TSTP Solution File: SEU810^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU810^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n002.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 03:30:27 EDT 2024
% Result : Theorem 1.81s 0.80s
% Output : CNFRefutation 1.81s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU810^1 : TPTP v8.2.0. Released v3.7.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n002.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Sun May 19 17:18:08 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.23/0.51 Running higher-order theorem proving
% 0.23/0.51 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
% 1.81/0.80 # Version: 3.1.0-ho
% 1.81/0.80 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.81/0.80 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.81/0.80 # Starting ehoh_best5 with 300s (1) cores
% 1.81/0.80 # Starting almost_fo_3_lam with 300s (1) cores
% 1.81/0.80 # Starting new_bool_5 with 300s (1) cores
% 1.81/0.80 # Starting pre_casc_3 with 300s (1) cores
% 1.81/0.80 # Starting ho_unfolding_8 with 300s (1) cores
% 1.81/0.80 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.81/0.80 # Starting new_bool_3 with 300s (1) cores
% 1.81/0.80 # Starting new_ho_5 with 300s (1) cores
% 1.81/0.80 # new_ho_10_cnf2 with pid 31733 completed with status 0
% 1.81/0.80 # Result found by new_ho_10_cnf2
% 1.81/0.80 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.81/0.80 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.81/0.80 # Starting ehoh_best5 with 300s (1) cores
% 1.81/0.80 # Starting almost_fo_3_lam with 300s (1) cores
% 1.81/0.80 # Starting new_bool_5 with 300s (1) cores
% 1.81/0.80 # Starting pre_casc_3 with 300s (1) cores
% 1.81/0.80 # Starting ho_unfolding_8 with 300s (1) cores
% 1.81/0.80 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.81/0.80 # No SInE strategy applied
% 1.81/0.80 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.81/0.80 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.81/0.80 # Starting ho_unfolding_8 with 61s (1) cores
% 1.81/0.80 # ho_unfolding_8 with pid 31740 completed with status 0
% 1.81/0.80 # Result found by ho_unfolding_8
% 1.81/0.80 # Preprocessing class: HSLMSLSSLLLCHFA.
% 1.81/0.80 # Scheduled 8 strats onto 8 cores with 300 seconds (2400 total)
% 1.81/0.80 # Starting ehoh_best5 with 300s (1) cores
% 1.81/0.80 # Starting almost_fo_3_lam with 300s (1) cores
% 1.81/0.80 # Starting new_bool_5 with 300s (1) cores
% 1.81/0.80 # Starting pre_casc_3 with 300s (1) cores
% 1.81/0.80 # Starting ho_unfolding_8 with 300s (1) cores
% 1.81/0.80 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.81/0.80 # No SInE strategy applied
% 1.81/0.80 # Search class: HGHSM-FSLM32-MHFMMSBN
% 1.81/0.80 # Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 1.81/0.80 # Starting ho_unfolding_8 with 61s (1) cores
% 1.81/0.80 # Preprocessing time : 0.062 s
% 1.81/0.80 # Presaturation interreduction done
% 1.81/0.80
% 1.81/0.80 # Proof found!
% 1.81/0.80 # SZS status Theorem
% 1.81/0.80 # SZS output start CNFRefutation
% 1.81/0.80 thf(decl_22, type, in: $i > $i > $o).
% 1.81/0.80 thf(decl_23, type, exu: ($i > $o) > $o).
% 1.81/0.80 thf(decl_24, type, setextAx: $o).
% 1.81/0.80 thf(decl_25, type, emptyset: $i).
% 1.81/0.80 thf(decl_26, type, emptysetAx: $o).
% 1.81/0.80 thf(decl_27, type, setadjoin: $i > $i > $i).
% 1.81/0.80 thf(decl_28, type, setadjoinAx: $o).
% 1.81/0.80 thf(decl_29, type, powerset: $i > $i).
% 1.81/0.80 thf(decl_30, type, powersetAx: $o).
% 1.81/0.80 thf(decl_31, type, setunion: $i > $i).
% 1.81/0.80 thf(decl_32, type, setunionAx: $o).
% 1.81/0.80 thf(decl_33, type, omega: $i).
% 1.81/0.80 thf(decl_34, type, omega0Ax: $o).
% 1.81/0.80 thf(decl_35, type, omegaSAx: $o).
% 1.81/0.80 thf(decl_36, type, omegaIndAx: $o).
% 1.81/0.80 thf(decl_37, type, replAx: $o).
% 1.81/0.80 thf(decl_38, type, foundationAx: $o).
% 1.81/0.80 thf(decl_39, type, wellorderingAx: $o).
% 1.81/0.80 thf(decl_40, type, descr: ($i > $o) > $i).
% 1.81/0.80 thf(decl_41, type, descrp: $o).
% 1.81/0.80 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_43, type, dsetconstrI: $o).
% 1.81/0.80 thf(decl_44, type, dsetconstrEL: $o).
% 1.81/0.80 thf(decl_45, type, dsetconstrER: $o).
% 1.81/0.80 thf(decl_46, type, exuE1: $o).
% 1.81/0.80 thf(decl_47, type, prop2set: $o > $i).
% 1.81/0.80 thf(decl_48, type, prop2setE: $o).
% 1.81/0.80 thf(decl_49, type, emptysetE: $o).
% 1.81/0.80 thf(decl_50, type, emptysetimpfalse: $o).
% 1.81/0.80 thf(decl_51, type, notinemptyset: $o).
% 1.81/0.80 thf(decl_52, type, exuE3e: $o).
% 1.81/0.80 thf(decl_53, type, setext: $o).
% 1.81/0.80 thf(decl_54, type, emptyI: $o).
% 1.81/0.80 thf(decl_55, type, noeltsimpempty: $o).
% 1.81/0.80 thf(decl_56, type, setbeta: $o).
% 1.81/0.80 thf(decl_57, type, nonempty: $i > $o).
% 1.81/0.80 thf(decl_58, type, nonemptyE1: $o).
% 1.81/0.80 thf(decl_59, type, nonemptyI: $o).
% 1.81/0.80 thf(decl_60, type, nonemptyI1: $o).
% 1.81/0.80 thf(decl_61, type, setadjoinIL: $o).
% 1.81/0.80 thf(decl_62, type, emptyinunitempty: $o).
% 1.81/0.80 thf(decl_63, type, setadjoinIR: $o).
% 1.81/0.80 thf(decl_64, type, setadjoinE: $o).
% 1.81/0.80 thf(decl_65, type, setadjoinOr: $o).
% 1.81/0.80 thf(decl_66, type, setoftrueEq: $o).
% 1.81/0.80 thf(decl_67, type, powersetI: $o).
% 1.81/0.80 thf(decl_68, type, emptyinPowerset: $o).
% 1.81/0.80 thf(decl_69, type, emptyInPowerset: $o).
% 1.81/0.80 thf(decl_70, type, powersetE: $o).
% 1.81/0.80 thf(decl_71, type, setunionI: $o).
% 1.81/0.80 thf(decl_72, type, setunionE: $o).
% 1.81/0.80 thf(decl_73, type, subPowSU: $o).
% 1.81/0.80 thf(decl_74, type, exuE2: $o).
% 1.81/0.80 thf(decl_75, type, nonemptyImpWitness: $o).
% 1.81/0.80 thf(decl_76, type, uniqinunit: $o).
% 1.81/0.80 thf(decl_77, type, notinsingleton: $o).
% 1.81/0.80 thf(decl_78, type, eqinunit: $o).
% 1.81/0.80 thf(decl_79, type, singletonsswitch: $o).
% 1.81/0.80 thf(decl_80, type, upairsetE: $o).
% 1.81/0.80 thf(decl_81, type, upairsetIL: $o).
% 1.81/0.80 thf(decl_82, type, upairsetIR: $o).
% 1.81/0.80 thf(decl_83, type, emptyE1: $o).
% 1.81/0.80 thf(decl_84, type, vacuousDall: $o).
% 1.81/0.80 thf(decl_85, type, quantDeMorgan1: $o).
% 1.81/0.80 thf(decl_86, type, quantDeMorgan2: $o).
% 1.81/0.80 thf(decl_87, type, quantDeMorgan3: $o).
% 1.81/0.80 thf(decl_88, type, quantDeMorgan4: $o).
% 1.81/0.80 thf(decl_89, type, prop2setI: $o).
% 1.81/0.80 thf(decl_90, type, set2prop: $i > $o).
% 1.81/0.80 thf(decl_91, type, prop2set2propI: $o).
% 1.81/0.80 thf(decl_92, type, notdexE: $o).
% 1.81/0.80 thf(decl_93, type, notdallE: $o).
% 1.81/0.80 thf(decl_94, type, exuI1: $o).
% 1.81/0.80 thf(decl_95, type, exuI3: $o).
% 1.81/0.80 thf(decl_96, type, exuI2: $o).
% 1.81/0.80 thf(decl_97, type, inCongP: $o).
% 1.81/0.80 thf(decl_98, type, in__Cong: $o).
% 1.81/0.80 thf(decl_99, type, exuE3u: $o).
% 1.81/0.80 thf(decl_100, type, exu__Cong: $o).
% 1.81/0.80 thf(decl_101, type, emptyset__Cong: $o).
% 1.81/0.80 thf(decl_102, type, setadjoin__Cong: $o).
% 1.81/0.80 thf(decl_103, type, powerset__Cong: $o).
% 1.81/0.80 thf(decl_104, type, setunion__Cong: $o).
% 1.81/0.80 thf(decl_105, type, omega__Cong: $o).
% 1.81/0.80 thf(decl_106, type, exuEu: $o).
% 1.81/0.80 thf(decl_107, type, descr__Cong: $o).
% 1.81/0.80 thf(decl_108, type, dsetconstr__Cong: $o).
% 1.81/0.80 thf(decl_109, type, subset: $i > $i > $o).
% 1.81/0.80 thf(decl_112, type, subsetI1: $o).
% 1.81/0.80 thf(decl_113, type, eqimpsubset2: $o).
% 1.81/0.80 thf(decl_114, type, eqimpsubset1: $o).
% 1.81/0.80 thf(decl_115, type, subsetI2: $o).
% 1.81/0.80 thf(decl_116, type, emptysetsubset: $o).
% 1.81/0.80 thf(decl_117, type, subsetE: $o).
% 1.81/0.80 thf(decl_118, type, subsetE2: $o).
% 1.81/0.80 thf(decl_119, type, notsubsetI: $o).
% 1.81/0.80 thf(decl_120, type, notequalI1: $o).
% 1.81/0.80 thf(decl_121, type, notequalI2: $o).
% 1.81/0.80 thf(decl_122, type, subsetRefl: $o).
% 1.81/0.80 thf(decl_123, type, subsetTrans: $o).
% 1.81/0.80 thf(decl_124, type, setadjoinSub: $o).
% 1.81/0.80 thf(decl_125, type, setadjoinSub2: $o).
% 1.81/0.80 thf(decl_126, type, subset2powerset: $o).
% 1.81/0.80 thf(decl_127, type, setextsub: $o).
% 1.81/0.80 thf(decl_128, type, subsetemptysetimpeq: $o).
% 1.81/0.80 thf(decl_129, type, powersetI1: $o).
% 1.81/0.80 thf(decl_130, type, powersetE1: $o).
% 1.81/0.80 thf(decl_131, type, inPowerset: $o).
% 1.81/0.80 thf(decl_132, type, powersetsubset: $o).
% 1.81/0.80 thf(decl_133, type, sepInPowerset: $o).
% 1.81/0.80 thf(decl_134, type, sepSubset: $o).
% 1.81/0.80 thf(decl_135, type, binunion: $i > $i > $i).
% 1.81/0.80 thf(decl_136, type, binunionIL: $o).
% 1.81/0.80 thf(decl_137, type, upairset2IR: $o).
% 1.81/0.80 thf(decl_138, type, binunionIR: $o).
% 1.81/0.80 thf(decl_139, type, binunionEcases: $o).
% 1.81/0.80 thf(decl_140, type, binunionE: $o).
% 1.81/0.80 thf(decl_141, type, binunionLsub: $o).
% 1.81/0.80 thf(decl_142, type, binunionRsub: $o).
% 1.81/0.80 thf(decl_143, type, binintersect: $i > $i > $i).
% 1.81/0.80 thf(decl_144, type, binintersectI: $o).
% 1.81/0.80 thf(decl_145, type, binintersectSubset5: $o).
% 1.81/0.80 thf(decl_146, type, binintersectEL: $o).
% 1.81/0.80 thf(decl_147, type, binintersectLsub: $o).
% 1.81/0.80 thf(decl_148, type, binintersectSubset2: $o).
% 1.81/0.80 thf(decl_149, type, binintersectSubset3: $o).
% 1.81/0.80 thf(decl_150, type, binintersectER: $o).
% 1.81/0.80 thf(decl_151, type, disjointsetsI1: $o).
% 1.81/0.80 thf(decl_152, type, binintersectRsub: $o).
% 1.81/0.80 thf(decl_153, type, binintersectSubset4: $o).
% 1.81/0.80 thf(decl_154, type, binintersectSubset1: $o).
% 1.81/0.80 thf(decl_155, type, bs114d: $o).
% 1.81/0.80 thf(decl_157, type, setminus: $i > $i > $i).
% 1.81/0.80 thf(decl_158, type, setminusI: $o).
% 1.81/0.80 thf(decl_159, type, setminusEL: $o).
% 1.81/0.80 thf(decl_160, type, setminusER: $o).
% 1.81/0.80 thf(decl_161, type, setminusSubset2: $o).
% 1.81/0.80 thf(decl_162, type, setminusERneg: $o).
% 1.81/0.80 thf(decl_163, type, setminusELneg: $o).
% 1.81/0.80 thf(decl_164, type, setminusILneg: $o).
% 1.81/0.80 thf(decl_165, type, setminusIRneg: $o).
% 1.81/0.80 thf(decl_166, type, setminusLsub: $o).
% 1.81/0.80 thf(decl_167, type, setminusSubset1: $o).
% 1.81/0.80 thf(decl_168, type, symdiff: $i > $i > $i).
% 1.81/0.80 thf(decl_169, type, symdiffE: $o).
% 1.81/0.80 thf(decl_170, type, symdiffI1: $o).
% 1.81/0.80 thf(decl_171, type, symdiffI2: $o).
% 1.81/0.80 thf(decl_172, type, symdiffIneg1: $o).
% 1.81/0.80 thf(decl_173, type, symdiffIneg2: $o).
% 1.81/0.80 thf(decl_174, type, iskpair: $i > $o).
% 1.81/0.80 thf(decl_175, type, secondinupair: $o).
% 1.81/0.80 thf(decl_176, type, setukpairIL: $o).
% 1.81/0.80 thf(decl_177, type, setukpairIR: $o).
% 1.81/0.80 thf(decl_178, type, kpairiskpair: $o).
% 1.81/0.80 thf(decl_179, type, kpair: $i > $i > $i).
% 1.81/0.80 thf(decl_180, type, kpairp: $o).
% 1.81/0.80 thf(decl_181, type, cartprod: $i > $i > $i).
% 1.81/0.80 thf(decl_182, type, singletonsubset: $o).
% 1.81/0.80 thf(decl_183, type, singletoninpowerset: $o).
% 1.81/0.80 thf(decl_184, type, singletoninpowunion: $o).
% 1.81/0.80 thf(decl_185, type, upairset2E: $o).
% 1.81/0.80 thf(decl_186, type, upairsubunion: $o).
% 1.81/0.80 thf(decl_187, type, upairinpowunion: $o).
% 1.81/0.80 thf(decl_188, type, ubforcartprodlem1: $o).
% 1.81/0.80 thf(decl_189, type, ubforcartprodlem2: $o).
% 1.81/0.80 thf(decl_190, type, ubforcartprodlem3: $o).
% 1.81/0.80 thf(decl_191, type, cartprodpairin: $o).
% 1.81/0.80 thf(decl_192, type, cartprodmempair1: $o).
% 1.81/0.80 thf(decl_193, type, cartprodmempair: $o).
% 1.81/0.80 thf(decl_194, type, setunionE2: $o).
% 1.81/0.80 thf(decl_195, type, setunionsingleton1: $o).
% 1.81/0.80 thf(decl_196, type, setunionsingleton2: $o).
% 1.81/0.80 thf(decl_197, type, setunionsingleton: $o).
% 1.81/0.80 thf(decl_198, type, singleton: $i > $o).
% 1.81/0.80 thf(decl_199, type, singletonprop: $o).
% 1.81/0.80 thf(decl_200, type, ex1: $i > ($i > $o) > $o).
% 1.81/0.80 thf(decl_201, type, ex1E1: $o).
% 1.81/0.80 thf(decl_202, type, ex1I: $o).
% 1.81/0.80 thf(decl_203, type, ex1I2: $o).
% 1.81/0.80 thf(decl_204, type, singletonsuniq: $o).
% 1.81/0.80 thf(decl_209, type, setukpairinjL1: $o).
% 1.81/0.80 thf(decl_210, type, kfstsingleton: $o).
% 1.81/0.80 thf(decl_211, type, theprop: $o).
% 1.81/0.80 thf(decl_212, type, kfst: $i > $i).
% 1.81/0.80 thf(decl_213, type, kfstpairEq: $o).
% 1.81/0.80 thf(decl_214, type, cartprodfstin: $o).
% 1.81/0.80 thf(decl_215, type, setukpairinjL2: $o).
% 1.81/0.80 thf(decl_216, type, setukpairinjL: $o).
% 1.81/0.80 thf(decl_217, type, setukpairinjR11: $o).
% 1.81/0.80 thf(decl_218, type, setukpairinjR12: $o).
% 1.81/0.80 thf(decl_219, type, setukpairinjR1: $o).
% 1.81/0.80 thf(decl_220, type, upairequniteq: $o).
% 1.81/0.80 thf(decl_221, type, setukpairinjR2: $o).
% 1.81/0.80 thf(decl_222, type, setukpairinjR: $o).
% 1.81/0.80 thf(decl_223, type, ksndsingleton: $o).
% 1.81/0.80 thf(decl_224, type, ksnd: $i > $i).
% 1.81/0.80 thf(decl_225, type, ksndpairEq: $o).
% 1.81/0.80 thf(decl_226, type, kpairsurjEq: $o).
% 1.81/0.80 thf(decl_227, type, cartprodsndin: $o).
% 1.81/0.80 thf(decl_228, type, cartprodpairmemEL: $o).
% 1.81/0.80 thf(decl_229, type, cartprodpairmemER: $o).
% 1.81/0.80 thf(decl_230, type, cartprodmempaircEq: $o).
% 1.81/0.80 thf(decl_231, type, cartprodfstpairEq: $o).
% 1.81/0.80 thf(decl_232, type, cartprodsndpairEq: $o).
% 1.81/0.80 thf(decl_233, type, cartprodpairsurjEq: $o).
% 1.81/0.80 thf(decl_234, type, breln: $i > $i > $i > $o).
% 1.81/0.80 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.81/0.80 thf(decl_236, type, dpsetconstrI: $o).
% 1.81/0.80 thf(decl_237, type, dpsetconstrSub: $o).
% 1.81/0.80 thf(decl_238, type, setOfPairsIsBReln: $o).
% 1.81/0.80 thf(decl_239, type, dpsetconstrERa: $o).
% 1.81/0.80 thf(decl_240, type, dpsetconstrEL1: $o).
% 1.81/0.80 thf(decl_241, type, dpsetconstrEL2: $o).
% 1.81/0.80 thf(decl_242, type, dpsetconstrER: $o).
% 1.81/0.80 thf(decl_243, type, func: $i > $i > $i > $o).
% 1.81/0.80 thf(decl_244, type, funcSet: $i > $i > $i).
% 1.81/0.80 thf(decl_245, type, funcImageSingleton: $o).
% 1.81/0.80 thf(decl_246, type, apProp: $o).
% 1.81/0.80 thf(decl_247, type, ap: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_248, type, app: $o).
% 1.81/0.80 thf(decl_249, type, infuncsetfunc: $o).
% 1.81/0.80 thf(decl_250, type, ap2p: $o).
% 1.81/0.80 thf(decl_251, type, funcinfuncset: $o).
% 1.81/0.80 thf(decl_252, type, lamProp: $o).
% 1.81/0.80 thf(decl_253, type, lam: $i > $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_254, type, lamp: $o).
% 1.81/0.80 thf(decl_255, type, lam2p: $o).
% 1.81/0.80 thf(decl_256, type, brelnall1: $o).
% 1.81/0.80 thf(decl_257, type, brelnall2: $o).
% 1.81/0.80 thf(decl_258, type, ex1E2: $o).
% 1.81/0.80 thf(decl_259, type, funcGraphProp1: $o).
% 1.81/0.80 thf(decl_260, type, funcGraphProp3: $o).
% 1.81/0.80 thf(decl_261, type, funcGraphProp2: $o).
% 1.81/0.80 thf(decl_262, type, funcextLem: $o).
% 1.81/0.80 thf(decl_263, type, funcGraphProp4: $o).
% 1.81/0.80 thf(decl_264, type, subbreln: $o).
% 1.81/0.80 thf(decl_265, type, eqbreln: $o).
% 1.81/0.80 thf(decl_266, type, funcext: $o).
% 1.81/0.80 thf(decl_267, type, funcext2: $o).
% 1.81/0.80 thf(decl_268, type, ap2apEq1: $o).
% 1.81/0.80 thf(decl_269, type, ap2apEq2: $o).
% 1.81/0.80 thf(decl_270, type, beta1: $o).
% 1.81/0.80 thf(decl_271, type, eta1: $o).
% 1.81/0.80 thf(decl_272, type, lam2lamEq: $o).
% 1.81/0.80 thf(decl_273, type, beta2: $o).
% 1.81/0.80 thf(decl_274, type, eta2: $o).
% 1.81/0.80 thf(decl_275, type, iffalseProp1: $o).
% 1.81/0.80 thf(decl_276, type, iffalseProp2: $o).
% 1.81/0.80 thf(decl_277, type, iftrueProp1: $o).
% 1.81/0.80 thf(decl_278, type, iftrueProp2: $o).
% 1.81/0.80 thf(decl_279, type, ifSingleton: $o).
% 1.81/0.80 thf(decl_280, type, if: $i > $o > $i > $i > $i).
% 1.81/0.80 thf(decl_281, type, ifp: $o).
% 1.81/0.80 thf(decl_282, type, theeq: $o).
% 1.81/0.80 thf(decl_283, type, iftrue: $o).
% 1.81/0.80 thf(decl_284, type, iffalse: $o).
% 1.81/0.80 thf(decl_285, type, iftrueorfalse: $o).
% 1.81/0.80 thf(decl_286, type, binintersectT_lem: $o).
% 1.81/0.80 thf(decl_287, type, binunionT_lem: $o).
% 1.81/0.80 thf(decl_288, type, powersetT_lem: $o).
% 1.81/0.80 thf(decl_289, type, setminusT_lem: $o).
% 1.81/0.80 thf(decl_290, type, complementT_lem: $o).
% 1.81/0.80 thf(decl_291, type, setextT: $o).
% 1.81/0.80 thf(decl_292, type, subsetTI: $o).
% 1.81/0.80 thf(decl_293, type, powersetTI1: $o).
% 1.81/0.80 thf(decl_294, type, powersetTE1: $o).
% 1.81/0.80 thf(decl_295, type, complementTI1: $o).
% 1.81/0.80 thf(decl_296, type, complementTE1: $o).
% 1.81/0.80 thf(decl_297, type, binintersectTELcontra: $o).
% 1.81/0.80 thf(decl_298, type, binintersectTERcontra: $o).
% 1.81/0.80 thf(decl_299, type, contrasubsetT: $o).
% 1.81/0.80 thf(decl_300, type, contrasubsetT1: $o).
% 1.81/0.80 thf(decl_301, type, contrasubsetT2: $o).
% 1.81/0.80 thf(decl_302, type, contrasubsetT3: $o).
% 1.81/0.80 thf(decl_303, type, doubleComplementI1: $o).
% 1.81/0.80 thf(decl_304, type, doubleComplementE1: $o).
% 1.81/0.80 thf(decl_305, type, doubleComplementSub1: $o).
% 1.81/0.80 thf(decl_306, type, doubleComplementSub2: $o).
% 1.81/0.80 thf(decl_307, type, doubleComplementEq: $o).
% 1.81/0.80 thf(decl_308, type, complementTnotintersectT: $o).
% 1.81/0.80 thf(decl_309, type, complementImpComplementIntersect: $o).
% 1.81/0.80 thf(decl_310, type, complementSubsetComplementIntersect: $o).
% 1.81/0.80 thf(decl_311, type, complementInPowersetComplementIntersect: $o).
% 1.81/0.80 thf(decl_312, type, contraSubsetComplement: $o).
% 1.81/0.80 thf(decl_313, type, complementTcontraSubset: $o).
% 1.81/0.80 thf(decl_314, type, binunionTILcontra: $o).
% 1.81/0.80 thf(decl_315, type, binunionTIRcontra: $o).
% 1.81/0.80 thf(decl_316, type, inIntersectImpInUnion: $o).
% 1.81/0.80 thf(decl_317, type, inIntersectImpInUnion2: $o).
% 1.81/0.80 thf(decl_318, type, inIntersectImpInIntersectUnions: $o).
% 1.81/0.80 thf(decl_319, type, intersectInPowersetIntersectUnions: $o).
% 1.81/0.80 thf(decl_320, type, inComplementUnionImpNotIn1: $o).
% 1.81/0.80 thf(decl_321, type, inComplementUnionImpInComplement1: $o).
% 1.81/0.80 thf(decl_322, type, binunionTE: $o).
% 1.81/0.80 thf(decl_323, type, binunionTEcontra: $o).
% 1.81/0.80 thf(decl_324, type, demorgan2a1: $o).
% 1.81/0.80 thf(decl_325, type, complementUnionInPowersetComplement: $o).
% 1.81/0.80 thf(decl_326, type, demorgan2a2: $o).
% 1.81/0.80 thf(decl_327, type, demorgan1a: $o).
% 1.81/0.80 thf(decl_328, type, demorgan1b: $o).
% 1.81/0.80 thf(decl_329, type, demorgan1: $o).
% 1.81/0.80 thf(decl_330, type, demorgan2a: $o).
% 1.81/0.80 thf(decl_331, type, demorgan2b2: $o).
% 1.81/0.80 thf(decl_332, type, demorgan2b: $o).
% 1.81/0.80 thf(decl_333, type, demorgan2: $o).
% 1.81/0.80 thf(decl_334, type, woz13rule0: $o).
% 1.81/0.80 thf(decl_335, type, woz13rule1: $o).
% 1.81/0.80 thf(decl_336, type, woz13rule2: $o).
% 1.81/0.80 thf(decl_337, type, woz13rule3: $o).
% 1.81/0.80 thf(decl_338, type, woz13rule4: $o).
% 1.81/0.80 thf(decl_339, type, woz1_1: $o).
% 1.81/0.80 thf(decl_340, type, woz1_2: $o).
% 1.81/0.80 thf(decl_341, type, woz1_3: $o).
% 1.81/0.80 thf(decl_342, type, woz1_4: $o).
% 1.81/0.80 thf(decl_343, type, woz1_5: $o).
% 1.81/0.80 thf(decl_344, type, breln1: $i > $i > $o).
% 1.81/0.80 thf(decl_345, type, breln1all2: $o).
% 1.81/0.80 thf(decl_346, type, breln1Set: $i > $i).
% 1.81/0.80 thf(decl_347, type, breln1SetBreln1: $o).
% 1.81/0.80 thf(decl_353, type, reflwellordering: $i > $i > $o).
% 1.81/0.80 thf(decl_354, type, choice2fnsingleton: $o).
% 1.81/0.80 thf(decl_355, type, setOfPairsIsBReln1: $o).
% 1.81/0.80 thf(decl_356, type, breln1all1: $o).
% 1.81/0.80 thf(decl_357, type, subbreln1: $o).
% 1.81/0.80 thf(decl_358, type, eqbreln1: $o).
% 1.81/0.80 thf(decl_359, type, breln1invset: $i > $i > $i).
% 1.81/0.80 thf(decl_360, type, breln1invprop: $o).
% 1.81/0.80 thf(decl_361, type, breln1invI: $o).
% 1.81/0.80 thf(decl_362, type, breln1invE: $o).
% 1.81/0.80 thf(decl_363, type, breln1compset: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_364, type, breln1compprop: $o).
% 1.81/0.80 thf(decl_365, type, breln1compI: $o).
% 1.81/0.80 thf(decl_366, type, breln1compE: $o).
% 1.81/0.80 thf(decl_367, type, breln1compEex: $o).
% 1.81/0.80 thf(decl_368, type, breln1unionprop: $o).
% 1.81/0.80 thf(decl_369, type, breln1unionIL: $o).
% 1.81/0.80 thf(decl_370, type, breln1unionIR: $o).
% 1.81/0.80 thf(decl_371, type, breln1unionI: $o).
% 1.81/0.80 thf(decl_372, type, breln1unionE: $o).
% 1.81/0.80 thf(decl_373, type, breln1unionEcases: $o).
% 1.81/0.80 thf(decl_374, type, breln1unionCommutes: $o).
% 1.81/0.80 thf(decl_375, type, woz2Ex: $o).
% 1.81/0.80 thf(decl_376, type, woz2W: $o).
% 1.81/0.80 thf(decl_377, type, woz2A: $o).
% 1.81/0.80 thf(decl_378, type, woz2B: $o).
% 1.81/0.80 thf(decl_379, type, image1Ex: $o).
% 1.81/0.80 thf(decl_380, type, image1Ex1: $o).
% 1.81/0.80 thf(decl_381, type, image1: $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_382, type, image1Equiv: $o).
% 1.81/0.80 thf(decl_383, type, image1E: $o).
% 1.81/0.80 thf(decl_384, type, image1I: $o).
% 1.81/0.80 thf(decl_385, type, injective: $i > $i > $i > $o).
% 1.81/0.80 thf(decl_386, type, injFuncSet: $i > $i > $i).
% 1.81/0.80 thf(decl_387, type, injFuncInInjFuncSet: $o).
% 1.81/0.80 thf(decl_388, type, injFuncSetFuncIn: $o).
% 1.81/0.80 thf(decl_389, type, injFuncSetFuncInj: $o).
% 1.81/0.80 thf(decl_390, type, surjective: $i > $i > $i > $o).
% 1.81/0.80 thf(decl_391, type, surjFuncSet: $i > $i > $i).
% 1.81/0.80 thf(decl_392, type, surjFuncSetFuncIn: $o).
% 1.81/0.80 thf(decl_393, type, surjFuncSetFuncSurj: $o).
% 1.81/0.80 thf(decl_394, type, leftInvIsSurj: $o).
% 1.81/0.80 thf(decl_395, type, surjCantorThm: $o).
% 1.81/0.80 thf(decl_396, type, foundation2: $o).
% 1.81/0.80 thf(decl_397, type, notinself: $o).
% 1.81/0.80 thf(decl_398, type, notinself2: $o).
% 1.81/0.80 thf(decl_399, type, omegaS: $i > $i).
% 1.81/0.80 thf(decl_400, type, omegaSp: $o).
% 1.81/0.80 thf(decl_401, type, omegaSclos: $o).
% 1.81/0.80 thf(decl_402, type, epred1_0: $o).
% 1.81/0.80 thf(decl_403, type, esk1_2: $i > $i > $i).
% 1.81/0.80 thf(decl_404, type, esk2_2: $i > $i > $i).
% 1.81/0.80 thf(decl_405, type, esk3_2: $i > $i > $i).
% 1.81/0.80 thf(decl_406, type, esk4_1: $i > $i).
% 1.81/0.80 thf(decl_407, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.81/0.80 thf(decl_408, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.81/0.80 thf(decl_409, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.81/0.80 thf(decl_410, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.81/0.80 thf(decl_411, type, esk9_1: $i > $i).
% 1.81/0.80 thf(decl_412, type, esk10_2: ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_413, type, esk11_2: ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_414, type, esk12_1: ($i > $o) > $i).
% 1.81/0.80 thf(decl_415, type, esk13_2: ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_416, type, esk14_1: ($i > $o) > $i).
% 1.81/0.80 thf(decl_417, type, esk15_2: $i > $i > $i).
% 1.81/0.80 thf(decl_418, type, esk16_2: $i > $i > $i).
% 1.81/0.80 thf(decl_419, type, esk17_1: $i > $i).
% 1.81/0.80 thf(decl_420, type, esk18_1: $i > $i).
% 1.81/0.80 thf(decl_421, type, esk19_1: $i > $i).
% 1.81/0.80 thf(decl_422, type, esk20_2: $i > $i > $i).
% 1.81/0.80 thf(decl_423, type, esk21_3: $i > $i > $o > $i).
% 1.81/0.80 thf(decl_424, type, esk22_2: ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_425, type, esk23_1: ($i > $o) > $i).
% 1.81/0.80 thf(decl_426, type, esk24_1: $i > $i).
% 1.81/0.80 thf(decl_427, type, esk25_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_428, type, esk26_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_429, type, esk27_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_430, type, esk28_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_431, type, esk29_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_432, type, esk30_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_433, type, esk31_2: ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_434, type, esk32_1: ($i > $o) > $i).
% 1.81/0.80 thf(decl_435, type, esk33_1: ($i > $o) > $i).
% 1.81/0.80 thf(decl_436, type, esk34_1: ($i > $o) > $i).
% 1.81/0.80 thf(decl_437, type, esk35_1: ($i > $o) > $i).
% 1.81/0.80 thf(decl_438, type, esk36_2: ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_439, type, esk37_1: ($i > $o) > $i).
% 1.81/0.80 thf(decl_440, type, esk38_2: ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_441, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.80 thf(decl_442, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.80 thf(decl_443, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_444, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.80 thf(decl_445, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_446, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.80 thf(decl_447, type, esk45_2: ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_448, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.80 thf(decl_449, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.81/0.80 thf(decl_450, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_451, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_452, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.81/0.80 thf(decl_453, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.81/0.80 thf(decl_454, type, esk52_2: $i > $i > $i).
% 1.81/0.80 thf(decl_455, type, esk53_2: $i > $i > $i).
% 1.81/0.80 thf(decl_456, type, esk54_2: $i > $i > $i).
% 1.81/0.80 thf(decl_457, type, esk55_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_458, type, esk56_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_459, type, esk57_2: $i > $i > $i).
% 1.81/0.80 thf(decl_460, type, esk58_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_461, type, esk59_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_462, type, esk60_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_463, type, esk61_3: $i > ($i > $o) > $i > $i).
% 1.81/0.80 thf(decl_464, type, esk62_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_465, type, esk63_2: $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_466, type, esk64_3: $i > $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_467, type, esk65_3: $i > $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_468, type, esk66_3: $i > $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_469, type, esk67_4: $i > $i > $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_470, type, esk68_4: $i > $i > $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_471, type, esk69_4: $i > $i > $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_472, type, esk70_4: $i > $i > $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_473, type, esk71_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_474, type, esk72_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_475, type, esk73_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_476, type, esk74_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_477, type, esk75_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_478, type, esk76_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_479, type, esk77_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_480, type, esk78_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_481, type, esk79_4: $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_482, type, esk80_3: $i > $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_483, type, esk81_3: $i > $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_484, type, esk82_3: $i > $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_485, type, esk83_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_486, type, esk84_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_487, type, esk85_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_488, type, esk86_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_489, type, esk87_3: $i > $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_490, type, esk88_3: $i > $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_491, type, esk89_3: $i > $i > ($i > $i > $o) > $i).
% 1.81/0.80 thf(decl_492, type, esk90_3: $i > $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_493, type, esk91_3: $i > $i > ($i > $o) > $i).
% 1.81/0.80 thf(decl_494, type, esk92_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_495, type, esk93_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_496, type, esk94_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_497, type, esk95_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_498, type, esk96_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_499, type, esk97_3: $i > $i > $i > $i).
% 1.81/0.80 thf(decl_500, type, esk98_5: $i > $i > $i > $i > $i > $i).
% 1.81/0.80 thf(decl_501, type, esk99_6: $i > $i > $i > $i > $i > $o > $i).
% 1.81/0.80 thf(decl_502, type, esk100_2: $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_503, type, esk101_3: $i > ($i > $i) > $i > $i).
% 1.81/0.80 thf(decl_504, type, esk102_2: $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_505, type, esk103_3: $i > ($i > $i) > $i > $i).
% 1.81/0.80 thf(decl_506, type, esk104_3: $i > ($i > $i) > $i > $i).
% 1.81/0.80 thf(decl_507, type, esk105_3: $i > ($i > $i) > $i > $i).
% 1.81/0.80 thf(decl_508, type, esk106_3: $i > ($i > $i) > $i > $i).
% 1.81/0.80 thf(decl_509, type, esk107_3: $i > ($i > $i) > $i > $i).
% 1.81/0.80 thf(decl_510, type, esk108_3: $i > $i > ($i > $i) > $i).
% 1.81/0.80 thf(decl_511, type, esk109_4: $i > $i > ($i > $i) > $i > $i).
% 1.81/0.80 thf(decl_512, type, esk110_1: $i > $i).
% 1.81/0.80 thf(decl_513, type, esk111_0: $i).
% 1.81/0.80 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', replAx)).
% 1.81/0.80 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu)).
% 1.81/0.80 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descrp)).
% 1.81/0.80 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE1)).
% 1.81/0.80 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3e)).
% 1.81/0.80 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonempty)).
% 1.81/0.80 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI)).
% 1.81/0.80 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE2)).
% 1.81/0.80 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI1)).
% 1.81/0.80 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI3)).
% 1.81/0.80 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI2)).
% 1.81/0.80 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3u)).
% 1.81/0.80 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu__Cong)).
% 1.81/0.80 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuEu)).
% 1.81/0.80 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descr__Cong)).
% 1.81/0.80 thf(image1Ex1, axiom, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', image1Ex1)).
% 1.81/0.80 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrI)).
% 1.81/0.80 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrEL)).
% 1.81/0.80 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrER)).
% 1.81/0.80 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setbeta)).
% 1.81/0.80 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyE1)).
% 1.81/0.80 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI1)).
% 1.81/0.80 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setoftrueEq)).
% 1.81/0.80 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyImpWitness)).
% 1.81/0.80 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyE1)).
% 1.81/0.80 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstr__Cong)).
% 1.81/0.80 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepInPowerset)).
% 1.81/0.80 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepSubset)).
% 1.81/0.80 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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonprop)).
% 1.81/0.80 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1E1)).
% 1.81/0.80 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I)).
% 1.81/0.80 thf(ex1I2, axiom, ((ex1I2)<=>![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)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I2)).
% 1.81/0.80 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstsingleton)).
% 1.81/0.80 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndsingleton)).
% 1.81/0.80 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrI)).
% 1.81/0.80 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X23 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrSub)).
% 1.81/0.80 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln)).
% 1.81/0.80 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ X14 @ X18)))))=>(X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrERa)).
% 1.81/0.80 thf(dpsetconstrEL1, axiom, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL1)).
% 1.81/0.80 thf(dpsetconstrEL2, axiom, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL2)).
% 1.81/0.80 thf(dpsetconstrER, axiom, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X28 @ X14 @ X18)))))=>(X28 @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrER)).
% 1.81/0.80 thf(funcImageSingleton, axiom, ((funcImageSingleton)<=>![X4:$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)).
% 1.81/0.80 thf(apProp, axiom, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[X3:$i]:((in @ (kpair @ X2 @ X3) @ X29))))) @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', apProp)).
% 1.81/0.80 thf(lamProp, axiom, ((lamProp)<=>![X4:$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)).
% 1.81/0.80 thf(lamp, axiom, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X2:$i]:(X31 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', lamp)).
% 1.81/0.80 thf(lam2p, axiom, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[X2:$i]:(X32 @ X2))) @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', lam2p)).
% 1.81/0.80 thf(ex1E2, axiom, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1E2)).
% 1.81/0.80 thf(beta1, axiom, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X36 @ X3))) @ X2)=(X36 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', beta1)).
% 1.81/0.80 thf(eta1, axiom, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eta1)).
% 1.81/0.80 thf(lam2lamEq, axiom, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2)))=(lam @ X4 @ X5 @ (^[X2:$i]:(X37 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', lam2lamEq)).
% 1.81/0.80 thf(beta2, axiom, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[X3:$i]:(X38 @ X3))) @ X2)=(X38 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', beta2)).
% 1.81/0.80 thf(eta2, axiom, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[X2:$i]:(ap @ X4 @ X5 @ X29 @ X2)))=(X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eta2)).
% 1.81/0.80 thf(iffalseProp1, axiom, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X39)&((X14)=(X2)))|(~((X39))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iffalseProp1)).
% 1.81/0.80 thf(iffalseProp2, axiom, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[X14:$i]:((((X40)&((X14)=(X2)))|(~((X40))&((X14)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iffalseProp2)).
% 1.81/0.80 thf(iftrueProp1, axiom, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X14:$i]:((((X41)&((X14)=(X2)))|(~((X41))&((X14)=(X3)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrueProp1)).
% 1.81/0.80 thf(iftrueProp2, axiom, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[X14:$i]:((((X42)&((X14)=(X2)))|(~((X42))&((X14)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrueProp2)).
% 1.81/0.80 thf(ifSingleton, axiom, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[X14:$i]:((((X43)&((X14)=(X2)))|(~((X43))&((X14)=(X3))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ifSingleton)).
% 1.81/0.80 thf(choice2fnsingleton, axiom, ((choice2fnsingleton)<=>![X4:$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:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ X3 @ X14) @ X33))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', choice2fnsingleton)).
% 1.81/0.80 thf(setOfPairsIsBReln1, axiom, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[X2:$i, X3:$i]:((X53 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln1)).
% 1.81/0.80 thf(image1Equiv, axiom, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X59 @ X3))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', image1Equiv)).
% 1.81/0.80 thf(image1E, axiom, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X60 @ X3))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', image1E)).
% 1.81/0.80 thf(image1I, axiom, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[X3:$i]:(X61 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', image1I)).
% 1.81/0.80 thf(foundation2, axiom, ((foundation2)<=>![X4:$i]:(((nonempty @ X4)=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', foundation2)).
% 1.81/0.80 thf(peano0notS, 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)=>((breln1compE)=>((breln1compEex)=>((breln1unionprop)=>((breln1unionIL)=>((breln1unionIR)=>((breln1unionI)=>((breln1unionE)=>((breln1unionEcases)=>((breln1unionCommutes)=>((woz2Ex)=>((woz2W)=>((woz2A)=>((woz2B)=>((image1Ex)=>((image1Ex1)=>((image1Equiv)=>((image1E)=>((image1I)=>((injFuncInInjFuncSet)=>((injFuncSetFuncIn)=>((injFuncSetFuncInj)=>((surjFuncSetFuncIn)=>((surjFuncSetFuncSurj)=>((leftInvIsSurj)=>((surjCantorThm)=>((foundation2)=>((notinself)=>((notinself2)=>((omegaSp)=>((omegaSclos)=>![X2:$i]:(((in @ X2 @ omega)=>((omegaS @ X2)!=(emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', peano0notS)).
% 1.81/0.80 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextAx)).
% 1.81/0.80 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetAx)).
% 1.81/0.80 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinAx)).
% 1.81/0.80 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetAx)).
% 1.81/0.80 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionAx)).
% 1.81/0.80 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega0Ax)).
% 1.81/0.80 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSAx)).
% 1.81/0.80 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaIndAx)).
% 1.81/0.80 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', foundationAx)).
% 1.81/0.80 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', wellorderingAx)).
% 1.81/0.80 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setE)).
% 1.81/0.80 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetE)).
% 1.81/0.80 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetimpfalse)).
% 1.81/0.80 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinemptyset)).
% 1.81/0.80 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setext)).
% 1.81/0.80 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyI)).
% 1.81/0.80 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', noeltsimpempty)).
% 1.81/0.80 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIL)).
% 1.81/0.80 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinunitempty)).
% 1.81/0.80 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIR)).
% 1.81/0.80 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinE)).
% 1.81/0.80 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinOr)).
% 1.81/0.80 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI)).
% 1.81/0.80 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinPowerset)).
% 1.81/0.80 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyInPowerset)).
% 1.81/0.80 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE)).
% 1.81/0.80 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionI)).
% 1.81/0.80 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE)).
% 1.81/0.80 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subPowSU)).
% 1.81/0.80 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', uniqinunit)).
% 1.81/0.80 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinsingleton)).
% 1.81/0.80 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqinunit)).
% 1.81/0.80 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsswitch)).
% 1.81/0.80 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetE)).
% 1.81/0.80 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIL)).
% 1.81/0.80 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIR)).
% 1.81/0.80 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', vacuousDall)).
% 1.81/0.80 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan1)).
% 1.81/0.80 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan2)).
% 1.81/0.80 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan3)).
% 1.81/0.80 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan4)).
% 1.81/0.80 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setI)).
% 1.81/0.80 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2set2propI)).
% 1.81/0.80 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdexE)).
% 1.81/0.80 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdallE)).
% 1.81/0.80 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inCongP)).
% 1.81/0.80 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', in__Cong)).
% 1.81/0.80 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyset__Cong)).
% 1.81/0.80 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoin__Cong)).
% 1.81/0.80 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powerset__Cong)).
% 1.81/0.80 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunion__Cong)).
% 1.81/0.80 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega__Cong)).
% 1.81/0.80 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI1)).
% 1.81/0.80 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset2)).
% 1.81/0.80 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset1)).
% 1.81/0.80 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI2)).
% 1.81/0.80 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetsubset)).
% 1.81/0.80 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE)).
% 1.81/0.80 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE2)).
% 1.81/0.80 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notsubsetI)).
% 1.81/0.80 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI1)).
% 1.81/0.80 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI2)).
% 1.81/0.80 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetRefl)).
% 1.81/0.80 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTrans)).
% 1.81/0.80 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub)).
% 1.81/0.80 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub2)).
% 1.81/0.80 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subset2powerset)).
% 1.81/0.80 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextsub)).
% 1.81/0.80 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetemptysetimpeq)).
% 1.81/0.80 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI1)).
% 1.81/0.80 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE1)).
% 1.81/0.80 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inPowerset)).
% 1.81/0.80 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetsubset)).
% 1.81/0.80 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIL)).
% 1.81/0.80 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2IR)).
% 1.81/0.80 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIR)).
% 1.81/0.80 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionEcases)).
% 1.81/0.80 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionE)).
% 1.81/0.80 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionLsub)).
% 1.81/0.80 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionRsub)).
% 1.81/0.80 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectI)).
% 1.81/0.80 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset5)).
% 1.81/0.80 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectEL)).
% 1.81/0.80 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectLsub)).
% 1.81/0.80 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset2)).
% 1.81/0.80 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset3)).
% 1.81/0.80 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectER)).
% 1.81/0.80 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', disjointsetsI1)).
% 1.81/0.80 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectRsub)).
% 1.81/0.80 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset4)).
% 1.81/0.80 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset1)).
% 1.81/0.80 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bs114d)).
% 1.81/0.80 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusI)).
% 1.81/0.80 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusEL)).
% 1.81/0.80 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusER)).
% 1.81/0.80 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset2)).
% 1.81/0.80 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusERneg)).
% 1.81/0.80 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusELneg)).
% 1.81/0.80 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusILneg)).
% 1.81/0.80 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusIRneg)).
% 1.81/0.80 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusLsub)).
% 1.81/0.80 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset1)).
% 1.81/0.80 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffE)).
% 1.81/0.80 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI1)).
% 1.81/0.80 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI2)).
% 1.81/0.80 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg1)).
% 1.81/0.80 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg2)).
% 1.81/0.80 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', secondinupair)).
% 1.81/0.80 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIL)).
% 1.81/0.80 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIR)).
% 1.81/0.80 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairiskpair)).
% 1.81/0.80 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairp)).
% 1.81/0.80 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsubset)).
% 1.81/0.80 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowerset)).
% 1.81/0.80 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowunion)).
% 1.81/0.80 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2E)).
% 1.81/0.80 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsubunion)).
% 1.81/0.80 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairinpowunion)).
% 1.81/0.80 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem1)).
% 1.81/0.80 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem2)).
% 1.81/0.80 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem3)).
% 1.81/0.80 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairin)).
% 1.81/0.80 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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)).
% 1.81/0.80 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair)).
% 1.81/0.80 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE2)).
% 1.81/0.80 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton1)).
% 1.81/0.80 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton2)).
% 1.81/0.80 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton)).
% 1.81/0.80 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsuniq)).
% 1.81/0.80 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL1)).
% 1.81/0.80 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theprop)).
% 1.81/0.80 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstpairEq)).
% 1.81/0.80 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstin)).
% 1.81/0.80 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL2)).
% 1.81/0.80 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL)).
% 1.81/0.80 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR11)).
% 1.81/0.80 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR12)).
% 1.81/0.80 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR1)).
% 1.81/0.80 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairequniteq)).
% 1.81/0.80 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR2)).
% 1.81/0.80 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR)).
% 1.81/0.80 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndpairEq)).
% 1.81/0.80 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairsurjEq)).
% 1.81/0.80 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndin)).
% 1.81/0.80 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemEL)).
% 1.81/0.80 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemER)).
% 1.81/0.80 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempaircEq)).
% 1.81/0.80 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstpairEq)).
% 1.81/0.80 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndpairEq)).
% 1.81/0.80 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairsurjEq)).
% 1.81/0.80 thf(app, axiom, ((app)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', app)).
% 1.81/0.80 thf(infuncsetfunc, axiom, ((infuncsetfunc)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>(func @ X4 @ X5 @ X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', infuncsetfunc)).
% 1.81/0.80 thf(ap2p, axiom, ((ap2p)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (ap @ X4 @ X5 @ X29 @ X2) @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ap2p)).
% 1.81/0.80 thf(funcinfuncset, axiom, ((funcinfuncset)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcinfuncset)).
% 1.81/0.80 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)).
% 1.81/0.80 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)).
% 1.81/0.80 thf(funcGraphProp1, axiom, ((funcGraphProp1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcGraphProp1)).
% 1.81/0.80 thf(funcGraphProp3, axiom, ((funcGraphProp3)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (kpair @ X2 @ (ap @ X4 @ X5 @ X29 @ X2)) @ X29)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcGraphProp3)).
% 1.81/0.80 thf(funcGraphProp2, axiom, ((funcGraphProp2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcGraphProp2)).
% 1.81/0.80 thf(funcextLem, axiom, ((funcextLem)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X34)=>(in @ (kpair @ X2 @ X3) @ X29)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcextLem)).
% 1.81/0.80 thf(funcGraphProp4, axiom, ((funcGraphProp4)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X29)=>((ap @ X4 @ X5 @ X29 @ X2)=(X3)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcGraphProp4)).
% 1.81/0.80 thf(subbreln, axiom, ((subbreln)<=>![X4:$i, X5:$i, X33:$i]:(((breln @ X4 @ X5 @ X33)=>![X35:$i]:(((breln @ X4 @ X5 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subbreln)).
% 1.81/0.80 thf(eqbreln, axiom, ((eqbreln)<=>![X4:$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:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ X33))))))=>((X33)=(X35))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqbreln)).
% 1.81/0.80 thf(funcext, axiom, ((funcext)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X34:$i]:(((func @ X4 @ X5 @ X34)=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcext)).
% 1.81/0.80 thf(funcext2, axiom, ((funcext2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X34:$i]:(((in @ X34 @ (funcSet @ X4 @ X5))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X34 @ X2))))=>((X29)=(X34)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', funcext2)).
% 1.81/0.80 thf(ap2apEq1, axiom, ((ap2apEq1)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ap2apEq1)).
% 1.81/0.80 thf(ap2apEq2, axiom, ((ap2apEq2)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ X29 @ X2)=(ap @ X4 @ X5 @ X29 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ap2apEq2)).
% 1.81/0.80 thf(ifp, axiom, ((ifp)<=>![X4:$i, X44:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X44)) @ X2 @ X3) @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ifp)).
% 1.81/0.80 thf(theeq, axiom, ((theeq)<=>![X21:$i]:(((singleton @ X21)=>![X2:$i]:(((in @ X2 @ X21)=>((setunion @ X21)=(X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theeq)).
% 1.81/0.80 thf(iftrue, axiom, ((iftrue)<=>![X4:$i, X45:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X45)=>((if @ X4 @ ((X45)) @ X2 @ X3)=(X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrue)).
% 1.81/0.80 thf(iffalse, axiom, ((iffalse)<=>![X4:$i, X46:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X46))=>((if @ X4 @ ((X46)) @ X2 @ X3)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iffalse)).
% 1.81/0.80 thf(iftrueorfalse, axiom, ((iftrueorfalse)<=>![X4:$i, X47:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(in @ (if @ X4 @ ((X47)) @ X2 @ X3) @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', iftrueorfalse)).
% 1.81/0.80 thf(binintersectT_lem, axiom, ((binintersectT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectT_lem)).
% 1.81/0.80 thf(binunionT_lem, axiom, ((binunionT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (binunion @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionT_lem)).
% 1.81/0.80 thf(powersetT_lem, axiom, ((powersetT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (powerset @ X21) @ (powerset @ (powerset @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetT_lem)).
% 1.81/0.80 thf(setminusT_lem, axiom, ((setminusT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X21 @ X48) @ (powerset @ X4))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusT_lem)).
% 1.81/0.80 thf(complementT_lem, axiom, ((complementT_lem)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementT_lem)).
% 1.81/0.80 thf(setextT, axiom, ((setextT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ X21))))=>((X21)=(X48))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextT)).
% 1.81/0.80 thf(subsetTI, axiom, ((subsetTI)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTI)).
% 1.81/0.80 thf(powersetTI1, axiom, ((powersetTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ X48))))=>(in @ X21 @ (powerset @ X48)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetTI1)).
% 1.81/0.80 thf(powersetTE1, axiom, ((powersetTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X21 @ (powerset @ X48))=>((in @ X2 @ X21)=>(in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetTE1)).
% 1.81/0.80 thf(complementTI1, axiom, ((complementTI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>~((in @ X2 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTI1)).
% 1.81/0.80 thf(complementTE1, axiom, ((complementTE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTE1)).
% 1.81/0.80 thf(binintersectTELcontra, axiom, ((binintersectTELcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectTELcontra)).
% 1.81/0.80 thf(binintersectTERcontra, axiom, ((binintersectTERcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectTERcontra)).
% 1.81/0.80 thf(contrasubsetT, axiom, ((contrasubsetT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ (setminus @ X4 @ X48))=>((in @ X2 @ X48)=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contrasubsetT)).
% 1.81/0.80 thf(contrasubsetT1, axiom, ((contrasubsetT1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((subset @ X21 @ X48)=>(~((in @ X2 @ X48))=>~((in @ X2 @ X21))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contrasubsetT1)).
% 1.81/0.80 thf(contrasubsetT2, axiom, ((contrasubsetT2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ X48)=>(subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contrasubsetT2)).
% 1.81/0.80 thf(contrasubsetT3, axiom, ((contrasubsetT3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ (setminus @ X4 @ X48) @ (setminus @ X4 @ X21))=>(subset @ X21 @ X48))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contrasubsetT3)).
% 1.81/0.80 thf(doubleComplementI1, axiom, ((doubleComplementI1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X21)=>(in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementI1)).
% 1.81/0.80 thf(doubleComplementE1, axiom, ((doubleComplementE1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (setminus @ X4 @ X21)))=>(in @ X2 @ X21))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementE1)).
% 1.81/0.80 thf(doubleComplementSub1, axiom, ((doubleComplementSub1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ X21 @ (setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementSub1)).
% 1.81/0.80 thf(doubleComplementSub2, axiom, ((doubleComplementSub2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ (setminus @ X4 @ X21)) @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementSub2)).
% 1.81/0.80 thf(doubleComplementEq, axiom, ((doubleComplementEq)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>((X21)=(setminus @ X4 @ (setminus @ X4 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', doubleComplementEq)).
% 1.81/0.80 thf(complementTnotintersectT, axiom, ((complementTnotintersectT)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>~((in @ X2 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTnotintersectT)).
% 1.81/0.80 thf(complementImpComplementIntersect, axiom, ((complementImpComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementImpComplementIntersect)).
% 1.81/0.80 thf(complementSubsetComplementIntersect, axiom, ((complementSubsetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(subset @ (setminus @ X4 @ X21) @ (setminus @ X4 @ (binintersect @ X21 @ X48)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementSubsetComplementIntersect)).
% 1.81/0.80 thf(complementInPowersetComplementIntersect, axiom, ((complementInPowersetComplementIntersect)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementInPowersetComplementIntersect)).
% 1.81/0.80 thf(contraSubsetComplement, axiom, ((contraSubsetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X48)=>(in @ X2 @ (setminus @ X4 @ X21))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', contraSubsetComplement)).
% 1.81/0.80 thf(complementTcontraSubset, axiom, ((complementTcontraSubset)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementTcontraSubset)).
% 1.81/0.80 thf(binunionTILcontra, axiom, ((binunionTILcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionTILcontra)).
% 1.81/0.80 thf(binunionTIRcontra, axiom, ((binunionTIRcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X48)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionTIRcontra)).
% 1.81/0.80 thf(inIntersectImpInUnion, axiom, ((inIntersectImpInUnion)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X21 @ X49)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inIntersectImpInUnion)).
% 1.81/0.80 thf(inIntersectImpInUnion2, axiom, ((inIntersectImpInUnion2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binunion @ X48 @ X49)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inIntersectImpInUnion2)).
% 1.81/0.80 thf(inIntersectImpInIntersectUnions, axiom, ((inIntersectImpInIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inIntersectImpInIntersectUnions)).
% 1.81/0.80 thf(intersectInPowersetIntersectUnions, axiom, ((intersectInPowersetIntersectUnions)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', intersectInPowersetIntersectUnions)).
% 1.81/0.80 thf(inComplementUnionImpNotIn1, axiom, ((inComplementUnionImpNotIn1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>~((in @ X2 @ X21)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inComplementUnionImpNotIn1)).
% 1.81/0.80 thf(inComplementUnionImpInComplement1, axiom, ((inComplementUnionImpInComplement1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inComplementUnionImpInComplement1)).
% 1.81/0.80 thf(binunionTE, axiom, ((binunionTE)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X50:$o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ X21 @ X48))=>(((in @ X2 @ X21)=>(X50))=>(((in @ X2 @ X48)=>(X50))=>(X50))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionTE)).
% 1.81/0.80 thf(binunionTEcontra, axiom, ((binunionTEcontra)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X21))=>(~((in @ X2 @ X48))=>~((in @ X2 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionTEcontra)).
% 1.81/0.80 thf(demorgan2a1, axiom, ((demorgan2a1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X21)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2a1)).
% 1.81/0.80 thf(complementUnionInPowersetComplement, axiom, ((complementUnionInPowersetComplement)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', complementUnionInPowersetComplement)).
% 1.81/0.80 thf(demorgan2a2, axiom, ((demorgan2a2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (setminus @ X4 @ X48)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2a2)).
% 1.81/0.80 thf(demorgan1a, axiom, ((demorgan1a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48)))=>(in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan1a)).
% 1.81/0.80 thf(demorgan1b, axiom, ((demorgan1b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan1b)).
% 1.81/0.80 thf(demorgan1, axiom, ((demorgan1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ X21 @ X48))=(binunion @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan1)).
% 1.81/0.80 thf(demorgan2a, axiom, ((demorgan2a)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))=>(in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2a)).
% 1.81/0.80 thf(demorgan2b2, axiom, ((demorgan2b2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (setminus @ X4 @ X21))=>((in @ X2 @ (setminus @ X4 @ X48))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2b2)).
% 1.81/0.80 thf(demorgan2b, axiom, ((demorgan2b)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))=>(in @ X2 @ (setminus @ X4 @ (binunion @ X21 @ X48))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2b)).
% 1.81/0.80 thf(demorgan2, axiom, ((demorgan2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((setminus @ X4 @ (binunion @ X21 @ X48))=(binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', demorgan2)).
% 1.81/0.80 thf(woz13rule0, axiom, ((woz13rule0)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X2:$i]:(((in @ X2 @ (binintersect @ X21 @ X48))=>(in @ X2 @ X4)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule0)).
% 1.81/0.80 thf(woz13rule1, axiom, ((woz13rule1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule1)).
% 1.81/0.80 thf(woz13rule2, axiom, ((woz13rule2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X48 @ X49)=>(subset @ (binintersect @ X21 @ X48) @ X49))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule2)).
% 1.81/0.80 thf(woz13rule3, axiom, ((woz13rule3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>((subset @ X21 @ X48)=>((subset @ X21 @ X49)=>(subset @ X21 @ (binintersect @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule3)).
% 1.81/0.80 thf(woz13rule4, axiom, ((woz13rule4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((subset @ X21 @ X49)=>((subset @ X48 @ X51)=>(subset @ (binintersect @ X21 @ X48) @ (binintersect @ X49 @ X51))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz13rule4)).
% 1.81/0.80 thf(woz1_1, axiom, ((woz1_1)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ X21) @ (powerset @ (setminus @ X4 @ (binintersect @ X21 @ X48))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz1_1)).
% 1.81/0.80 thf(woz1_2, axiom, ((woz1_2)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>![X51:$i]:(((in @ X51 @ (powerset @ X4))=>((setminus @ X4 @ (binintersect @ (binunion @ X21 @ X48) @ (binunion @ X49 @ X51)))=(binunion @ (binintersect @ (setminus @ X4 @ X21) @ (setminus @ X4 @ X48)) @ (binintersect @ (setminus @ X4 @ X49) @ (setminus @ X4 @ X51))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz1_2)).
% 1.81/0.80 thf(woz1_3, axiom, ((woz1_3)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>![X49:$i]:(((in @ X49 @ (powerset @ X4))=>(in @ (binintersect @ X21 @ X48) @ (powerset @ (binintersect @ (binunion @ X21 @ X49) @ (binunion @ X48 @ X49))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz1_3)).
% 1.81/0.80 thf(woz1_4, axiom, ((woz1_4)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>((subset @ X21 @ (setminus @ X4 @ X48))=>(subset @ X48 @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz1_4)).
% 1.81/0.80 thf(woz1_5, axiom, ((woz1_5)<=>![X4:$i, X21:$i]:(((in @ X21 @ (powerset @ X4))=>![X48:$i]:(((in @ X48 @ (powerset @ X4))=>(in @ (setminus @ X4 @ (binunion @ X21 @ X48)) @ (powerset @ (setminus @ X4 @ X21)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz1_5)).
% 1.81/0.80 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)).
% 1.81/0.80 thf(breln1SetBreln1, axiom, ((breln1SetBreln1)<=>![X4:$i, X33:$i]:(((in @ X33 @ (breln1Set @ X4))=>(breln1 @ X4 @ X33)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1SetBreln1)).
% 1.81/0.80 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)).
% 1.81/0.80 thf(subbreln1, axiom, ((subbreln1)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X33)=>(in @ (kpair @ X2 @ X3) @ X35))))))=>(subset @ X33 @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subbreln1)).
% 1.81/0.80 thf(eqbreln1, axiom, ((eqbreln1)<=>![X4:$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)).
% 1.81/0.80 thf(breln1invprop, axiom, ((breln1invprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>(breln1 @ X4 @ (breln1invset @ X4 @ X33))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1invprop)).
% 1.81/0.80 thf(breln1invI, axiom, ((breln1invI)<=>![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)).
% 1.81/0.80 thf(breln1invE, axiom, ((breln1invE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X3 @ X2) @ (breln1invset @ X4 @ X33))=>(in @ (kpair @ X2 @ X3) @ X33))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1invE)).
% 1.81/0.80 thf(breln1compprop, axiom, ((breln1compprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (breln1compset @ X4 @ X33 @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1compprop)).
% 1.81/0.80 thf(breln1compI, axiom, ((breln1compI)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (breln1compset @ X4 @ X33 @ X35))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1compI)).
% 1.81/0.80 thf(breln1compE, axiom, ((breln1compE)<=>![X4:$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:$i]:((((in @ X14 @ X4)&(in @ (kpair @ X2 @ X14) @ X33))&(in @ (kpair @ X14 @ X3) @ X35))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1compE)).
% 1.81/0.80 thf(breln1compEex, axiom, ((breln1compEex)<=>![X4:$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))=>![X54:$o]:((![X14:$i]:(((in @ X14 @ X4)=>((in @ (kpair @ X2 @ X14) @ X33)=>((in @ (kpair @ X14 @ X3) @ X35)=>(X54)))))=>(X54))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1compEex)).
% 1.81/0.80 thf(breln1unionprop, axiom, ((breln1unionprop)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>(breln1 @ X4 @ (binunion @ X33 @ X35))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionprop)).
% 1.81/0.80 thf(breln1unionIL, axiom, ((breln1unionIL)<=>![X4:$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) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionIL)).
% 1.81/0.80 thf(breln1unionIR, axiom, ((breln1unionIR)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ X35)=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionIR)).
% 1.81/0.80 thf(breln1unionI, axiom, ((breln1unionI)<=>![X4:$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))=>(in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionI)).
% 1.81/0.80 thf(breln1unionE, axiom, ((breln1unionE)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((in @ (kpair @ X2 @ X3) @ (binunion @ X33 @ X35))=>((in @ (kpair @ X2 @ X3) @ X33)|(in @ (kpair @ X2 @ X3) @ X35)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionE)).
% 1.81/0.80 thf(breln1unionEcases, axiom, ((breln1unionEcases)<=>![X4:$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) @ (binunion @ X33 @ X35))=>![X55:$o]:((((in @ (kpair @ X2 @ X3) @ X33)=>(X55))=>(((in @ (kpair @ X2 @ X3) @ X35)=>(X55))=>(X55)))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionEcases)).
% 1.81/0.80 thf(breln1unionCommutes, axiom, ((breln1unionCommutes)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((binunion @ X33 @ X35)=(binunion @ X35 @ X33))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln1unionCommutes)).
% 1.81/0.80 thf(woz2Ex, axiom, ((woz2Ex)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>((X33)=(breln1invset @ X4 @ (breln1invset @ X4 @ X33)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz2Ex)).
% 1.81/0.80 thf(woz2W, axiom, ((woz2W)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>((breln1invset @ X4 @ (breln1compset @ X4 @ X33 @ X35))=(breln1compset @ X4 @ (breln1invset @ X4 @ X35) @ (breln1invset @ X4 @ X33)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz2W)).
% 1.81/0.80 thf(woz2A, axiom, ((woz2A)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1compset @ X4 @ X33 @ X56) @ (breln1compset @ X4 @ X35 @ X56)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz2A)).
% 1.81/0.80 thf(woz2B, axiom, ((woz2B)<=>![X4:$i, X33:$i]:(((breln1 @ X4 @ X33)=>![X35:$i]:(((breln1 @ X4 @ X35)=>![X56:$i]:(((breln1 @ X4 @ X56)=>((breln1compset @ X4 @ (binunion @ X33 @ X35) @ X56)=(binunion @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X35))) @ (breln1invset @ X4 @ (breln1compset @ X4 @ (breln1invset @ X4 @ X56) @ (breln1invset @ X4 @ X33)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', woz2B)).
% 1.81/0.80 thf(image1Ex, axiom, ((image1Ex)<=>![X4:$i, X57:$i > $i]:(?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X57 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', image1Ex)).
% 1.81/0.80 thf(injFuncInInjFuncSet, axiom, ((injFuncInInjFuncSet)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((injective @ X4 @ X5 @ X29)=>(in @ X29 @ (injFuncSet @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', injFuncInInjFuncSet)).
% 1.81/0.80 thf(injFuncSetFuncIn, axiom, ((injFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', injFuncSetFuncIn)).
% 1.81/0.80 thf(injFuncSetFuncInj, axiom, ((injFuncSetFuncInj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (injFuncSet @ X2 @ X3))=>(injective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', injFuncSetFuncInj)).
% 1.81/0.80 thf(surjFuncSetFuncIn, axiom, ((surjFuncSetFuncIn)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X4 @ X5))=>(in @ X29 @ (funcSet @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', surjFuncSetFuncIn)).
% 1.81/0.80 thf(surjFuncSetFuncSurj, axiom, ((surjFuncSetFuncSurj)<=>![X2:$i, X3:$i, X29:$i]:(((in @ X29 @ (surjFuncSet @ X2 @ X3))=>(surjective @ X2 @ X3 @ X29)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', surjFuncSetFuncSurj)).
% 1.81/0.80 thf(leftInvIsSurj, axiom, ((leftInvIsSurj)<=>![X4:$i, X5:$i, X62:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X62 @ X2) @ X5)))=>![X34:$i]:(((in @ X34 @ (funcSet @ X5 @ X4))=>(![X2:$i]:(((in @ X2 @ X4)=>((ap @ X5 @ X4 @ X34 @ (X62 @ X2))=(X2))))=>(surjective @ X5 @ X4 @ X34))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', leftInvIsSurj)).
% 1.81/0.80 thf(surjCantorThm, axiom, ((surjCantorThm)<=>![X4:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ (powerset @ X4)))=>~((surjective @ X4 @ (powerset @ X4) @ X29))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', surjCantorThm)).
% 1.81/0.80 thf(notinself, axiom, ((notinself)<=>![X4:$i]:(~((in @ X4 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinself)).
% 1.81/0.80 thf(notinself2, axiom, ((notinself2)<=>![X4:$i, X5:$i]:(((in @ X4 @ X5)=>~((in @ X5 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinself2)).
% 1.81/0.80 thf(omegaSp, axiom, ((omegaSp)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (omegaS @ X2) @ omega)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSp)).
% 1.81/0.80 thf(omegaSclos, axiom, ((omegaSclos)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSclos)).
% 1.81/0.80 thf(omegaS, axiom, ((omegaS)=(^[X2:$i]:(setadjoin @ X2 @ X2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaS)).
% 1.81/0.80 thf(c_0_330, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.81/0.80 thf(c_0_331, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.81/0.80 thf(c_0_332, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.81/0.80 thf(c_0_333, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.81/0.80 thf(c_0_334, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.81/0.80 thf(c_0_335, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.81/0.80 thf(c_0_336, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.81/0.80 thf(c_0_337, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.81/0.80 thf(c_0_338, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.81/0.80 thf(c_0_339, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.81/0.80 thf(c_0_340, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.81/0.80 thf(c_0_341, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.81/0.80 thf(c_0_342, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.81/0.80 thf(c_0_343, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.81/0.80 thf(c_0_344, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.81/0.80 thf(c_0_345, plain, ((image1Ex1)<=>![X4:$i, X58:$i > $i]:((exu @ (^[Z0/* 6 */:$i]:(![X2:$i]:(((in @ X2 @ Z0)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3))))))))))), inference(fof_simplification,[status(thm)],[image1Ex1])).
% 1.81/0.80 thf(c_0_346, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X1132:$i]:((((X6 @ X2 @ X1132))&![X1133:$i]:((((X6 @ X2 @ X1133))=>((X1132)=(X1133)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_330, c_0_331])).
% 1.81/0.80 thf(c_0_347, plain, ((descrp)=(![X1:$i > $o]:(((?[X1134:$i]:((((X1 @ X1134))&![X1135:$i]:((((X1 @ X1135))=>((X1134)=(X1135)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_332, c_0_331])).
% 1.81/0.80 thf(c_0_348, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.81/0.80 thf(c_0_349, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.81/0.80 thf(c_0_350, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.81/0.80 thf(c_0_351, plain, ((exuE1)=(![X1:$i > $o]:(((?[X1136:$i]:((((X1 @ X1136))&![X1137:$i]:((((X1 @ X1137))=>((X1136)=(X1137)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_333, c_0_331])).
% 1.81/0.80 thf(c_0_352, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X1138:$i]:((((X1 @ X1138))&![X1139:$i]:((((X1 @ X1139))=>((X1138)=(X1139)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_334, c_0_331])).
% 1.81/0.80 thf(c_0_353, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.81/0.80 thf(c_0_354, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_335])).
% 1.81/0.80 thf(c_0_355, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_336, c_0_335])).
% 1.81/0.80 thf(c_0_356, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_335])).
% 1.81/0.80 thf(c_0_357, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.81/0.80 thf(c_0_358, plain, ((exuE2)=(![X1:$i > $o]:(((?[X1140:$i]:((((X1 @ X1140))&![X1141:$i]:((((X1 @ X1141))=>((X1140)=(X1141)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_337, c_0_331])).
% 1.81/0.80 thf(c_0_359, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_335])).
% 1.81/0.80 thf(c_0_360, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 1.81/0.80 thf(c_0_361, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X1142:$i]:((((X1 @ X1142))&![X1143:$i]:((((X1 @ X1143))=>((X1142)=(X1143))))))))))), inference(apply_def,[status(thm)],[c_0_338, c_0_331])).
% 1.81/0.80 thf(c_0_362, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X1144:$i]:((((X1 @ X1144))&![X1145:$i]:((((X1 @ X1145))=>((X1144)=(X1145)))))))))))), inference(apply_def,[status(thm)],[c_0_339, c_0_331])).
% 1.81/0.80 thf(c_0_363, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X1146:$i]:((((X1 @ X1146))&![X1147:$i]:((((X1 @ X1147))=>((X1146)=(X1147))))))))))), inference(apply_def,[status(thm)],[c_0_340, c_0_331])).
% 1.81/0.80 thf(c_0_364, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X1148:$i]:((((X1 @ X1148))&![X1149:$i]:((((X1 @ X1149))=>((X1148)=(X1149)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_341, c_0_331])).
% 1.81/0.80 thf(c_0_365, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1150:$i]:((((X1 @ X1150))&![X1151:$i]:((((X1 @ X1151))=>((X1150)=(X1151)))))))<=>(?[X1152:$i]:((((X17 @ X1152))&![X1153:$i]:((((X17 @ X1153))=>((X1152)=(X1153)))))))))))), inference(apply_def,[status(thm)],[c_0_342, c_0_331])).
% 1.81/0.80 thf(c_0_366, plain, ((exuEu)=(![X1:$i > $o]:(((?[X1154:$i]:((((X1 @ X1154))&![X1155:$i]:((((X1 @ X1155))=>((X1154)=(X1155)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_343, c_0_331])).
% 1.81/0.80 thf(c_0_367, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X1156:$i]:((((X1 @ X1156))&![X1157:$i]:((((X1 @ X1157))=>((X1156)=(X1157)))))))=>((?[X1158:$i]:((((X17 @ X1158))&![X1159:$i]:((((X17 @ X1159))=>((X1158)=(X1159)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_344, c_0_331])).
% 1.81/0.80 thf(c_0_368, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.81/0.80 thf(c_0_369, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.81/0.80 thf(c_0_370, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.81/0.80 thf(c_0_371, 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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.81/0.80 thf(c_0_372, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 1.81/0.80 thf(c_0_373, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 1.81/0.80 thf(c_0_374, plain, ((ex1I2)<=>![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)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 1.81/0.80 thf(c_0_375, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.81/0.80 thf(c_0_376, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.81/0.80 thf(c_0_377, plain, ((dpsetconstrI)<=>![X4:$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:$i]:((X22 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 1.81/0.80 thf(c_0_378, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X23:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 1.81/0.80 thf(c_0_379, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 1.81/0.80 thf(c_0_380, plain, ((dpsetconstrERa)<=>![X4:$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:$i]:((X25 @ Z0 @ Z1)))))=>(X25 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 1.81/0.80 thf(c_0_381, plain, ((dpsetconstrEL1)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL1])).
% 1.81/0.80 thf(c_0_382, plain, ((dpsetconstrEL2)<=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X27 @ Z0 @ Z1)))))=>(in @ X3 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrEL2])).
% 1.81/0.80 thf(c_0_383, plain, ((dpsetconstrER)<=>![X4:$i, X5:$i, X28:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X28 @ Z0 @ Z1)))))=>(X28 @ X2 @ X3)))), inference(fof_simplification,[status(thm)],[dpsetconstrER])).
% 1.81/0.80 thf(c_0_384, plain, ((funcImageSingleton)<=>![X4:$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])).
% 1.81/0.80 thf(c_0_385, plain, ((apProp)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>![X2:$i]:(((in @ X2 @ X4)=>(in @ (setunion @ (dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((in @ (kpair @ X2 @ Z0) @ X29))))) @ X5)))))), inference(fof_simplification,[status(thm)],[apProp])).
% 1.81/0.80 thf(c_0_386, plain, ((lamProp)<=>![X4:$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])).
% 1.81/0.80 thf(c_0_387, plain, ((lamp)<=>![X4:$i, X5:$i, X31:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X31 @ X2) @ X5)))=>(func @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X31 @ Z0))))))), inference(fof_simplification,[status(thm)],[lamp])).
% 1.81/0.80 thf(c_0_388, plain, ((lam2p)<=>![X4:$i, X5:$i, X32:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X32 @ X2) @ X5)))=>(in @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X32 @ Z0))) @ (funcSet @ X4 @ X5))))), inference(fof_simplification,[status(thm)],[lam2p])).
% 1.81/0.80 thf(c_0_389, plain, ((ex1E2)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))))), inference(fof_simplification,[status(thm)],[ex1E2])).
% 1.81/0.80 thf(c_0_390, plain, ((beta1)<=>![X4:$i, X5:$i, X36:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X36 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X36 @ Z0))) @ X2)=(X36 @ X2))))))), inference(fof_simplification,[status(thm)],[beta1])).
% 1.81/0.80 thf(c_0_391, plain, ((eta1)<=>![X4:$i, X5:$i, X29:$i]:(((func @ X4 @ X5 @ X29)=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta1])).
% 1.81/0.80 thf(c_0_392, plain, ((lam2lamEq)<=>![X4:$i, X5:$i, X37:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X37 @ X2) @ X5)))=>((lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0)))=(lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X37 @ Z0))))))), inference(fof_simplification,[status(thm)],[lam2lamEq])).
% 1.81/0.80 thf(c_0_393, plain, ((beta2)<=>![X4:$i, X5:$i, X38:$i > $i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ (X38 @ X2) @ X5)))=>![X2:$i]:(((in @ X2 @ X4)=>((ap @ X4 @ X5 @ (lam @ X4 @ X5 @ (^[Z0/* 17 */:$i]:(X38 @ Z0))) @ X2)=(X38 @ X2))))))), inference(fof_simplification,[status(thm)],[beta2])).
% 1.81/0.80 thf(c_0_394, plain, ((eta2)<=>![X4:$i, X5:$i, X29:$i]:(((in @ X29 @ (funcSet @ X4 @ X5))=>((lam @ X4 @ X5 @ (^[Z0/* 247 */:$i]:(ap @ X4 @ X5 @ X29 @ Z0)))=(X29))))), inference(fof_simplification,[status(thm)],[eta2])).
% 1.81/0.80 thf(c_0_395, plain, ((iffalseProp1)<=>![X4:$i, X39:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X39))=>(in @ X3 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X39)&((Z0)=(X2)))|(~((X39))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iffalseProp1])).
% 1.81/0.80 thf(c_0_396, plain, ((iffalseProp2)<=>![X4:$i, X40:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(~((X40))=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X40)&((Z0)=(X2)))|(~((X40))&((Z0)=(X3)))))))=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iffalseProp2])).
% 1.81/0.80 thf(c_0_397, plain, ((iftrueProp1)<=>![X4:$i, X41:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X41)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X41)&((Z0)=(X2)))|(~((X41))&((Z0)=(X3)))))))))))))), inference(fof_simplification,[status(thm)],[iftrueProp1])).
% 1.81/0.80 thf(c_0_398, plain, ((iftrueProp2)<=>![X4:$i, X42:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X42)=>((dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X42)&((Z0)=(X2)))|(~((X42))&((Z0)=(X3)))))))=(setadjoin @ X2 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[iftrueProp2])).
% 1.81/0.80 thf(c_0_399, plain, ((ifSingleton)<=>![X4:$i, X43:$o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 9 */:$i]:((((X43)&((Z0)=(X2)))|(~((X43))&((Z0)=(X3))))))))))))), inference(fof_simplification,[status(thm)],[ifSingleton])).
% 1.81/0.80 thf(c_0_400, plain, ((choice2fnsingleton)<=>![X4:$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:$i]:(((in @ X14 @ X5)=>((X52 @ X2 @ X14)=>(in @ (kpair @ Z0 @ X14) @ X33))))))))))))))))), inference(fof_simplification,[status(thm)],[choice2fnsingleton])).
% 1.81/0.80 thf(c_0_401, plain, ((setOfPairsIsBReln1)<=>![X4:$i, X53:$i > $i > $o]:((breln1 @ X4 @ (dpsetconstr @ X4 @ X4 @ (^[Z0/* 19 */:$i, Z1:$i]:((X53 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln1])).
% 1.81/0.80 thf(c_0_402, plain, ((image1Ex1)=(![X4:$i, X58:$i > $i]:((?[X1160:$i]:(((![X2:$i]:(((in @ X2 @ X1160)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))&![X1161:$i]:(((![X2:$i]:(((in @ X2 @ X1161)<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X58 @ X3)))))))=>((X1160)=(X1161)))))))))), inference(apply_def,[status(thm)],[c_0_345, c_0_331])).
% 1.81/0.80 thf(c_0_403, plain, ((image1Equiv)<=>![X4:$i, X59:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X59 @ Z0))))<=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X59 @ X3))))))), inference(fof_simplification,[status(thm)],[image1Equiv])).
% 1.81/0.80 thf(c_0_404, plain, ((image1E)<=>![X4:$i, X60:$i > $i, X2:$i]:(((in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X60 @ Z0))))=>?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X60 @ X3))))))), inference(fof_simplification,[status(thm)],[image1E])).
% 1.81/0.80 thf(c_0_405, plain, ((image1I)<=>![X4:$i, X61:$i > $i, X2:$i]:((?[X3:$i]:(((in @ X3 @ X4)&((X2)=(X61 @ X3))))=>(in @ X2 @ (image1 @ X4 @ (^[Z0/* 17 */:$i]:(X61 @ Z0))))))), inference(fof_simplification,[status(thm)],[image1I])).
% 1.81/0.80 thf(c_0_406, axiom, ((foundation2)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X21:$i]:(((in @ X21 @ X4)&((binintersect @ X21 @ X4)=(emptyset)))))))), inference(apply_def,[status(thm)],[foundation2, c_0_335])).
% 1.81/0.80 thf(c_0_407, plain, ((epred1_0)<=>![X1191:$i]:(?[X1192:$i]:((((![X1193:$i]:(((in @ X1193 @ X1192)=>![X1194:$i]:(((in @ X1194 @ X1193)=>(in @ X1194 @ X1191)))))&![X1195:$i, X1196:$i]:((((in @ X1195 @ X1191)&(in @ X1196 @ X1191))=>(![X1197:$i]:(((in @ X1197 @ X1192)=>((in @ X1195 @ X1197)<=>(in @ X1196 @ X1197))))=>((X1195)=(X1196))))))&![X1198:$i, X1199:$i]:((((in @ X1198 @ X1192)&(in @ X1199 @ X1192))=>(![X1200:$i]:(((in @ X1200 @ X1198)=>(in @ X1200 @ X1199)))|![X1201:$i]:(((in @ X1201 @ X1199)=>(in @ X1201 @ X1198)))))))&![X1202:$i]:(((![X1203:$i]:(((in @ X1203 @ X1202)=>(in @ X1203 @ X1191)))&?[X1204:$i]:((in @ X1204 @ X1202)))=>?[X1205:$i, X1206:$i]:(((((in @ X1205 @ X1192)&(in @ X1206 @ X1202))&~(?[X1207:$i]:(((in @ X1207 @ X1205)&(in @ X1207 @ X1202)))))&![X1208:$i]:(((in @ X1208 @ X1192)=>(![X1209:$i]:(((in @ X1209 @ X1208)=>(in @ X1209 @ X1205)))|(in @ X1206 @ X1208)))))))))))), introduced(definition)).
% 1.81/0.80 thf(c_0_408, negated_conjecture, ~((![X1162:$i, X1163:$i]:((![X1164:$i]:(((in @ X1164 @ X1162)<=>(in @ X1164 @ X1163)))=>((X1162)=(X1163))))=>(![X1165:$i]:(~(in @ X1165 @ emptyset))=>(![X1166:$i, X1167:$i, X1168:$i]:(((in @ X1168 @ (setadjoin @ X1166 @ X1167))<=>(((X1168)=(X1166))|(in @ X1168 @ X1167))))=>(![X1169:$i, X1170:$i]:(((in @ X1170 @ (powerset @ X1169))<=>![X1171:$i]:(((in @ X1171 @ X1170)=>(in @ X1171 @ X1169)))))=>(![X1172:$i, X1173:$i]:(((in @ X1173 @ (setunion @ X1172))<=>?[X1174:$i]:(((in @ X1173 @ X1174)&(in @ X1174 @ X1172)))))=>((in @ emptyset @ omega)=>(![X1175:$i]:(((in @ X1175 @ omega)=>(in @ (setadjoin @ X1175 @ X1175) @ omega)))=>(![X1176:$i]:((((in @ emptyset @ X1176)&![X1177:$i]:((((in @ X1177 @ omega)&(in @ X1177 @ X1176))=>(in @ (setadjoin @ X1177 @ X1177) @ X1176))))=>![X1178:$i]:(((in @ X1178 @ omega)=>(in @ X1178 @ X1176)))))=>(![X1179:$i > $i > $o, X1180:$i]:((![X1181:$i]:(((in @ X1181 @ X1180)=>?[X1182:$i]:(((X1179 @ X1181 @ X1182)&![X1183:$i]:(((X1179 @ X1181 @ X1183)=>((X1182)=(X1183))))))))=>?[X1184:$i]:(![X1185:$i]:(((in @ X1185 @ X1184)<=>?[X1186:$i]:(((in @ X1186 @ X1180)&(X1179 @ X1186 @ X1185))))))))=>(![X1187:$i]:((?[X1188:$i]:((in @ X1188 @ X1187))=>?[X1189:$i]:(((in @ X1189 @ X1187)&~(?[X1190:$i]:(((in @ X1190 @ X1189)&(in @ X1190 @ X1187))))))))=>((epred1_0)=>(![X1210:$i > $o]:((?[X1211:$i]:(((X1210 @ X1211)&![X1212:$i]:(((X1210 @ X1212)=>((X1211)=(X1212))))))=>(X1210 @ (descr @ (^[Z0/* 17 */:$i]:(X1210 @ Z0))))))=>(![X1213:$i, X1214:$i > $o, X1215:$i]:(((in @ X1215 @ X1213)=>((X1214 @ X1215)=>(in @ X1215 @ (dsetconstr @ X1213 @ X1214)))))=>(![X1216:$i, X1217:$i > $o, X1218:$i]:(((in @ X1218 @ (dsetconstr @ X1216 @ X1217))=>(in @ X1218 @ X1216)))=>(![X1219:$i, X1220:$i > $o, X1221:$i]:(((in @ X1221 @ (dsetconstr @ X1219 @ X1220))=>(X1220 @ X1221)))=>(![X1222:$i > $o]:((?[X1223:$i]:(((X1222 @ X1223)&![X1224:$i]:(((X1222 @ X1224)=>((X1223)=(X1224))))))=>?[X1225:$i]:(((X1222 @ X1225)&![X1226:$i]:(((X1222 @ X1226)=>((X1225)=(X1226))))))))=>(![X1227:$o, X1228:$i]:(((in @ X1228 @ (prop2set @ ((X1227))))=>(X1227)))=>(![X1229:$i]:(((in @ X1229 @ emptyset)=>![X1230:$o]:((X1230))))=>(![X1231:$i]:(((in @ X1231 @ emptyset)=>~($true)))=>(![X1232:$i]:(~(in @ X1232 @ emptyset))=>(![X1233:$i > $o]:((?[X1234:$i]:(((X1233 @ X1234)&![X1235:$i]:(((X1233 @ X1235)=>((X1234)=(X1235))))))=>?[X1236:$i]:((X1233 @ X1236))))=>(![X1237:$i, X1238:$i]:((![X1239:$i]:(((in @ X1239 @ X1237)=>(in @ X1239 @ X1238)))=>(![X1240:$i]:(((in @ X1240 @ X1238)=>(in @ X1240 @ X1237)))=>((X1237)=(X1238)))))=>(![X1241:$i]:((![X1242:$i]:(~(in @ X1242 @ X1241))=>((X1241)=(emptyset))))=>(![X1243:$i]:((![X1244:$i]:(~(in @ X1244 @ X1243))=>((X1243)=(emptyset))))=>(![X1245:$i, X1246:$i > $o, X1247:$i]:(((in @ X1247 @ X1245)=>((in @ X1247 @ (dsetconstr @ X1245 @ X1246))<=>(X1246 @ X1247))))=>(![X1248:$i]:((((X1248)!=(emptyset))=>?[X1249:$i]:((in @ X1249 @ X1248))))=>(![X1250:$i, X1251:$i > $o, X1252:$i]:(((in @ X1252 @ X1250)=>((X1251 @ X1252)=>((dsetconstr @ X1250 @ X1251)!=(emptyset)))))=>(![X1253:$i]:((?[X1254:$i]:((in @ X1254 @ X1253))=>((X1253)!=(emptyset))))=>(![X1255:$i, X1256:$i]:((in @ X1255 @ (setadjoin @ X1255 @ X1256)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X1257:$i, X1258:$i, X1259:$i]:(((in @ X1259 @ X1258)=>(in @ X1259 @ (setadjoin @ X1257 @ X1258))))=>(![X1260:$i, X1261:$i, X1262:$i]:(((in @ X1262 @ (setadjoin @ X1260 @ X1261))=>![X1263:$o]:(((((X1262)=(X1260))=>(X1263))=>(((in @ X1262 @ X1261)=>(X1263))=>(X1263))))))=>(![X1264:$i, X1265:$i, X1266:$i]:(((in @ X1266 @ (setadjoin @ X1264 @ X1265))=>(((X1266)=(X1264))|(in @ X1266 @ X1265))))=>(![X1267:$i]:(((dsetconstr @ X1267 @ (^[Z0/* 1 */:$i]:($true)))=(X1267)))=>(![X1268:$i, X1269:$i]:((![X1270:$i]:(((in @ X1270 @ X1269)=>(in @ X1270 @ X1268)))=>(in @ X1269 @ (powerset @ X1268))))=>(![X1271:$i]:((in @ emptyset @ (powerset @ X1271)))=>(![X1272:$i]:((in @ emptyset @ (powerset @ X1272)))=>(![X1273:$i, X1274:$i, X1275:$i]:(((in @ X1274 @ (powerset @ X1273))=>((in @ X1275 @ X1274)=>(in @ X1275 @ X1273))))=>(![X1276:$i, X1277:$i, X1278:$i]:(((in @ X1277 @ X1278)=>((in @ X1278 @ X1276)=>(in @ X1277 @ (setunion @ X1276)))))=>(![X1279:$i, X1280:$i]:(((in @ X1280 @ (setunion @ X1279))=>![X1281:$o]:((![X1282:$i]:(((in @ X1280 @ X1282)=>((in @ X1282 @ X1279)=>(X1281))))=>(X1281)))))=>(![X1283:$i, X1284:$i]:(((in @ X1284 @ X1283)=>(in @ X1284 @ (powerset @ (setunion @ X1283)))))=>(![X1285:$i > $o]:((?[X1286:$i]:(((X1285 @ X1286)&![X1287:$i]:(((X1285 @ X1287)=>((X1286)=(X1287))))))=>?[X1288:$i]:(![X1289:$i]:(((X1285 @ X1289)<=>((X1289)=(X1288)))))))=>(![X1290:$i]:((((X1290)!=(emptyset))=>?[X1291:$i]:(((in @ X1291 @ X1290)&$true))))=>(![X1292:$i, X1293:$i]:(((in @ X1292 @ (setadjoin @ X1293 @ emptyset))=>((X1292)=(X1293))))=>(![X1294:$i, X1295:$i]:((((X1294)!=(X1295))=>~(in @ X1295 @ (setadjoin @ X1294 @ emptyset))))=>(![X1296:$i, X1297:$i]:((((X1296)=(X1297))=>(in @ X1296 @ (setadjoin @ X1297 @ emptyset))))=>(![X1298:$i, X1299:$i]:(((in @ X1298 @ (setadjoin @ X1299 @ emptyset))=>(in @ X1299 @ (setadjoin @ X1298 @ emptyset))))=>(![X1300:$i, X1301:$i, X1302:$i]:(((in @ X1302 @ (setadjoin @ X1300 @ (setadjoin @ X1301 @ emptyset)))=>(((X1302)=(X1300))|((X1302)=(X1301)))))=>(![X1303:$i, X1304:$i]:((in @ X1303 @ (setadjoin @ X1303 @ (setadjoin @ X1304 @ emptyset))))=>(![X1305:$i, X1306:$i]:((in @ X1306 @ (setadjoin @ X1305 @ (setadjoin @ X1306 @ emptyset))))=>(![X1307:$i, X1308:$i > $o]:((?[X1309:$i]:(((in @ X1309 @ X1307)&(X1308 @ X1309)))=>(((dsetconstr @ X1307 @ X1308)=(emptyset))=>~($true))))=>(![X1310:$i > $o, X1311:$i]:(((in @ X1311 @ emptyset)=>(X1310 @ X1311)))=>(![X1312:$i, X1313:$i > $o]:((~(![X1314:$i]:(((in @ X1314 @ X1312)=>(X1313 @ X1314))))=>?[X1315:$i]:(((in @ X1315 @ X1312)&~((X1313 @ X1315))))))=>(![X1316:$i, X1317:$i > $o]:((![X1318:$i]:(((in @ X1318 @ X1316)=>~((X1317 @ X1318))))=>~(?[X1319:$i]:(((in @ X1319 @ X1316)&(X1317 @ X1319))))))=>(![X1320:$i, X1321:$i > $o]:((~(?[X1322:$i]:(((in @ X1322 @ X1320)&(X1321 @ X1322))))=>![X1323:$i]:(((in @ X1323 @ X1320)=>~((X1321 @ X1323))))))=>(![X1324:$i, X1325:$i > $o]:((?[X1326:$i]:(((in @ X1326 @ X1324)&~((X1325 @ X1326))))=>~(![X1327:$i]:(((in @ X1327 @ X1324)=>(X1325 @ X1327))))))=>(![X1328:$o]:(((X1328)=>(in @ emptyset @ (prop2set @ ((X1328))))))=>(![X1329:$o]:(((X1329)=>(set2prop @ (prop2set @ ((X1329))))))=>(![X1330:$i, X1331:$i > $o]:((~(?[X1332:$i]:(((in @ X1332 @ X1330)&(X1331 @ X1332))))=>![X1333:$i]:(((in @ X1333 @ X1330)=>~((X1331 @ X1333))))))=>(![X1334:$i, X1335:$i > $o]:((~(![X1336:$i]:(((in @ X1336 @ X1334)=>(X1335 @ X1336))))=>?[X1337:$i]:(((in @ X1337 @ X1334)&~((X1335 @ X1337))))))=>(![X1338:$i > $o]:((?[X1339:$i]:(((X1338 @ X1339)&![X1340:$i]:(((X1338 @ X1340)=>((X1339)=(X1340))))))=>?[X1341:$i]:(((X1338 @ X1341)&![X1342:$i]:(((X1338 @ X1342)=>((X1341)=(X1342))))))))=>(![X1343:$i > $o]:((?[X1344:$i]:((X1343 @ X1344))=>(![X1345:$i, X1346:$i]:(((X1343 @ X1345)=>((X1343 @ X1346)=>((X1345)=(X1346)))))=>?[X1347:$i]:(((X1343 @ X1347)&![X1348:$i]:(((X1343 @ X1348)=>((X1347)=(X1348)))))))))=>(![X1349:$i > $o]:((?[X1350:$i]:(![X1351:$i]:(((X1349 @ X1351)<=>((X1351)=(X1350)))))=>?[X1352:$i]:(((X1349 @ X1352)&![X1353:$i]:(((X1349 @ X1353)=>((X1352)=(X1353))))))))=>(![X1354:$i, X1355:$i]:((((X1354)=(X1355))=>![X1356:$i, X1357:$i]:((((X1356)=(X1357))=>((in @ X1356 @ X1354)=>(in @ X1357 @ X1355))))))=>(![X1358:$i, X1359:$i]:((((X1358)=(X1359))=>![X1360:$i, X1361:$i]:((((X1360)=(X1361))=>((in @ X1360 @ X1358)<=>(in @ X1361 @ X1359))))))=>(![X1362:$i > $o]:((?[X1363:$i]:(((X1362 @ X1363)&![X1364:$i]:(((X1362 @ X1364)=>((X1363)=(X1364))))))=>![X1365:$i, X1366:$i]:(((X1362 @ X1365)=>((X1362 @ X1366)=>((X1365)=(X1366)))))))=>(![X1367:$i > $o, X1368:$i > $o]:((![X1369:$i, X1370:$i]:((((X1369)=(X1370))=>((X1367 @ X1369)<=>(X1368 @ X1370))))=>(?[X1371:$i]:(((X1367 @ X1371)&![X1372:$i]:(((X1367 @ X1372)=>((X1371)=(X1372))))))<=>?[X1373:$i]:(((X1368 @ X1373)&![X1374:$i]:(((X1368 @ X1374)=>((X1373)=(X1374)))))))))=>(((emptyset)=(emptyset))=>(![X1375:$i, X1376:$i]:((((X1375)=(X1376))=>![X1377:$i, X1378:$i]:((((X1377)=(X1378))=>((setadjoin @ X1375 @ X1377)=(setadjoin @ X1376 @ X1378))))))=>(![X1379:$i, X1380:$i]:((((X1379)=(X1380))=>((powerset @ X1379)=(powerset @ X1380))))=>(![X1381:$i, X1382:$i]:((((X1381)=(X1382))=>((setunion @ X1381)=(setunion @ X1382))))=>(((omega)=(omega))=>(![X1383:$i > $o]:((?[X1384:$i]:(((X1383 @ X1384)&![X1385:$i]:(((X1383 @ X1385)=>((X1384)=(X1385))))))=>![X1386:$i, X1387:$i]:(((X1383 @ X1386)=>((X1383 @ X1387)=>((X1386)=(X1387)))))))=>(![X1388:$i > $o, X1389:$i > $o]:((![X1390:$i, X1391:$i]:((((X1390)=(X1391))=>((X1388 @ X1390)<=>(X1389 @ X1391))))=>(?[X1392:$i]:(((X1388 @ X1392)&![X1393:$i]:(((X1388 @ X1393)=>((X1392)=(X1393))))))=>(?[X1394:$i]:(((X1389 @ X1394)&![X1395:$i]:(((X1389 @ X1395)=>((X1394)=(X1395))))))=>((descr @ X1388)=(descr @ X1389))))))=>(![X1396:$i, X1397:$i]:((((X1396)=(X1397))=>![X1398:$i > $o, X1399:$i > $o]:((![X1400:$i]:(((in @ X1400 @ X1396)=>![X1401:$i]:(((in @ X1401 @ X1397)=>(((X1400)=(X1401))=>((X1398 @ X1400)<=>(X1399 @ X1401)))))))=>((dsetconstr @ X1396 @ X1398)=(dsetconstr @ X1397 @ X1399))))))=>(![X1402:$i, X1403:$i]:((![X1404:$i]:(((in @ X1404 @ X1402)=>(in @ X1404 @ X1403)))=>(subset @ X1402 @ X1403)))=>(![X1405:$i, X1406:$i]:((((X1405)=(X1406))=>(subset @ X1406 @ X1405)))=>(![X1407:$i, X1408:$i]:((((X1407)=(X1408))=>(subset @ X1407 @ X1408)))=>(![X1409:$i, X1410:$i]:((![X1411:$i]:(((in @ X1411 @ X1409)=>(in @ X1411 @ X1410)))=>(subset @ X1409 @ X1410)))=>(![X1412:$i]:((subset @ emptyset @ X1412))=>(![X1413:$i, X1414:$i, X1415:$i]:(((subset @ X1413 @ X1414)=>((in @ X1415 @ X1413)=>(in @ X1415 @ X1414))))=>(![X1416:$i, X1417:$i, X1418:$i]:(((subset @ X1416 @ X1417)=>(~(in @ X1418 @ X1417)=>~(in @ X1418 @ X1416))))=>(![X1419:$i, X1420:$i, X1421:$i]:(((in @ X1421 @ X1419)=>(~(in @ X1421 @ X1420)=>~(subset @ X1419 @ X1420))))=>(![X1422:$i, X1423:$i]:((~(subset @ X1422 @ X1423)=>((X1422)!=(X1423))))=>(![X1424:$i, X1425:$i, X1426:$i]:(((in @ X1426 @ X1424)=>(~(in @ X1426 @ X1425)=>((X1424)!=(X1425)))))=>(![X1427:$i]:((subset @ X1427 @ X1427))=>(![X1428:$i, X1429:$i, X1430:$i]:(((subset @ X1428 @ X1429)=>((subset @ X1429 @ X1430)=>(subset @ X1428 @ X1430))))=>(![X1431:$i, X1432:$i]:((subset @ X1432 @ (setadjoin @ X1431 @ X1432)))=>(![X1433:$i, X1434:$i, X1435:$i]:(((subset @ X1433 @ X1435)=>(subset @ X1433 @ (setadjoin @ X1434 @ X1435))))=>(![X1436:$i, X1437:$i]:(((subset @ X1436 @ X1437)=>(in @ X1436 @ (powerset @ X1437))))=>(![X1438:$i, X1439:$i]:(((subset @ X1438 @ X1439)=>((subset @ X1439 @ X1438)=>((X1438)=(X1439)))))=>(![X1440:$i]:(((subset @ X1440 @ emptyset)=>((X1440)=(emptyset))))=>(![X1441:$i, X1442:$i]:(((subset @ X1442 @ X1441)=>(in @ X1442 @ (powerset @ X1441))))=>(![X1443:$i, X1444:$i]:(((in @ X1444 @ (powerset @ X1443))=>(subset @ X1444 @ X1443)))=>(![X1445:$i]:((in @ X1445 @ (powerset @ X1445)))=>(![X1446:$i, X1447:$i]:(((subset @ X1446 @ X1447)=>(subset @ (powerset @ X1446) @ (powerset @ X1447))))=>(![X1448:$i, X1449:$i > $o]:((in @ (dsetconstr @ X1448 @ X1449) @ (powerset @ X1448)))=>(![X1450:$i, X1451:$i > $o]:((subset @ (dsetconstr @ X1450 @ X1451) @ X1450))=>(![X1452:$i, X1453:$i, X1454:$i]:(((in @ X1454 @ X1452)=>(in @ X1454 @ (binunion @ X1452 @ X1453))))=>(![X1455:$i, X1456:$i]:((in @ X1456 @ (setadjoin @ X1455 @ (setadjoin @ X1456 @ emptyset))))=>(![X1457:$i, X1458:$i, X1459:$i]:(((in @ X1459 @ X1458)=>(in @ X1459 @ (binunion @ X1457 @ X1458))))=>(![X1460:$i, X1461:$i, X1462:$i, X1463:$o]:(((in @ X1462 @ (binunion @ X1460 @ X1461))=>(((in @ X1462 @ X1460)=>(X1463))=>(((in @ X1462 @ X1461)=>(X1463))=>(X1463)))))=>(![X1464:$i, X1465:$i, X1466:$i]:(((in @ X1466 @ (binunion @ X1464 @ X1465))=>((in @ X1466 @ X1464)|(in @ X1466 @ X1465))))=>(![X1467:$i, X1468:$i]:((subset @ X1467 @ (binunion @ X1467 @ X1468)))=>(![X1469:$i, X1470:$i]:((subset @ X1470 @ (binunion @ X1469 @ X1470)))=>(![X1471:$i, X1472:$i, X1473:$i]:(((in @ X1473 @ X1471)=>((in @ X1473 @ X1472)=>(in @ X1473 @ (binintersect @ X1471 @ X1472)))))=>(![X1474:$i, X1475:$i, X1476:$i]:(((subset @ X1476 @ X1474)=>((subset @ X1476 @ X1475)=>(subset @ X1476 @ (binintersect @ X1474 @ X1475)))))=>(![X1477:$i, X1478:$i, X1479:$i]:(((in @ X1479 @ (binintersect @ X1477 @ X1478))=>(in @ X1479 @ X1477)))=>(![X1480:$i, X1481:$i]:((subset @ (binintersect @ X1480 @ X1481) @ X1480))=>(![X1482:$i, X1483:$i]:(((subset @ X1482 @ X1483)=>((binintersect @ X1482 @ X1483)=(X1482))))=>(![X1484:$i, X1485:$i]:((((binintersect @ X1484 @ X1485)=(X1485))=>(subset @ X1485 @ X1484)))=>(![X1486:$i, X1487:$i, X1488:$i]:(((in @ X1488 @ (binintersect @ X1486 @ X1487))=>(in @ X1488 @ X1487)))=>(![X1489:$i, X1490:$i]:((~(?[X1491:$i]:(((in @ X1491 @ X1489)&(in @ X1491 @ X1490))))=>((binintersect @ X1489 @ X1490)=(emptyset))))=>(![X1492:$i, X1493:$i]:((subset @ 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@ (setminus @ X1515 @ X1516))=>(~(in @ X1517 @ X1516)=>~(in @ X1517 @ X1515))))=>(![X1518:$i, X1519:$i, X1520:$i]:((~(in @ X1520 @ X1518)=>~(in @ X1520 @ (setminus @ X1518 @ X1519))))=>(![X1521:$i, X1522:$i, X1523:$i]:(((in @ X1523 @ X1522)=>~(in @ X1523 @ (setminus @ X1521 @ X1522))))=>(![X1524:$i, X1525:$i]:((subset @ (setminus @ X1524 @ X1525) @ X1524))=>(![X1526:$i, X1527:$i]:((((setminus @ X1526 @ X1527)=(emptyset))=>(subset @ X1526 @ X1527)))=>(![X1528:$i, X1529:$i, X1530:$i]:(((in @ X1530 @ (symdiff @ X1528 @ X1529))=>![X1531:$o]:((((in @ X1530 @ X1528)=>(~(in @ X1530 @ X1529)=>(X1531)))=>((~(in @ X1530 @ X1528)=>((in @ X1530 @ X1529)=>(X1531)))=>(X1531))))))=>(![X1532:$i, X1533:$i, X1534:$i]:(((in @ X1534 @ X1532)=>(~(in @ X1534 @ X1533)=>(in @ X1534 @ (symdiff @ X1532 @ X1533)))))=>(![X1535:$i, X1536:$i, X1537:$i]:((~(in @ X1537 @ X1535)=>((in @ X1537 @ X1536)=>(in @ X1537 @ (symdiff @ X1535 @ X1536)))))=>(![X1538:$i, X1539:$i, X1540:$i]:(((in @ X1540 @ X1538)=>((in @ X1540 @ 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$o]:((![X2100:$i]:(((in @ X2100 @ X2097)=>![X2101:$i]:(((in @ X2101 @ X2097)=>((in @ (kpair @ X2100 @ X2101) @ X2098)=>(X2099 @ (kpair @ X2100 @ X2101)))))))=>![X2102:$i]:(((in @ X2102 @ X2098)=>(X2099 @ X2102)))))))=>(![X2103:$i, X2104:$i]:(((in @ X2104 @ (breln1Set @ X2103))=>(breln1 @ X2103 @ X2104)))=>(![X2105:$i, X2106:$i, X2107:$i > $i > $o]:((![X2108:$i]:(((in @ X2108 @ X2105)=>?[X2109:$i]:(((in @ X2109 @ X2106)&(X2107 @ X2108 @ X2109)))))=>![X2110:$i]:(((in @ X2110 @ (breln1Set @ X2106))=>((reflwellordering @ X2106 @ X2110)=>![X2111:$i]:(((in @ X2111 @ X2105)=>(singleton @ (dsetconstr @ X2106 @ (^[Z0/* 8 */:$i]:((X2107 @ X2111 @ Z0&![X2112:$i]:(((in @ X2112 @ X2106)=>(X2107 @ X2111 @ X2112=>(in @ (kpair @ Z0 @ X2112) @ X2110))))))))))))))))=>(![X2113:$i, X2114:$i > $i > $o]:((breln1 @ X2113 @ (dpsetconstr @ X2113 @ X2113 @ X2114)))=>(![X2115:$i, X2116:$i]:(((breln1 @ X2115 @ X2116)=>![X2117:$i > $o]:((![X2118:$i]:(((in @ X2118 @ X2115)=>![X2119:$i]:(((in @ X2119 @ X2115)=>((in 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omega)))=>(![X2264:$i]:(((in @ X2264 @ omega)=>(in @ (setadjoin @ X2264 @ X2264) @ omega)))=>![X2:$i]:(((in @ X2 @ omega)=>((omegaS @ X2)!=(emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[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(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(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(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(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(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(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(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)],[peano0notS]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_346]), foundationAx]), wellorderingAx]), c_0_347]), c_0_348]), c_0_349]), c_0_350]), c_0_351]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_352]), setext]), emptyI]), noeltsimpempty]), c_0_353]), c_0_354]), c_0_355]), c_0_356]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_357]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_358]), c_0_359]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_360]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_361]), c_0_362]), c_0_363]), inCongP]), in__Cong]), c_0_364]), c_0_365]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_366]), c_0_367]), c_0_368]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_369]), c_0_370]), 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]), c_0_371]), c_0_372]), c_0_373]), c_0_374]), singletonsuniq]), setukpairinjL1]), c_0_375]), theprop]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_376]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_377]), c_0_378]), c_0_379]), c_0_380]), c_0_381]), c_0_382]), c_0_383]), c_0_384]), c_0_385]), app]), infuncsetfunc]), ap2p]), funcinfuncset]), c_0_386]), c_0_387]), c_0_388]), brelnall1]), brelnall2]), c_0_389]), funcGraphProp1]), funcGraphProp3]), funcGraphProp2]), funcextLem]), funcGraphProp4]), subbreln]), eqbreln]), funcext]), funcext2]), ap2apEq1]), ap2apEq2]), c_0_390]), c_0_391]), c_0_392]), c_0_393]), c_0_394]), c_0_395]), c_0_396]), c_0_397]), c_0_398]), c_0_399]), 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]), c_0_400]), c_0_401]), breln1all1]), subbreln1]), eqbreln1]), breln1invprop]), breln1invI]), breln1invE]), breln1compprop]), breln1compI]), breln1compE]), breln1compEex]), breln1unionprop]), breln1unionIL]), breln1unionIR]), breln1unionI]), breln1unionE]), breln1unionEcases]), breln1unionCommutes]), woz2Ex]), woz2W]), woz2A]), woz2B]), image1Ex]), c_0_402]), c_0_403]), c_0_404]), c_0_405]), injFuncInInjFuncSet]), injFuncSetFuncIn]), injFuncSetFuncInj]), surjFuncSetFuncIn]), surjFuncSetFuncSurj]), leftInvIsSurj]), surjCantorThm]), c_0_406]), notinself]), notinself2]), omegaSp]), omegaSclos])])]), c_0_407])).
% 1.81/0.80 thf(c_0_409, plain, ![X2265:$i]:(((omegaS @ X2265)=(setadjoin @ X2265 @ X2265))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[omegaS])])).
% 1.81/0.80 thf(c_0_410, negated_conjecture, ![X2267:$i, X2268:$i, X2270:$i, X2271:$i, X2272:$i, X2273:$i, X2274:$i, X2275:$i, X2276:$i, X2277:$i, X2278:$i, X2280:$i, X2281:$i, X2283:$i, X2284:$i, X2285:$i, X2286:$i, X2287:$i, X2289:$i, X2290:$i > $i > $o, X2291:$i, X2293:$i, X2296:$i, X2298:$i, X2299:$i, X2300:$i, X2301:$i, X2303:$i, X2304:$i > $o, X2305:$i, X2307:$i, X2308:$i > $o, X2309:$i, X2310:$i, X2311:$i > $o, X2312:$i, X2313:$i, X2314:$i > $o, X2315:$i, X2316:$i > $o, X2317:$i, X2320:$i, X2321:$o, X2322:$i, X2323:$i, X2324:$o, X2325:$i, X2326:$i, X2327:$i > $o, X2328:$i, X2331:$i, X2332:$i, X2335:$i, X2337:$i, X2339:$i, X2340:$i > $o, X2341:$i, X2342:$i, X2344:$i, X2345:$i > $o, X2346:$i, X2347:$i, X2348:$i, X2349:$i, X2350:$i, X2351:$i, X2352:$i, X2353:$i, X2354:$i, X2355:$i, X2356:$i, X2357:$o, X2358:$i, X2359:$i, X2360:$i, X2361:$i, X2362:$i, X2363:$i, X2365:$i, X2366:$i, X2367:$i, X2368:$i, X2369:$i, X2370:$i, X2371:$i, X2372:$i, X2373:$i, X2374:$i, X2375:$o, X2377:$i, X2378:$i, X2379:$i > $o, X2380:$i, X2383:$i, X2384:$i, X2385:$i, X2387:$i, X2388:$i, X2389:$i, X2390:$i, X2391:$i, X2392:$i, X2393:$i, X2394:$i, X2395:$i, X2396:$i, X2397:$i, X2398:$i, X2399:$i, X2400:$i, X2401:$i, X2402:$i, X2403:$i > $o, X2404:$i, X2405:$i > $o, X2406:$i, X2407:$i, X2408:$i > $o, X2409:$i, X2411:$i, X2412:$i > $o, X2414:$i, X2415:$i, X2416:$i > $o, X2418:$i, X2419:$i, X2420:$i > $o, X2421:$i, X2423:$o, X2424:$o, X2425:$i, X2426:$i > $o, X2428:$i, X2429:$i, X2430:$i > $o, X2431:$i, X2433:$i > $o, X2434:$i, X2437:$i, X2438:$i > $o, X2439:$i, X2443:$i, X2444:$i > $o, X2445:$i, X2448:$i, X2449:$i, X2450:$i, X2451:$i, X2452:$i, X2453:$i, X2454:$i, X2455:$i, X2456:$i, X2457:$i > $o, X2458:$i, X2460:$i, X2461:$i, X2462:$i > $o, X2463:$i > $o, X2466:$i, X2469:$i, X2470:$i, X2473:$i, X2474:$i, X2475:$i, X2476:$i, X2477:$i, X2478:$i, X2479:$i, X2480:$i, X2481:$i, X2482:$i > $o, X2483:$i, X2485:$i, X2486:$i, X2487:$i > $o, X2488:$i > $o, X2491:$i, X2493:$i, X2495:$i, X2496:$i, X2497:$i > $o, X2498:$i > $o, X2501:$i, X2502:$i, X2504:$i, X2505:$i, X2506:$i, X2507:$i, X2508:$i, X2509:$i, X2511:$i, X2512:$i, X2513:$i, X2514:$i, X2515:$i, X2516:$i, X2517:$i, X2518:$i, X2519:$i, X2520:$i, X2521:$i, X2522:$i, X2523:$i, X2524:$i, X2525:$i, X2526:$i, X2527:$i, X2528:$i, X2529:$i, X2530:$i, X2531:$i, X2532:$i, X2533:$i, X2534:$i, X2535:$i, X2536:$i, X2537:$i, X2538:$i, X2539:$i, X2540:$i, X2541:$i, X2542:$i, X2543:$i, X2544:$i, X2545:$i, X2546:$i, X2547:$i, X2548:$i > $o, X2549:$i, X2550:$i > $o, X2551:$i, X2552:$i, X2553:$i, X2554:$i, X2555:$i, X2556:$i, X2557:$i, X2558:$i, X2559:$i, X2560:$i, X2561:$i, X2562:$o, X2563:$i, X2564:$i, X2565:$i, X2566:$i, X2567:$i, X2568:$i, X2569:$i, X2570:$i, X2571:$i, X2572:$i, X2573:$i, X2574:$i, X2575:$i, X2576:$i, X2577:$i, X2578:$i, X2579:$i, X2580:$i, X2581:$i, X2582:$i, X2583:$i, X2584:$i, X2585:$i, X2586:$i, X2587:$i, X2588:$i, X2589:$i, X2591:$i, X2592:$i, X2593:$i, X2594:$i, X2595:$i, X2596:$i, X2597:$i, X2598:$i, X2599:$i, X2600:$i, X2601:$i, X2602:$i, X2603:$i, X2604:$i, X2605:$i, X2606:$i, X2607:$i, X2608:$i, X2609:$i, X2610:$i, X2611:$i, X2612:$i, X2613:$i, X2614:$i, X2615:$i, X2616:$i, X2617:$i, X2618:$i, X2619:$i, X2620:$i, X2621:$i, X2622:$i, X2623:$i, X2624:$i, X2625:$i, X2626:$i, X2627:$i, X2628:$i, X2629:$i, X2630:$o, X2631:$i, X2632:$i, X2633:$i, X2634:$i, X2635:$i, X2636:$i, X2637:$i, X2638:$i, X2639:$i, X2640:$i, X2641:$i, X2642:$i, X2643:$i, X2644:$i, X2645:$i, X2646:$i, X2647:$i, X2648:$i, X2649:$i, X2650:$i, X2651:$i, X2652:$i, X2653:$i, X2654:$i, X2655:$i, X2656:$i, X2657:$i, X2658:$i, X2659:$i, X2660:$i, X2661:$i, X2662:$i, X2663:$i, X2664:$i, X2665:$i, X2666:$i, X2667:$i, X2668:$i, X2669:$i, X2670:$i, X2671:$i, X2672:$i, X2673:$i, X2674:$i, X2675:$i, X2676:$i, X2677:$i, X2678:$i, X2679:$i, X2680:$i, X2681:$i, X2682:$i, X2683:$i, X2684:$i, X2685:$i, X2686:$i, X2687:$i, X2688:$i, X2689:$i, X2692:$i, X2693:$i, X2694:$i, X2695:$i, X2696:$i, X2698:$i, X2699:$i, X2700:$i, X2701:$i, X2702:$i > $o, X2705:$i, X2706:$i, X2707:$i > $o, X2709:$i, X2710:$i > $o, X2711:$i, X2713:$i, X2714:$i > $o, X2717:$i, X2718:$i, X2719:$i, X2720:$i, X2721:$i, X2722:$i, X2723:$i, X2724:$i, X2725:$i, X2726:$i, X2727:$i, X2728:$i, X2729:$i, X2730:$i, X2731:$i, X2732:$i, X2733:$i, X2734:$i, X2735:$i, X2736:$i, X2737:$i, X2738:$i, X2739:$i, X2740:$i, X2741:$i, X2742:$i, X2743:$i, X2744:$i, X2745:$i, X2746:$i, X2747:$i, X2748:$i, X2749:$i, X2750:$i, X2751:$i, X2752:$i, X2753:$i, X2754:$i, X2755:$i, X2756:$i, X2757:$i, X2758:$i, X2759:$i, X2760:$i, X2761:$i, X2762:$i, X2763:$i, X2764:$i, X2765:$i, X2766:$i, X2767:$i, X2768:$i, X2769:$i, X2770:$i, X2771:$i, X2772:$i, X2773:$i, X2774:$i, X2775:$i, X2776:$i, X2777:$i, X2778:$i, X2779:$i, X2780:$i, X2781:$i, X2782:$i, X2783:$i, X2784:$i, X2785:$i, X2786:$i, X2787:$i, X2788:$i, X2789:$i > $i > $o, X2790:$i, X2791:$i, X2792:$i, X2793:$i, X2794:$i > $i > $o, X2795:$i, X2796:$i, X2797:$i > $i > $o, X2798:$i, X2799:$i, X2800:$i > $i > $o, X2801:$i, X2802:$i, X2803:$i, X2804:$i, X2805:$i > $i > $o, X2806:$i, X2807:$i, X2808:$i, X2809:$i, X2810:$i > $i > $o, X2811:$i, X2812:$i, X2813:$i, X2814:$i, X2815:$i > $i > $o, X2816:$i, X2817:$i, X2818:$i, X2819:$i, X2820:$i, X2821:$i, X2822:$i, X2823:$i, X2824:$i, X2825:$i, X2826:$i, X2827:$i, X2828:$i, X2829:$i, X2830:$i, X2831:$i, X2832:$i, X2833:$i, X2834:$i, X2835:$i, X2836:$i, X2837:$i, X2838:$i, X2839:$i, X2840:$i, X2841:$i, X2842:$i > $i, X2844:$i, X2845:$i, X2846:$i > $i, X2848:$i, X2849:$i, X2850:$i > $i, X2852:$i, X2853:$i, X2854:$i, X2855:$i > $o, X2858:$i, X2859:$i, X2860:$i, X2861:$i, X2862:$i > $o, X2865:$i, X2866:$i, X2867:$i > $o, X2868:$i, X2869:$i, X2870:$i, X2871:$i, X2872:$i, X2873:$i, X2874:$i, X2875:$i, X2876:$i, X2877:$i, X2878:$i, X2879:$i, X2880:$i, X2881:$i, X2882:$i, X2883:$i, X2884:$i, X2885:$i, X2886:$i, X2888:$i, X2889:$i, X2890:$i, X2891:$i, X2892:$i, X2893:$i, X2894:$i, X2895:$i, X2896:$i, X2897:$i, X2898:$i, X2901:$i, X2902:$i, X2903:$i, X2904:$i, X2909:$i, X2910:$i, X2911:$i, X2912:$i, X2914:$i, X2915:$i, X2916:$i, X2917:$i, X2919:$i, X2920:$i, X2921:$i, X2922:$i, X2923:$i, X2924:$i, X2925:$i, X2926:$i, X2927:$i, X2928:$i, X2929:$i > $i, X2931:$i, X2932:$i, X2933:$i, X2934:$i, X2935:$i, X2936:$i, X2937:$i > $i, X2939:$i, X2940:$i, X2941:$i > $i, X2943:$i, X2944:$i, X2945:$i, X2946:$i, X2947:$i, X2948:$o, X2949:$i, X2950:$i, X2951:$i, X2952:$o, X2953:$i, X2954:$i, X2955:$i, X2956:$o, X2957:$i, X2958:$i, X2959:$i, X2960:$o, X2961:$i, X2962:$i, X2963:$i, X2964:$o, X2965:$i, X2966:$i, X2967:$i, X2968:$o, X2969:$i, X2970:$i, X2971:$i, X2972:$i, X2973:$i, X2974:$o, X2975:$i, X2976:$i, X2977:$i, X2978:$o, X2979:$i, X2980:$i, X2981:$i, X2982:$o, X2983:$i, X2984:$i, X2985:$i, X2986:$i, X2987:$i, X2988:$i, X2989:$i, X2990:$i, X2991:$i, X2992:$i, X2993:$i, X2994:$i, X2995:$i, X2996:$i, X2997:$i, X2998:$i, X2999:$i, X3000:$i, X3003:$i, X3004:$i, X3005:$i, X3007:$i, X3008:$i, X3009:$i, X3011:$i, X3012:$i, X3013:$i, X3014:$i, X3015:$i, X3016:$i, X3017:$i, X3018:$i, X3019:$i, X3020:$i, X3021:$i, X3022:$i, X3023:$i, X3024:$i, X3025:$i, X3026:$i, X3027:$i, X3028:$i, X3029:$i, X3030:$i, X3031:$i, X3032:$i, X3033:$i, X3034:$i, X3035:$i, X3036:$i, X3037:$i, X3038:$i, X3039:$i, X3040:$i, X3041:$i, X3042:$i, X3043:$i, X3044:$i, X3045:$i, X3046:$i, X3047:$i, X3048:$i, X3049:$i, X3050:$i, X3051:$i, X3052:$i, X3053:$i, X3054:$i, X3055:$i, X3056:$i, X3057:$i, X3058:$i, X3059:$i, X3060:$i, X3061:$i, X3062:$i, X3063:$i, X3064:$i, X3065:$i, X3066:$i, X3067:$i, X3068:$i, X3069:$i, X3070:$i, X3071:$i, X3072:$i, X3073:$i, X3074:$i, X3075:$i, X3076:$i, X3077:$i, X3078:$i, X3079:$i, X3080:$i, X3081:$i, X3082:$i, X3083:$i, X3084:$i, X3085:$i, X3086:$i, X3087:$i, X3088:$i, X3089:$i, X3090:$i, X3091:$i, X3092:$i, X3093:$i, X3094:$i, X3095:$i, X3096:$i, X3097:$i, X3098:$i, X3099:$i, X3100:$i, X3101:$i, X3102:$i, X3103:$i, X3104:$i, X3105:$i, X3106:$i, X3107:$i, X3108:$i, X3109:$i, X3110:$i, X3111:$i, X3112:$i, X3113:$i, X3114:$o, X3115:$i, X3116:$i, X3117:$i, X3118:$i, X3119:$i, X3120:$i, X3121:$i, X3122:$i, X3123:$i, X3124:$i, X3125:$i, X3126:$i, X3127:$i, X3128:$i, X3129:$i, X3130:$i, X3131:$i, X3132:$i, X3133:$i, X3134:$i, X3135:$i, X3136:$i, X3137:$i, X3138:$i, X3139:$i, X3140:$i, X3141:$i, X3142:$i, X3143:$i, X3144:$i, X3145:$i, X3146:$i, X3147:$i, X3148:$i, X3149:$i, X3150:$i, X3151:$i, X3152:$i, X3153:$i, X3154:$i, X3155:$i, X3156:$i, X3157:$i, X3158:$i, X3159:$i, X3160:$i, X3161:$i, X3162:$i, X3163:$i, X3164:$i, X3165:$i, X3166:$i, X3167:$i, X3168:$i, X3169:$i, X3170:$i, X3171:$i, X3172:$i, X3173:$i, X3174:$i, X3175:$i, X3176:$i, X3177:$i, X3178:$i, X3179:$i, X3180:$i, X3181:$i, X3182:$i, X3183:$i, X3184:$i, X3185:$i, X3186:$i, X3187:$i, X3188:$i, X3189:$i, X3190:$i, X3191:$i, X3192:$i, X3193:$i, X3194:$i, X3195:$i, X3196:$i, X3197:$i, X3198:$i > $o, X3201:$i, X3202:$i, X3203:$i, X3204:$i, X3205:$i, X3206:$i > $i > $o, X3208:$i, X3209:$i, X3210:$i, X3211:$i, X3212:$i > $i > $o, X3213:$i, X3214:$i, X3215:$i > $o, X3218:$i, X3219:$i, X3220:$i, X3221:$i, X3224:$i, X3225:$i, X3226:$i, X3231:$i, X3232:$i, X3233:$i, X3234:$i, X3235:$i, X3236:$i, X3237:$i, X3238:$i, X3239:$i, X3240:$i, X3241:$i, X3242:$i, X3243:$i, X3244:$i, X3245:$i, X3246:$i, X3247:$i, X3248:$i, X3249:$i, X3250:$i, X3251:$i, X3252:$i, X3253:$i, X3254:$i, X3256:$i, X3257:$i, X3258:$i, X3259:$i, X3260:$i, X3261:$o, X3263:$i, X3264:$i, X3265:$i, X3266:$i, X3267:$i, X3268:$i, X3269:$i, X3270:$i, X3271:$i, X3272:$i, X3273:$i, X3274:$i, X3275:$i, X3276:$i, X3277:$i, X3278:$i, X3279:$i, X3280:$i, X3281:$i, X3282:$i, X3283:$i, X3284:$i, X3285:$i, X3286:$i, X3287:$i, X3288:$i, X3289:$i, X3290:$i, X3291:$o, X3292:$i, X3293:$i, X3294:$i, X3295:$i, X3296:$i, X3297:$i, X3298:$i, X3299:$i, X3300:$i, X3301:$i, X3302:$i, X3303:$i, X3304:$i, X3305:$i, X3306:$i, X3307:$i, X3308:$i, X3309:$i > $i, X3311:$i, X3313:$i, X3314:$i, X3315:$i, X3316:$i > $i, X3318:$i, X3320:$i, X3321:$i, X3322:$i, X3324:$i, X3326:$i, X3327:$i > $i, X3328:$i, X3330:$i, X3331:$i > $i, X3332:$i, 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@ X3225 @ X3226)) @ X3225)|((X3225)=(X3226))|(in @ (esk94_3 @ X3224 @ X3225 @ X3226) @ X3224)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225)))))&((((in @ (esk96_3 @ X3224 @ X3225 @ X3226) @ X3224)|((X3225)=(X3226))|(in @ (esk95_3 @ X3224 @ X3225 @ X3226) @ X3224)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(((in @ (esk97_3 @ X3224 @ X3225 @ X3226) @ X3224)|((X3225)=(X3226))|(in @ (esk95_3 @ X3224 @ X3225 @ X3226) @ X3224)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(((in @ (kpair @ (esk96_3 @ X3224 @ X3225 @ X3226) @ (esk97_3 @ X3224 @ X3225 @ X3226)) @ X3226)|((X3225)=(X3226))|(in @ (esk95_3 @ X3224 @ X3225 @ X3226) @ X3224)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(~(in @ (kpair @ (esk96_3 @ X3224 @ X3225 @ X3226) @ (esk97_3 @ X3224 @ X3225 @ X3226)) @ X3225)|((X3225)=(X3226))|(in @ (esk95_3 @ X3224 @ X3225 @ X3226) @ X3224)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225)))))&((((in @ (esk96_3 @ X3224 @ X3225 @ X3226) @ X3224)|((X3225)=(X3226))|(in @ (kpair @ (esk94_3 @ X3224 @ X3225 @ X3226) @ (esk95_3 @ X3224 @ X3225 @ X3226)) @ X3225)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(((in @ (esk97_3 @ X3224 @ X3225 @ X3226) @ X3224)|((X3225)=(X3226))|(in @ (kpair @ (esk94_3 @ X3224 @ X3225 @ X3226) @ (esk95_3 @ X3224 @ X3225 @ X3226)) @ X3225)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(((in @ (kpair @ (esk96_3 @ X3224 @ X3225 @ X3226) @ (esk97_3 @ X3224 @ X3225 @ X3226)) @ X3226)|((X3225)=(X3226))|(in @ (kpair @ (esk94_3 @ X3224 @ X3225 @ X3226) @ (esk95_3 @ X3224 @ X3225 @ X3226)) @ X3225)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(~(in @ (kpair @ (esk96_3 @ X3224 @ X3225 @ X3226) @ (esk97_3 @ X3224 @ X3225 @ X3226)) @ X3225)|((X3225)=(X3226))|(in @ (kpair @ (esk94_3 @ X3224 @ X3225 @ X3226) @ (esk95_3 @ X3224 @ X3225 @ X3226)) @ X3225)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225)))))&(((in @ (esk96_3 @ X3224 @ X3225 @ X3226) @ X3224)|((X3225)=(X3226))|~(in @ (kpair @ (esk94_3 @ X3224 @ X3225 @ X3226) @ (esk95_3 @ X3224 @ X3225 @ X3226)) @ X3226)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(((in @ (esk97_3 @ X3224 @ X3225 @ X3226) @ X3224)|((X3225)=(X3226))|~(in @ (kpair @ (esk94_3 @ X3224 @ X3225 @ X3226) @ (esk95_3 @ X3224 @ X3225 @ X3226)) @ X3226)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(((in @ (kpair @ (esk96_3 @ X3224 @ X3225 @ X3226) @ (esk97_3 @ X3224 @ X3225 @ X3226)) @ X3226)|((X3225)=(X3226))|~(in @ (kpair @ (esk94_3 @ X3224 @ X3225 @ X3226) @ (esk95_3 @ X3224 @ X3225 @ X3226)) @ X3226)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))&(~(in @ (kpair @ (esk96_3 @ X3224 @ X3225 @ X3226) @ (esk97_3 @ X3224 @ X3225 @ X3226)) @ X3225)|((X3225)=(X3226))|~(in @ (kpair @ (esk94_3 @ X3224 @ X3225 @ X3226) @ (esk95_3 @ X3224 @ X3225 @ X3226)) @ X3226)|~(breln1 @ X3224 @ X3226)|~(breln1 @ X3224 @ X3225))))))))&((~(breln1 @ X3231 @ X3232)|(breln1 @ X3231 @ (breln1invset @ X3231 @ X3232)))&((~(breln1 @ X3233 @ X3234)|(~(in @ X3235 @ X3233)|(~(in @ X3236 @ X3233)|(~(in @ (kpair @ X3235 @ X3236) @ X3234)|(in @ (kpair @ X3236 @ X3235) @ (breln1invset @ X3233 @ X3234))))))&((~(breln1 @ X3237 @ X3238)|(~(in @ X3239 @ X3237)|(~(in @ X3240 @ X3237)|(~(in @ (kpair @ X3240 @ X3239) @ (breln1invset @ X3237 @ X3238))|(in @ (kpair @ X3239 @ X3240) @ X3238)))))&((~(breln1 @ X3241 @ X3242)|(~(breln1 @ X3241 @ X3243)|(breln1 @ X3241 @ (breln1compset @ X3241 @ X3242 @ X3243))))&((~(breln1 @ X3244 @ X3245)|(~(breln1 @ X3244 @ X3246)|(~(in @ X3247 @ X3244)|(~(in @ X3248 @ X3244)|(~(in @ X3249 @ X3244)|(~(in @ (kpair @ X3247 @ X3249) @ X3245)|(~(in @ (kpair @ X3249 @ X3248) @ X3246)|(in @ (kpair @ X3247 @ X3248) @ (breln1compset @ X3244 @ X3245 @ X3246)))))))))&(((((in @ (esk98_5 @ X3250 @ X3251 @ X3252 @ X3253 @ X3254) @ X3250)|~(in @ (kpair @ X3253 @ X3254) @ (breln1compset @ X3250 @ X3251 @ X3252))|~(in @ X3254 @ X3250)|~(in @ X3253 @ X3250)|~(breln1 @ X3250 @ X3252)|~(breln1 @ X3250 @ X3251))&((in @ (kpair @ X3253 @ (esk98_5 @ X3250 @ X3251 @ X3252 @ X3253 @ X3254)) @ X3251)|~(in @ (kpair @ X3253 @ X3254) @ (breln1compset @ X3250 @ X3251 @ X3252))|~(in @ X3254 @ X3250)|~(in @ X3253 @ X3250)|~(breln1 @ X3250 @ X3252)|~(breln1 @ X3250 @ X3251)))&((in @ (kpair @ (esk98_5 @ X3250 @ X3251 @ X3252 @ X3253 @ X3254) @ X3254) @ X3252)|~(in @ (kpair @ X3253 @ X3254) @ (breln1compset @ X3250 @ X3251 @ X3252))|~(in @ X3254 @ X3250)|~(in @ X3253 @ X3250)|~(breln1 @ X3250 @ X3252)|~(breln1 @ X3250 @ X3251)))&((((in @ (esk99_6 @ X3256 @ X3257 @ X3258 @ X3259 @ X3260 @ X3261) @ X3256)|(X3261)|~(in @ (kpair @ X3259 @ X3260) @ (breln1compset @ X3256 @ X3257 @ X3258))|~(in @ X3260 @ X3256)|~(in @ X3259 @ X3256)|~(breln1 @ X3256 @ X3258)|~(breln1 @ X3256 @ X3257))&(((in @ (kpair @ X3259 @ (esk99_6 @ X3256 @ X3257 @ X3258 @ X3259 @ X3260 @ X3261)) @ X3257)|(X3261)|~(in @ (kpair @ X3259 @ X3260) @ (breln1compset @ X3256 @ X3257 @ X3258))|~(in @ X3260 @ X3256)|~(in @ X3259 @ X3256)|~(breln1 @ X3256 @ X3258)|~(breln1 @ X3256 @ X3257))&(((in @ (kpair @ (esk99_6 @ X3256 @ X3257 @ X3258 @ X3259 @ X3260 @ X3261) @ X3260) @ X3258)|(X3261)|~(in @ (kpair @ X3259 @ X3260) @ (breln1compset @ X3256 @ X3257 @ X3258))|~(in @ X3260 @ X3256)|~(in @ X3259 @ X3256)|~(breln1 @ X3256 @ X3258)|~(breln1 @ X3256 @ X3257))&(~(X3261)|(X3261)|~(in @ (kpair @ X3259 @ X3260) @ (breln1compset @ X3256 @ X3257 @ X3258))|~(in @ X3260 @ X3256)|~(in @ X3259 @ X3256)|~(breln1 @ X3256 @ X3258)|~(breln1 @ X3256 @ X3257)))))&((~(breln1 @ X3263 @ X3264)|(~(breln1 @ X3263 @ X3265)|(breln1 @ X3263 @ (binunion @ X3264 @ X3265))))&((~(breln1 @ X3266 @ X3267)|(~(breln1 @ X3266 @ X3268)|(~(in @ X3269 @ X3266)|(~(in @ X3270 @ X3266)|(~(in @ (kpair @ X3269 @ X3270) @ X3267)|(in @ (kpair @ X3269 @ X3270) @ (binunion @ X3267 @ X3268)))))))&((~(breln1 @ X3271 @ X3272)|(~(breln1 @ X3271 @ X3273)|(~(in @ X3274 @ X3271)|(~(in @ X3275 @ X3271)|(~(in @ (kpair @ X3274 @ X3275) @ X3273)|(in @ (kpair @ X3274 @ X3275) @ (binunion @ X3272 @ X3273)))))))&(((~(in @ (kpair @ X3279 @ X3280) @ X3277)|(in @ (kpair @ X3279 @ X3280) @ (binunion @ X3277 @ X3278))|~(in @ X3280 @ X3276)|~(in @ X3279 @ X3276)|~(breln1 @ X3276 @ X3278)|~(breln1 @ X3276 @ X3277))&(~(in @ (kpair @ X3279 @ X3280) @ X3278)|(in @ (kpair @ X3279 @ X3280) @ (binunion @ X3277 @ X3278))|~(in @ X3280 @ X3276)|~(in @ X3279 @ X3276)|~(breln1 @ X3276 @ X3278)|~(breln1 @ X3276 @ X3277)))&((~(breln1 @ X3281 @ X3282)|(~(breln1 @ X3281 @ X3283)|(~(in @ X3284 @ X3281)|(~(in @ X3285 @ X3281)|(~(in @ (kpair @ X3284 @ X3285) @ (binunion @ X3282 @ X3283))|((in @ (kpair @ X3284 @ X3285) @ X3282)|(in @ (kpair @ X3284 @ X3285) @ X3283)))))))&(((((in @ (kpair @ X3289 @ X3290) @ X3288)|(X3291)|(in @ (kpair @ X3289 @ X3290) @ X3287)|~(in @ (kpair @ X3289 @ X3290) @ (binunion @ X3287 @ X3288))|~(in @ X3290 @ X3286)|~(in @ X3289 @ X3286)|~(breln1 @ X3286 @ X3288)|~(breln1 @ X3286 @ X3287))&(~(X3291)|(X3291)|(in @ (kpair @ X3289 @ X3290) @ X3287)|~(in @ (kpair @ X3289 @ X3290) @ (binunion @ X3287 @ X3288))|~(in @ X3290 @ X3286)|~(in @ X3289 @ X3286)|~(breln1 @ X3286 @ X3288)|~(breln1 @ X3286 @ X3287)))&(((in @ (kpair @ X3289 @ X3290) @ X3288)|(X3291)|~(X3291)|~(in @ (kpair @ X3289 @ X3290) @ (binunion @ X3287 @ X3288))|~(in @ X3290 @ X3286)|~(in @ X3289 @ X3286)|~(breln1 @ X3286 @ X3288)|~(breln1 @ X3286 @ X3287))&(~(X3291)|(X3291)|~(X3291)|~(in @ (kpair @ X3289 @ X3290) @ (binunion @ X3287 @ X3288))|~(in @ X3290 @ X3286)|~(in @ X3289 @ X3286)|~(breln1 @ X3286 @ X3288)|~(breln1 @ X3286 @ X3287))))&((~(breln1 @ X3292 @ X3293)|(~(breln1 @ X3292 @ X3294)|((binunion @ X3293 @ X3294)=(binunion @ X3294 @ X3293))))&((~(breln1 @ X3295 @ X3296)|((X3296)=(breln1invset @ X3295 @ (breln1invset @ X3295 @ X3296))))&((~(breln1 @ X3297 @ X3298)|(~(breln1 @ X3297 @ X3299)|((breln1invset @ X3297 @ (breln1compset @ X3297 @ X3298 @ X3299))=(breln1compset @ X3297 @ (breln1invset @ X3297 @ X3299) @ (breln1invset @ X3297 @ X3298)))))&((~(breln1 @ X3300 @ X3301)|(~(breln1 @ X3300 @ X3302)|(~(breln1 @ X3300 @ X3303)|((breln1compset @ X3300 @ (binunion @ X3301 @ X3302) @ X3303)=(binunion @ (breln1compset @ X3300 @ X3301 @ X3303) @ (breln1compset @ X3300 @ X3302 @ X3303))))))&((~(breln1 @ X3304 @ X3305)|(~(breln1 @ X3304 @ X3306)|(~(breln1 @ X3304 @ X3307)|((breln1compset @ X3304 @ (binunion @ X3305 @ X3306) @ X3307)=(binunion @ (breln1invset @ X3304 @ (breln1compset @ X3304 @ (breln1invset @ X3304 @ X3307) @ (breln1invset @ X3304 @ X3306))) @ (breln1invset @ X3304 @ (breln1compset @ X3304 @ (breln1invset @ X3304 @ X3307) @ (breln1invset @ X3304 @ X3305))))))))&(((((in @ (esk101_3 @ X3308 @ X3309 @ X3311) @ X3308)|~(in @ X3311 @ (esk100_2 @ X3308 @ X3309)))&(((X3311)=(X3309 @ (esk101_3 @ X3308 @ X3309 @ X3311)))|~(in @ X3311 @ (esk100_2 @ X3308 @ X3309))))&(~(in @ X3314 @ X3308)|((X3313)!=(X3309 @ X3314))|(in @ X3313 @ (esk100_2 @ X3308 @ X3309))))&((((((in @ (esk103_3 @ X3315 @ X3316 @ X3318) @ X3315)|~(in @ X3318 @ (esk102_2 @ X3315 @ X3316)))&(((X3318)=(X3316 @ (esk103_3 @ X3315 @ X3316 @ X3318)))|~(in @ X3318 @ (esk102_2 @ X3315 @ X3316))))&(~(in @ X3321 @ X3315)|((X3320)!=(X3316 @ X3321))|(in @ X3320 @ (esk102_2 @ X3315 @ X3316))))&((~(in @ (esk104_3 @ X3315 @ X3316 @ X3322) @ X3322)|(~(in @ X3324 @ X3315)|((esk104_3 @ X3315 @ X3316 @ X3322)!=(X3316 @ X3324)))|((esk102_2 @ X3315 @ X3316)=(X3322)))&(((in @ (esk105_3 @ X3315 @ X3316 @ X3322) @ X3315)|(in @ (esk104_3 @ X3315 @ X3316 @ X3322) @ X3322)|((esk102_2 @ X3315 @ X3316)=(X3322)))&(((esk104_3 @ X3315 @ X3316 @ X3322)=(X3316 @ (esk105_3 @ X3315 @ X3316 @ X3322)))|(in @ (esk104_3 @ X3315 @ X3316 @ X3322) @ X3322)|((esk102_2 @ X3315 @ X3316)=(X3322))))))&(((((in @ (esk106_3 @ X3326 @ X3327 @ X3328) @ X3326)|~(in @ X3328 @ (image1 @ X3326 @ X3327)))&(((X3328)=(X3327 @ (esk106_3 @ X3326 @ X3327 @ X3328)))|~(in @ X3328 @ (image1 @ X3326 @ X3327))))&(~(in @ X3333 @ X3330)|((X3332)!=(X3331 @ X3333))|(in @ X3332 @ (image1 @ X3330 @ X3331))))&((((in @ (esk107_3 @ X3334 @ X3335 @ X3336) @ X3334)|~(in @ X3336 @ (image1 @ X3334 @ X3335)))&(((X3336)=(X3335 @ (esk107_3 @ X3334 @ X3335 @ X3336)))|~(in @ X3336 @ (image1 @ X3334 @ X3335))))&((~(in @ X3341 @ X3338)|((X3340)!=(X3339 @ X3341))|(in @ X3340 @ (image1 @ X3338 @ X3339)))&((~(in @ X3344 @ (funcSet @ X3342 @ X3343))|(~(injective @ X3342 @ X3343 @ X3344)|(in @ X3344 @ (injFuncSet @ X3342 @ X3343))))&((~(in @ X3347 @ (injFuncSet @ X3345 @ X3346))|(in @ X3347 @ (funcSet @ X3345 @ X3346)))&((~(in @ X3350 @ (injFuncSet @ X3348 @ X3349))|(injective @ X3348 @ X3349 @ X3350))&((~(in @ X3353 @ (surjFuncSet @ X3351 @ X3352))|(in @ X3353 @ (funcSet @ X3351 @ X3352)))&((~(in @ X3356 @ (surjFuncSet @ X3354 @ X3355))|(surjective @ X3354 @ X3355 @ X3356))&(((((in @ (esk109_4 @ X3357 @ X3358 @ X3359 @ X3361) @ X3357)|(surjective @ X3358 @ X3357 @ X3361)|~(in @ X3361 @ (funcSet @ X3358 @ X3357))|(in @ (esk108_3 @ X3357 @ X3358 @ X3359) @ X3357))&(((ap @ X3358 @ X3357 @ X3361 @ (X3359 @ (esk109_4 @ X3357 @ X3358 @ X3359 @ X3361)))!=(esk109_4 @ X3357 @ X3358 @ X3359 @ X3361))|(surjective @ X3358 @ X3357 @ X3361)|~(in @ X3361 @ (funcSet @ X3358 @ X3357))|(in @ (esk108_3 @ X3357 @ X3358 @ X3359) @ X3357)))&(((in @ (esk109_4 @ X3357 @ X3358 @ X3359 @ X3361) @ X3357)|(surjective @ X3358 @ X3357 @ X3361)|~(in @ X3361 @ (funcSet @ X3358 @ X3357))|~(in @ (X3359 @ (esk108_3 @ X3357 @ X3358 @ X3359)) @ X3358))&(((ap @ X3358 @ X3357 @ X3361 @ (X3359 @ (esk109_4 @ X3357 @ X3358 @ X3359 @ X3361)))!=(esk109_4 @ X3357 @ X3358 @ X3359 @ X3361))|(surjective @ X3358 @ X3357 @ X3361)|~(in @ X3361 @ (funcSet @ X3358 @ X3357))|~(in @ (X3359 @ (esk108_3 @ X3357 @ X3358 @ X3359)) @ X3358))))&((~(in @ X3364 @ (funcSet @ X3363 @ (powerset @ X3363)))|~(surjective @ X3363 @ (powerset @ X3363) @ X3364))&((((in @ (esk110_1 @ X3365) @ X3365)|((X3365)=(emptyset)))&(((binintersect @ (esk110_1 @ X3365) @ X3365)=(emptyset))|((X3365)=(emptyset))))&(~(in @ X3367 @ X3367)&((~(in @ X3368 @ X3369)|~(in @ X3369 @ X3368))&((~(in @ X3370 @ omega)|(in @ (omegaS @ X3370) @ omega))&((~(in @ X3371 @ omega)|(in @ (setadjoin @ X3371 @ X3371) @ omega))&((in @ esk111_0 @ omega)&((omegaS @ esk111_0)=(emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_408])])])])])])])).
% 1.81/0.80 thf(c_0_411, plain, ![X2266:$i]:(((omegaS @ X2266)=(setadjoin @ X2266 @ X2266))), inference(variable_rename,[status(thm)],[c_0_409])).
% 1.81/0.80 thf(c_0_412, negated_conjecture, ((omegaS @ esk111_0)=(emptyset)), inference(split_conjunct,[status(thm)],[c_0_410])).
% 1.81/0.80 thf(c_0_413, plain, ![X2:$i]:(((omegaS @ X2)=(setadjoin @ X2 @ X2))), inference(split_conjunct,[status(thm)],[c_0_411])).
% 1.81/0.80 thf(c_0_414, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(split_conjunct,[status(thm)],[c_0_410])).
% 1.81/0.80 thf(c_0_415, negated_conjecture, ((setadjoin @ esk111_0 @ esk111_0)=(emptyset)), inference(rw,[status(thm)],[c_0_412, c_0_413])).
% 1.81/0.80 thf(c_0_416, negated_conjecture, ![X2:$i]:(~((in @ X2 @ emptyset))), inference(split_conjunct,[status(thm)],[c_0_410])).
% 1.81/0.80 thf(c_0_417, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_414, c_0_415]), c_0_416]), ['proof']).
% 1.81/0.80 # SZS output end CNFRefutation
% 1.81/0.80 # Parsed axioms : 710
% 1.81/0.80 # Removed by relevancy pruning/SinE : 0
% 1.81/0.80 # Initial clauses : 967
% 1.81/0.80 # Removed in clause preprocessing : 421
% 1.81/0.80 # Initial clauses in saturation : 546
% 1.81/0.80 # Processed clauses : 600
% 1.81/0.80 # ...of these trivial : 9
% 1.81/0.80 # ...subsumed : 52
% 1.81/0.80 # ...remaining for further processing : 539
% 1.81/0.80 # Other redundant clauses eliminated : 23
% 1.81/0.80 # Clauses deleted for lack of memory : 0
% 1.81/0.80 # Backward-subsumed : 0
% 1.81/0.80 # Backward-rewritten : 2
% 1.81/0.80 # Generated clauses : 48
% 1.81/0.80 # ...of the previous two non-redundant : 39
% 1.81/0.80 # ...aggressively subsumed : 0
% 1.81/0.80 # Contextual simplify-reflections : 14
% 1.81/0.80 # Paramodulations : 21
% 1.81/0.80 # Factorizations : 0
% 1.81/0.80 # NegExts : 0
% 1.81/0.80 # Equation resolutions : 25
% 1.81/0.80 # Disequality decompositions : 0
% 1.81/0.80 # Total rewrite steps : 34
% 1.81/0.80 # ...of those cached : 18
% 1.81/0.80 # Propositional unsat checks : 0
% 1.81/0.80 # Propositional check models : 0
% 1.81/0.80 # Propositional check unsatisfiable : 0
% 1.81/0.80 # Propositional clauses : 0
% 1.81/0.80 # Propositional clauses after purity: 0
% 1.81/0.80 # Propositional unsat core size : 0
% 1.81/0.80 # Propositional preprocessing time : 0.000
% 1.81/0.80 # Propositional encoding time : 0.000
% 1.81/0.80 # Propositional solver time : 0.000
% 1.81/0.80 # Success case prop preproc time : 0.000
% 1.81/0.80 # Success case prop encoding time : 0.000
% 1.81/0.80 # Success case prop solver time : 0.000
% 1.81/0.80 # Current number of processed clauses : 36
% 1.81/0.80 # Positive orientable unit clauses : 21
% 1.81/0.80 # Positive unorientable unit clauses: 0
% 1.81/0.80 # Negative unit clauses : 3
% 1.81/0.80 # Non-unit-clauses : 12
% 1.81/0.80 # Current number of unprocessed clauses: 462
% 1.81/0.80 # ...number of literals in the above : 1578
% 1.81/0.80 # Current number of archived formulas : 0
% 1.81/0.80 # Current number of archived clauses : 481
% 1.81/0.80 # Clause-clause subsumption calls (NU) : 60863
% 1.81/0.80 # Rec. Clause-clause subsumption calls : 18321
% 1.81/0.80 # Non-unit clause-clause subsumptions : 61
% 1.81/0.80 # Unit Clause-clause subsumption calls : 558
% 1.81/0.80 # Rewrite failures with RHS unbound : 0
% 1.81/0.80 # BW rewrite match attempts : 29
% 1.81/0.80 # BW rewrite match successes : 3
% 1.81/0.80 # Condensation attempts : 0
% 1.81/0.80 # Condensation successes : 0
% 1.81/0.80 # Termbank termtop insertions : 114838
% 1.81/0.80 # Search garbage collected termcells : 36858
% 1.81/0.80
% 1.81/0.80 # -------------------------------------------------
% 1.81/0.80 # User time : 0.215 s
% 1.81/0.80 # System time : 0.026 s
% 1.81/0.80 # Total time : 0.241 s
% 1.81/0.80 # Maximum resident set size: 10576 pages
% 1.81/0.80
% 1.81/0.80 # -------------------------------------------------
% 1.81/0.80 # User time : 0.234 s
% 1.81/0.80 # System time : 0.032 s
% 1.81/0.80 # Total time : 0.266 s
% 1.81/0.80 # Maximum resident set size: 2884 pages
% 1.81/0.80 % E---3.1 exiting
% 1.81/0.80 % E exiting
%------------------------------------------------------------------------------