TSTP Solution File: SEU668^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU668^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n013.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 03:28:59 EDT 2024
% Result : Theorem 0.90s 0.63s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU668^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 16:15:53 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.20/0.48 Running higher-order theorem proving
% 0.20/0.48 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
% 0.90/0.63 # Version: 3.1.0-ho
% 0.90/0.63 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.90/0.63 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.63 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.90/0.63 # Starting pre_casc_3 with 300s (1) cores
% 0.90/0.63 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.90/0.63 # Starting full_lambda_10 with 300s (1) cores
% 0.90/0.63 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.90/0.63 # ehoh_best_nonlift_rwall with pid 9535 completed with status 0
% 0.90/0.63 # Result found by ehoh_best_nonlift_rwall
% 0.90/0.63 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.90/0.63 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.63 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.90/0.63 # Starting pre_casc_3 with 300s (1) cores
% 0.90/0.63 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.90/0.63 # Starting full_lambda_10 with 300s (1) cores
% 0.90/0.63 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.90/0.63 # No SInE strategy applied
% 0.90/0.63 # Search class: HGHSM-FSLM31-DHSMMSBN
% 0.90/0.63 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 0.90/0.63 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.90/0.63 # Starting new_ho_10_cnf2 with 174s (1) cores
% 0.90/0.63 # new_ho_10_cnf2 with pid 9538 completed with status 0
% 0.90/0.63 # Result found by new_ho_10_cnf2
% 0.90/0.63 # Preprocessing class: HSLMSLSSLLLCHSA.
% 0.90/0.63 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 0.90/0.63 # Starting ho_unfolding_5 with 1200s (4) cores
% 0.90/0.63 # Starting pre_casc_3 with 300s (1) cores
% 0.90/0.63 # Starting new_ho_10_cnf2 with 300s (1) cores
% 0.90/0.63 # Starting full_lambda_10 with 300s (1) cores
% 0.90/0.63 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.90/0.63 # No SInE strategy applied
% 0.90/0.63 # Search class: HGHSM-FSLM31-DHSMMSBN
% 0.90/0.63 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 0.90/0.63 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.90/0.63 # Starting new_ho_10_cnf2 with 174s (1) cores
% 0.90/0.63 # Preprocessing time : 0.007 s
% 0.90/0.63 # Presaturation interreduction done
% 0.90/0.63
% 0.90/0.63 # Proof found!
% 0.90/0.63 # SZS status Theorem
% 0.90/0.63 # SZS output start CNFRefutation
% 0.90/0.63 thf(decl_22, type, in: $i > $i > $o).
% 0.90/0.63 thf(decl_23, type, exu: ($i > $o) > $o).
% 0.90/0.63 thf(decl_24, type, setextAx: $o).
% 0.90/0.63 thf(decl_25, type, emptyset: $i).
% 0.90/0.63 thf(decl_26, type, emptysetAx: $o).
% 0.90/0.63 thf(decl_27, type, setadjoin: $i > $i > $i).
% 0.90/0.63 thf(decl_28, type, setadjoinAx: $o).
% 0.90/0.63 thf(decl_29, type, powerset: $i > $i).
% 0.90/0.63 thf(decl_30, type, powersetAx: $o).
% 0.90/0.63 thf(decl_31, type, setunion: $i > $i).
% 0.90/0.63 thf(decl_32, type, setunionAx: $o).
% 0.90/0.63 thf(decl_33, type, omega: $i).
% 0.90/0.63 thf(decl_34, type, omega0Ax: $o).
% 0.90/0.63 thf(decl_35, type, omegaSAx: $o).
% 0.90/0.63 thf(decl_36, type, omegaIndAx: $o).
% 0.90/0.63 thf(decl_37, type, replAx: $o).
% 0.90/0.63 thf(decl_38, type, foundationAx: $o).
% 0.90/0.63 thf(decl_39, type, wellorderingAx: $o).
% 0.90/0.63 thf(decl_40, type, descr: ($i > $o) > $i).
% 0.90/0.63 thf(decl_41, type, descrp: $o).
% 0.90/0.63 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_43, type, dsetconstrI: $o).
% 0.90/0.63 thf(decl_44, type, dsetconstrEL: $o).
% 0.90/0.63 thf(decl_45, type, dsetconstrER: $o).
% 0.90/0.63 thf(decl_46, type, exuE1: $o).
% 0.90/0.63 thf(decl_47, type, prop2set: $o > $i).
% 0.90/0.63 thf(decl_48, type, prop2setE: $o).
% 0.90/0.63 thf(decl_49, type, emptysetE: $o).
% 0.90/0.63 thf(decl_50, type, emptysetimpfalse: $o).
% 0.90/0.63 thf(decl_51, type, notinemptyset: $o).
% 0.90/0.63 thf(decl_52, type, exuE3e: $o).
% 0.90/0.63 thf(decl_53, type, setext: $o).
% 0.90/0.63 thf(decl_54, type, emptyI: $o).
% 0.90/0.63 thf(decl_55, type, noeltsimpempty: $o).
% 0.90/0.63 thf(decl_56, type, setbeta: $o).
% 0.90/0.63 thf(decl_57, type, nonempty: $i > $o).
% 0.90/0.63 thf(decl_58, type, nonemptyE1: $o).
% 0.90/0.63 thf(decl_59, type, nonemptyI: $o).
% 0.90/0.63 thf(decl_60, type, nonemptyI1: $o).
% 0.90/0.63 thf(decl_61, type, setadjoinIL: $o).
% 0.90/0.63 thf(decl_62, type, emptyinunitempty: $o).
% 0.90/0.63 thf(decl_63, type, setadjoinIR: $o).
% 0.90/0.63 thf(decl_64, type, setadjoinE: $o).
% 0.90/0.63 thf(decl_65, type, setadjoinOr: $o).
% 0.90/0.63 thf(decl_66, type, setoftrueEq: $o).
% 0.90/0.63 thf(decl_67, type, powersetI: $o).
% 0.90/0.63 thf(decl_68, type, emptyinPowerset: $o).
% 0.90/0.63 thf(decl_69, type, emptyInPowerset: $o).
% 0.90/0.63 thf(decl_70, type, powersetE: $o).
% 0.90/0.63 thf(decl_71, type, setunionI: $o).
% 0.90/0.63 thf(decl_72, type, setunionE: $o).
% 0.90/0.63 thf(decl_73, type, subPowSU: $o).
% 0.90/0.63 thf(decl_74, type, exuE2: $o).
% 0.90/0.63 thf(decl_75, type, nonemptyImpWitness: $o).
% 0.90/0.63 thf(decl_76, type, uniqinunit: $o).
% 0.90/0.63 thf(decl_77, type, notinsingleton: $o).
% 0.90/0.63 thf(decl_78, type, eqinunit: $o).
% 0.90/0.63 thf(decl_79, type, singletonsswitch: $o).
% 0.90/0.63 thf(decl_80, type, upairsetE: $o).
% 0.90/0.63 thf(decl_81, type, upairsetIL: $o).
% 0.90/0.63 thf(decl_82, type, upairsetIR: $o).
% 0.90/0.63 thf(decl_83, type, emptyE1: $o).
% 0.90/0.63 thf(decl_84, type, vacuousDall: $o).
% 0.90/0.63 thf(decl_85, type, quantDeMorgan1: $o).
% 0.90/0.63 thf(decl_86, type, quantDeMorgan2: $o).
% 0.90/0.63 thf(decl_87, type, quantDeMorgan3: $o).
% 0.90/0.63 thf(decl_88, type, quantDeMorgan4: $o).
% 0.90/0.63 thf(decl_89, type, prop2setI: $o).
% 0.90/0.63 thf(decl_90, type, set2prop: $i > $o).
% 0.90/0.63 thf(decl_91, type, prop2set2propI: $o).
% 0.90/0.63 thf(decl_92, type, notdexE: $o).
% 0.90/0.63 thf(decl_93, type, notdallE: $o).
% 0.90/0.63 thf(decl_94, type, exuI1: $o).
% 0.90/0.63 thf(decl_95, type, exuI3: $o).
% 0.90/0.63 thf(decl_96, type, exuI2: $o).
% 0.90/0.63 thf(decl_97, type, inCongP: $o).
% 0.90/0.63 thf(decl_98, type, in__Cong: $o).
% 0.90/0.63 thf(decl_99, type, exuE3u: $o).
% 0.90/0.63 thf(decl_100, type, exu__Cong: $o).
% 0.90/0.63 thf(decl_101, type, emptyset__Cong: $o).
% 0.90/0.63 thf(decl_102, type, setadjoin__Cong: $o).
% 0.90/0.63 thf(decl_103, type, powerset__Cong: $o).
% 0.90/0.63 thf(decl_104, type, setunion__Cong: $o).
% 0.90/0.63 thf(decl_105, type, omega__Cong: $o).
% 0.90/0.63 thf(decl_106, type, exuEu: $o).
% 0.90/0.63 thf(decl_107, type, descr__Cong: $o).
% 0.90/0.63 thf(decl_108, type, dsetconstr__Cong: $o).
% 0.90/0.63 thf(decl_109, type, subset: $i > $i > $o).
% 0.90/0.63 thf(decl_112, type, subsetI1: $o).
% 0.90/0.63 thf(decl_113, type, eqimpsubset2: $o).
% 0.90/0.63 thf(decl_114, type, eqimpsubset1: $o).
% 0.90/0.63 thf(decl_115, type, subsetI2: $o).
% 0.90/0.63 thf(decl_116, type, emptysetsubset: $o).
% 0.90/0.63 thf(decl_117, type, subsetE: $o).
% 0.90/0.63 thf(decl_118, type, subsetE2: $o).
% 0.90/0.63 thf(decl_119, type, notsubsetI: $o).
% 0.90/0.63 thf(decl_120, type, notequalI1: $o).
% 0.90/0.63 thf(decl_121, type, notequalI2: $o).
% 0.90/0.63 thf(decl_122, type, subsetRefl: $o).
% 0.90/0.63 thf(decl_123, type, subsetTrans: $o).
% 0.90/0.63 thf(decl_124, type, setadjoinSub: $o).
% 0.90/0.63 thf(decl_125, type, setadjoinSub2: $o).
% 0.90/0.63 thf(decl_126, type, subset2powerset: $o).
% 0.90/0.63 thf(decl_127, type, setextsub: $o).
% 0.90/0.63 thf(decl_128, type, subsetemptysetimpeq: $o).
% 0.90/0.63 thf(decl_129, type, powersetI1: $o).
% 0.90/0.63 thf(decl_130, type, powersetE1: $o).
% 0.90/0.63 thf(decl_131, type, inPowerset: $o).
% 0.90/0.63 thf(decl_132, type, powersetsubset: $o).
% 0.90/0.63 thf(decl_133, type, sepInPowerset: $o).
% 0.90/0.63 thf(decl_134, type, sepSubset: $o).
% 0.90/0.63 thf(decl_135, type, binunion: $i > $i > $i).
% 0.90/0.63 thf(decl_136, type, binunionIL: $o).
% 0.90/0.63 thf(decl_137, type, upairset2IR: $o).
% 0.90/0.63 thf(decl_138, type, binunionIR: $o).
% 0.90/0.63 thf(decl_139, type, binunionEcases: $o).
% 0.90/0.63 thf(decl_140, type, binunionE: $o).
% 0.90/0.63 thf(decl_141, type, binunionLsub: $o).
% 0.90/0.63 thf(decl_142, type, binunionRsub: $o).
% 0.90/0.63 thf(decl_143, type, binintersect: $i > $i > $i).
% 0.90/0.63 thf(decl_144, type, binintersectI: $o).
% 0.90/0.63 thf(decl_145, type, binintersectSubset5: $o).
% 0.90/0.63 thf(decl_146, type, binintersectEL: $o).
% 0.90/0.63 thf(decl_147, type, binintersectLsub: $o).
% 0.90/0.63 thf(decl_148, type, binintersectSubset2: $o).
% 0.90/0.63 thf(decl_149, type, binintersectSubset3: $o).
% 0.90/0.63 thf(decl_150, type, binintersectER: $o).
% 0.90/0.63 thf(decl_151, type, disjointsetsI1: $o).
% 0.90/0.63 thf(decl_152, type, binintersectRsub: $o).
% 0.90/0.63 thf(decl_153, type, binintersectSubset4: $o).
% 0.90/0.63 thf(decl_154, type, binintersectSubset1: $o).
% 0.90/0.63 thf(decl_155, type, bs114d: $o).
% 0.90/0.63 thf(decl_157, type, setminus: $i > $i > $i).
% 0.90/0.63 thf(decl_158, type, setminusI: $o).
% 0.90/0.63 thf(decl_159, type, setminusEL: $o).
% 0.90/0.63 thf(decl_160, type, setminusER: $o).
% 0.90/0.63 thf(decl_161, type, setminusSubset2: $o).
% 0.90/0.63 thf(decl_162, type, setminusERneg: $o).
% 0.90/0.63 thf(decl_163, type, setminusELneg: $o).
% 0.90/0.63 thf(decl_164, type, setminusILneg: $o).
% 0.90/0.63 thf(decl_165, type, setminusIRneg: $o).
% 0.90/0.63 thf(decl_166, type, setminusLsub: $o).
% 0.90/0.63 thf(decl_167, type, setminusSubset1: $o).
% 0.90/0.63 thf(decl_168, type, symdiff: $i > $i > $i).
% 0.90/0.63 thf(decl_169, type, symdiffE: $o).
% 0.90/0.63 thf(decl_170, type, symdiffI1: $o).
% 0.90/0.63 thf(decl_171, type, symdiffI2: $o).
% 0.90/0.63 thf(decl_172, type, symdiffIneg1: $o).
% 0.90/0.63 thf(decl_173, type, symdiffIneg2: $o).
% 0.90/0.63 thf(decl_174, type, iskpair: $i > $o).
% 0.90/0.63 thf(decl_175, type, secondinupair: $o).
% 0.90/0.63 thf(decl_176, type, setukpairIL: $o).
% 0.90/0.63 thf(decl_177, type, setukpairIR: $o).
% 0.90/0.63 thf(decl_178, type, kpairiskpair: $o).
% 0.90/0.63 thf(decl_179, type, kpair: $i > $i > $i).
% 0.90/0.63 thf(decl_180, type, kpairp: $o).
% 0.90/0.63 thf(decl_181, type, cartprod: $i > $i > $i).
% 0.90/0.63 thf(decl_182, type, singletonsubset: $o).
% 0.90/0.63 thf(decl_183, type, singletoninpowerset: $o).
% 0.90/0.63 thf(decl_184, type, singletoninpowunion: $o).
% 0.90/0.63 thf(decl_185, type, upairset2E: $o).
% 0.90/0.63 thf(decl_186, type, upairsubunion: $o).
% 0.90/0.63 thf(decl_187, type, upairinpowunion: $o).
% 0.90/0.63 thf(decl_188, type, ubforcartprodlem1: $o).
% 0.90/0.63 thf(decl_189, type, ubforcartprodlem2: $o).
% 0.90/0.63 thf(decl_190, type, ubforcartprodlem3: $o).
% 0.90/0.63 thf(decl_191, type, cartprodpairin: $o).
% 0.90/0.63 thf(decl_192, type, cartprodmempair1: $o).
% 0.90/0.63 thf(decl_193, type, cartprodmempair: $o).
% 0.90/0.63 thf(decl_194, type, setunionE2: $o).
% 0.90/0.63 thf(decl_195, type, setunionsingleton1: $o).
% 0.90/0.63 thf(decl_196, type, setunionsingleton2: $o).
% 0.90/0.63 thf(decl_197, type, setunionsingleton: $o).
% 0.90/0.63 thf(decl_198, type, singleton: $i > $o).
% 0.90/0.63 thf(decl_199, type, singletonprop: $o).
% 0.90/0.63 thf(decl_200, type, ex1: $i > ($i > $o) > $o).
% 0.90/0.63 thf(decl_201, type, ex1E1: $o).
% 0.90/0.63 thf(decl_202, type, ex1I: $o).
% 0.90/0.63 thf(decl_203, type, ex1I2: $o).
% 0.90/0.63 thf(decl_204, type, singletonsuniq: $o).
% 0.90/0.63 thf(decl_209, type, setukpairinjL1: $o).
% 0.90/0.63 thf(decl_210, type, kfstsingleton: $o).
% 0.90/0.63 thf(decl_211, type, theprop: $o).
% 0.90/0.63 thf(decl_212, type, kfst: $i > $i).
% 0.90/0.63 thf(decl_213, type, kfstpairEq: $o).
% 0.90/0.63 thf(decl_214, type, cartprodfstin: $o).
% 0.90/0.63 thf(decl_215, type, setukpairinjL2: $o).
% 0.90/0.63 thf(decl_216, type, setukpairinjL: $o).
% 0.90/0.63 thf(decl_217, type, setukpairinjR11: $o).
% 0.90/0.63 thf(decl_218, type, setukpairinjR12: $o).
% 0.90/0.63 thf(decl_219, type, setukpairinjR1: $o).
% 0.90/0.63 thf(decl_220, type, upairequniteq: $o).
% 0.90/0.63 thf(decl_221, type, setukpairinjR2: $o).
% 0.90/0.63 thf(decl_222, type, setukpairinjR: $o).
% 0.90/0.63 thf(decl_223, type, ksndsingleton: $o).
% 0.90/0.63 thf(decl_224, type, ksnd: $i > $i).
% 0.90/0.63 thf(decl_225, type, ksndpairEq: $o).
% 0.90/0.63 thf(decl_226, type, kpairsurjEq: $o).
% 0.90/0.63 thf(decl_227, type, cartprodsndin: $o).
% 0.90/0.63 thf(decl_228, type, cartprodpairmemEL: $o).
% 0.90/0.63 thf(decl_229, type, cartprodpairmemER: $o).
% 0.90/0.63 thf(decl_230, type, cartprodmempaircEq: $o).
% 0.90/0.63 thf(decl_231, type, cartprodfstpairEq: $o).
% 0.90/0.63 thf(decl_232, type, cartprodsndpairEq: $o).
% 0.90/0.63 thf(decl_233, type, cartprodpairsurjEq: $o).
% 0.90/0.63 thf(decl_234, type, breln: $i > $i > $i > $o).
% 0.90/0.63 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 0.90/0.63 thf(decl_236, type, dpsetconstrI: $o).
% 0.90/0.63 thf(decl_237, type, dpsetconstrSub: $o).
% 0.90/0.63 thf(decl_238, type, setOfPairsIsBReln: $o).
% 0.90/0.63 thf(decl_239, type, epred1_0: $o).
% 0.90/0.63 thf(decl_240, type, esk1_2: $i > $i > $i).
% 0.90/0.63 thf(decl_241, type, esk2_2: $i > $i > $i).
% 0.90/0.63 thf(decl_242, type, esk3_2: $i > $i > $i).
% 0.90/0.63 thf(decl_243, type, esk4_1: $i > $i).
% 0.90/0.63 thf(decl_244, type, esk5_2: ($i > $i > $o) > $i > $i).
% 0.90/0.63 thf(decl_245, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 0.90/0.63 thf(decl_246, type, esk7_2: ($i > $i > $o) > $i > $i).
% 0.90/0.63 thf(decl_247, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 0.90/0.63 thf(decl_248, type, esk9_1: $i > $i).
% 0.90/0.63 thf(decl_249, type, esk10_2: ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_250, type, esk11_2: ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_251, type, esk12_1: ($i > $o) > $i).
% 0.90/0.63 thf(decl_252, type, esk13_2: ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_253, type, esk14_1: ($i > $o) > $i).
% 0.90/0.63 thf(decl_254, type, esk15_2: $i > $i > $i).
% 0.90/0.63 thf(decl_255, type, esk16_2: $i > $i > $i).
% 0.90/0.63 thf(decl_256, type, esk17_1: $i > $i).
% 0.90/0.63 thf(decl_257, type, esk18_1: $i > $i).
% 0.90/0.63 thf(decl_258, type, esk19_1: $i > $i).
% 0.90/0.63 thf(decl_259, type, esk20_2: $i > $i > $i).
% 0.90/0.63 thf(decl_260, type, esk21_3: $i > $i > $o > $i).
% 0.90/0.63 thf(decl_261, type, esk22_2: ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_262, type, esk23_1: ($i > $o) > $i).
% 0.90/0.63 thf(decl_263, type, esk24_1: $i > $i).
% 0.90/0.63 thf(decl_264, type, esk25_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_265, type, esk26_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_266, type, esk27_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_267, type, esk28_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_268, type, esk29_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_269, type, esk30_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_270, type, esk31_2: ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_271, type, esk32_1: ($i > $o) > $i).
% 0.90/0.63 thf(decl_272, type, esk33_1: ($i > $o) > $i).
% 0.90/0.63 thf(decl_273, type, esk34_1: ($i > $o) > $i).
% 0.90/0.63 thf(decl_274, type, esk35_1: ($i > $o) > $i).
% 0.90/0.63 thf(decl_275, type, esk36_2: ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_276, type, esk37_1: ($i > $o) > $i).
% 0.90/0.63 thf(decl_277, type, esk38_2: ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_278, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 0.90/0.63 thf(decl_279, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 0.90/0.63 thf(decl_280, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_281, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 0.90/0.63 thf(decl_282, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_283, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 0.90/0.63 thf(decl_284, type, esk45_2: ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_285, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 0.90/0.63 thf(decl_286, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 0.90/0.63 thf(decl_287, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_288, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_289, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.90/0.63 thf(decl_290, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 0.90/0.63 thf(decl_291, type, esk52_2: $i > $i > $i).
% 0.90/0.63 thf(decl_292, type, esk53_2: $i > $i > $i).
% 0.90/0.63 thf(decl_293, type, esk54_2: $i > $i > $i).
% 0.90/0.63 thf(decl_294, type, esk55_3: $i > $i > $i > $i).
% 0.90/0.63 thf(decl_295, type, esk56_3: $i > $i > $i > $i).
% 0.90/0.63 thf(decl_296, type, esk57_2: $i > $i > $i).
% 0.90/0.63 thf(decl_297, type, esk58_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_298, type, esk59_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_299, type, esk60_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_300, type, esk61_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_301, type, esk62_3: $i > ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_302, type, esk63_3: $i > ($i > $o) > $i > $i).
% 0.90/0.63 thf(decl_303, type, esk64_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_304, type, esk65_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_305, type, esk66_2: $i > ($i > $o) > $i).
% 0.90/0.63 thf(decl_306, type, esk67_1: $i > $i).
% 0.90/0.63 thf(decl_307, type, esk68_1: $i > $i).
% 0.90/0.63 thf(decl_308, type, esk69_0: $i).
% 0.90/0.63 thf(decl_309, type, esk70_0: $i).
% 0.90/0.63 thf(decl_310, type, epred2_0: $i > $i > $o).
% 0.90/0.63 thf(decl_311, type, esk71_0: $i).
% 0.90/0.63 thf(decl_312, type, esk72_0: $i).
% 0.90/0.63 thf(decl_318, type, esk78_0: $i).
% 0.90/0.63 thf(decl_319, type, esk79_0: $i).
% 0.90/0.63 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1)).
% 0.90/0.63 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singleton)).
% 0.90/0.63 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', replAx)).
% 0.90/0.63 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu)).
% 0.90/0.63 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descrp)).
% 0.90/0.63 thf(exuE1, axiom, ((exuE1)<=>![X1:$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)).
% 0.90/0.63 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3e)).
% 0.90/0.63 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonempty)).
% 0.90/0.63 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI)).
% 0.90/0.63 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE2)).
% 0.90/0.63 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)).
% 0.90/0.63 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI3)).
% 0.90/0.63 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI2)).
% 0.90/0.63 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)).
% 0.90/0.63 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu__Cong)).
% 0.90/0.63 thf(exuEu, axiom, ((exuEu)<=>![X1:$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)).
% 0.90/0.63 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descr__Cong)).
% 0.90/0.63 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$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:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonprop)).
% 0.90/0.63 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1E1)).
% 0.90/0.63 thf(ex1I, axiom, ((ex1I)<=>![X4:$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)).
% 0.90/0.63 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I2)).
% 0.90/0.63 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstsingleton)).
% 0.90/0.63 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndsingleton)).
% 0.90/0.63 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X23 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrI)).
% 0.90/0.63 thf(dpsetconstr, axiom, ((dpsetconstr)=(^[X4:$i, X5:$i, X22:$i > $i > $o]:(dsetconstr @ (cartprod @ X4 @ X5) @ (^[X18:$i]:(?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:((((in @ X3 @ X5)&(X22 @ X2 @ X3))&((X18)=(kpair @ X2 @ X3))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstr)).
% 0.90/0.63 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrSub)).
% 0.90/0.63 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X25:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln)).
% 0.90/0.63 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln)).
% 0.90/0.63 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrI)).
% 0.90/0.63 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrEL)).
% 0.90/0.63 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrER)).
% 0.90/0.63 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setbeta)).
% 0.90/0.63 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyE1)).
% 0.90/0.63 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI1)).
% 0.90/0.63 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setoftrueEq)).
% 0.90/0.63 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyImpWitness)).
% 0.90/0.63 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$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)).
% 0.90/0.63 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstr__Cong)).
% 0.90/0.63 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepInPowerset)).
% 0.90/0.63 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)).
% 0.90/0.63 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theprop)).
% 0.90/0.63 thf(dpsetconstrERa, 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)=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(X26 @ X2 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrERa)).
% 0.90/0.63 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextAx)).
% 0.90/0.63 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetAx)).
% 0.90/0.63 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinAx)).
% 0.90/0.63 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetAx)).
% 0.90/0.63 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionAx)).
% 0.90/0.63 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega0Ax)).
% 0.90/0.63 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSAx)).
% 0.90/0.63 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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)).
% 0.90/0.63 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)).
% 0.90/0.63 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', wellorderingAx)).
% 0.90/0.63 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setE)).
% 0.90/0.63 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetE)).
% 0.90/0.63 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetimpfalse)).
% 0.90/0.63 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinemptyset)).
% 0.90/0.63 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)).
% 0.90/0.63 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyI)).
% 0.90/0.63 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', noeltsimpempty)).
% 0.90/0.63 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIL)).
% 0.90/0.63 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinunitempty)).
% 0.90/0.63 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIR)).
% 0.90/0.63 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinE)).
% 0.90/0.63 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinOr)).
% 0.90/0.63 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI)).
% 0.90/0.63 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinPowerset)).
% 0.90/0.63 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyInPowerset)).
% 0.90/0.63 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE)).
% 0.90/0.63 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionI)).
% 0.90/0.63 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE)).
% 0.90/0.63 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subPowSU)).
% 0.90/0.63 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', uniqinunit)).
% 0.90/0.63 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinsingleton)).
% 0.90/0.63 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqinunit)).
% 0.90/0.63 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsswitch)).
% 0.90/0.63 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetE)).
% 0.90/0.63 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIL)).
% 0.90/0.63 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIR)).
% 0.90/0.63 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', vacuousDall)).
% 0.90/0.63 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan1)).
% 0.90/0.63 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan2)).
% 0.90/0.63 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan3)).
% 0.90/0.63 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan4)).
% 0.90/0.63 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setI)).
% 0.90/0.63 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2set2propI)).
% 0.90/0.63 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdexE)).
% 0.90/0.63 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdallE)).
% 0.90/0.63 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inCongP)).
% 0.90/0.63 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', in__Cong)).
% 0.90/0.63 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyset__Cong)).
% 0.90/0.63 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoin__Cong)).
% 0.90/0.63 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powerset__Cong)).
% 0.90/0.63 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunion__Cong)).
% 0.90/0.63 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega__Cong)).
% 0.90/0.63 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI1)).
% 0.90/0.63 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset2)).
% 0.90/0.63 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset1)).
% 0.90/0.63 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI2)).
% 0.90/0.63 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetsubset)).
% 0.90/0.63 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE)).
% 0.90/0.63 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE2)).
% 0.90/0.63 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notsubsetI)).
% 0.90/0.63 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI1)).
% 0.90/0.63 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI2)).
% 0.90/0.63 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetRefl)).
% 0.90/0.63 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTrans)).
% 0.90/0.63 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub)).
% 0.90/0.63 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub2)).
% 0.90/0.63 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subset2powerset)).
% 0.90/0.63 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextsub)).
% 0.90/0.63 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetemptysetimpeq)).
% 0.90/0.63 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI1)).
% 0.90/0.63 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE1)).
% 0.90/0.63 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inPowerset)).
% 0.90/0.63 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetsubset)).
% 0.90/0.63 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIL)).
% 0.90/0.63 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2IR)).
% 0.90/0.63 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIR)).
% 0.90/0.63 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionEcases)).
% 0.90/0.63 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionE)).
% 0.90/0.63 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionLsub)).
% 0.90/0.63 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionRsub)).
% 0.90/0.63 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectI)).
% 0.90/0.63 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset5)).
% 0.90/0.63 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectEL)).
% 0.90/0.63 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectLsub)).
% 0.90/0.63 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset2)).
% 0.90/0.63 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset3)).
% 0.90/0.63 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectER)).
% 0.90/0.63 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', disjointsetsI1)).
% 0.90/0.63 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectRsub)).
% 0.90/0.63 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset4)).
% 0.90/0.63 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset1)).
% 0.90/0.63 thf(bs114d, axiom, ((bs114d)<=>![X4:$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)).
% 0.90/0.63 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusI)).
% 0.90/0.63 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusEL)).
% 0.90/0.63 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusER)).
% 0.90/0.63 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset2)).
% 0.90/0.63 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusERneg)).
% 0.90/0.63 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusELneg)).
% 0.90/0.63 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusILneg)).
% 0.90/0.63 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusIRneg)).
% 0.90/0.63 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusLsub)).
% 0.90/0.63 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset1)).
% 0.90/0.63 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffE)).
% 0.90/0.63 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI1)).
% 0.90/0.63 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI2)).
% 0.90/0.63 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg1)).
% 0.90/0.63 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg2)).
% 0.90/0.63 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', secondinupair)).
% 0.90/0.63 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIL)).
% 0.90/0.63 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIR)).
% 0.90/0.63 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairiskpair)).
% 0.90/0.63 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairp)).
% 0.90/0.63 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsubset)).
% 0.90/0.63 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowerset)).
% 0.90/0.63 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowunion)).
% 0.90/0.63 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2E)).
% 0.90/0.63 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsubunion)).
% 0.90/0.63 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairinpowunion)).
% 0.90/0.63 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem1)).
% 0.90/0.63 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem2)).
% 0.90/0.63 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem3)).
% 0.90/0.63 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairin)).
% 0.90/0.63 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$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)).
% 0.90/0.63 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair)).
% 0.90/0.63 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE2)).
% 0.90/0.63 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton1)).
% 0.90/0.63 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton2)).
% 0.90/0.63 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton)).
% 0.90/0.63 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsuniq)).
% 0.90/0.63 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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)).
% 0.90/0.63 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstpairEq)).
% 0.90/0.63 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstin)).
% 0.90/0.63 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL2)).
% 0.90/0.63 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL)).
% 0.90/0.63 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR11)).
% 0.90/0.63 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR12)).
% 0.90/0.63 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR1)).
% 0.90/0.63 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairequniteq)).
% 0.90/0.63 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)).
% 0.90/0.63 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)).
% 0.90/0.63 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndpairEq)).
% 0.90/0.63 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairsurjEq)).
% 0.90/0.63 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndin)).
% 0.90/0.63 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)).
% 0.90/0.63 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)).
% 0.90/0.63 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)).
% 0.90/0.63 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)).
% 0.90/0.63 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)).
% 0.90/0.63 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairsurjEq)).
% 0.90/0.63 thf(c_0_191, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X570:$i]:(((in @ X570 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X570 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 0.90/0.63 thf(c_0_192, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 0.90/0.63 thf(c_0_193, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 0.90/0.63 thf(c_0_194, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 0.90/0.63 thf(c_0_195, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 0.90/0.63 thf(c_0_196, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 0.90/0.63 thf(c_0_197, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 0.90/0.63 thf(c_0_198, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 0.90/0.63 thf(c_0_199, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 0.90/0.63 thf(c_0_200, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 0.90/0.63 thf(c_0_201, 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])).
% 0.90/0.63 thf(c_0_202, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 0.90/0.63 thf(c_0_203, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 0.90/0.63 thf(c_0_204, 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])).
% 0.90/0.63 thf(c_0_205, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 0.90/0.63 thf(c_0_206, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 0.90/0.63 thf(c_0_207, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 0.90/0.63 thf(c_0_208, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 0.90/0.63 thf(c_0_209, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 0.90/0.63 thf(c_0_210, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X570:$i]:(((in @ X570 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X570 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_192])).
% 0.90/0.63 thf(c_0_211, 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])).
% 0.90/0.63 thf(c_0_212, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 0.90/0.63 thf(c_0_213, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 0.90/0.63 thf(c_0_214, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.90/0.63 thf(c_0_215, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 0.90/0.63 thf(c_0_216, plain, ((dpsetconstr)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i > $i > $o]:(dsetconstr @ (cartprod @ Z0 @ Z1) @ (^[Z3/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&?[X3:$i]:((((in @ X3 @ Z1)&(Z2 @ X2 @ X3))&((Z3)=(kpair @ X2 @ X3))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstr])).
% 0.90/0.63 thf(c_0_217, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 0.90/0.63 thf(c_0_218, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X25:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 0.90/0.63 thf(c_0_219, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 0.90/0.63 thf(c_0_220, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X541:$i]:((((X6 @ X2 @ X541))&![X542:$i]:((((X6 @ X2 @ X542))=>((X541)=(X542)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_193, c_0_194])).
% 0.90/0.63 thf(c_0_221, plain, ((descrp)=(![X1:$i > $o]:(((?[X543:$i]:((((X1 @ X543))&![X544:$i]:((((X1 @ X544))=>((X543)=(X544)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_194])).
% 0.90/0.63 thf(c_0_222, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 0.90/0.63 thf(c_0_223, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 0.90/0.63 thf(c_0_224, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.90/0.63 thf(c_0_225, plain, ((exuE1)=(![X1:$i > $o]:(((?[X545:$i]:((((X1 @ X545))&![X546:$i]:((((X1 @ X546))=>((X545)=(X546)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_194])).
% 0.90/0.63 thf(c_0_226, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X547:$i]:((((X1 @ X547))&![X548:$i]:((((X1 @ X548))=>((X547)=(X548)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_197, c_0_194])).
% 0.90/0.63 thf(c_0_227, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 0.90/0.63 thf(c_0_228, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_198])).
% 0.90/0.63 thf(c_0_229, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_199, c_0_198])).
% 0.90/0.63 thf(c_0_230, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_198])).
% 0.90/0.63 thf(c_0_231, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 0.90/0.63 thf(c_0_232, plain, ((exuE2)=(![X1:$i > $o]:(((?[X549:$i]:((((X1 @ X549))&![X550:$i]:((((X1 @ X550))=>((X549)=(X550)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_200, c_0_194])).
% 0.90/0.63 thf(c_0_233, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_198])).
% 0.90/0.63 thf(c_0_234, 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])).
% 0.90/0.63 thf(c_0_235, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X551:$i]:((((X1 @ X551))&![X552:$i]:((((X1 @ X552))=>((X551)=(X552))))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_194])).
% 0.90/0.63 thf(c_0_236, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X553:$i]:((((X1 @ X553))&![X554:$i]:((((X1 @ X554))=>((X553)=(X554)))))))))))), inference(apply_def,[status(thm)],[c_0_202, c_0_194])).
% 0.90/0.63 thf(c_0_237, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X555:$i]:((((X1 @ X555))&![X556:$i]:((((X1 @ X556))=>((X555)=(X556))))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_194])).
% 0.90/0.63 thf(c_0_238, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X557:$i]:((((X1 @ X557))&![X558:$i]:((((X1 @ X558))=>((X557)=(X558)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_204, c_0_194])).
% 0.90/0.63 thf(c_0_239, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X559:$i]:((((X1 @ X559))&![X560:$i]:((((X1 @ X560))=>((X559)=(X560)))))))<=>(?[X561:$i]:((((X17 @ X561))&![X562:$i]:((((X17 @ X562))=>((X561)=(X562)))))))))))), inference(apply_def,[status(thm)],[c_0_205, c_0_194])).
% 0.90/0.63 thf(c_0_240, plain, ((exuEu)=(![X1:$i > $o]:(((?[X563:$i]:((((X1 @ X563))&![X564:$i]:((((X1 @ X564))=>((X563)=(X564)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_206, c_0_194])).
% 0.90/0.63 thf(c_0_241, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X565:$i]:((((X1 @ X565))&![X566:$i]:((((X1 @ X566))=>((X565)=(X566)))))))=>((?[X567:$i]:((((X17 @ X567))&![X568:$i]:((((X17 @ X568))=>((X567)=(X568)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_207, c_0_194])).
% 0.90/0.63 thf(c_0_242, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 0.90/0.63 thf(c_0_243, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 0.90/0.63 thf(c_0_244, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 0.90/0.63 thf(c_0_245, 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)))=>(?[X569:$i]:(((in @ X569 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X569 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_208, c_0_192])).
% 0.90/0.63 thf(c_0_246, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X571:$i]:(((in @ X571 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X571 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_209, c_0_210])).
% 0.90/0.63 thf(c_0_247, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X572:$i]:(((in @ X572 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X572 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_211, c_0_210])).
% 0.90/0.63 thf(c_0_248, 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)))=>(?[X573:$i]:(((in @ X573 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X573 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_212, c_0_210])).
% 0.90/0.63 thf(c_0_249, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X574:$i]:(((in @ X574 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X574 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_213, c_0_192])).
% 0.90/0.63 thf(c_0_250, axiom, ((theprop)=(![X21:$i]:(((?[X575:$i]:(((in @ X575 @ X21)&((X21)=(setadjoin @ X575 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_192])).
% 0.90/0.63 thf(c_0_251, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X576:$i]:(((in @ X576 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X576 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_214, c_0_192])).
% 0.90/0.63 thf(c_0_252, plain, ((dpsetconstrI)=(![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dsetconstr @ (cartprod @ X4 @ X5) @ (^[Z0/* 5 */:$i]:(?[X577:$i]:(((in @ X577 @ X4)&?[X578:$i]:((((in @ X578 @ X5)&((X23 @ X577 @ X578)))&((Z0)=(kpair @ X577 @ X578))))))))))))))))), inference(apply_def,[status(thm)],[c_0_215, c_0_216])).
% 0.90/0.63 thf(c_0_253, plain, ((dpsetconstrSub)=(![X4:$i, X5:$i, X24:$i > $i > $o]:((subset @ (dsetconstr @ (cartprod @ X4 @ X5) @ (^[Z0/* 5 */:$i]:(?[X579:$i]:(((in @ X579 @ X4)&?[X580:$i]:((((in @ X580 @ X5)&((X24 @ X579 @ X580)))&((Z0)=(kpair @ X579 @ X580))))))))) @ (cartprod @ X4 @ X5))))), inference(apply_def,[status(thm)],[c_0_217, c_0_216])).
% 0.90/0.63 thf(c_0_254, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X25:$i > $i > $o]:(((subset @ (dsetconstr @ (cartprod @ X4 @ X5) @ (^[Z0/* 5 */:$i]:(?[X581:$i]:(((in @ X581 @ X4)&?[X582:$i]:((((in @ X582 @ X5)&((X25 @ X581 @ X582)))&((Z0)=(kpair @ X581 @ X582))))))))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_218, c_0_219]), c_0_216])).
% 0.90/0.63 thf(c_0_255, plain, ((epred1_0)<=>![X612:$i]:(?[X613:$i]:((((![X614:$i]:(((in @ X614 @ X613)=>![X615:$i]:(((in @ X615 @ X614)=>(in @ X615 @ X612)))))&![X616:$i, X617:$i]:((((in @ X616 @ X612)&(in @ X617 @ X612))=>(![X618:$i]:(((in @ X618 @ X613)=>((in @ X616 @ X618)<=>(in @ X617 @ X618))))=>((X616)=(X617))))))&![X619:$i, X620:$i]:((((in @ X619 @ X613)&(in @ X620 @ X613))=>(![X621:$i]:(((in @ X621 @ X619)=>(in @ X621 @ X620)))|![X622:$i]:(((in @ X622 @ X620)=>(in @ X622 @ X619)))))))&![X623:$i]:(((![X624:$i]:(((in @ X624 @ X623)=>(in @ X624 @ X612)))&?[X625:$i]:((in @ X625 @ X623)))=>?[X626:$i, X627:$i]:(((((in @ X626 @ X613)&(in @ X627 @ X623))&~(?[X628:$i]:(((in @ X628 @ X626)&(in @ X628 @ X623)))))&![X629:$i]:(((in @ X629 @ X613)=>(![X630:$i]:(((in @ X630 @ X629)=>(in @ X630 @ X626)))|(in @ X627 @ X629)))))))))))), introduced(definition)).
% 0.90/0.63 thf(c_0_256, negated_conjecture, ~((![X583:$i, X584:$i]:((![X585:$i]:(((in @ X585 @ X583)<=>(in @ X585 @ X584)))=>((X583)=(X584))))=>(![X586:$i]:(~(in @ X586 @ emptyset))=>(![X587:$i, X588:$i, X589:$i]:(((in @ X589 @ (setadjoin @ X587 @ X588))<=>(((X589)=(X587))|(in @ X589 @ X588))))=>(![X590:$i, X591:$i]:(((in @ X591 @ (powerset @ X590))<=>![X592:$i]:(((in @ X592 @ X591)=>(in @ X592 @ X590)))))=>(![X593:$i, X594:$i]:(((in @ X594 @ (setunion @ X593))<=>?[X595:$i]:(((in @ X594 @ X595)&(in @ X595 @ X593)))))=>((in @ emptyset @ omega)=>(![X596:$i]:(((in @ X596 @ omega)=>(in @ (setadjoin @ X596 @ X596) @ omega)))=>(![X597:$i]:((((in @ emptyset @ X597)&![X598:$i]:((((in @ X598 @ omega)&(in @ X598 @ X597))=>(in @ (setadjoin @ X598 @ X598) @ X597))))=>![X599:$i]:(((in @ X599 @ omega)=>(in @ X599 @ X597)))))=>(![X600:$i > $i > $o, X601:$i]:((![X602:$i]:(((in @ X602 @ X601)=>?[X603:$i]:(((X600 @ X602 @ X603)&![X604:$i]:(((X600 @ X602 @ X604)=>((X603)=(X604))))))))=>?[X605:$i]:(![X606:$i]:(((in @ X606 @ X605)<=>?[X607:$i]:(((in @ X607 @ X601)&(X600 @ X607 @ X606))))))))=>(![X608:$i]:((?[X609:$i]:((in @ X609 @ X608))=>?[X610:$i]:(((in @ X610 @ X608)&~(?[X611:$i]:(((in @ X611 @ X610)&(in @ X611 @ X608))))))))=>((epred1_0)=>(![X631:$i > $o]:((?[X632:$i]:(((X631 @ X632)&![X633:$i]:(((X631 @ X633)=>((X632)=(X633))))))=>(X631 @ (descr @ (^[Z0/* 17 */:$i]:(X631 @ Z0))))))=>(![X634:$i, X635:$i > $o, X636:$i]:(((in @ X636 @ X634)=>((X635 @ X636)=>(in @ X636 @ (dsetconstr @ X634 @ X635)))))=>(![X637:$i, X638:$i > $o, X639:$i]:(((in @ X639 @ (dsetconstr @ X637 @ X638))=>(in @ X639 @ X637)))=>(![X640:$i, X641:$i > $o, X642:$i]:(((in @ X642 @ (dsetconstr @ X640 @ X641))=>(X641 @ X642)))=>(![X643:$i > $o]:((?[X644:$i]:(((X643 @ X644)&![X645:$i]:(((X643 @ X645)=>((X644)=(X645))))))=>?[X646:$i]:(((X643 @ X646)&![X647:$i]:(((X643 @ X647)=>((X646)=(X647))))))))=>(![X648:$o, X649:$i]:(((in @ X649 @ (prop2set @ ((X648))))=>(X648)))=>(![X650:$i]:(((in @ X650 @ emptyset)=>![X651:$o]:((X651))))=>(![X652:$i]:(((in @ X652 @ emptyset)=>~($true)))=>(![X653:$i]:(~(in @ X653 @ emptyset))=>(![X654:$i > $o]:((?[X655:$i]:(((X654 @ X655)&![X656:$i]:(((X654 @ X656)=>((X655)=(X656))))))=>?[X657:$i]:((X654 @ X657))))=>(![X658:$i, X659:$i]:((![X660:$i]:(((in @ X660 @ X658)=>(in @ X660 @ X659)))=>(![X661:$i]:(((in @ X661 @ X659)=>(in @ X661 @ X658)))=>((X658)=(X659)))))=>(![X662:$i]:((![X663:$i]:(~(in @ X663 @ X662))=>((X662)=(emptyset))))=>(![X664:$i]:((![X665:$i]:(~(in @ X665 @ X664))=>((X664)=(emptyset))))=>(![X666:$i, X667:$i > $o, X668:$i]:(((in @ X668 @ X666)=>((in @ X668 @ (dsetconstr @ X666 @ X667))<=>(X667 @ X668))))=>(![X669:$i]:((((X669)!=(emptyset))=>?[X670:$i]:((in @ X670 @ X669))))=>(![X671:$i, X672:$i > $o, X673:$i]:(((in @ X673 @ X671)=>((X672 @ X673)=>((dsetconstr @ X671 @ X672)!=(emptyset)))))=>(![X674:$i]:((?[X675:$i]:((in @ X675 @ X674))=>((X674)!=(emptyset))))=>(![X676:$i, X677:$i]:((in @ X676 @ (setadjoin @ X676 @ X677)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X678:$i, X679:$i, X680:$i]:(((in @ X680 @ X679)=>(in @ X680 @ (setadjoin @ X678 @ X679))))=>(![X681:$i, X682:$i, X683:$i]:(((in @ X683 @ (setadjoin @ X681 @ X682))=>![X684:$o]:(((((X683)=(X681))=>(X684))=>(((in @ X683 @ X682)=>(X684))=>(X684))))))=>(![X685:$i, X686:$i, X687:$i]:(((in @ X687 @ (setadjoin @ X685 @ X686))=>(((X687)=(X685))|(in @ X687 @ X686))))=>(![X688:$i]:(((dsetconstr @ X688 @ (^[Z0/* 1 */:$i]:($true)))=(X688)))=>(![X689:$i, X690:$i]:((![X691:$i]:(((in @ X691 @ X690)=>(in @ X691 @ X689)))=>(in @ X690 @ (powerset @ X689))))=>(![X692:$i]:((in @ emptyset @ (powerset @ X692)))=>(![X693:$i]:((in @ emptyset @ (powerset @ X693)))=>(![X694:$i, X695:$i, X696:$i]:(((in @ X695 @ (powerset @ X694))=>((in @ X696 @ X695)=>(in @ X696 @ X694))))=>(![X697:$i, X698:$i, X699:$i]:(((in @ X698 @ X699)=>((in @ X699 @ X697)=>(in @ X698 @ (setunion @ X697)))))=>(![X700:$i, X701:$i]:(((in @ X701 @ (setunion @ X700))=>![X702:$o]:((![X703:$i]:(((in @ X701 @ X703)=>((in @ X703 @ X700)=>(X702))))=>(X702)))))=>(![X704:$i, X705:$i]:(((in @ X705 @ X704)=>(in @ X705 @ (powerset @ (setunion @ X704)))))=>(![X706:$i > $o]:((?[X707:$i]:(((X706 @ X707)&![X708:$i]:(((X706 @ X708)=>((X707)=(X708))))))=>?[X709:$i]:(![X710:$i]:(((X706 @ X710)<=>((X710)=(X709)))))))=>(![X711:$i]:((((X711)!=(emptyset))=>?[X712:$i]:(((in @ X712 @ X711)&$true))))=>(![X713:$i, X714:$i]:(((in @ X713 @ (setadjoin @ X714 @ emptyset))=>((X713)=(X714))))=>(![X715:$i, X716:$i]:((((X715)!=(X716))=>~(in @ X716 @ (setadjoin @ X715 @ emptyset))))=>(![X717:$i, X718:$i]:((((X717)=(X718))=>(in @ X717 @ (setadjoin @ X718 @ emptyset))))=>(![X719:$i, X720:$i]:(((in @ X719 @ (setadjoin @ X720 @ emptyset))=>(in @ X720 @ (setadjoin @ X719 @ emptyset))))=>(![X721:$i, X722:$i, X723:$i]:(((in @ X723 @ (setadjoin @ X721 @ (setadjoin @ X722 @ emptyset)))=>(((X723)=(X721))|((X723)=(X722)))))=>(![X724:$i, X725:$i]:((in @ X724 @ (setadjoin @ X724 @ (setadjoin @ X725 @ emptyset))))=>(![X726:$i, X727:$i]:((in @ X727 @ (setadjoin @ X726 @ (setadjoin @ X727 @ emptyset))))=>(![X728:$i, X729:$i > $o]:((?[X730:$i]:(((in @ X730 @ X728)&(X729 @ X730)))=>(((dsetconstr @ X728 @ X729)=(emptyset))=>~($true))))=>(![X731:$i > $o, X732:$i]:(((in @ X732 @ emptyset)=>(X731 @ X732)))=>(![X733:$i, X734:$i > $o]:((~(![X735:$i]:(((in @ X735 @ X733)=>(X734 @ X735))))=>?[X736:$i]:(((in @ X736 @ X733)&~((X734 @ X736))))))=>(![X737:$i, X738:$i > $o]:((![X739:$i]:(((in @ X739 @ X737)=>~((X738 @ X739))))=>~(?[X740:$i]:(((in @ X740 @ X737)&(X738 @ X740))))))=>(![X741:$i, X742:$i > $o]:((~(?[X743:$i]:(((in @ X743 @ X741)&(X742 @ X743))))=>![X744:$i]:(((in @ X744 @ X741)=>~((X742 @ X744))))))=>(![X745:$i, X746:$i > $o]:((?[X747:$i]:(((in @ X747 @ X745)&~((X746 @ X747))))=>~(![X748:$i]:(((in @ X748 @ X745)=>(X746 @ X748))))))=>(![X749:$o]:(((X749)=>(in @ emptyset @ (prop2set @ ((X749))))))=>(![X750:$o]:(((X750)=>(set2prop @ (prop2set @ ((X750))))))=>(![X751:$i, X752:$i > $o]:((~(?[X753:$i]:(((in @ X753 @ X751)&(X752 @ X753))))=>![X754:$i]:(((in @ X754 @ X751)=>~((X752 @ X754))))))=>(![X755:$i, X756:$i > $o]:((~(![X757:$i]:(((in @ X757 @ X755)=>(X756 @ X757))))=>?[X758:$i]:(((in @ X758 @ X755)&~((X756 @ X758))))))=>(![X759:$i > $o]:((?[X760:$i]:(((X759 @ X760)&![X761:$i]:(((X759 @ X761)=>((X760)=(X761))))))=>?[X762:$i]:(((X759 @ X762)&![X763:$i]:(((X759 @ X763)=>((X762)=(X763))))))))=>(![X764:$i > $o]:((?[X765:$i]:((X764 @ X765))=>(![X766:$i, X767:$i]:(((X764 @ X766)=>((X764 @ X767)=>((X766)=(X767)))))=>?[X768:$i]:(((X764 @ X768)&![X769:$i]:(((X764 @ X769)=>((X768)=(X769)))))))))=>(![X770:$i > $o]:((?[X771:$i]:(![X772:$i]:(((X770 @ X772)<=>((X772)=(X771)))))=>?[X773:$i]:(((X770 @ X773)&![X774:$i]:(((X770 @ X774)=>((X773)=(X774))))))))=>(![X775:$i, X776:$i]:((((X775)=(X776))=>![X777:$i, X778:$i]:((((X777)=(X778))=>((in @ X777 @ X775)=>(in @ X778 @ X776))))))=>(![X779:$i, X780:$i]:((((X779)=(X780))=>![X781:$i, X782:$i]:((((X781)=(X782))=>((in @ X781 @ X779)<=>(in @ X782 @ X780))))))=>(![X783:$i > $o]:((?[X784:$i]:(((X783 @ X784)&![X785:$i]:(((X783 @ X785)=>((X784)=(X785))))))=>![X786:$i, X787:$i]:(((X783 @ X786)=>((X783 @ X787)=>((X786)=(X787)))))))=>(![X788:$i > $o, X789:$i > $o]:((![X790:$i, X791:$i]:((((X790)=(X791))=>((X788 @ X790)<=>(X789 @ X791))))=>(?[X792:$i]:(((X788 @ X792)&![X793:$i]:(((X788 @ X793)=>((X792)=(X793))))))<=>?[X794:$i]:(((X789 @ X794)&![X795:$i]:(((X789 @ X795)=>((X794)=(X795)))))))))=>(((emptyset)=(emptyset))=>(![X796:$i, X797:$i]:((((X796)=(X797))=>![X798:$i, X799:$i]:((((X798)=(X799))=>((setadjoin @ X796 @ X798)=(setadjoin @ X797 @ X799))))))=>(![X800:$i, X801:$i]:((((X800)=(X801))=>((powerset @ X800)=(powerset @ X801))))=>(![X802:$i, X803:$i]:((((X802)=(X803))=>((setunion @ X802)=(setunion @ X803))))=>(((omega)=(omega))=>(![X804:$i > $o]:((?[X805:$i]:(((X804 @ X805)&![X806:$i]:(((X804 @ X806)=>((X805)=(X806))))))=>![X807:$i, X808:$i]:(((X804 @ X807)=>((X804 @ 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X836:$i]:(((subset @ X834 @ X835)=>((in @ X836 @ X834)=>(in @ X836 @ X835))))=>(![X837:$i, X838:$i, X839:$i]:(((subset @ X837 @ X838)=>(~(in @ X839 @ X838)=>~(in @ X839 @ X837))))=>(![X840:$i, X841:$i, X842:$i]:(((in @ X842 @ X840)=>(~(in @ X842 @ X841)=>~(subset @ X840 @ X841))))=>(![X843:$i, X844:$i]:((~(subset @ X843 @ X844)=>((X843)!=(X844))))=>(![X845:$i, X846:$i, X847:$i]:(((in @ X847 @ X845)=>(~(in @ X847 @ X846)=>((X845)!=(X846)))))=>(![X848:$i]:((subset @ X848 @ X848))=>(![X849:$i, X850:$i, X851:$i]:(((subset @ X849 @ X850)=>((subset @ X850 @ X851)=>(subset @ X849 @ X851))))=>(![X852:$i, X853:$i]:((subset @ X853 @ (setadjoin @ X852 @ X853)))=>(![X854:$i, X855:$i, X856:$i]:(((subset @ X854 @ X856)=>(subset @ X854 @ (setadjoin @ X855 @ X856))))=>(![X857:$i, X858:$i]:(((subset @ X857 @ X858)=>(in @ X857 @ (powerset @ X858))))=>(![X859:$i, X860:$i]:(((subset @ X859 @ X860)=>((subset @ X860 @ X859)=>((X859)=(X860)))))=>(![X861:$i]:(((subset @ X861 @ 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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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[dpsetconstrERa])]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_220]), foundationAx]), wellorderingAx]), c_0_221]), c_0_222]), c_0_223]), c_0_224]), c_0_225]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_226]), setext]), emptyI]), noeltsimpempty]), c_0_227]), c_0_228]), c_0_229]), c_0_230]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_231]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_232]), c_0_233]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_234]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_235]), c_0_236]), c_0_237]), inCongP]), in__Cong]), c_0_238]), c_0_239]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_240]), c_0_241]), c_0_242]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_243]), c_0_244]), 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_245]), c_0_246]), c_0_247]), c_0_248]), singletonsuniq]), setukpairinjL1]), c_0_249]), c_0_250]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_251]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_216]), c_0_252]), c_0_253]), c_0_254])])]), c_0_255])).
% 0.90/0.63 thf(c_0_257, negated_conjecture, ![X1135:$i, X1136:$i, X1138:$i, X1139:$i, X1140:$i, X1141:$i, X1142:$i, X1143:$i, X1144:$i, X1145:$i, X1146:$i, X1148:$i, X1149:$i, X1151:$i, X1152:$i, X1153:$i, X1154:$i, X1155:$i, X1157:$i, X1158:$i > $i > $o, X1159:$i, X1161:$i, X1164:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1171:$i, X1172:$i > $o, X1173:$i, X1175:$i, X1176:$i > $o, X1177:$i, X1178:$i, X1179:$i > $o, X1180:$i, X1181:$i, X1182:$i > $o, X1183:$i, X1184:$i > $o, X1185:$i, X1188:$i, X1189:$o, X1190:$i, X1191:$i, X1192:$o, X1193:$i, X1194:$i, X1195:$i > $o, X1196:$i, X1199:$i, X1200:$i, X1203:$i, X1205:$i, X1207:$i, X1208:$i > $o, X1209:$i, X1210:$i, X1212:$i, X1213:$i > $o, X1214:$i, X1215:$i, X1216:$i, X1217:$i, X1218:$i, X1219:$i, X1220:$i, X1221:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$o, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$i, X1241:$i, X1242:$i, X1243:$o, X1245:$i, X1246:$i, X1247:$i > $o, X1248:$i, X1251:$i, X1252:$i, X1253:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$i, X1259:$i, X1260:$i, X1261:$i, X1262:$i, X1263:$i, X1264:$i, X1265:$i, X1266:$i, X1267:$i, X1268:$i, X1269:$i, X1270:$i, X1271:$i > $o, X1272:$i, X1273:$i > $o, X1274:$i, X1275:$i, X1276:$i > $o, X1277:$i, X1279:$i, X1280:$i > $o, X1282:$i, X1283:$i, X1284:$i > $o, X1286:$i, X1287:$i, X1288:$i > $o, X1289:$i, X1291:$o, X1292:$o, X1293:$i, X1294:$i > $o, X1296:$i, X1297:$i, X1298:$i > $o, X1299:$i, X1301:$i > $o, X1302:$i, X1305:$i, X1306:$i > $o, X1307:$i, X1311:$i, X1312:$i > $o, X1313:$i, X1316:$i, X1317:$i, X1318:$i, X1319:$i, X1320:$i, X1321:$i, X1322:$i, X1323:$i, X1324:$i, X1325:$i > $o, X1326:$i, X1328:$i, X1329:$i, X1330:$i > $o, X1331:$i > $o, X1334:$i, X1337:$i, X1338:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1345:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i > $o, X1351:$i, X1353:$i, X1354:$i, X1355:$i > $o, X1356:$i > $o, X1359:$i, X1361:$i, X1363:$i, X1364:$i, X1365:$i > $o, X1366:$i > $o, X1369:$i, X1370:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i, X1384:$i, X1385:$i, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i > $o, X1417:$i, X1418:$i > $o, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$o, X1431:$i, X1432:$i, X1433:$i, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$i, X1446:$i, X1447:$i, X1448:$i, X1449:$i, X1450:$i, X1451:$i, X1452:$i, X1453:$i, X1454:$i, X1455:$i, X1456:$i, X1457:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$i, X1473:$i, X1474:$i, X1475:$i, X1476:$i, X1477:$i, X1478:$i, X1479:$i, X1480:$i, X1481:$i, X1482:$i, X1483:$i, X1484:$i, X1485:$i, X1486:$i, X1487:$i, X1488:$i, X1489:$i, X1490:$i, X1491:$i, X1492:$i, X1493:$i, X1494:$i, X1495:$i, X1496:$i, X1497:$i, X1498:$o, X1499:$i, X1500:$i, X1501:$i, X1502:$i, X1503:$i, X1504:$i, X1505:$i, X1506:$i, X1507:$i, X1508:$i, X1509:$i, X1510:$i, X1511:$i, X1512:$i, X1513:$i, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i > $o, X1573:$i, X1575:$i, X1576:$i > $o, X1577:$i, X1579:$i, X1580:$i > $o, X1581:$i, X1584:$i, X1585:$i > $o, X1588:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1597:$i, X1598:$i, X1599:$i, X1600:$i, X1601:$i, X1602:$i, X1603:$i, X1604:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1611:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1647:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i > $i > $o, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i > $i > $o, X1670:$i, X1671:$i, X1672:$i > $i > $o]:((((~(in @ (esk1_2 @ X1135 @ X1136) @ X1135)|~(in @ (esk1_2 @ X1135 @ X1136) @ X1136)|((X1135)=(X1136)))&((in @ (esk1_2 @ X1135 @ X1136) @ X1135)|(in @ (esk1_2 @ X1135 @ X1136) @ X1136)|((X1135)=(X1136))))&(~(in @ X1138 @ emptyset)&(((~(in @ X1141 @ (setadjoin @ X1139 @ X1140))|(((X1141)=(X1139))|(in @ X1141 @ X1140)))&((((X1141)!=(X1139))|(in @ X1141 @ (setadjoin @ X1139 @ X1140)))&(~(in @ X1141 @ X1140)|(in @ X1141 @ (setadjoin @ X1139 @ X1140)))))&(((~(in @ X1143 @ (powerset @ X1142))|(~(in @ X1144 @ X1143)|(in @ X1144 @ X1142)))&(((in @ (esk2_2 @ X1145 @ X1146) @ X1146)|(in @ X1146 @ (powerset @ X1145)))&(~(in @ (esk2_2 @ X1145 @ X1146) @ X1145)|(in @ X1146 @ (powerset @ X1145)))))&(((((in @ X1149 @ (esk3_2 @ X1148 @ X1149))|~(in @ X1149 @ (setunion @ X1148)))&((in @ (esk3_2 @ X1148 @ X1149) @ X1148)|~(in @ X1149 @ (setunion @ X1148))))&(~(in @ X1152 @ X1153)|~(in @ X1153 @ X1151)|(in @ X1152 @ (setunion @ X1151))))&((in @ emptyset @ omega)&((~(in @ X1154 @ omega)|(in @ (setadjoin @ X1154 @ X1154) @ omega))&(((((in @ 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@ X1548)|(in @ (kpair @ X1549 @ X1550) @ (powerset @ (powerset @ (binunion @ X1547 @ X1548))))))&((~(in @ X1553 @ X1551)|(~(in @ X1554 @ X1552)|(in @ (kpair @ X1553 @ X1554) @ (cartprod @ X1551 @ X1552))))&((((in @ (esk55_3 @ X1555 @ X1556 @ X1557) @ X1555)|~(in @ X1557 @ (cartprod @ X1555 @ X1556)))&(((in @ (esk56_3 @ X1555 @ X1556 @ X1557) @ X1556)|~(in @ X1557 @ (cartprod @ X1555 @ X1556)))&(((X1557)=(kpair @ (esk55_3 @ X1555 @ X1556 @ X1557) @ (esk56_3 @ X1555 @ X1556 @ X1557)))|~(in @ X1557 @ (cartprod @ X1555 @ X1556)))))&((~(in @ X1562 @ (cartprod @ X1560 @ X1561))|(iskpair @ X1562))&((((in @ (esk57_2 @ X1563 @ X1564) @ X1563)|~(in @ X1564 @ (setunion @ X1563)))&((in @ X1564 @ (esk57_2 @ X1563 @ X1564))|~(in @ X1564 @ (setunion @ X1563))))&((subset @ (setunion @ (setadjoin @ X1566 @ emptyset)) @ X1566)&((subset @ X1567 @ (setunion @ (setadjoin @ X1567 @ emptyset)))&(((setunion @ (setadjoin @ X1568 @ emptyset))=(X1568))&(((((in @ (esk60_2 @ X1569 @ X1570) @ (dsetconstr @ X1569 @ X1570))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|(in @ (esk58_2 @ X1569 @ X1570) @ X1569))&(((dsetconstr @ X1569 @ X1570)=(setadjoin @ (esk60_2 @ X1569 @ X1570) @ emptyset))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|(in @ (esk58_2 @ X1569 @ X1570) @ X1569)))&((((in @ (esk60_2 @ X1569 @ X1570) @ (dsetconstr @ X1569 @ X1570))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|(in @ (esk59_2 @ X1569 @ X1570) @ X1569))&(((dsetconstr @ X1569 @ X1570)=(setadjoin @ (esk60_2 @ X1569 @ X1570) @ emptyset))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|(in @ (esk59_2 @ X1569 @ X1570) @ X1569)))&((((in @ (esk60_2 @ X1569 @ X1570) @ (dsetconstr @ X1569 @ X1570))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|(X1570 @ (esk58_2 @ X1569 @ X1570)))&(((dsetconstr @ X1569 @ X1570)=(setadjoin @ (esk60_2 @ X1569 @ X1570) @ emptyset))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|(X1570 @ (esk58_2 @ X1569 @ X1570))))&((((in @ (esk60_2 @ X1569 @ X1570) @ (dsetconstr @ X1569 @ X1570))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|(X1570 @ (esk59_2 @ X1569 @ X1570)))&(((dsetconstr @ X1569 @ X1570)=(setadjoin @ (esk60_2 @ X1569 @ X1570) @ emptyset))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|(X1570 @ (esk59_2 @ X1569 @ X1570))))&(((in @ (esk60_2 @ X1569 @ X1570) @ (dsetconstr @ X1569 @ X1570))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|((esk58_2 @ X1569 @ X1570)!=(esk59_2 @ X1569 @ X1570)))&(((dsetconstr @ X1569 @ X1570)=(setadjoin @ (esk60_2 @ X1569 @ X1570) @ emptyset))|(~(in @ X1573 @ X1569)|~(X1570 @ X1573))|((esk58_2 @ X1569 @ X1570)!=(esk59_2 @ X1569 @ X1570))))))))&((((in @ (esk61_2 @ X1575 @ X1576) @ X1575)|(~(in @ X1577 @ (dsetconstr @ X1575 @ X1576))|((dsetconstr @ X1575 @ X1576)!=(setadjoin @ X1577 @ emptyset))))&((X1576 @ (esk61_2 @ X1575 @ X1576))|(~(in @ X1577 @ (dsetconstr @ X1575 @ X1576))|((dsetconstr @ X1575 @ X1576)!=(setadjoin @ X1577 @ emptyset)))))&(((((in @ (esk63_3 @ X1579 @ X1580 @ X1581) @ (dsetconstr @ X1579 @ X1580))|(in @ (esk62_3 @ X1579 @ X1580 @ X1581) @ X1579)|~(X1580 @ X1581)|~(in @ X1581 @ X1579))&(((dsetconstr @ X1579 @ X1580)=(setadjoin @ (esk63_3 @ X1579 @ X1580 @ X1581) @ emptyset))|(in @ (esk62_3 @ X1579 @ X1580 @ X1581) @ X1579)|~(X1580 @ X1581)|~(in @ X1581 @ X1579)))&((((in @ (esk63_3 @ X1579 @ X1580 @ X1581) @ (dsetconstr @ X1579 @ X1580))|(X1580 @ (esk62_3 @ X1579 @ X1580 @ X1581))|~(X1580 @ X1581)|~(in @ X1581 @ X1579))&(((dsetconstr @ X1579 @ X1580)=(setadjoin @ (esk63_3 @ X1579 @ X1580 @ X1581) @ emptyset))|(X1580 @ (esk62_3 @ X1579 @ X1580 @ X1581))|~(X1580 @ X1581)|~(in @ X1581 @ X1579)))&(((in @ (esk63_3 @ X1579 @ X1580 @ X1581) @ (dsetconstr @ X1579 @ X1580))|((esk62_3 @ X1579 @ X1580 @ X1581)!=(X1581))|~(X1580 @ X1581)|~(in @ X1581 @ X1579))&(((dsetconstr @ X1579 @ X1580)=(setadjoin @ (esk63_3 @ X1579 @ X1580 @ X1581) @ emptyset))|((esk62_3 @ X1579 @ X1580 @ X1581)!=(X1581))|~(X1580 @ X1581)|~(in @ X1581 @ X1579)))))&(((((in @ (esk66_2 @ X1584 @ X1585) @ (dsetconstr @ X1584 @ X1585))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|(in @ (esk64_2 @ X1584 @ X1585) @ X1584))&(((dsetconstr @ X1584 @ X1585)=(setadjoin @ (esk66_2 @ X1584 @ X1585) @ emptyset))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|(in @ (esk64_2 @ X1584 @ X1585) @ X1584)))&((((in @ (esk66_2 @ X1584 @ X1585) @ (dsetconstr @ X1584 @ X1585))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|(in @ (esk65_2 @ X1584 @ X1585) @ X1584))&(((dsetconstr @ X1584 @ X1585)=(setadjoin @ (esk66_2 @ X1584 @ X1585) @ emptyset))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|(in @ (esk65_2 @ X1584 @ X1585) @ X1584)))&((((in @ (esk66_2 @ X1584 @ X1585) @ (dsetconstr @ X1584 @ X1585))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|(X1585 @ (esk64_2 @ X1584 @ X1585)))&(((dsetconstr @ X1584 @ X1585)=(setadjoin @ (esk66_2 @ X1584 @ X1585) @ emptyset))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|(X1585 @ (esk64_2 @ X1584 @ X1585))))&((((in @ (esk66_2 @ X1584 @ X1585) @ (dsetconstr @ X1584 @ X1585))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|(X1585 @ (esk65_2 @ X1584 @ X1585)))&(((dsetconstr @ X1584 @ X1585)=(setadjoin @ (esk66_2 @ X1584 @ X1585) @ emptyset))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|(X1585 @ (esk65_2 @ X1584 @ X1585))))&(((in @ (esk66_2 @ X1584 @ X1585) @ (dsetconstr @ X1584 @ X1585))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|((esk64_2 @ X1584 @ X1585)!=(esk65_2 @ X1584 @ X1585)))&(((dsetconstr @ X1584 @ X1585)=(setadjoin @ (esk66_2 @ X1584 @ X1585) @ emptyset))|(~(in @ X1588 @ X1584)|~(X1585 @ X1588))|((esk64_2 @ X1584 @ X1585)!=(esk65_2 @ X1584 @ X1585))))))))&((((setadjoin @ X1590 @ emptyset)!=(setadjoin @ X1591 @ emptyset))|((X1590)=(X1591)))&((~(in @ (setadjoin @ X1594 @ emptyset) @ (setadjoin @ (setadjoin @ X1592 @ emptyset) @ (setadjoin @ (setadjoin @ X1592 @ (setadjoin @ X1593 @ emptyset)) @ emptyset)))|((X1592)=(X1594)))&((((in @ (esk67_1 @ X1595) @ (dsetconstr @ (setunion @ X1595) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1595)))))|~(iskpair @ X1595))&(((dsetconstr @ (setunion @ X1595) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1595))))=(setadjoin @ (esk67_1 @ X1595) @ emptyset))|~(iskpair @ X1595)))&((~(in @ X1598 @ X1597)|((X1597)!=(setadjoin @ X1598 @ emptyset))|(in @ (setunion @ X1597) @ X1597))&(((kfst @ (kpair @ X1599 @ X1600))=(X1599))&((~(in @ X1603 @ (cartprod @ X1601 @ X1602))|(in @ (kfst @ X1603) @ X1601))&((((setadjoin @ (setadjoin @ X1604 @ emptyset) @ (setadjoin @ (setadjoin @ X1604 @ (setadjoin @ X1605 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1606 @ emptyset) @ (setadjoin @ (setadjoin @ X1606 @ (setadjoin @ X1607 @ emptyset)) @ emptyset)))|((X1604)=(X1606)))&((((kpair @ X1608 @ X1609)!=(kpair @ X1610 @ X1611))|((X1608)=(X1610)))&((((X1612)!=(X1613))|((setadjoin @ X1612 @ (setadjoin @ X1613 @ emptyset))=(setadjoin @ X1612 @ emptyset)))&((((X1614)!=(X1615))|((setadjoin @ (setadjoin @ X1614 @ emptyset) @ (setadjoin @ (setadjoin @ X1614 @ (setadjoin @ X1615 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1614 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1616 @ emptyset) @ (setadjoin @ (setadjoin @ X1616 @ (setadjoin @ X1617 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1618 @ emptyset) @ (setadjoin @ (setadjoin @ X1618 @ (setadjoin @ X1619 @ emptyset)) @ emptyset)))|(((X1618)!=(X1619))|((X1617)=(X1619))))&((((setadjoin @ X1620 @ (setadjoin @ X1621 @ emptyset))!=(setadjoin @ X1622 @ emptyset))|((X1620)=(X1621)))&((((setadjoin @ (setadjoin @ X1623 @ emptyset) @ (setadjoin @ (setadjoin @ X1623 @ (setadjoin @ X1624 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1625 @ emptyset) @ (setadjoin @ (setadjoin @ X1625 @ (setadjoin @ X1626 @ emptyset)) @ emptyset)))|((X1624)=(X1626)))&((((kpair @ X1627 @ X1628)!=(kpair @ X1629 @ X1630))|((X1628)=(X1630)))&((((in @ (esk68_1 @ X1631) @ (dsetconstr @ (setunion @ X1631) @ (^[Z0/* 3 */:$i]:(((X1631)=(kpair @ (kfst @ X1631) @ Z0))))))|~(iskpair @ X1631))&(((dsetconstr @ (setunion @ X1631) @ (^[Z0/* 3 */:$i]:(((X1631)=(kpair @ (kfst @ X1631) @ Z0)))))=(setadjoin @ (esk68_1 @ X1631) @ emptyset))|~(iskpair @ X1631)))&(((ksnd @ (kpair @ X1633 @ X1634))=(X1634))&((~(iskpair @ X1635)|((kpair @ (kfst @ X1635) @ (ksnd @ X1635))=(X1635)))&((~(in @ X1638 @ (cartprod @ X1636 @ X1637))|(in @ (ksnd @ X1638) @ X1637))&((~(in @ (kpair @ X1641 @ X1642) @ (cartprod @ X1639 @ X1640))|(in @ X1641 @ X1639))&((~(in @ (kpair @ X1645 @ X1646) @ (cartprod @ X1643 @ X1644))|(in @ X1646 @ X1644))&((~(in @ X1649 @ X1647)|(~(in @ X1650 @ X1648)|((kpair @ X1649 @ X1650)=(kpair @ X1649 @ X1650))))&((~(in @ X1653 @ X1651)|(~(in @ X1654 @ X1652)|((kfst @ (kpair @ X1653 @ X1654))=(X1653))))&((~(in @ X1657 @ X1655)|(~(in @ X1658 @ X1656)|((ksnd @ (kpair @ X1657 @ X1658))=(X1658))))&((~(in @ X1661 @ (cartprod @ X1659 @ X1660))|((kpair @ (kfst @ X1661) @ (ksnd @ X1661))=(X1661)))&((~(in @ X1665 @ X1662)|(~(in @ X1666 @ X1663)|(~(X1664 @ X1665 @ X1666)|(in @ (kpair @ X1665 @ X1666) @ (dsetconstr @ (cartprod @ X1662 @ X1663) @ (^[Z0/* 5 */:$i]:(?[X1121:$i]:(((in @ X1121 @ X1662)&?[X1122:$i]:((((in @ X1122 @ X1663)&X1664 @ X1121 @ X1122)&((Z0)=(kpair @ X1121 @ X1122)))))))))))))&((subset @ (dsetconstr @ (cartprod @ X1667 @ X1668) @ (^[Z0/* 5 */:$i]:(?[X1126:$i]:(((in @ X1126 @ X1667)&?[X1127:$i]:((((in @ X1127 @ X1668)&X1669 @ X1126 @ X1127)&((Z0)=(kpair @ X1126 @ X1127))))))))) @ (cartprod @ X1667 @ X1668))&((subset @ (dsetconstr @ (cartprod @ X1670 @ X1671) @ (^[Z0/* 5 */:$i]:(?[X1131:$i]:(((in @ X1131 @ X1670)&?[X1132:$i]:((((in @ X1132 @ X1671)&X1672 @ X1131 @ X1132)&((Z0)=(kpair @ X1131 @ X1132))))))))) @ (cartprod @ X1670 @ X1671))&((in @ esk71_0 @ esk69_0)&((in @ esk72_0 @ esk70_0)&((in @ (kpair @ esk71_0 @ esk72_0) @ (dsetconstr @ (cartprod @ esk69_0 @ esk70_0) @ (^[Z0/* 5 */:$i]:(?[X1133:$i]:(((in @ X1133 @ esk69_0)&?[X1134:$i]:((((in @ X1134 @ esk70_0)&epred2_0 @ X1133 @ X1134)&((Z0)=(kpair @ X1133 @ X1134))))))))))&~(epred2_0 @ esk71_0 @ esk72_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_256])])])])])])])).
% 0.90/0.63 thf(c_0_258, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_257])).
% 0.90/0.63 thf(c_0_259, negated_conjecture, (in @ (kpair @ esk71_0 @ esk72_0) @ (dsetconstr @ (cartprod @ esk69_0 @ esk70_0) @ (^[Z0/* 5 */:$i]:(?[X1701:$i]:(((in @ X1701 @ esk69_0)&?[X1702:$i]:((((in @ X1702 @ esk70_0)&(epred2_0 @ X1701 @ X1702))&((Z0)=(kpair @ X1701 @ X1702)))))))))), inference(split_conjunct,[status(thm)],[c_0_257])).
% 0.90/0.63 thf(c_0_260, negated_conjecture, ?[X1703:$i]:(((in @ X1703 @ esk69_0)&?[X1704:$i]:((((in @ X1704 @ esk70_0)&(epred2_0 @ X1703 @ X1704))&((kpair @ esk71_0 @ esk72_0)=(kpair @ X1703 @ X1704)))))), inference(spm,[status(thm)],[c_0_258, c_0_259])).
% 0.90/0.63 thf(c_0_261, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_257])).
% 0.90/0.63 thf(c_0_262, negated_conjecture, ((kpair @ esk71_0 @ esk72_0)=(kpair @ esk78_0 @ esk79_0)), inference(dynamic_cnf,[status(thm)],[c_0_260])).
% 0.90/0.63 thf(c_0_263, negated_conjecture, ((esk72_0)=(esk79_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_261, c_0_262]), c_0_261])).
% 0.90/0.63 thf(c_0_264, negated_conjecture, ~((epred2_0 @ esk71_0 @ esk72_0)), inference(split_conjunct,[status(thm)],[c_0_257])).
% 0.90/0.63 thf(c_0_265, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_257])).
% 0.90/0.63 thf(c_0_266, negated_conjecture, ((kpair @ esk71_0 @ esk79_0)=(kpair @ esk78_0 @ esk79_0)), inference(rw,[status(thm)],[c_0_262, c_0_263])).
% 0.90/0.63 thf(c_0_267, negated_conjecture, ~((epred2_0 @ esk71_0 @ esk79_0)), inference(rw,[status(thm)],[c_0_264, c_0_263])).
% 0.90/0.63 thf(c_0_268, negated_conjecture, ((esk71_0)=(esk78_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_265, c_0_266]), c_0_265])).
% 0.90/0.63 thf(c_0_269, negated_conjecture, (epred2_0 @ esk78_0 @ esk79_0), inference(dynamic_cnf,[status(thm)],[c_0_260])).
% 0.90/0.63 thf(c_0_270, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_267, c_0_268]), c_0_269])]), ['proof']).
% 0.90/0.63 # SZS output end CNFRefutation
% 0.90/0.63 # Parsed axioms : 408
% 0.90/0.63 # Removed by relevancy pruning/SinE : 0
% 0.90/0.63 # Initial clauses : 556
% 0.90/0.63 # Removed in clause preprocessing : 242
% 0.90/0.63 # Initial clauses in saturation : 314
% 0.90/0.63 # Processed clauses : 410
% 0.90/0.63 # ...of these trivial : 10
% 0.90/0.63 # ...subsumed : 32
% 0.90/0.63 # ...remaining for further processing : 368
% 0.90/0.63 # Other redundant clauses eliminated : 19
% 0.90/0.63 # Clauses deleted for lack of memory : 0
% 0.90/0.63 # Backward-subsumed : 0
% 0.90/0.63 # Backward-rewritten : 9
% 0.90/0.63 # Generated clauses : 140
% 0.90/0.63 # ...of the previous two non-redundant : 100
% 0.90/0.63 # ...aggressively subsumed : 0
% 0.90/0.63 # Contextual simplify-reflections : 0
% 0.90/0.63 # Paramodulations : 116
% 0.90/0.63 # Factorizations : 0
% 0.90/0.63 # NegExts : 0
% 0.90/0.63 # Equation resolutions : 20
% 0.90/0.63 # Disequality decompositions : 0
% 0.90/0.63 # Total rewrite steps : 75
% 0.90/0.63 # ...of those cached : 43
% 0.90/0.63 # Propositional unsat checks : 0
% 0.90/0.63 # Propositional check models : 0
% 0.90/0.63 # Propositional check unsatisfiable : 0
% 0.90/0.63 # Propositional clauses : 0
% 0.90/0.63 # Propositional clauses after purity: 0
% 0.90/0.63 # Propositional unsat core size : 0
% 0.90/0.63 # Propositional preprocessing time : 0.000
% 0.90/0.63 # Propositional encoding time : 0.000
% 0.90/0.63 # Propositional solver time : 0.000
% 0.90/0.63 # Success case prop preproc time : 0.000
% 0.90/0.63 # Success case prop encoding time : 0.000
% 0.90/0.63 # Success case prop solver time : 0.000
% 0.90/0.63 # Current number of processed clauses : 71
% 0.90/0.63 # Positive orientable unit clauses : 35
% 0.90/0.63 # Positive unorientable unit clauses: 0
% 0.90/0.63 # Negative unit clauses : 1
% 0.90/0.63 # Non-unit-clauses : 35
% 0.90/0.63 # Current number of unprocessed clauses: 271
% 0.90/0.63 # ...number of literals in the above : 872
% 0.90/0.63 # Current number of archived formulas : 0
% 0.90/0.63 # Current number of archived clauses : 281
% 0.90/0.63 # Clause-clause subsumption calls (NU) : 12737
% 0.90/0.63 # Rec. Clause-clause subsumption calls : 5385
% 0.90/0.63 # Non-unit clause-clause subsumptions : 26
% 0.90/0.63 # Unit Clause-clause subsumption calls : 78
% 0.90/0.63 # Rewrite failures with RHS unbound : 0
% 0.90/0.63 # BW rewrite match attempts : 18
% 0.90/0.63 # BW rewrite match successes : 5
% 0.90/0.63 # Condensation attempts : 410
% 0.90/0.63 # Condensation successes : 6
% 0.90/0.63 # Termbank termtop insertions : 55496
% 0.90/0.63 # Search garbage collected termcells : 18178
% 0.90/0.63
% 0.90/0.63 # -------------------------------------------------
% 0.90/0.63 # User time : 0.100 s
% 0.90/0.63 # System time : 0.015 s
% 0.90/0.63 # Total time : 0.115 s
% 0.90/0.63 # Maximum resident set size: 5948 pages
% 0.90/0.63
% 0.90/0.63 # -------------------------------------------------
% 0.90/0.63 # User time : 0.109 s
% 0.90/0.63 # System time : 0.019 s
% 0.90/0.63 # Total time : 0.128 s
% 0.90/0.63 # Maximum resident set size: 2208 pages
% 0.90/0.63 % E---3.1 exiting
% 0.90/0.63 % E exiting
%------------------------------------------------------------------------------