl_193, type, cartprodmempair: $o).
% 3.26/0.87 thf(decl_194, type, setunionE2: $o).
% 3.26/0.87 thf(decl_195, type, setunionsingleton1: $o).
% 3.26/0.87 thf(decl_196, type, setunionsingleton2: $o).
% 3.26/0.87 thf(decl_197, type, setunionsingleton: $o).
% 3.26/0.87 thf(decl_198, type, singleton: $i > $o).
% 3.26/0.87 thf(decl_199, type, singletonprop: $o).
% 3.26/0.87 thf(decl_201, type, ex1E1: $o).
% 3.26/0.87 thf(decl_202, type, ex1I: $o).
% 3.26/0.87 thf(decl_203, type, ex1I2: $o).
% 3.26/0.87 thf(decl_204, type, singletonsuniq: $o).
% 3.26/0.87 thf(decl_209, type, setukpairinjL1: $o).
% 3.26/0.87 thf(decl_210, type, kfstsingleton: $o).
% 3.26/0.87 thf(decl_211, type, theprop: $o).
% 3.26/0.87 thf(decl_212, type, kfst: $i > $i).
% 3.26/0.87 thf(decl_213, type, kfstpairEq: $o).
% 3.26/0.87 thf(decl_214, type, cartprodfstin: $o).
% 3.26/0.87 thf(decl_215, type, setukpairinjL2: $o).
% 3.26/0.87 thf(decl_216, type, setukpairinjL: $o).
% 3.26/0.87 thf(decl_217, type, setukpairinjR11: $o).
% 3.26/0.87 thf(decl_218, type, setukpairinjR12: $o).
% 3.26/0.87 thf(decl_219, type, setukpairinjR1: $o).
% 3.26/0.87 thf(decl_220, type, upairequniteq: $o).
% 3.26/0.87 thf(decl_221, type, setukpairinjR2: $o).
% 3.26/0.87 thf(decl_222, type, setukpairinjR: $o).
% 3.26/0.87 thf(decl_223, type, ksndsingleton: $o).
% 3.26/0.87 thf(decl_224, type, ksnd: $i > $i).
% 3.26/0.87 thf(decl_225, type, ksndpairEq: $o).
% 3.26/0.87 thf(decl_226, type, kpairsurjEq: $o).
% 3.26/0.87 thf(decl_227, type, cartprodsndin: $o).
% 3.26/0.87 thf(decl_228, type, cartprodpairmemEL: $o).
% 3.26/0.87 thf(decl_229, type, cartprodpairmemER: $o).
% 3.26/0.87 thf(decl_230, type, cartprodmempaircEq: $o).
% 3.26/0.87 thf(decl_231, type, cartprodfstpairEq: $o).
% 3.26/0.87 thf(decl_232, type, cartprodsndpairEq: $o).
% 3.26/0.87 thf(decl_233, type, cartprodpairsurjEq: $o).
% 3.26/0.87 thf(decl_234, type, breln: $i > $i > $i > $o).
% 3.26/0.87 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 3.26/0.87 thf(decl_236, type, dpsetconstrI: $o).
% 3.26/0.87 thf(decl_237, type, dpsetconstrSub: $o).
% 3.26/0.87 thf(decl_238, type, setOfPairsIsBReln: $o).
% 3.26/0.87 thf(decl_239, type, dpsetconstrERa: $o).
% 3.26/0.87 thf(decl_240, type, dpsetconstrEL1: $o).
% 3.26/0.87 thf(decl_241, type, dpsetconstrEL2: $o).
% 3.26/0.87 thf(decl_242, type, dpsetconstrER: $o).
% 3.26/0.87 thf(decl_243, type, func: $i > $i > $i > $o).
% 3.26/0.87 thf(decl_245, type, funcImageSingleton: $o).
% 3.26/0.87 thf(decl_246, type, apProp: $o).
% 3.26/0.87 thf(decl_248, type, app: $o).
% 3.26/0.87 thf(decl_249, type, infuncsetfunc: $o).
% 3.26/0.87 thf(decl_250, type, ap2p: $o).
% 3.26/0.87 thf(decl_251, type, funcinfuncset: $o).
% 3.26/0.87 thf(decl_252, type, lamProp: $o).
% 3.26/0.87 thf(decl_254, type, lamp: $o).
% 3.26/0.87 thf(decl_255, type, lam2p: $o).
% 3.26/0.87 thf(decl_256, type, brelnall1: $o).
% 3.26/0.87 thf(decl_257, type, brelnall2: $o).
% 3.26/0.87 thf(decl_258, type, ex1E2: $o).
% 3.26/0.87 thf(decl_259, type, funcGraphProp1: $o).
% 3.26/0.87 thf(decl_260, type, funcGraphProp3: $o).
% 3.26/0.87 thf(decl_261, type, funcGraphProp2: $o).
% 3.26/0.87 thf(decl_262, type, funcextLem: $o).
% 3.26/0.87 thf(decl_263, type, funcGraphProp4: $o).
% 3.26/0.87 thf(decl_264, type, subbreln: $o).
% 3.26/0.87 thf(decl_265, type, eqbreln: $o).
% 3.26/0.87 thf(decl_266, type, funcext: $o).
% 3.26/0.87 thf(decl_267, type, funcext2: $o).
% 3.26/0.87 thf(decl_268, type, ap2apEq1: $o).
% 3.26/0.87 thf(decl_269, type, ap2apEq2: $o).
% 3.26/0.87 thf(decl_270, type, beta1: $o).
% 3.26/0.87 thf(decl_271, type, eta1: $o).
% 3.26/0.87 thf(decl_272, type, lam2lamEq: $o).
% 3.26/0.87 thf(decl_273, type, beta2: $o).
% 3.26/0.87 thf(decl_274, type, eta2: $o).
% 3.26/0.87 thf(decl_275, type, iffalseProp1: $o).
% 3.26/0.87 thf(decl_276, type, iffalseProp2: $o).
% 3.26/0.87 thf(decl_277, type, iftrueProp1: $o).
% 3.26/0.87 thf(decl_278, type, iftrueProp2: $o).
% 3.26/0.87 thf(decl_279, type, ifSingleton: $o).
% 3.26/0.87 thf(decl_281, type, ifp: $o).
% 3.26/0.87 thf(decl_282, type, theeq: $o).
% 3.26/0.87 thf(decl_283, type, iftrue: $o).
% 3.26/0.87 thf(decl_284, type, iffalse: $o).
% 3.26/0.87 thf(decl_285, type, iftrueorfalse: $o).
% 3.26/0.87 thf(decl_286, type, binintersectT_lem: $o).
% 3.26/0.87 thf(decl_287, type, binunionT_lem: $o).
% 3.26/0.87 thf(decl_288, type, powersetT_lem: $o).
% 3.26/0.87 thf(decl_289, type, setminusT_lem: $o).
% 3.26/0.87 thf(decl_290, type, complementT_lem: $o).
% 3.26/0.87 thf(decl_291, type, setextT: $o).
% 3.26/0.87 thf(decl_292, type, subsetTI: $o).
% 3.26/0.87 thf(decl_293, type, powersetTI1: $o).
% 3.26/0.87 thf(decl_294, type, powersetTE1: $o).
% 3.26/0.87 thf(decl_295, type, complementTI1: $o).
% 3.26/0.87 thf(decl_296, type, complementTE1: $o).
% 3.26/0.87 thf(decl_297, type, binintersectTELcontra: $o).
% 3.26/0.87 thf(decl_298, type, binintersectTERcontra: $o).
% 3.26/0.87 thf(decl_299, type, contrasubsetT: $o).
% 3.26/0.87 thf(decl_300, type, contrasubsetT1: $o).
% 3.26/0.87 thf(decl_301, type, contrasubsetT2: $o).
% 3.26/0.87 thf(decl_302, type, contrasubsetT3: $o).
% 3.26/0.87 thf(decl_303, type, doubleComplementI1: $o).
% 3.26/0.87 thf(decl_304, type, doubleComplementE1: $o).
% 3.26/0.87 thf(decl_305, type, doubleComplementSub1: $o).
% 3.26/0.87 thf(decl_306, type, doubleComplementSub2: $o).
% 3.26/0.87 thf(decl_307, type, doubleComplementEq: $o).
% 3.26/0.87 thf(decl_308, type, complementTnotintersectT: $o).
% 3.26/0.87 thf(decl_309, type, complementImpComplementIntersect: $o).
% 3.26/0.87 thf(decl_310, type, complementSubsetComplementIntersect: $o).
% 3.26/0.87 thf(decl_311, type, complementInPowersetComplementIntersect: $o).
% 3.26/0.87 thf(decl_312, type, contraSubsetComplement: $o).
% 3.26/0.87 thf(decl_313, type, complementTcontraSubset: $o).
% 3.26/0.87 thf(decl_314, type, binunionTILcontra: $o).
% 3.26/0.87 thf(decl_315, type, binunionTIRcontra: $o).
% 3.26/0.87 thf(decl_316, type, inIntersectImpInUnion: $o).
% 3.26/0.87 thf(decl_317, type, inIntersectImpInUnion2: $o).
% 3.26/0.87 thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
% 3.26/0.87 thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
% 3.26/0.87 thf(decl_320, type, inComplementUnionImpNotIn1: $o).
% 3.26/0.87 thf(decl_321, type, inComplementUnionImpInComplement1: $o).
% 3.26/0.87 thf(decl_322, type, binunionTE: $o).
% 3.26/0.87 thf(decl_323, type, binunionTEcontra: $o).
% 3.26/0.87 thf(decl_324, type, demorgan2a1: $o).
% 3.26/0.87 thf(decl_325, type, complementUnionInPowersetComplement: $o).
% 3.26/0.87 thf(decl_326, type, demorgan2a2: $o).
% 3.26/0.87 thf(decl_327, type, demorgan1a: $o).
% 3.26/0.87 thf(decl_328, type, demorgan1b: $o).
% 3.26/0.87 thf(decl_329, type, demorgan1: $o).
% 3.26/0.87 thf(decl_330, type, demorgan2a: $o).
% 3.26/0.87 thf(decl_331, type, demorgan2b2: $o).
% 3.26/0.87 thf(decl_332, type, demorgan2b: $o).
% 3.26/0.87 thf(decl_333, type, demorgan2: $o).
% 3.26/0.87 thf(decl_334, type, woz13rule0: $o).
% 3.26/0.87 thf(decl_335, type, woz13rule1: $o).
% 3.26/0.87 thf(decl_336, type, woz13rule2: $o).
% 3.26/0.87 thf(decl_337, type, woz13rule3: $o).
% 3.26/0.87 thf(decl_338, type, woz13rule4: $o).
% 3.26/0.87 thf(decl_339, type, woz1_1: $o).
% 3.26/0.87 thf(decl_340, type, woz1_2: $o).
% 3.26/0.87 thf(decl_341, type, woz1_3: $o).
% 3.26/0.87 thf(decl_342, type, woz1_4: $o).
% 3.26/0.87 thf(decl_343, type, woz1_5: $o).
% 3.26/0.87 thf(decl_344, type, breln1: $i > $i > $o).
% 3.26/0.87 thf(decl_345, type, breln1all2: $o).
% 3.26/0.87 thf(decl_346, type, breln1Set: $i > $i).
% 3.26/0.87 thf(decl_347, type, breln1SetBreln1: $o).
% 3.26/0.87 thf(decl_353, type, reflwellordering: $i > $i > $o).
% 3.26/0.87 thf(decl_354, type, choice2fnsingleton: $o).
% 3.26/0.87 thf(decl_355, type, setOfPairsIsBReln1: $o).
% 3.26/0.87 thf(decl_356, type, breln1all1: $o).
% 3.26/0.87 thf(decl_357, type, subbreln1: $o).
% 3.26/0.87 thf(decl_358, type, eqbreln1: $o).
% 3.26/0.87 thf(decl_359, type, breln1invset: $i > $i > $i).
% 3.26/0.87 thf(decl_360, type, breln1invprop: $o).
% 3.26/0.87 thf(decl_361, type, esk1_3: $i > $i > $i > $i).
% 3.26/0.87 thf(decl_362, type, esk2_3: $i > $i > $i > $i).
% 3.26/0.87 thf(decl_363, type, esk3_2: $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_364, type, esk4_2: $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_365, type, esk5_3: $i > $i > ($i > $i) > $i).
% 3.26/0.87 thf(decl_366, type, esk6_4: $i > $i > $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_367, type, esk7_4: $i > $i > $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_368, type, esk8_4: $i > $i > $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_369, type, esk9_4: $i > $i > $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_370, type, esk10_4: $i > $i > $i > $i > $i).
% 3.26/0.87 thf(decl_371, type, esk11_4: $i > $i > $i > $i > $i).
% 3.26/0.87 thf(decl_372, type, esk12_4: $i > $i > $i > $i > $i).
% 3.26/0.87 thf(decl_373, type, esk13_4: $i > $i > $i > $i > $i).
% 3.26/0.87 thf(decl_374, type, esk14_4: $i > $i > $i > $i > $i).
% 3.26/0.87 thf(decl_375, type, esk15_4: $i > $i > $i > $i > $i).
% 3.26/0.87 thf(decl_376, type, esk16_3: $i > $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_377, type, esk17_3: $i > $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_378, type, esk18_3: $i > $i > ($i > $i > $o) > $i).
% 3.26/0.87 thf(decl_379, type, esk19_3: $i > $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_380, type, esk20_3: $i > $i > ($i > $o) > $i).
% 3.26/0.87 thf(decl_381, type, esk21_3: $i > $i > $i > $i).
% 3.26/0.87 thf(decl_382, type, esk22_3: $i > $i > $i > $i).
% 3.26/0.87 thf(decl_383, type, esk23_3: $i > $i > $i > $i).
% 3.26/0.87 thf(decl_384, type, esk24_3: $i > $i > $i > $i).
% 3.26/0.87 thf(decl_385, type, esk25_3: $i > $i > $i > $i).
% 3.26/0.87 thf(decl_386, type, esk26_3: $i > $i > $i > $i).
% 3.26/0.87 thf(decl_387, type, esk27_0: $i).
% 3.26/0.87 thf(decl_388, type, esk28_0: $i).
% 3.26/0.87 thf(decl_389, type, esk29_0: $i).
% 3.26/0.87 thf(decl_390, type, esk30_0: $i).
% 3.26/0.87 thf(decl_397, type, epred7_1: $i > $i > $i > $o).
% 3.26/0.87 thf(breln1, axiom, ((breln1)=(^[X4:$i, X33:$i]:((breln @ X4 @ X4 @ X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1)).
% 3.26/0.87 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln)).
% 3.26/0.87 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln)).
% 3.26/0.87 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln1)).
% 3.26/0.87 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1invprop)).
% 3.26/0.87 thf(brelnall2, axiom, ((brelnall2)<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', brelnall2)).
% 3.26/0.87 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/sandbox2/benchmark/theBenchmark.p', brelnall1)).
% 3.26/0.87 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/sandbox2/benchmark/theBenchmark.p', lamProp)).
% 3.26/0.87 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:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrER)).
% 3.26/0.87 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL2)).
% 3.26/0.87 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL1)).
% 3.26/0.87 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrERa)).
% 3.26/0.87 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrSub)).
% 3.26/0.87 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrI)).
% 3.26/0.87 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$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) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqbreln1)).
% 3.26/0.87 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subbreln1)).
% 3.26/0.87 thf(breln1all1, axiom, ((breln1all1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1all1)).
% 3.26/0.87 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ifSingleton)).
% 3.26/0.87 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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/sandbox2/benchmark/theBenchmark.p', funcImageSingleton)).
% 3.26/0.87 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndsingleton)).
% 3.26/0.87 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstsingleton)).
% 3.26/0.87 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonprop)).
% 3.26/0.87 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$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:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', choice2fnsingleton)).
% 3.26/0.87 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqbreln)).
% 3.26/0.87 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subbreln)).
% 3.26/0.87 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1SetBreln1)).
% 3.26/0.87 thf(breln1all2, axiom, ((breln1all2)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1all2)).
% 3.26/0.87 thf(breln1invI, 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)=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1invI)).
% 3.26/0.87 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/sandbox2/benchmark/theBenchmark.p', cartprodsndpairEq)).
% 3.26/0.87 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndpairEq)).
% 3.26/0.87 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/sandbox2/benchmark/theBenchmark.p', cartprodfstpairEq)).
% 3.26/0.87 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstpairEq)).
% 3.26/0.87 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairsurjEq)).
% 3.26/0.87 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairp)).
% 3.26/0.87 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairiskpair)).
% 3.26/0.87 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theeq)).
% 3.26/0.87 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theprop)).
% 3.26/0.87 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairsurjEq)).
% 3.26/0.87 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemER)).
% 3.26/0.87 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemEL)).
% 3.26/0.87 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndin)).
% 3.26/0.87 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstin)).
% 3.26/0.87 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair)).
% 3.26/0.87 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair1)).
% 3.26/0.87 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairin)).
% 3.26/0.87 thf(breln1invset, axiom, ((breln1invset)=(^[X4:$i, X33:$i]:(dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((in @ (kpair @ X3 @ X2) @ X33)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1invset)).
% 3.26/0.87 thf(c_0_46, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(fof_simplification,[status(thm)],[breln1])).
% 3.26/0.87 thf(c_0_47, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 3.26/0.87 thf(c_0_48, plain, ((breln1)=(^[Z0/* 19 */:$i, Z1:$i]:(((subset @ Z1 @ (cartprod @ Z0 @ Z0)))))), inference(apply_def,[status(thm)],[c_0_46, c_0_47])).
% 3.26/0.87 thf(c_0_49, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 3.26/0.87 thf(c_0_50, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
% 3.26/0.87 thf(c_0_51, axiom, ((breln1invprop)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>((subset @ (breln1invset @ X4 @ X33) @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1invprop, c_0_48])).
% 3.26/0.87 thf(c_0_52, axiom, ((brelnall2)=(![X4:$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_47])).
% 3.26/0.87 thf(c_0_53, 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_47])).
% 3.26/0.87 thf(c_0_54, 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])).
% 3.26/0.87 thf(c_0_55, 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:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 3.26/0.87 thf(c_0_56, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 3.26/0.87 thf(c_0_57, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 3.26/0.87 thf(c_0_58, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 3.26/0.87 thf(c_0_59, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X24:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[c_0_49, c_0_47])).
% 3.26/0.87 thf(c_0_60, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 3.26/0.87 thf(c_0_61, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 3.26/0.87 thf(c_0_62, axiom, ((eqbreln1)=(![X4:$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) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln1, c_0_48])).
% 3.26/0.87 thf(c_0_63, axiom, ((subbreln1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X4)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln1, c_0_48])).
% 3.26/0.87 thf(c_0_64, axiom, ((breln1all1)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[breln1all1, c_0_48])).
% 3.26/0.87 thf(c_0_65, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 3.26/0.87 thf(c_0_66, plain, ((funcImageSingleton)<=>![X4:$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])).
% 3.26/0.87 thf(c_0_67, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 3.26/0.87 thf(c_0_68, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 3.26/0.87 thf(c_0_69, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 3.26/0.87 thf(c_0_70, plain, ((choice2fnsingleton)<=>![X4:$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:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
% 3.26/0.87 thf(c_0_71, axiom, ((eqbreln)=(![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35)))))))))), inference(apply_def,[status(thm)],[eqbreln, c_0_47])).
% 3.26/0.87 thf(c_0_72, axiom, ((subbreln)=(![X4:$i, X5:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X5)))=>![X35:$i]:((((subset @ X35 @ (cartprod @ X4 @ X5)))=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35)))))))), inference(apply_def,[status(thm)],[subbreln, c_0_47])).
% 3.26/0.87 thf(c_0_73, plain, ((setOfPairsIsBReln1)=(![X4:$i, X53:$i > $i > $o]:(((subset @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X4)))))), inference(apply_def,[status(thm)],[c_0_50, c_0_48])).
% 3.26/0.87 thf(c_0_74, axiom, ((breln1SetBreln1)=(![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>((subset @ X33 @ (cartprod @ X4 @ X4))))))), inference(apply_def,[status(thm)],[breln1SetBreln1, c_0_48])).
% 3.26/0.87 thf(c_0_75, axiom, ((breln1all2)=(![X4:$i, X33:$i]:((((subset @ X33 @ (cartprod @ X4 @ X4)))=>![X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(X1 @ (kpair @ X2 @ X3)))))))=>![X2:$i]:(((in @ X2 @ X33)=>(X1 @ X2))))))))), inference(apply_def,[status(thm)],[breln1all2, c_0_48])).
% 3.26/0.87 thf(c_0_76, 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)=>(![X222:$i, X223:$i]:((iskpair @ (setadjoin @ (setadjoin @ X222 @ emptyset) @ (setadjoin @ (setadjoin @ X222 @ (setadjoin @ X223 @ emptyset)) @ emptyset))))=>(![X224:$i, X225:$i]:((iskpair @ (kpair @ X224 @ X225)))=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>(![X226:$i, X227:$i, X228:$i]:(((in @ X228 @ X226)=>![X229:$i]:(((in @ X229 @ X227)=>(in @ (kpair @ X228 @ X229) @ (cartprod @ X226 @ X227))))))=>(![X230:$i, X231:$i, X232:$i]:(((in @ X232 @ (cartprod @ X230 @ X231))=>?[X233:$i]:(((in @ X233 @ X230)&?[X234:$i]:(((in @ X234 @ X231)&((X232)=(kpair @ X233 @ X234))))))))=>(![X235:$i, X236:$i, X237:$i]:(((in @ X237 @ (cartprod @ X235 @ X236))=>(iskpair @ X237)))=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>(![X238:$i, X239:$i > $o]:((![X240:$i]:(((in @ X240 @ X238)=>![X241:$i]:(((in @ X241 @ X238)=>((X239 @ X240)=>((X239 @ X241)=>((X240)=(X241))))))))=>(?[X242:$i]:(((in @ X242 @ X238)&(X239 @ X242)))=>(singleton @ (dsetconstr @ X238 @ X239)))))=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>(![X243:$i]:(((iskpair @ X243)=>(singleton @ (dsetconstr @ (setunion @ X243) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X243)))))))=>(![X244:$i]:(((singleton @ X244)=>(in @ (setunion @ X244) @ X244)))=>(![X245:$i, X246:$i]:(((kfst @ (kpair @ X245 @ X246))=(X245)))=>(![X247:$i, X248:$i, X249:$i]:(((in @ X249 @ (cartprod @ X247 @ X248))=>(in @ (kfst @ X249) @ X247)))=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>(![X250:$i]:(((iskpair @ X250)=>(singleton @ (dsetconstr @ (setunion @ X250) @ (^[Z0/* 3 */:$i]:(((X250)=(kpair @ (kfst @ X250) @ Z0))))))))=>(![X251:$i, X252:$i]:(((ksnd @ (kpair @ X251 @ X252))=(X252)))=>(![X253:$i]:(((iskpair @ X253)=>((kpair @ (kfst @ X253) @ (ksnd @ X253))=(X253))))=>(![X254:$i, X255:$i, X256:$i]:(((in @ X256 @ (cartprod @ X254 @ X255))=>(in @ (ksnd @ X256) @ X255)))=>(![X257:$i, X258:$i, X259:$i, X260:$i]:(((in @ (kpair @ X259 @ X260) @ (cartprod @ X257 @ X258))=>(in @ X259 @ X257)))=>(![X261:$i, X262:$i, X263:$i, X264:$i]:(((in @ (kpair @ X263 @ X264) @ (cartprod @ X261 @ X262))=>(in @ X264 @ X262)))=>((cartprodmempaircEq)=>(![X265:$i, X266:$i, X267:$i]:(((in @ X267 @ X265)=>![X268:$i]:(((in @ X268 @ X266)=>((kfst @ (kpair @ X267 @ X268))=(X267))))))=>(![X269:$i, X270:$i, X271:$i]:(((in @ X271 @ X269)=>![X272:$i]:(((in @ X272 @ X270)=>((ksnd @ (kpair @ X271 @ X272))=(X272))))))=>(![X273:$i, X274:$i, X275:$i]:(((in @ X275 @ (cartprod @ X273 @ X274))=>((kpair @ (kfst @ X275) @ (ksnd @ X275))=(X275))))=>(![X276:$i, X277:$i, X278:$i > $i > $o, X279:$i]:(((in @ X279 @ X276)=>![X280:$i]:(((in @ X280 @ X277)=>((X278 @ X279 @ X280)=>(in @ (kpair @ X279 @ X280) @ (dpsetconstr @ X276 @ X277 @ X278)))))))=>(![X281:$i, X282:$i, X283:$i > $i > $o]:((subset @ (dpsetconstr @ X281 @ X282 @ X283) @ (cartprod @ X281 @ X282)))=>(![X284:$i, X285:$i, X286:$i > $i > $o]:((subset @ (dpsetconstr @ X284 @ X285 @ X286) @ (cartprod @ X284 @ X285)))=>(![X287:$i, X288:$i, X289:$i > $i > $o, X290:$i]:(((in @ X290 @ X287)=>![X291:$i]:(((in @ X291 @ X288)=>((in @ (kpair @ X290 @ X291) @ (dpsetconstr @ X287 @ X288 @ X289))=>(X289 @ X290 @ X291))))))=>(![X292:$i, X293:$i, X294:$i > $i > $o, X295:$i, X296:$i]:(((in @ (kpair @ X295 @ X296) @ (dpsetconstr @ X292 @ X293 @ X294))=>(in @ X295 @ X292)))=>(![X297:$i, X298:$i, X299:$i > $i > $o, X300:$i, X301:$i]:(((in @ (kpair @ X300 @ X301) @ (dpsetconstr @ X297 @ X298 @ X299))=>(in @ X301 @ X298)))=>(![X302:$i, X303:$i, X304:$i > $i > $o, X305:$i, X306:$i]:(((in @ (kpair @ X305 @ X306) @ (dpsetconstr @ X302 @ X303 @ X304))=>(X304 @ X305 @ X306)))=>(![X307:$i, X308:$i, X309:$i]:(((func @ X307 @ X308 @ X309)=>![X310:$i]:(((in @ X310 @ X307)=>(singleton @ (dsetconstr @ X308 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X310 @ Z0) @ X309)))))))))=>((apProp)=>((app)=>((infuncsetfunc)=>((ap2p)=>((funcinfuncset)=>(![X311:$i, X312:$i, X313:$i > $i]:((![X314:$i]:(((in @ X314 @ X311)=>(in @ (X313 @ X314) @ X312)))=>(func @ X311 @ X312 @ (dpsetconstr @ X311 @ X312 @ (^[Z0/* 3 */:$i]:($eq @ (X313 @ Z0)))))))=>((lamp)=>((lam2p)=>(![X315:$i, X316:$i, X317:$i]:(((subset @ X317 @ (cartprod @ X315 @ X316))=>![X318:$i > $o]:((![X319:$i]:(((in @ X319 @ X315)=>![X320:$i]:(((in @ X320 @ X316)=>((in @ (kpair @ X319 @ X320) @ X317)=>(X318 @ (kpair @ X319 @ X320)))))))=>![X321:$i]:(((in @ X321 @ X317)=>(X318 @ X321)))))))=>(![X322:$i, X323:$i, X324:$i]:(((subset @ X324 @ (cartprod @ X322 @ X323))=>![X325:$i > $o]:((![X326:$i]:(((in @ X326 @ X322)=>![X327:$i]:(((in @ X327 @ X323)=>((in @ (kpair @ X326 @ X327) @ X324)=>(X325 @ (kpair @ X326 @ X327)))))))=>![X328:$i]:(((in @ X328 @ X324)=>(X325 @ X328)))))))=>((ex1E2)=>((funcGraphProp1)=>((funcGraphProp3)=>((funcGraphProp2)=>((funcextLem)=>((funcGraphProp4)=>(![X329:$i, X330:$i, X331:$i]:(((subset @ X331 @ (cartprod @ X329 @ X330))=>![X332:$i]:(((subset @ X332 @ (cartprod @ X329 @ X330))=>(![X333:$i]:(((in @ X333 @ X329)=>![X334:$i]:(((in @ X334 @ X330)=>((in @ (kpair @ X333 @ X334) @ X331)=>(in @ (kpair @ X333 @ X334) @ X332))))))=>(subset @ X331 @ X332))))))=>(![X335:$i, X336:$i, X337:$i]:(((subset @ X337 @ (cartprod @ X335 @ X336))=>![X338:$i]:(((subset @ X338 @ (cartprod @ X335 @ X336))=>(![X339:$i]:(((in @ X339 @ X335)=>![X340:$i]:(((in @ X340 @ X336)=>((in @ (kpair @ X339 @ X340) @ X337)=>(in @ (kpair @ X339 @ X340) @ X338))))))=>(![X341:$i]:(((in @ X341 @ X335)=>![X342:$i]:(((in @ X342 @ X336)=>((in @ (kpair @ X341 @ X342) @ X338)=>(in @ (kpair @ X341 @ X342) @ X337))))))=>((X337)=(X338))))))))=>((funcext)=>((funcext2)=>((ap2apEq1)=>((ap2apEq2)=>((beta1)=>((eta1)=>((lam2lamEq)=>((beta2)=>((eta2)=>((iffalseProp1)=>((iffalseProp2)=>((iftrueProp1)=>((iftrueProp2)=>(![X343:$i, X344:$o, X345:$i]:(((in @ X345 @ X343)=>![X346:$i]:(((in @ X346 @ X343)=>(singleton @ (dsetconstr @ X343 @ (^[Z0/* 9 */:$i]:((((X344)&((Z0)=(X345)))|(~((X344))&((Z0)=(X346))))))))))))=>((ifp)=>(![X347:$i]:(((singleton @ X347)=>![X348:$i]:(((in @ X348 @ X347)=>((setunion @ X347)=(X348))))))=>((iftrue)=>((iffalse)=>((iftrueorfalse)=>((binintersectT_lem)=>((binunionT_lem)=>((powersetT_lem)=>((setminusT_lem)=>((complementT_lem)=>((setextT)=>((subsetTI)=>((powersetTI1)=>((powersetTE1)=>((complementTI1)=>((complementTE1)=>((binintersectTELcontra)=>((binintersectTERcontra)=>((contrasubsetT)=>((contrasubsetT1)=>((contrasubsetT2)=>((contrasubsetT3)=>((doubleComplementI1)=>((doubleComplementE1)=>((doubleComplementSub1)=>((doubleComplementSub2)=>((doubleComplementEq)=>((complementTnotintersectT)=>((complementImpComplementIntersect)=>((complementSubsetComplementIntersect)=>((complementInPowersetComplementIntersect)=>((contraSubsetComplement)=>((complementTcontraSubset)=>((binunionTILcontra)=>((binunionTIRcontra)=>((inIntersectImpInUnion)=>((inIntersectImpInUnion2)=>((inIntersectImpInIntersectUnions)=>((intersectInPowersetIntersectUnions)=>((inComplementUnionImpNotIn1)=>((inComplementUnionImpInComplement1)=>((binunionTE)=>((binunionTEcontra)=>((demorgan2a1)=>((complementUnionInPowersetComplement)=>((demorgan2a2)=>((demorgan1a)=>((demorgan1b)=>((demorgan1)=>((demorgan2a)=>((demorgan2b2)=>((demorgan2b)=>((demorgan2)=>((woz13rule0)=>((woz13rule1)=>((woz13rule2)=>((woz13rule3)=>((woz13rule4)=>((woz1_1)=>((woz1_2)=>((woz1_3)=>((woz1_4)=>((woz1_5)=>(![X349:$i, X350:$i]:(((subset @ X350 @ (cartprod @ X349 @ X349))=>![X351:$i > $o]:((![X352:$i]:(((in @ X352 @ X349)=>![X353:$i]:(((in @ X353 @ X349)=>((in @ (kpair @ X352 @ X353) @ X350)=>(X351 @ (kpair @ X352 @ X353)))))))=>![X354:$i]:(((in @ X354 @ X350)=>(X351 @ X354)))))))=>(![X355:$i, X356:$i]:(((in @ X356 @ (breln1Set @ X355))=>(subset @ X356 @ (cartprod @ X355 @ X355))))=>(![X357:$i, X358:$i, X359:$i > $i > $o]:((![X360:$i]:(((in @ X360 @ X357)=>?[X361:$i]:(((in @ X361 @ X358)&(X359 @ X360 @ X361)))))=>![X362:$i]:(((in @ X362 @ (breln1Set @ X358))=>((reflwellordering @ X358 @ X362)=>![X363:$i]:(((in @ X363 @ X357)=>(singleton @ (dsetconstr @ X358 @ (^[Z0/* 8 */:$i]:((X359 @ X363 @ Z0&![X364:$i]:(((in @ X364 @ X358)=>(X359 @ X363 @ X364=>(in @ (kpair @ Z0 @ X364) @ X362))))))))))))))))=>(![X365:$i, X366:$i > $i > $o]:((subset @ (dpsetconstr @ X365 @ X365 @ X366) @ (cartprod @ X365 @ X365)))=>(![X367:$i, X368:$i]:(((subset @ X368 @ (cartprod @ X367 @ X367))=>![X369:$i > $o]:((![X370:$i]:(((in @ X370 @ X367)=>![X371:$i]:(((in @ X371 @ X367)=>((in @ (kpair @ X370 @ X371) @ X368)=>(X369 @ (kpair @ X370 @ X371)))))))=>![X372:$i]:(((in @ X372 @ X368)=>(X369 @ X372)))))))=>(![X373:$i, X374:$i]:(((subset @ X374 @ (cartprod @ X373 @ X373))=>![X375:$i]:(((subset @ X375 @ (cartprod @ X373 @ X373))=>(![X376:$i]:(((in @ X376 @ X373)=>![X377:$i]:(((in @ X377 @ X373)=>((in @ (kpair @ X376 @ X377) @ X374)=>(in @ (kpair @ X376 @ X377) @ X375))))))=>(subset @ X374 @ X375))))))=>(![X378:$i, X379:$i]:(((subset @ X379 @ (cartprod @ X378 @ X378))=>![X380:$i]:(((subset @ X380 @ (cartprod @ X378 @ X378))=>(![X381:$i]:(((in @ X381 @ X378)=>![X382:$i]:(((in @ X382 @ X378)=>((in @ (kpair @ X381 @ X382) @ X379)=>(in @ (kpair @ X381 @ X382) @ X380))))))=>(![X383:$i]:(((in @ X383 @ X378)=>![X384:$i]:(((in @ X384 @ X378)=>((in @ (kpair @ X383 @ X384) @ X380)=>(in @ (kpair @ X383 @ X384) @ X379))))))=>((X379)=(X380))))))))=>(![X385:$i, X386:$i]:(((subset @ X386 @ (cartprod @ X385 @ X385))=>(subset @ (breln1invset @ X385 @ X386) @ (cartprod @ X385 @ X385))))=>![X4:$i, X33:$i]:(((subset @ X33 @ (cartprod @ X4 @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[breln1invI]), c_0_51]), c_0_52]), c_0_53]), 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]), cartprodsndpairEq]), ksndpairEq]), cartprodfstpairEq]), kfstpairEq]), kpairsurjEq]), kpairp]), kpairiskpair]), theeq]), c_0_65]), c_0_66]), c_0_67]), theprop]), c_0_68]), c_0_69]), cartprodpairsurjEq]), cartprodpairmemER]), cartprodpairmemEL]), cartprodsndin]), cartprodfstin]), cartprodmempair]), cartprodmempair1]), cartprodpairin]), c_0_70]), c_0_71]), c_0_72]), c_0_73]), c_0_74]), c_0_75]), c_0_48])])).
% 3.26/0.87 thf(c_0_77, plain, ![X387:$i, X388:$i]:(((breln1invset @ X387 @ X388)=(dpsetconstr @ X387 @ X387 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X388)))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[breln1invset])])).
% 3.26/0.87 thf(c_0_78, negated_conjecture, ![X389:$i, X390:$i, X391:$i, X392:$i, X393:$i, X394:$i, X395:$i, X396:$i, X397:$i, X398:$i, X399:$i, X402:$i, X403:$i, X404:$i, X405:$i, X406:$i > $o, X409:$i, X410:$i, X411:$i, X412:$i, X413:$i, X414:$i, X415:$i, X416:$i, X417:$i, X418:$i, X419:$i, X420:$i, X421:$i, X422:$i, X423:$i, X424:$i, X425:$i, X426:$i, X427:$i, X428:$i, X429:$i, X430:$i, X431:$i, X432:$i, X433:$i, X434:$i, X435:$i, X436:$i, X437:$i, X438:$i, X439:$i, X440:$i, X441:$i, X442:$i, X443:$i, X444:$i, X445:$i > $i > $o, X446:$i, X447:$i, X448:$i, X449:$i, X450:$i > $i > $o, X451:$i, X452:$i, X453:$i > $i > $o, X454:$i, X455:$i, X456:$i > $i > $o, X457:$i, X458:$i, X459:$i, X460:$i, X461:$i > $i > $o, X462:$i, X463:$i, X464:$i, X465:$i, X466:$i > $i > $o, X467:$i, X468:$i, X469:$i, X470:$i, X471:$i > $i > $o, X472:$i, X473:$i, X474:$i, X475:$i, X476:$i, X477:$i, X478:$i, X479:$i, X480:$i > $i, X482:$i, X483:$i, X484:$i, X485:$i > $o, X488:$i, X489:$i, X490:$i, X491:$i, X492:$i > $o, X495:$i, X496:$i, X497:$i, X498:$i, X499:$i, X502:$i, X503:$i, X504:$i, X505:$i, X510:$i, X511:$o, X512:$i, X513:$i, X514:$i, X515:$i, X516:$i, X517:$i, X518:$i > $o, X521:$i, X522:$i, X523:$i, X524:$i, X525:$i, X526:$i > $i > $o, X528:$i, X529:$i, X530:$i, X531:$i, X532:$i > $i > $o, X533:$i, X534:$i, X535:$i > $o, X538:$i, X539:$i, X540:$i, X541:$i, X544:$i, X545:$i, X546:$i, X551:$i, 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@ (setadjoin @ (setadjoin @ X389 @ emptyset) @ (setadjoin @ (setadjoin @ X389 @ (setadjoin @ X390 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X391 @ X392))&((singletonsubset)&((singletoninpowerset)&((singletoninpowunion)&((upairset2E)&((upairsubunion)&((upairinpowunion)&((ubforcartprodlem1)&((ubforcartprodlem2)&((ubforcartprodlem3)&((~(in @ X395 @ X393)|(~(in @ X396 @ X394)|(in @ (kpair @ X395 @ X396) @ (cartprod @ X393 @ X394))))&((((in @ (esk1_3 @ X397 @ X398 @ X399) @ X397)|~(in @ X399 @ (cartprod @ X397 @ X398)))&(((in @ (esk2_3 @ X397 @ X398 @ X399) @ X398)|~(in @ X399 @ (cartprod @ X397 @ X398)))&(((X399)=(kpair @ (esk1_3 @ X397 @ X398 @ X399) @ (esk2_3 @ X397 @ X398 @ X399)))|~(in @ X399 @ (cartprod @ X397 @ X398)))))&((~(in @ X404 @ (cartprod @ X402 @ X403))|(iskpair @ X404))&((setunionE2)&((setunionsingleton1)&((setunionsingleton2)&((setunionsingleton)&((((in @ (esk3_2 @ X405 @ X406) @ X405)|(~(in @ X409 @ X405)|~(X406 @ X409)|(singleton @ (dsetconstr @ X405 @ 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@ (esk16_3 @ X516 @ X517 @ X518) @ X516)|(~(in @ X521 @ X517)|(X518 @ X521))|~(subset @ X517 @ (cartprod @ X516 @ X516)))&(((in @ (esk17_3 @ X516 @ X517 @ X518) @ X516)|(~(in @ X521 @ X517)|(X518 @ X521))|~(subset @ X517 @ (cartprod @ X516 @ X516)))&(((in @ (kpair @ (esk16_3 @ X516 @ X517 @ X518) @ (esk17_3 @ X516 @ X517 @ X518)) @ X517)|(~(in @ X521 @ X517)|(X518 @ X521))|~(subset @ X517 @ (cartprod @ X516 @ X516)))&(~(X518 @ (kpair @ (esk16_3 @ X516 @ X517 @ X518) @ (esk17_3 @ X516 @ X517 @ X518)))|(~(in @ X521 @ X517)|(X518 @ X521))|~(subset @ X517 @ (cartprod @ X516 @ X516))))))&((~(in @ X523 @ (breln1Set @ X522))|(subset @ X523 @ (cartprod @ X522 @ X522)))&((((in @ (esk18_3 @ X524 @ X525 @ X526) @ X524)|(~(in @ X529 @ (breln1Set @ X525))|(~(reflwellordering @ X525 @ X529)|(~(in @ X530 @ X524)|(singleton @ (dsetconstr @ X525 @ (^[Z0/* 8 */:$i]:((X526 @ X530 @ Z0&![X364:$i]:(((in @ X364 @ X525)=>(X526 @ X530 @ X364=>(in @ (kpair @ Z0 @ X364) @ X529)))))))))))))&(~(in @ X528 @ X525)|~(X526 @ (esk18_3 @ X524 @ X525 @ X526) @ X528)|(~(in @ X529 @ (breln1Set @ X525))|(~(reflwellordering @ X525 @ X529)|(~(in @ X530 @ X524)|(singleton @ (dsetconstr @ X525 @ (^[Z0/* 8 */:$i]:((X526 @ X530 @ Z0&![X364:$i]:(((in @ X364 @ X525)=>(X526 @ X530 @ X364=>(in @ (kpair @ Z0 @ X364) @ X529))))))))))))))&((subset @ (dpsetconstr @ X531 @ X531 @ X532) @ (cartprod @ X531 @ X531))&((((in @ (esk19_3 @ X533 @ X534 @ X535) @ X533)|(~(in @ X538 @ X534)|(X535 @ X538))|~(subset @ X534 @ (cartprod @ X533 @ X533)))&(((in @ (esk20_3 @ X533 @ X534 @ X535) @ X533)|(~(in @ X538 @ X534)|(X535 @ X538))|~(subset @ X534 @ (cartprod @ X533 @ X533)))&(((in @ (kpair @ (esk19_3 @ X533 @ X534 @ X535) @ (esk20_3 @ X533 @ X534 @ X535)) @ X534)|(~(in @ X538 @ X534)|(X535 @ X538))|~(subset @ X534 @ (cartprod @ X533 @ X533)))&(~(X535 @ (kpair @ (esk19_3 @ X533 @ X534 @ X535) @ (esk20_3 @ X533 @ X534 @ X535)))|(~(in @ X538 @ X534)|(X535 @ X538))|~(subset @ X534 @ (cartprod @ X533 @ X533))))))&((((in @ (esk21_3 @ X539 @ X540 @ X541) @ X539)|(subset @ X540 @ X541)|~(subset @ X541 @ (cartprod @ X539 @ X539))|~(subset @ X540 @ (cartprod @ X539 @ X539)))&(((in @ (esk22_3 @ X539 @ X540 @ X541) @ X539)|(subset @ X540 @ X541)|~(subset @ X541 @ (cartprod @ X539 @ X539))|~(subset @ X540 @ (cartprod @ X539 @ X539)))&(((in @ (kpair @ (esk21_3 @ X539 @ X540 @ X541) @ (esk22_3 @ X539 @ X540 @ X541)) @ X540)|(subset @ X540 @ X541)|~(subset @ X541 @ (cartprod @ X539 @ X539))|~(subset @ X540 @ (cartprod @ X539 @ X539)))&(~(in @ (kpair @ (esk21_3 @ X539 @ X540 @ X541) @ (esk22_3 @ X539 @ X540 @ X541)) @ X541)|(subset @ X540 @ X541)|~(subset @ X541 @ (cartprod @ X539 @ X539))|~(subset @ X540 @ (cartprod @ X539 @ X539))))))&(((((in @ (esk25_3 @ X544 @ X545 @ X546) @ X544)|((X545)=(X546))|(in @ (esk23_3 @ X544 @ X545 @ X546) @ X544)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(((in @ (esk26_3 @ X544 @ X545 @ X546) @ X544)|((X545)=(X546))|(in @ (esk23_3 @ X544 @ X545 @ X546) @ X544)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(((in @ (kpair @ (esk25_3 @ X544 @ X545 @ X546) @ (esk26_3 @ X544 @ X545 @ X546)) @ X546)|((X545)=(X546))|(in @ (esk23_3 @ X544 @ X545 @ X546) @ X544)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(~(in @ (kpair @ (esk25_3 @ X544 @ X545 @ X546) @ (esk26_3 @ X544 @ X545 @ X546)) @ X545)|((X545)=(X546))|(in @ (esk23_3 @ X544 @ X545 @ X546) @ X544)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544))))))&((((in @ (esk25_3 @ X544 @ X545 @ X546) @ X544)|((X545)=(X546))|(in @ (esk24_3 @ X544 @ X545 @ X546) @ X544)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(((in @ (esk26_3 @ X544 @ X545 @ X546) @ X544)|((X545)=(X546))|(in @ (esk24_3 @ X544 @ X545 @ X546) @ X544)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(((in @ (kpair @ (esk25_3 @ X544 @ X545 @ X546) @ (esk26_3 @ X544 @ X545 @ X546)) @ X546)|((X545)=(X546))|(in @ (esk24_3 @ X544 @ X545 @ X546) @ X544)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(~(in @ (kpair @ (esk25_3 @ X544 @ X545 @ X546) @ (esk26_3 @ X544 @ X545 @ X546)) @ X545)|((X545)=(X546))|(in @ (esk24_3 @ X544 @ X545 @ X546) @ X544)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544))))))&((((in @ (esk25_3 @ X544 @ X545 @ X546) @ X544)|((X545)=(X546))|(in @ (kpair @ (esk23_3 @ X544 @ X545 @ X546) @ (esk24_3 @ X544 @ X545 @ X546)) @ X545)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(((in @ (esk26_3 @ X544 @ X545 @ X546) @ X544)|((X545)=(X546))|(in @ (kpair @ (esk23_3 @ X544 @ X545 @ X546) @ (esk24_3 @ X544 @ X545 @ X546)) @ X545)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(((in @ (kpair @ (esk25_3 @ X544 @ X545 @ X546) @ (esk26_3 @ X544 @ X545 @ X546)) @ X546)|((X545)=(X546))|(in @ (kpair @ (esk23_3 @ X544 @ X545 @ X546) @ (esk24_3 @ X544 @ X545 @ X546)) @ X545)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(~(in @ (kpair @ (esk25_3 @ X544 @ X545 @ X546) @ (esk26_3 @ X544 @ X545 @ X546)) @ X545)|((X545)=(X546))|(in @ (kpair @ (esk23_3 @ X544 @ X545 @ X546) @ (esk24_3 @ X544 @ X545 @ X546)) @ X545)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544))))))&(((in @ (esk25_3 @ X544 @ X545 @ X546) @ X544)|((X545)=(X546))|~(in @ (kpair @ (esk23_3 @ X544 @ X545 @ X546) @ (esk24_3 @ X544 @ X545 @ X546)) @ X546)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(((in @ (esk26_3 @ X544 @ X545 @ X546) @ X544)|((X545)=(X546))|~(in @ (kpair @ (esk23_3 @ X544 @ X545 @ X546) @ (esk24_3 @ X544 @ X545 @ X546)) @ X546)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(((in @ (kpair @ (esk25_3 @ X544 @ X545 @ X546) @ (esk26_3 @ X544 @ X545 @ X546)) @ X546)|((X545)=(X546))|~(in @ (kpair @ (esk23_3 @ X544 @ X545 @ X546) @ (esk24_3 @ X544 @ X545 @ X546)) @ X546)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))&(~(in @ (kpair @ (esk25_3 @ X544 @ X545 @ X546) @ (esk26_3 @ X544 @ X545 @ X546)) @ X545)|((X545)=(X546))|~(in @ (kpair @ (esk23_3 @ X544 @ X545 @ X546) @ (esk24_3 @ X544 @ X545 @ X546)) @ X546)|~(subset @ X546 @ (cartprod @ X544 @ X544))|~(subset @ X545 @ (cartprod @ X544 @ X544)))))))))&((~(subset @ X552 @ (cartprod @ X551 @ X551))|(subset @ (breln1invset @ X551 @ X552) @ (cartprod @ X551 @ X551)))&((subset @ esk28_0 @ (cartprod @ esk27_0 @ esk27_0))&((in @ esk29_0 @ esk27_0)&((in @ esk30_0 @ esk27_0)&((in @ (kpair @ esk29_0 @ esk30_0) @ esk28_0)&~(in @ (kpair @ esk30_0 @ esk29_0) @ (breln1invset @ esk27_0 @ esk28_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_76])])])])])])).
% 3.26/0.87 thf(c_0_79, plain, ![X557:$i, X558:$i]:(((breln1invset @ X557 @ X558)=(dpsetconstr @ X557 @ X557 @ (^[Z0/* 19 */:$i, Z1:$i]:((in @ (kpair @ Z1 @ Z0) @ X558)))))), inference(variable_rename,[status(thm)],[c_0_77])).
% 3.26/0.87 thf(c_0_80, plain, ![X570:$i, X569:$i, X3:$i]:(((epred7_1 @ X3 @ X569 @ X570)<=>(in @ (kpair @ X570 @ X569) @ X3))), introduced(definition)).
% 3.26/0.87 thf(c_0_81, negated_conjecture, ![X3:$i, X2:$i, X6:$i > $i > $o, X5:$i, X4:$i]:(((in @ (kpair @ X2 @ X4) @ (dpsetconstr @ X3 @ X5 @ X6))|~((in @ X2 @ X3))|~((in @ X4 @ X5))|~((X6 @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_78])).
% 3.26/0.87 thf(c_0_82, plain, ![X2:$i, X3:$i]:(((breln1invset @ X2 @ X3)=(dpsetconstr @ X2 @ X2 @ (epred7_1 @ X3)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_79]), c_0_80])).
% 3.26/0.87 thf(c_0_83, negated_conjecture, ~((in @ (kpair @ esk30_0 @ esk29_0) @ (breln1invset @ esk27_0 @ esk28_0))), inference(split_conjunct,[status(thm)],[c_0_78])).
% 3.26/0.87 thf(c_0_84, negated_conjecture, ![X2:$i, X3:$i, X5:$i, X4:$i]:(((in @ (kpair @ X2 @ X3) @ (breln1invset @ X4 @ X5))|~((epred7_1 @ X5 @ X2 @ X3))|~((in @ X3 @ X4))|~((in @ X2 @ X4)))), inference(spm,[status(thm)],[c_0_81, c_0_82])).
% 3.26/0.87 thf(c_0_85, negated_conjecture, (in @ esk29_0 @ esk27_0), inference(split_conjunct,[status(thm)],[c_0_78])).
% 3.26/0.87 thf(c_0_86, negated_conjecture, (in @ esk30_0 @ esk27_0), inference(split_conjunct,[status(thm)],[c_0_78])).
% 3.26/0.87 thf(c_0_87, plain, ![X571:$i, X572:$i, X573:$i]:(((~(epred7_1 @ X573 @ X572 @ X571)|(in @ (kpair @ X571 @ X572) @ X573))&(~(in @ (kpair @ X571 @ X572) @ X573)|(epred7_1 @ X573 @ X572 @ X571)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
% 3.26/0.87 thf(c_0_88, negated_conjecture, ~((epred7_1 @ esk28_0 @ esk30_0 @ esk29_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_85]), c_0_86])])).
% 3.26/0.87 thf(c_0_89, plain, ![X2:$i, X3:$i, X4:$i]:(((epred7_1 @ X4 @ X3 @ X2)|~((in @ (kpair @ X2 @ X3) @ X4)))), inference(split_conjunct,[status(thm)],[c_0_87])).
% 3.26/0.87 thf(c_0_90, negated_conjecture, (in @ (kpair @ esk29_0 @ esk30_0) @ esk28_0), inference(split_conjunct,[status(thm)],[c_0_78])).
% 3.26/0.87 thf(c_0_91, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88, c_0_89]), c_0_90])]), ['proof']).
% 3.26/0.87 # SZS output end CNFRefutation
% 3.26/0.87 # Parsed axioms : 637
% 3.26/0.87 # Removed by relevancy pruning/SinE : 591
% 3.26/0.87 # Initial clauses : 374
% 3.26/0.87 # Removed in clause preprocessing : 1
% 3.26/0.87 # Initial clauses in saturation : 373
% 3.26/0.87 # Processed clauses : 1314
% 3.26/0.87 # ...of these trivial : 4
% 3.26/0.87 # ...subsumed : 156
% 3.26/0.87 # ...remaining for further processing : 1154
% 3.26/0.87 # Other redundant clauses eliminated : 7
% 3.26/0.87 # Clauses deleted for lack of memory : 0
% 3.26/0.87 # Backward-subsumed : 11
% 3.26/0.87 # Backward-rewritten : 0
% 3.26/0.87 # Generated clauses : 8305
% 3.26/0.87 # ...of the previous two non-redundant : 7980
% 3.26/0.87 # ...aggressively subsumed : 0
% 3.26/0.87 # Contextual simplify-reflections : 7
% 3.26/0.87 # Paramodulations : 8289
% 3.26/0.87 # Factorizations : 0
% 3.26/0.87 # NegExts : 4
% 3.26/0.87 # Equation resolutions : 7
% 3.26/0.87 # Disequality decompositions : 0
% 3.26/0.87 # Total rewrite steps : 1354
% 3.26/0.87 # ...of those cached : 1162
% 3.26/0.87 # Propositional unsat checks : 0
% 3.26/0.87 # Propositional check models : 0
% 3.26/0.87 # Propositional check unsatisfiable : 0
% 3.26/0.87 # Propositional clauses : 0
% 3.26/0.87 # Propositional clauses after purity: 0
% 3.26/0.87 # Propositional unsat core size : 0
% 3.26/0.87 # Propositional preprocessing time : 0.000
% 3.26/0.87 # Propositional encoding time : 0.000
% 3.26/0.87 # Propositional solver time : 0.000
% 3.26/0.87 # Success case prop preproc time : 0.000
% 3.26/0.87 # Success case prop encoding time : 0.000
% 3.26/0.87 # Success case prop solver time : 0.000
% 3.26/0.87 # Current number of processed clauses : 772
% 3.26/0.87 # Positive orientable unit clauses : 270
% 3.26/0.87 # Positive unorientable unit clauses: 0
% 3.26/0.87 # Negative unit clauses : 2
% 3.26/0.87 # Non-unit-clauses : 500
% 3.26/0.87 # Current number of unprocessed clauses: 7387
% 3.26/0.87 # ...number of literals in the above : 38581
% 3.26/0.87 # Current number of archived formulas : 0
% 3.26/0.87 # Current number of archived clauses : 380
% 3.26/0.87 # Clause-clause subsumption calls (NU) : 39755
% 3.26/0.87 # Rec. Clause-clause subsumption calls : 18546
% 3.26/0.87 # Non-unit clause-clause subsumptions : 173
% 3.26/0.87 # Unit Clause-clause subsumption calls : 2599
% 3.26/0.87 # Rewrite failures with RHS unbound : 0
% 3.26/0.87 # BW rewrite match attempts : 12
% 3.26/0.87 # BW rewrite match successes : 1
% 3.26/0.87 # Condensation attempts : 0
% 3.26/0.87 # Condensation successes : 0
% 3.26/0.87 # Termbank termtop insertions : 234966
% 3.26/0.87 # Search garbage collected termcells : 11807
% 3.26/0.87
% 3.26/0.87 # -------------------------------------------------
% 3.26/0.87 # User time : 0.343 s
% 3.26/0.87 # System time : 0.015 s
% 3.26/0.87 # Total time : 0.358 s
% 3.26/0.87 # Maximum resident set size: 5440 pages
% 3.26/0.87
% 3.26/0.87 # -------------------------------------------------
% 3.26/0.87 # User time : 0.361 s
% 3.26/0.87 # System time : 0.018 s
% 3.26/0.87 # Total time : 0.378 s
% 3.26/0.87 # Maximum resident set size: 2484 pages
% 3.26/0.87 % E---3.1 exiting
% 3.26/0.87 % E exiting
%------------------------------------------------------------------------------