TSTP Solution File: SEU665^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU665^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:28:58 EDT 2024
% Result : Theorem 1.05s 0.70s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU665^1 : TPTP v8.2.0. Released v3.7.0.
% 0.07/0.14 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n005.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun May 19 18:18:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.21/0.49 Running higher-order theorem proving
% 0.21/0.49 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.05/0.70 # Version: 3.1.0-ho
% 1.05/0.70 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.05/0.70 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.70 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.05/0.70 # Starting pre_casc_3 with 300s (1) cores
% 1.05/0.70 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.05/0.70 # Starting full_lambda_10 with 300s (1) cores
% 1.05/0.70 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.05/0.70 # ho_unfolding_5 with pid 5574 completed with status 0
% 1.05/0.70 # Result found by ho_unfolding_5
% 1.05/0.70 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.05/0.70 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.70 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.05/0.70 # No SInE strategy applied
% 1.05/0.70 # Search class: HGHSM-FSLM31-MHSMMSBN
% 1.05/0.70 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 1.05/0.70 # Starting new_ho_10_cnf2 with 626s (1) cores
% 1.05/0.70 # Starting ho_unfolding_5 with 121s (1) cores
% 1.05/0.70 # Starting new_bool_3 with 109s (1) cores
% 1.05/0.70 # Starting ho_unfolding_7 with 109s (1) cores
% 1.05/0.70 # ho_unfolding_7 with pid 5623 completed with status 0
% 1.05/0.70 # Result found by ho_unfolding_7
% 1.05/0.70 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.05/0.70 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.05/0.70 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.05/0.70 # No SInE strategy applied
% 1.05/0.70 # Search class: HGHSM-FSLM31-MHSMMSBN
% 1.05/0.70 # Scheduled 6 strats onto 4 cores with 1200 seconds (1200 total)
% 1.05/0.70 # Starting new_ho_10_cnf2 with 626s (1) cores
% 1.05/0.70 # Starting ho_unfolding_5 with 121s (1) cores
% 1.05/0.70 # Starting new_bool_3 with 109s (1) cores
% 1.05/0.70 # Starting ho_unfolding_7 with 109s (1) cores
% 1.05/0.70 # Preprocessing time : 0.008 s
% 1.05/0.70 # Presaturation interreduction done
% 1.05/0.70
% 1.05/0.70 # Proof found!
% 1.05/0.70 # SZS status Theorem
% 1.05/0.70 # SZS output start CNFRefutation
% 1.05/0.70 thf(decl_22, type, in: $i > $i > $o).
% 1.05/0.70 thf(decl_23, type, exu: ($i > $o) > $o).
% 1.05/0.70 thf(decl_24, type, setextAx: $o).
% 1.05/0.70 thf(decl_25, type, emptyset: $i).
% 1.05/0.70 thf(decl_26, type, emptysetAx: $o).
% 1.05/0.70 thf(decl_27, type, setadjoin: $i > $i > $i).
% 1.05/0.70 thf(decl_28, type, setadjoinAx: $o).
% 1.05/0.70 thf(decl_29, type, powerset: $i > $i).
% 1.05/0.70 thf(decl_30, type, powersetAx: $o).
% 1.05/0.70 thf(decl_31, type, setunion: $i > $i).
% 1.05/0.70 thf(decl_32, type, setunionAx: $o).
% 1.05/0.70 thf(decl_33, type, omega: $i).
% 1.05/0.70 thf(decl_34, type, omega0Ax: $o).
% 1.05/0.70 thf(decl_35, type, omegaSAx: $o).
% 1.05/0.70 thf(decl_36, type, omegaIndAx: $o).
% 1.05/0.70 thf(decl_37, type, replAx: $o).
% 1.05/0.70 thf(decl_38, type, foundationAx: $o).
% 1.05/0.70 thf(decl_39, type, wellorderingAx: $o).
% 1.05/0.70 thf(decl_40, type, descr: ($i > $o) > $i).
% 1.05/0.70 thf(decl_41, type, descrp: $o).
% 1.05/0.70 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_43, type, dsetconstrI: $o).
% 1.05/0.70 thf(decl_44, type, dsetconstrEL: $o).
% 1.05/0.70 thf(decl_45, type, dsetconstrER: $o).
% 1.05/0.70 thf(decl_46, type, exuE1: $o).
% 1.05/0.70 thf(decl_47, type, prop2set: $o > $i).
% 1.05/0.70 thf(decl_48, type, prop2setE: $o).
% 1.05/0.70 thf(decl_49, type, emptysetE: $o).
% 1.05/0.70 thf(decl_50, type, emptysetimpfalse: $o).
% 1.05/0.70 thf(decl_51, type, notinemptyset: $o).
% 1.05/0.70 thf(decl_52, type, exuE3e: $o).
% 1.05/0.70 thf(decl_53, type, setext: $o).
% 1.05/0.70 thf(decl_54, type, emptyI: $o).
% 1.05/0.70 thf(decl_55, type, noeltsimpempty: $o).
% 1.05/0.70 thf(decl_56, type, setbeta: $o).
% 1.05/0.70 thf(decl_57, type, nonempty: $i > $o).
% 1.05/0.70 thf(decl_58, type, nonemptyE1: $o).
% 1.05/0.70 thf(decl_59, type, nonemptyI: $o).
% 1.05/0.70 thf(decl_60, type, nonemptyI1: $o).
% 1.05/0.70 thf(decl_61, type, setadjoinIL: $o).
% 1.05/0.70 thf(decl_62, type, emptyinunitempty: $o).
% 1.05/0.70 thf(decl_63, type, setadjoinIR: $o).
% 1.05/0.70 thf(decl_64, type, setadjoinE: $o).
% 1.05/0.70 thf(decl_65, type, setadjoinOr: $o).
% 1.05/0.70 thf(decl_66, type, setoftrueEq: $o).
% 1.05/0.70 thf(decl_67, type, powersetI: $o).
% 1.05/0.70 thf(decl_68, type, emptyinPowerset: $o).
% 1.05/0.70 thf(decl_69, type, emptyInPowerset: $o).
% 1.05/0.70 thf(decl_70, type, powersetE: $o).
% 1.05/0.70 thf(decl_71, type, setunionI: $o).
% 1.05/0.70 thf(decl_72, type, setunionE: $o).
% 1.05/0.70 thf(decl_73, type, subPowSU: $o).
% 1.05/0.70 thf(decl_74, type, exuE2: $o).
% 1.05/0.70 thf(decl_75, type, nonemptyImpWitness: $o).
% 1.05/0.70 thf(decl_76, type, uniqinunit: $o).
% 1.05/0.70 thf(decl_77, type, notinsingleton: $o).
% 1.05/0.70 thf(decl_78, type, eqinunit: $o).
% 1.05/0.70 thf(decl_79, type, singletonsswitch: $o).
% 1.05/0.70 thf(decl_80, type, upairsetE: $o).
% 1.05/0.70 thf(decl_81, type, upairsetIL: $o).
% 1.05/0.70 thf(decl_82, type, upairsetIR: $o).
% 1.05/0.70 thf(decl_83, type, emptyE1: $o).
% 1.05/0.70 thf(decl_84, type, vacuousDall: $o).
% 1.05/0.70 thf(decl_85, type, quantDeMorgan1: $o).
% 1.05/0.70 thf(decl_86, type, quantDeMorgan2: $o).
% 1.05/0.70 thf(decl_87, type, quantDeMorgan3: $o).
% 1.05/0.70 thf(decl_88, type, quantDeMorgan4: $o).
% 1.05/0.70 thf(decl_89, type, prop2setI: $o).
% 1.05/0.70 thf(decl_90, type, set2prop: $i > $o).
% 1.05/0.70 thf(decl_91, type, prop2set2propI: $o).
% 1.05/0.70 thf(decl_92, type, notdexE: $o).
% 1.05/0.70 thf(decl_93, type, notdallE: $o).
% 1.05/0.70 thf(decl_94, type, exuI1: $o).
% 1.05/0.70 thf(decl_95, type, exuI3: $o).
% 1.05/0.70 thf(decl_96, type, exuI2: $o).
% 1.05/0.70 thf(decl_97, type, inCongP: $o).
% 1.05/0.70 thf(decl_98, type, in__Cong: $o).
% 1.05/0.70 thf(decl_99, type, exuE3u: $o).
% 1.05/0.70 thf(decl_100, type, exu__Cong: $o).
% 1.05/0.70 thf(decl_101, type, emptyset__Cong: $o).
% 1.05/0.70 thf(decl_102, type, setadjoin__Cong: $o).
% 1.05/0.70 thf(decl_103, type, powerset__Cong: $o).
% 1.05/0.70 thf(decl_104, type, setunion__Cong: $o).
% 1.05/0.70 thf(decl_105, type, omega__Cong: $o).
% 1.05/0.70 thf(decl_106, type, exuEu: $o).
% 1.05/0.70 thf(decl_107, type, descr__Cong: $o).
% 1.05/0.70 thf(decl_108, type, dsetconstr__Cong: $o).
% 1.05/0.70 thf(decl_109, type, subset: $i > $i > $o).
% 1.05/0.70 thf(decl_112, type, subsetI1: $o).
% 1.05/0.70 thf(decl_113, type, eqimpsubset2: $o).
% 1.05/0.70 thf(decl_114, type, eqimpsubset1: $o).
% 1.05/0.70 thf(decl_115, type, subsetI2: $o).
% 1.05/0.70 thf(decl_116, type, emptysetsubset: $o).
% 1.05/0.70 thf(decl_117, type, subsetE: $o).
% 1.05/0.70 thf(decl_118, type, subsetE2: $o).
% 1.05/0.70 thf(decl_119, type, notsubsetI: $o).
% 1.05/0.70 thf(decl_120, type, notequalI1: $o).
% 1.05/0.70 thf(decl_121, type, notequalI2: $o).
% 1.05/0.70 thf(decl_122, type, subsetRefl: $o).
% 1.05/0.70 thf(decl_123, type, subsetTrans: $o).
% 1.05/0.70 thf(decl_124, type, setadjoinSub: $o).
% 1.05/0.70 thf(decl_125, type, setadjoinSub2: $o).
% 1.05/0.70 thf(decl_126, type, subset2powerset: $o).
% 1.05/0.70 thf(decl_127, type, setextsub: $o).
% 1.05/0.70 thf(decl_128, type, subsetemptysetimpeq: $o).
% 1.05/0.70 thf(decl_129, type, powersetI1: $o).
% 1.05/0.70 thf(decl_130, type, powersetE1: $o).
% 1.05/0.70 thf(decl_131, type, inPowerset: $o).
% 1.05/0.70 thf(decl_132, type, powersetsubset: $o).
% 1.05/0.70 thf(decl_133, type, sepInPowerset: $o).
% 1.05/0.70 thf(decl_134, type, sepSubset: $o).
% 1.05/0.70 thf(decl_135, type, binunion: $i > $i > $i).
% 1.05/0.70 thf(decl_136, type, binunionIL: $o).
% 1.05/0.70 thf(decl_137, type, upairset2IR: $o).
% 1.05/0.70 thf(decl_138, type, binunionIR: $o).
% 1.05/0.70 thf(decl_139, type, binunionEcases: $o).
% 1.05/0.70 thf(decl_140, type, binunionE: $o).
% 1.05/0.70 thf(decl_141, type, binunionLsub: $o).
% 1.05/0.70 thf(decl_142, type, binunionRsub: $o).
% 1.05/0.70 thf(decl_143, type, binintersect: $i > $i > $i).
% 1.05/0.70 thf(decl_144, type, binintersectI: $o).
% 1.05/0.70 thf(decl_145, type, binintersectSubset5: $o).
% 1.05/0.70 thf(decl_146, type, binintersectEL: $o).
% 1.05/0.70 thf(decl_147, type, binintersectLsub: $o).
% 1.05/0.70 thf(decl_148, type, binintersectSubset2: $o).
% 1.05/0.70 thf(decl_149, type, binintersectSubset3: $o).
% 1.05/0.70 thf(decl_150, type, binintersectER: $o).
% 1.05/0.70 thf(decl_151, type, disjointsetsI1: $o).
% 1.05/0.70 thf(decl_152, type, binintersectRsub: $o).
% 1.05/0.70 thf(decl_153, type, binintersectSubset4: $o).
% 1.05/0.70 thf(decl_154, type, binintersectSubset1: $o).
% 1.05/0.70 thf(decl_155, type, bs114d: $o).
% 1.05/0.70 thf(decl_157, type, setminus: $i > $i > $i).
% 1.05/0.70 thf(decl_158, type, setminusI: $o).
% 1.05/0.70 thf(decl_159, type, setminusEL: $o).
% 1.05/0.70 thf(decl_160, type, setminusER: $o).
% 1.05/0.70 thf(decl_161, type, setminusSubset2: $o).
% 1.05/0.70 thf(decl_162, type, setminusERneg: $o).
% 1.05/0.70 thf(decl_163, type, setminusELneg: $o).
% 1.05/0.70 thf(decl_164, type, setminusILneg: $o).
% 1.05/0.70 thf(decl_165, type, setminusIRneg: $o).
% 1.05/0.70 thf(decl_166, type, setminusLsub: $o).
% 1.05/0.70 thf(decl_167, type, setminusSubset1: $o).
% 1.05/0.70 thf(decl_168, type, symdiff: $i > $i > $i).
% 1.05/0.70 thf(decl_169, type, symdiffE: $o).
% 1.05/0.70 thf(decl_170, type, symdiffI1: $o).
% 1.05/0.70 thf(decl_171, type, symdiffI2: $o).
% 1.05/0.70 thf(decl_172, type, symdiffIneg1: $o).
% 1.05/0.70 thf(decl_173, type, symdiffIneg2: $o).
% 1.05/0.70 thf(decl_174, type, iskpair: $i > $o).
% 1.05/0.70 thf(decl_175, type, secondinupair: $o).
% 1.05/0.70 thf(decl_176, type, setukpairIL: $o).
% 1.05/0.70 thf(decl_177, type, setukpairIR: $o).
% 1.05/0.70 thf(decl_178, type, kpairiskpair: $o).
% 1.05/0.70 thf(decl_179, type, kpair: $i > $i > $i).
% 1.05/0.70 thf(decl_180, type, kpairp: $o).
% 1.05/0.70 thf(decl_181, type, cartprod: $i > $i > $i).
% 1.05/0.70 thf(decl_182, type, singletonsubset: $o).
% 1.05/0.70 thf(decl_183, type, singletoninpowerset: $o).
% 1.05/0.70 thf(decl_184, type, singletoninpowunion: $o).
% 1.05/0.70 thf(decl_185, type, upairset2E: $o).
% 1.05/0.70 thf(decl_186, type, upairsubunion: $o).
% 1.05/0.70 thf(decl_187, type, upairinpowunion: $o).
% 1.05/0.70 thf(decl_188, type, ubforcartprodlem1: $o).
% 1.05/0.70 thf(decl_189, type, ubforcartprodlem2: $o).
% 1.05/0.70 thf(decl_190, type, ubforcartprodlem3: $o).
% 1.05/0.70 thf(decl_191, type, cartprodpairin: $o).
% 1.05/0.70 thf(decl_192, type, cartprodmempair1: $o).
% 1.05/0.70 thf(decl_193, type, cartprodmempair: $o).
% 1.05/0.70 thf(decl_194, type, setunionE2: $o).
% 1.05/0.70 thf(decl_195, type, setunionsingleton1: $o).
% 1.05/0.70 thf(decl_196, type, setunionsingleton2: $o).
% 1.05/0.70 thf(decl_197, type, setunionsingleton: $o).
% 1.05/0.70 thf(decl_198, type, singleton: $i > $o).
% 1.05/0.70 thf(decl_199, type, singletonprop: $o).
% 1.05/0.70 thf(decl_200, type, ex1: $i > ($i > $o) > $o).
% 1.05/0.70 thf(decl_201, type, ex1E1: $o).
% 1.05/0.70 thf(decl_202, type, ex1I: $o).
% 1.05/0.70 thf(decl_203, type, ex1I2: $o).
% 1.05/0.70 thf(decl_204, type, singletonsuniq: $o).
% 1.05/0.70 thf(decl_209, type, setukpairinjL1: $o).
% 1.05/0.70 thf(decl_210, type, kfstsingleton: $o).
% 1.05/0.70 thf(decl_211, type, theprop: $o).
% 1.05/0.70 thf(decl_212, type, kfst: $i > $i).
% 1.05/0.70 thf(decl_213, type, kfstpairEq: $o).
% 1.05/0.70 thf(decl_214, type, cartprodfstin: $o).
% 1.05/0.70 thf(decl_215, type, setukpairinjL2: $o).
% 1.05/0.70 thf(decl_216, type, setukpairinjL: $o).
% 1.05/0.70 thf(decl_217, type, setukpairinjR11: $o).
% 1.05/0.70 thf(decl_218, type, setukpairinjR12: $o).
% 1.05/0.70 thf(decl_219, type, setukpairinjR1: $o).
% 1.05/0.70 thf(decl_220, type, upairequniteq: $o).
% 1.05/0.70 thf(decl_221, type, setukpairinjR2: $o).
% 1.05/0.70 thf(decl_222, type, setukpairinjR: $o).
% 1.05/0.70 thf(decl_223, type, ksndsingleton: $o).
% 1.05/0.70 thf(decl_224, type, ksnd: $i > $i).
% 1.05/0.70 thf(decl_225, type, ksndpairEq: $o).
% 1.05/0.70 thf(decl_226, type, kpairsurjEq: $o).
% 1.05/0.70 thf(decl_227, type, cartprodsndin: $o).
% 1.05/0.70 thf(decl_228, type, cartprodpairmemEL: $o).
% 1.05/0.70 thf(decl_229, type, cartprodpairmemER: $o).
% 1.05/0.70 thf(decl_230, type, cartprodmempaircEq: $o).
% 1.05/0.70 thf(decl_231, type, cartprodfstpairEq: $o).
% 1.05/0.70 thf(decl_232, type, cartprodsndpairEq: $o).
% 1.05/0.70 thf(decl_233, type, cartprodpairsurjEq: $o).
% 1.05/0.70 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.05/0.70 thf(decl_236, type, epred1_0: $o).
% 1.05/0.70 thf(decl_237, type, esk1_2: $i > $i > $i).
% 1.05/0.70 thf(decl_238, type, esk2_2: $i > $i > $i).
% 1.05/0.70 thf(decl_239, type, esk3_2: $i > $i > $i).
% 1.05/0.70 thf(decl_240, type, esk4_1: $i > $i).
% 1.05/0.70 thf(decl_241, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.05/0.70 thf(decl_242, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.05/0.70 thf(decl_243, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.05/0.70 thf(decl_244, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.05/0.70 thf(decl_245, type, esk9_1: $i > $i).
% 1.05/0.70 thf(decl_246, type, esk10_2: ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_247, type, esk11_2: ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_248, type, esk12_1: ($i > $o) > $i).
% 1.05/0.70 thf(decl_249, type, esk13_2: ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_250, type, esk14_1: ($i > $o) > $i).
% 1.05/0.70 thf(decl_251, type, esk15_2: $i > $i > $i).
% 1.05/0.70 thf(decl_252, type, esk16_2: $i > $i > $i).
% 1.05/0.70 thf(decl_253, type, esk17_1: $i > $i).
% 1.05/0.70 thf(decl_254, type, esk18_1: $i > $i).
% 1.05/0.70 thf(decl_255, type, esk19_1: $i > $i).
% 1.05/0.70 thf(decl_256, type, esk20_2: $i > $i > $i).
% 1.05/0.70 thf(decl_257, type, esk21_3: $i > $i > $o > $i).
% 1.05/0.70 thf(decl_258, type, esk22_2: ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_259, type, esk23_1: ($i > $o) > $i).
% 1.05/0.70 thf(decl_260, type, esk24_1: $i > $i).
% 1.05/0.70 thf(decl_261, type, esk25_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_262, type, esk26_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_263, type, esk27_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_264, type, esk28_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_265, type, esk29_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_266, type, esk30_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_267, type, esk31_2: ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_268, type, esk32_1: ($i > $o) > $i).
% 1.05/0.70 thf(decl_269, type, esk33_1: ($i > $o) > $i).
% 1.05/0.70 thf(decl_270, type, esk34_1: ($i > $o) > $i).
% 1.05/0.70 thf(decl_271, type, esk35_1: ($i > $o) > $i).
% 1.05/0.70 thf(decl_272, type, esk36_2: ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_273, type, esk37_1: ($i > $o) > $i).
% 1.05/0.70 thf(decl_274, type, esk38_2: ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_275, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.05/0.70 thf(decl_276, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.05/0.70 thf(decl_277, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_278, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.05/0.70 thf(decl_279, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_280, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.05/0.70 thf(decl_281, type, esk45_2: ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_282, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.05/0.70 thf(decl_283, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.05/0.70 thf(decl_284, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_285, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_286, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.05/0.70 thf(decl_287, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.05/0.70 thf(decl_288, type, esk52_2: $i > $i > $i).
% 1.05/0.70 thf(decl_289, type, esk53_2: $i > $i > $i).
% 1.05/0.70 thf(decl_290, type, esk54_2: $i > $i > $i).
% 1.05/0.70 thf(decl_291, type, esk55_3: $i > $i > $i > $i).
% 1.05/0.70 thf(decl_292, type, esk56_3: $i > $i > $i > $i).
% 1.05/0.70 thf(decl_293, type, esk57_2: $i > $i > $i).
% 1.05/0.70 thf(decl_294, type, esk58_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_295, type, esk59_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_296, type, esk60_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_297, type, esk61_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_298, type, esk62_3: $i > ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_299, type, esk63_3: $i > ($i > $o) > $i > $i).
% 1.05/0.70 thf(decl_300, type, esk64_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_301, type, esk65_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_302, type, esk66_2: $i > ($i > $o) > $i).
% 1.05/0.70 thf(decl_303, type, esk67_1: $i > $i).
% 1.05/0.70 thf(decl_304, type, esk68_1: $i > $i).
% 1.05/0.70 thf(decl_305, type, esk69_0: $i).
% 1.05/0.70 thf(decl_306, type, esk70_0: $i).
% 1.05/0.70 thf(decl_307, type, epred2_0: $i > $i > $o).
% 1.05/0.70 thf(decl_308, type, esk71_0: $i).
% 1.05/0.70 thf(decl_309, type, esk72_0: $i).
% 1.05/0.70 thf(decl_315, type, epred3_3: ($i > $i > $o) > $i > $i > $i > $o).
% 1.05/0.70 thf(decl_319, type, esk78_4: $i > $i > $i > ($i > $i > $o) > $i).
% 1.05/0.70 thf(decl_320, type, esk79_4: $i > $i > $i > ($i > $i > $o) > $i).
% 1.05/0.70 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1)).
% 1.05/0.70 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singleton)).
% 1.05/0.70 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', replAx)).
% 1.05/0.70 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu)).
% 1.05/0.70 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descrp)).
% 1.05/0.70 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE1)).
% 1.05/0.70 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE3e)).
% 1.05/0.70 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonempty)).
% 1.05/0.70 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI)).
% 1.05/0.70 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuE2)).
% 1.05/0.70 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/sandbox/benchmark/theBenchmark.p', exuI1)).
% 1.05/0.70 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI3)).
% 1.05/0.70 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuI2)).
% 1.05/0.70 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/sandbox/benchmark/theBenchmark.p', exuE3u)).
% 1.05/0.70 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:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exu__Cong)).
% 1.05/0.70 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', exuEu)).
% 1.05/0.70 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', descr__Cong)).
% 1.05/0.70 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonprop)).
% 1.05/0.70 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1E1)).
% 1.05/0.70 thf(ex1I, axiom, ((ex1I)<=>![X4:$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/sandbox/benchmark/theBenchmark.p', ex1I)).
% 1.05/0.70 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:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ex1I2)).
% 1.05/0.70 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstsingleton)).
% 1.05/0.70 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndsingleton)).
% 1.05/0.70 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrI)).
% 1.05/0.70 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrEL)).
% 1.05/0.70 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstrER)).
% 1.05/0.70 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setbeta)).
% 1.05/0.70 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyE1)).
% 1.05/0.70 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyI1)).
% 1.05/0.70 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setoftrueEq)).
% 1.05/0.70 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', nonemptyImpWitness)).
% 1.05/0.70 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyE1)).
% 1.05/0.70 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dsetconstr__Cong)).
% 1.05/0.70 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepInPowerset)).
% 1.05/0.70 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', sepSubset)).
% 1.05/0.70 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', theprop)).
% 1.05/0.70 thf(dpsetconstrI, 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)=>![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:$i]:((X23 @ X14 @ X18))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', dpsetconstrI)).
% 1.05/0.70 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextAx)).
% 1.05/0.70 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetAx)).
% 1.05/0.70 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinAx)).
% 1.05/0.70 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetAx)).
% 1.05/0.70 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionAx)).
% 1.05/0.70 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega0Ax)).
% 1.05/0.70 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omegaSAx)).
% 1.05/0.70 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/sandbox/benchmark/theBenchmark.p', omegaIndAx)).
% 1.05/0.70 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/sandbox/benchmark/theBenchmark.p', foundationAx)).
% 1.05/0.70 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', wellorderingAx)).
% 1.05/0.70 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setE)).
% 1.05/0.70 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetE)).
% 1.05/0.70 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetimpfalse)).
% 1.05/0.70 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinemptyset)).
% 1.05/0.70 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/sandbox/benchmark/theBenchmark.p', setext)).
% 1.05/0.70 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyI)).
% 1.05/0.70 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', noeltsimpempty)).
% 1.05/0.70 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIL)).
% 1.05/0.70 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinunitempty)).
% 1.05/0.70 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinIR)).
% 1.05/0.70 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinE)).
% 1.05/0.70 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinOr)).
% 1.05/0.70 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI)).
% 1.05/0.70 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyinPowerset)).
% 1.05/0.70 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyInPowerset)).
% 1.05/0.70 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE)).
% 1.05/0.70 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionI)).
% 1.05/0.70 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE)).
% 1.05/0.70 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subPowSU)).
% 1.05/0.70 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', uniqinunit)).
% 1.05/0.70 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notinsingleton)).
% 1.05/0.70 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqinunit)).
% 1.05/0.70 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsswitch)).
% 1.05/0.70 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetE)).
% 1.05/0.70 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIL)).
% 1.05/0.70 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsetIR)).
% 1.05/0.70 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', vacuousDall)).
% 1.05/0.70 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan1)).
% 1.05/0.70 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan2)).
% 1.05/0.70 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan3)).
% 1.05/0.70 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', quantDeMorgan4)).
% 1.05/0.70 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2setI)).
% 1.05/0.70 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', prop2set2propI)).
% 1.05/0.70 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdexE)).
% 1.05/0.70 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notdallE)).
% 1.05/0.70 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inCongP)).
% 1.05/0.70 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', in__Cong)).
% 1.05/0.70 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptyset__Cong)).
% 1.05/0.70 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoin__Cong)).
% 1.05/0.70 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powerset__Cong)).
% 1.05/0.70 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunion__Cong)).
% 1.05/0.70 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', omega__Cong)).
% 1.05/0.70 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI1)).
% 1.05/0.70 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset2)).
% 1.05/0.70 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', eqimpsubset1)).
% 1.05/0.70 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetI2)).
% 1.05/0.70 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', emptysetsubset)).
% 1.05/0.70 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE)).
% 1.05/0.70 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetE2)).
% 1.05/0.70 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notsubsetI)).
% 1.05/0.70 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI1)).
% 1.05/0.70 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', notequalI2)).
% 1.05/0.70 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetRefl)).
% 1.05/0.70 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetTrans)).
% 1.05/0.70 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub)).
% 1.05/0.70 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setadjoinSub2)).
% 1.05/0.70 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subset2powerset)).
% 1.05/0.70 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setextsub)).
% 1.05/0.70 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', subsetemptysetimpeq)).
% 1.05/0.70 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetI1)).
% 1.05/0.70 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetE1)).
% 1.05/0.70 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', inPowerset)).
% 1.05/0.70 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', powersetsubset)).
% 1.05/0.70 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIL)).
% 1.05/0.70 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2IR)).
% 1.05/0.70 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionIR)).
% 1.05/0.70 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionEcases)).
% 1.05/0.70 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionE)).
% 1.05/0.70 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionLsub)).
% 1.05/0.70 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binunionRsub)).
% 1.05/0.70 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectI)).
% 1.05/0.70 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset5)).
% 1.05/0.70 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectEL)).
% 1.05/0.70 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectLsub)).
% 1.05/0.70 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset2)).
% 1.05/0.70 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset3)).
% 1.05/0.70 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectER)).
% 1.05/0.70 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', disjointsetsI1)).
% 1.05/0.70 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectRsub)).
% 1.05/0.70 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset4)).
% 1.05/0.70 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', binintersectSubset1)).
% 1.05/0.70 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', bs114d)).
% 1.05/0.70 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusI)).
% 1.05/0.70 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusEL)).
% 1.05/0.70 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusER)).
% 1.05/0.70 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset2)).
% 1.05/0.70 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusERneg)).
% 1.05/0.70 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusELneg)).
% 1.05/0.70 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusILneg)).
% 1.05/0.70 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusIRneg)).
% 1.05/0.70 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusLsub)).
% 1.05/0.70 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setminusSubset1)).
% 1.05/0.70 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffE)).
% 1.05/0.70 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI1)).
% 1.05/0.70 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffI2)).
% 1.05/0.70 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg1)).
% 1.05/0.70 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', symdiffIneg2)).
% 1.05/0.70 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', secondinupair)).
% 1.05/0.70 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIL)).
% 1.05/0.70 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairIR)).
% 1.05/0.70 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairiskpair)).
% 1.05/0.70 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairp)).
% 1.05/0.70 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsubset)).
% 1.05/0.70 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowerset)).
% 1.05/0.70 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletoninpowunion)).
% 1.05/0.70 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairset2E)).
% 1.05/0.70 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairsubunion)).
% 1.05/0.70 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairinpowunion)).
% 1.05/0.70 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem1)).
% 1.05/0.70 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem2)).
% 1.05/0.70 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ubforcartprodlem3)).
% 1.05/0.70 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairin)).
% 1.05/0.70 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair1)).
% 1.05/0.70 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodmempair)).
% 1.05/0.70 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionE2)).
% 1.05/0.70 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton1)).
% 1.05/0.70 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton2)).
% 1.05/0.70 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setunionsingleton)).
% 1.05/0.70 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', singletonsuniq)).
% 1.05/0.70 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$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/sandbox/benchmark/theBenchmark.p', setukpairinjL1)).
% 1.05/0.70 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kfstpairEq)).
% 1.05/0.70 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstin)).
% 1.05/0.70 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL2)).
% 1.05/0.70 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjL)).
% 1.05/0.70 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR11)).
% 1.05/0.70 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR12)).
% 1.05/0.70 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR1)).
% 1.05/0.70 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', upairequniteq)).
% 1.05/0.70 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/sandbox/benchmark/theBenchmark.p', setukpairinjR2)).
% 1.05/0.70 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', setukpairinjR)).
% 1.05/0.70 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', ksndpairEq)).
% 1.05/0.70 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', kpairsurjEq)).
% 1.05/0.70 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndin)).
% 1.05/0.70 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemEL)).
% 1.05/0.70 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairmemER)).
% 1.05/0.70 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/sandbox/benchmark/theBenchmark.p', cartprodmempaircEq)).
% 1.05/0.70 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodfstpairEq)).
% 1.05/0.70 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodsndpairEq)).
% 1.05/0.70 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p', cartprodpairsurjEq)).
% 1.05/0.70 thf(dpsetconstr, axiom, ((dpsetconstr)=(^[X4:$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/sandbox/benchmark/theBenchmark.p', dpsetconstr)).
% 1.05/0.70 thf(c_0_187, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X556:$i]:(((in @ X556 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X556 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 1.05/0.70 thf(c_0_188, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 1.05/0.70 thf(c_0_189, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.05/0.70 thf(c_0_190, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.05/0.70 thf(c_0_191, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.05/0.70 thf(c_0_192, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.05/0.70 thf(c_0_193, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.05/0.70 thf(c_0_194, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.05/0.70 thf(c_0_195, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.05/0.70 thf(c_0_196, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.05/0.70 thf(c_0_197, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])).
% 1.05/0.70 thf(c_0_198, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.05/0.70 thf(c_0_199, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.05/0.70 thf(c_0_200, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])).
% 1.05/0.70 thf(c_0_201, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.05/0.70 thf(c_0_202, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.05/0.70 thf(c_0_203, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.05/0.70 thf(c_0_204, plain, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.05/0.70 thf(c_0_205, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 1.05/0.70 thf(c_0_206, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X556:$i]:(((in @ X556 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X556 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_187, c_0_188])).
% 1.05/0.70 thf(c_0_207, plain, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[ex1I])).
% 1.05/0.70 thf(c_0_208, plain, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 1.05/0.70 thf(c_0_209, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.05/0.70 thf(c_0_210, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.05/0.70 thf(c_0_211, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X527:$i]:((((X6 @ X2 @ X527))&![X528:$i]:((((X6 @ X2 @ X528))=>((X527)=(X528)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_189, c_0_190])).
% 1.05/0.70 thf(c_0_212, plain, ((descrp)=(![X1:$i > $o]:(((?[X529:$i]:((((X1 @ X529))&![X530:$i]:((((X1 @ X530))=>((X529)=(X530)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_191, c_0_190])).
% 1.05/0.70 thf(c_0_213, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.05/0.70 thf(c_0_214, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.05/0.70 thf(c_0_215, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.05/0.70 thf(c_0_216, plain, ((exuE1)=(![X1:$i > $o]:(((?[X531:$i]:((((X1 @ X531))&![X532:$i]:((((X1 @ X532))=>((X531)=(X532)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_190])).
% 1.05/0.70 thf(c_0_217, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X533:$i]:((((X1 @ X533))&![X534:$i]:((((X1 @ X534))=>((X533)=(X534)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_193, c_0_190])).
% 1.05/0.70 thf(c_0_218, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.05/0.70 thf(c_0_219, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_194])).
% 1.05/0.70 thf(c_0_220, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_195, c_0_194])).
% 1.05/0.70 thf(c_0_221, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_194])).
% 1.05/0.70 thf(c_0_222, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.05/0.70 thf(c_0_223, plain, ((exuE2)=(![X1:$i > $o]:(((?[X535:$i]:((((X1 @ X535))&![X536:$i]:((((X1 @ X536))=>((X535)=(X536)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_190])).
% 1.05/0.70 thf(c_0_224, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_194])).
% 1.05/0.70 thf(c_0_225, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])).
% 1.05/0.70 thf(c_0_226, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X537:$i]:((((X1 @ X537))&![X538:$i]:((((X1 @ X538))=>((X537)=(X538))))))))))), inference(apply_def,[status(thm)],[c_0_197, c_0_190])).
% 1.05/0.70 thf(c_0_227, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X539:$i]:((((X1 @ X539))&![X540:$i]:((((X1 @ X540))=>((X539)=(X540)))))))))))), inference(apply_def,[status(thm)],[c_0_198, c_0_190])).
% 1.05/0.70 thf(c_0_228, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X541:$i]:((((X1 @ X541))&![X542:$i]:((((X1 @ X542))=>((X541)=(X542))))))))))), inference(apply_def,[status(thm)],[c_0_199, c_0_190])).
% 1.05/0.70 thf(c_0_229, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X543:$i]:((((X1 @ X543))&![X544:$i]:((((X1 @ X544))=>((X543)=(X544)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_200, c_0_190])).
% 1.05/0.70 thf(c_0_230, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X545:$i]:((((X1 @ X545))&![X546:$i]:((((X1 @ X546))=>((X545)=(X546)))))))<=>(?[X547:$i]:((((X17 @ X547))&![X548:$i]:((((X17 @ X548))=>((X547)=(X548)))))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_190])).
% 1.05/0.70 thf(c_0_231, plain, ((exuEu)=(![X1:$i > $o]:(((?[X549:$i]:((((X1 @ X549))&![X550:$i]:((((X1 @ X550))=>((X549)=(X550)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_202, c_0_190])).
% 1.05/0.70 thf(c_0_232, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X551:$i]:((((X1 @ X551))&![X552:$i]:((((X1 @ X552))=>((X551)=(X552)))))))=>((?[X553:$i]:((((X17 @ X553))&![X554:$i]:((((X17 @ X554))=>((X553)=(X554)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_190])).
% 1.05/0.70 thf(c_0_233, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.05/0.70 thf(c_0_234, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.05/0.70 thf(c_0_235, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.05/0.70 thf(c_0_236, 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)))=>(?[X555:$i]:(((in @ X555 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X555 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_204, c_0_188])).
% 1.05/0.70 thf(c_0_237, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X557:$i]:(((in @ X557 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X557 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_205, c_0_206])).
% 1.05/0.70 thf(c_0_238, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X558:$i]:(((in @ X558 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X558 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_207, c_0_206])).
% 1.05/0.70 thf(c_0_239, 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)))=>(?[X559:$i]:(((in @ X559 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X559 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_208, c_0_206])).
% 1.05/0.70 thf(c_0_240, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X560:$i]:(((in @ X560 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X560 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_209, c_0_188])).
% 1.05/0.70 thf(c_0_241, axiom, ((theprop)=(![X21:$i]:(((?[X561:$i]:(((in @ X561 @ X21)&((X21)=(setadjoin @ X561 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_188])).
% 1.05/0.70 thf(c_0_242, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X562:$i]:(((in @ X562 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X562 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_210, c_0_188])).
% 1.05/0.70 thf(c_0_243, plain, ((epred1_0)<=>![X592:$i]:(?[X593:$i]:((((![X594:$i]:(((in @ X594 @ X593)=>![X595:$i]:(((in @ X595 @ X594)=>(in @ X595 @ X592)))))&![X596:$i, X597:$i]:((((in @ X596 @ X592)&(in @ X597 @ X592))=>(![X598:$i]:(((in @ X598 @ X593)=>((in @ X596 @ X598)<=>(in @ X597 @ X598))))=>((X596)=(X597))))))&![X599:$i, X600:$i]:((((in @ X599 @ X593)&(in @ X600 @ X593))=>(![X601:$i]:(((in @ X601 @ X599)=>(in @ X601 @ X600)))|![X602:$i]:(((in @ X602 @ X600)=>(in @ X602 @ X599)))))))&![X603:$i]:(((![X604:$i]:(((in @ X604 @ X603)=>(in @ X604 @ X592)))&?[X605:$i]:((in @ X605 @ X603)))=>?[X606:$i, X607:$i]:(((((in @ X606 @ X593)&(in @ X607 @ X603))&~(?[X608:$i]:(((in @ X608 @ X606)&(in @ X608 @ X603)))))&![X609:$i]:(((in @ X609 @ X593)=>(![X610:$i]:(((in @ X610 @ X609)=>(in @ X610 @ X606)))|(in @ X607 @ X609)))))))))))), introduced(definition)).
% 1.05/0.70 thf(c_0_244, negated_conjecture, ~((![X563:$i, X564:$i]:((![X565:$i]:(((in @ X565 @ X563)<=>(in @ X565 @ X564)))=>((X563)=(X564))))=>(![X566:$i]:(~(in @ X566 @ emptyset))=>(![X567:$i, X568:$i, X569:$i]:(((in @ X569 @ (setadjoin @ X567 @ X568))<=>(((X569)=(X567))|(in @ X569 @ X568))))=>(![X570:$i, X571:$i]:(((in @ X571 @ (powerset @ X570))<=>![X572:$i]:(((in @ X572 @ X571)=>(in @ X572 @ X570)))))=>(![X573:$i, X574:$i]:(((in @ X574 @ (setunion @ X573))<=>?[X575:$i]:(((in @ X574 @ X575)&(in @ X575 @ X573)))))=>((in @ emptyset @ omega)=>(![X576:$i]:(((in @ X576 @ omega)=>(in @ (setadjoin @ X576 @ X576) @ omega)))=>(![X577:$i]:((((in @ emptyset @ X577)&![X578:$i]:((((in @ X578 @ omega)&(in @ X578 @ X577))=>(in @ (setadjoin @ X578 @ X578) @ X577))))=>![X579:$i]:(((in @ X579 @ omega)=>(in @ X579 @ X577)))))=>(![X580:$i > $i > $o, X581:$i]:((![X582:$i]:(((in @ X582 @ X581)=>?[X583:$i]:(((X580 @ X582 @ X583)&![X584:$i]:(((X580 @ X582 @ X584)=>((X583)=(X584))))))))=>?[X585:$i]:(![X586:$i]:(((in @ X586 @ X585)<=>?[X587:$i]:(((in @ X587 @ X581)&(X580 @ X587 @ X586))))))))=>(![X588:$i]:((?[X589:$i]:((in @ X589 @ X588))=>?[X590:$i]:(((in @ X590 @ X588)&~(?[X591:$i]:(((in @ X591 @ X590)&(in @ X591 @ X588))))))))=>((epred1_0)=>(![X611:$i > $o]:((?[X612:$i]:(((X611 @ X612)&![X613:$i]:(((X611 @ X613)=>((X612)=(X613))))))=>(X611 @ (descr @ (^[Z0/* 17 */:$i]:(X611 @ Z0))))))=>(![X614:$i, X615:$i > $o, X616:$i]:(((in @ X616 @ X614)=>((X615 @ X616)=>(in @ X616 @ (dsetconstr @ X614 @ X615)))))=>(![X617:$i, X618:$i > $o, X619:$i]:(((in @ X619 @ (dsetconstr @ X617 @ X618))=>(in @ X619 @ X617)))=>(![X620:$i, X621:$i > $o, X622:$i]:(((in @ X622 @ (dsetconstr @ X620 @ X621))=>(X621 @ X622)))=>(![X623:$i > $o]:((?[X624:$i]:(((X623 @ X624)&![X625:$i]:(((X623 @ X625)=>((X624)=(X625))))))=>?[X626:$i]:(((X623 @ X626)&![X627:$i]:(((X623 @ X627)=>((X626)=(X627))))))))=>(![X628:$o, X629:$i]:(((in @ X629 @ (prop2set @ ((X628))))=>(X628)))=>(![X630:$i]:(((in @ X630 @ emptyset)=>![X631:$o]:((X631))))=>(![X632:$i]:(((in @ X632 @ emptyset)=>~($true)))=>(![X633:$i]:(~(in @ X633 @ emptyset))=>(![X634:$i > $o]:((?[X635:$i]:(((X634 @ X635)&![X636:$i]:(((X634 @ X636)=>((X635)=(X636))))))=>?[X637:$i]:((X634 @ X637))))=>(![X638:$i, X639:$i]:((![X640:$i]:(((in @ X640 @ X638)=>(in @ X640 @ X639)))=>(![X641:$i]:(((in @ X641 @ X639)=>(in @ X641 @ X638)))=>((X638)=(X639)))))=>(![X642:$i]:((![X643:$i]:(~(in @ X643 @ X642))=>((X642)=(emptyset))))=>(![X644:$i]:((![X645:$i]:(~(in @ X645 @ X644))=>((X644)=(emptyset))))=>(![X646:$i, X647:$i > $o, X648:$i]:(((in @ X648 @ X646)=>((in @ X648 @ (dsetconstr @ X646 @ X647))<=>(X647 @ X648))))=>(![X649:$i]:((((X649)!=(emptyset))=>?[X650:$i]:((in @ X650 @ X649))))=>(![X651:$i, X652:$i > $o, X653:$i]:(((in @ X653 @ X651)=>((X652 @ X653)=>((dsetconstr @ X651 @ X652)!=(emptyset)))))=>(![X654:$i]:((?[X655:$i]:((in @ X655 @ X654))=>((X654)!=(emptyset))))=>(![X656:$i, X657:$i]:((in @ X656 @ (setadjoin @ X656 @ X657)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X658:$i, X659:$i, X660:$i]:(((in @ X660 @ X659)=>(in @ X660 @ (setadjoin @ X658 @ X659))))=>(![X661:$i, X662:$i, X663:$i]:(((in @ X663 @ (setadjoin @ X661 @ X662))=>![X664:$o]:(((((X663)=(X661))=>(X664))=>(((in @ X663 @ X662)=>(X664))=>(X664))))))=>(![X665:$i, X666:$i, X667:$i]:(((in @ X667 @ (setadjoin @ X665 @ X666))=>(((X667)=(X665))|(in @ X667 @ X666))))=>(![X668:$i]:(((dsetconstr @ X668 @ (^[Z0/* 1 */:$i]:($true)))=(X668)))=>(![X669:$i, X670:$i]:((![X671:$i]:(((in @ X671 @ X670)=>(in @ X671 @ X669)))=>(in @ X670 @ (powerset @ X669))))=>(![X672:$i]:((in @ emptyset @ (powerset @ X672)))=>(![X673:$i]:((in @ emptyset @ (powerset @ X673)))=>(![X674:$i, X675:$i, X676:$i]:(((in @ X675 @ (powerset @ X674))=>((in @ X676 @ X675)=>(in @ X676 @ X674))))=>(![X677:$i, X678:$i, X679:$i]:(((in @ X678 @ X679)=>((in @ X679 @ X677)=>(in @ X678 @ (setunion @ X677)))))=>(![X680:$i, X681:$i]:(((in @ X681 @ (setunion @ X680))=>![X682:$o]:((![X683:$i]:(((in @ X681 @ X683)=>((in @ X683 @ X680)=>(X682))))=>(X682)))))=>(![X684:$i, X685:$i]:(((in @ X685 @ X684)=>(in @ X685 @ (powerset @ (setunion @ X684)))))=>(![X686:$i > $o]:((?[X687:$i]:(((X686 @ X687)&![X688:$i]:(((X686 @ X688)=>((X687)=(X688))))))=>?[X689:$i]:(![X690:$i]:(((X686 @ X690)<=>((X690)=(X689)))))))=>(![X691:$i]:((((X691)!=(emptyset))=>?[X692:$i]:(((in @ X692 @ X691)&$true))))=>(![X693:$i, X694:$i]:(((in @ X693 @ (setadjoin @ X694 @ emptyset))=>((X693)=(X694))))=>(![X695:$i, X696:$i]:((((X695)!=(X696))=>~(in @ X696 @ (setadjoin @ X695 @ emptyset))))=>(![X697:$i, X698:$i]:((((X697)=(X698))=>(in @ X697 @ (setadjoin @ X698 @ emptyset))))=>(![X699:$i, X700:$i]:(((in @ X699 @ (setadjoin @ X700 @ emptyset))=>(in @ X700 @ (setadjoin @ X699 @ emptyset))))=>(![X701:$i, X702:$i, X703:$i]:(((in @ X703 @ (setadjoin @ X701 @ (setadjoin @ X702 @ emptyset)))=>(((X703)=(X701))|((X703)=(X702)))))=>(![X704:$i, X705:$i]:((in @ X704 @ (setadjoin @ X704 @ (setadjoin @ X705 @ emptyset))))=>(![X706:$i, X707:$i]:((in @ X707 @ (setadjoin @ X706 @ (setadjoin @ X707 @ emptyset))))=>(![X708:$i, X709:$i > $o]:((?[X710:$i]:(((in @ X710 @ X708)&(X709 @ X710)))=>(((dsetconstr @ X708 @ X709)=(emptyset))=>~($true))))=>(![X711:$i > $o, X712:$i]:(((in @ X712 @ emptyset)=>(X711 @ X712)))=>(![X713:$i, X714:$i > $o]:((~(![X715:$i]:(((in @ X715 @ X713)=>(X714 @ X715))))=>?[X716:$i]:(((in @ X716 @ X713)&~((X714 @ X716))))))=>(![X717:$i, X718:$i > $o]:((![X719:$i]:(((in @ X719 @ X717)=>~((X718 @ X719))))=>~(?[X720:$i]:(((in @ X720 @ X717)&(X718 @ X720))))))=>(![X721:$i, X722:$i > $o]:((~(?[X723:$i]:(((in @ X723 @ X721)&(X722 @ X723))))=>![X724:$i]:(((in @ X724 @ X721)=>~((X722 @ X724))))))=>(![X725:$i, X726:$i > $o]:((?[X727:$i]:(((in @ X727 @ X725)&~((X726 @ X727))))=>~(![X728:$i]:(((in @ X728 @ X725)=>(X726 @ X728))))))=>(![X729:$o]:(((X729)=>(in @ emptyset @ (prop2set @ ((X729))))))=>(![X730:$o]:(((X730)=>(set2prop @ (prop2set @ ((X730))))))=>(![X731:$i, X732:$i > $o]:((~(?[X733:$i]:(((in @ X733 @ X731)&(X732 @ X733))))=>![X734:$i]:(((in @ X734 @ X731)=>~((X732 @ X734))))))=>(![X735:$i, X736:$i > $o]:((~(![X737:$i]:(((in @ X737 @ X735)=>(X736 @ X737))))=>?[X738:$i]:(((in @ X738 @ X735)&~((X736 @ X738))))))=>(![X739:$i > $o]:((?[X740:$i]:(((X739 @ X740)&![X741:$i]:(((X739 @ X741)=>((X740)=(X741))))))=>?[X742:$i]:(((X739 @ X742)&![X743:$i]:(((X739 @ X743)=>((X742)=(X743))))))))=>(![X744:$i > $o]:((?[X745:$i]:((X744 @ X745))=>(![X746:$i, X747:$i]:(((X744 @ X746)=>((X744 @ X747)=>((X746)=(X747)))))=>?[X748:$i]:(((X744 @ X748)&![X749:$i]:(((X744 @ X749)=>((X748)=(X749)))))))))=>(![X750:$i > $o]:((?[X751:$i]:(![X752:$i]:(((X750 @ X752)<=>((X752)=(X751)))))=>?[X753:$i]:(((X750 @ X753)&![X754:$i]:(((X750 @ X754)=>((X753)=(X754))))))))=>(![X755:$i, X756:$i]:((((X755)=(X756))=>![X757:$i, X758:$i]:((((X757)=(X758))=>((in @ X757 @ X755)=>(in @ X758 @ X756))))))=>(![X759:$i, X760:$i]:((((X759)=(X760))=>![X761:$i, X762:$i]:((((X761)=(X762))=>((in @ X761 @ X759)<=>(in @ X762 @ X760))))))=>(![X763:$i > $o]:((?[X764:$i]:(((X763 @ X764)&![X765:$i]:(((X763 @ X765)=>((X764)=(X765))))))=>![X766:$i, X767:$i]:(((X763 @ X766)=>((X763 @ X767)=>((X766)=(X767)))))))=>(![X768:$i > $o, X769:$i > $o]:((![X770:$i, X771:$i]:((((X770)=(X771))=>((X768 @ X770)<=>(X769 @ X771))))=>(?[X772:$i]:(((X768 @ X772)&![X773:$i]:(((X768 @ X773)=>((X772)=(X773))))))<=>?[X774:$i]:(((X769 @ X774)&![X775:$i]:(((X769 @ X775)=>((X774)=(X775)))))))))=>(((emptyset)=(emptyset))=>(![X776:$i, X777:$i]:((((X776)=(X777))=>![X778:$i, X779:$i]:((((X778)=(X779))=>((setadjoin @ X776 @ X778)=(setadjoin @ X777 @ X779))))))=>(![X780:$i, X781:$i]:((((X780)=(X781))=>((powerset @ X780)=(powerset @ X781))))=>(![X782:$i, X783:$i]:((((X782)=(X783))=>((setunion @ X782)=(setunion @ X783))))=>(((omega)=(omega))=>(![X784:$i > $o]:((?[X785:$i]:(((X784 @ X785)&![X786:$i]:(((X784 @ X786)=>((X785)=(X786))))))=>![X787:$i, X788:$i]:(((X784 @ X787)=>((X784 @ X788)=>((X787)=(X788)))))))=>(![X789:$i > $o, X790:$i > $o]:((![X791:$i, X792:$i]:((((X791)=(X792))=>((X789 @ X791)<=>(X790 @ X792))))=>(?[X793:$i]:(((X789 @ X793)&![X794:$i]:(((X789 @ X794)=>((X793)=(X794))))))=>(?[X795:$i]:(((X790 @ X795)&![X796:$i]:(((X790 @ X796)=>((X795)=(X796))))))=>((descr @ X789)=(descr @ X790))))))=>(![X797:$i, X798:$i]:((((X797)=(X798))=>![X799:$i > $o, X800:$i > $o]:((![X801:$i]:(((in @ X801 @ X797)=>![X802:$i]:(((in @ X802 @ X798)=>(((X801)=(X802))=>((X799 @ X801)<=>(X800 @ X802)))))))=>((dsetconstr @ X797 @ X799)=(dsetconstr @ X798 @ X800))))))=>(![X803:$i, X804:$i]:((![X805:$i]:(((in @ X805 @ X803)=>(in @ X805 @ X804)))=>(subset @ X803 @ X804)))=>(![X806:$i, X807:$i]:((((X806)=(X807))=>(subset @ X807 @ X806)))=>(![X808:$i, X809:$i]:((((X808)=(X809))=>(subset @ X808 @ X809)))=>(![X810:$i, X811:$i]:((![X812:$i]:(((in @ X812 @ X810)=>(in @ X812 @ X811)))=>(subset @ X810 @ X811)))=>(![X813:$i]:((subset @ emptyset @ X813))=>(![X814:$i, X815:$i, X816:$i]:(((subset @ X814 @ X815)=>((in @ X816 @ X814)=>(in @ X816 @ X815))))=>(![X817:$i, X818:$i, X819:$i]:(((subset @ X817 @ X818)=>(~(in @ X819 @ X818)=>~(in @ X819 @ X817))))=>(![X820:$i, X821:$i, X822:$i]:(((in @ X822 @ X820)=>(~(in @ X822 @ X821)=>~(subset @ X820 @ X821))))=>(![X823:$i, X824:$i]:((~(subset @ X823 @ X824)=>((X823)!=(X824))))=>(![X825:$i, X826:$i, X827:$i]:(((in @ X827 @ X825)=>(~(in @ X827 @ X826)=>((X825)!=(X826)))))=>(![X828:$i]:((subset @ X828 @ X828))=>(![X829:$i, X830:$i, X831:$i]:(((subset @ X829 @ X830)=>((subset @ X830 @ X831)=>(subset @ X829 @ X831))))=>(![X832:$i, X833:$i]:((subset @ X833 @ (setadjoin @ X832 @ X833)))=>(![X834:$i, X835:$i, X836:$i]:(((subset @ X834 @ X836)=>(subset @ X834 @ (setadjoin @ X835 @ X836))))=>(![X837:$i, X838:$i]:(((subset @ X837 @ X838)=>(in @ X837 @ (powerset @ X838))))=>(![X839:$i, X840:$i]:(((subset @ X839 @ X840)=>((subset @ X840 @ X839)=>((X839)=(X840)))))=>(![X841:$i]:(((subset @ X841 @ emptyset)=>((X841)=(emptyset))))=>(![X842:$i, X843:$i]:(((subset @ X843 @ X842)=>(in @ X843 @ (powerset @ X842))))=>(![X844:$i, X845:$i]:(((in @ X845 @ (powerset @ X844))=>(subset @ X845 @ X844)))=>(![X846:$i]:((in @ X846 @ (powerset @ X846)))=>(![X847:$i, X848:$i]:(((subset @ X847 @ X848)=>(subset @ (powerset @ X847) @ (powerset @ X848))))=>(![X849:$i, X850:$i > $o]:((in @ (dsetconstr @ X849 @ X850) @ (powerset @ X849)))=>(![X851:$i, X852:$i > $o]:((subset @ (dsetconstr @ X851 @ X852) @ X851))=>(![X853:$i, X854:$i, X855:$i]:(((in @ X855 @ X853)=>(in @ X855 @ (binunion @ X853 @ X854))))=>(![X856:$i, X857:$i]:((in @ X857 @ (setadjoin @ X856 @ (setadjoin @ X857 @ emptyset))))=>(![X858:$i, X859:$i, X860:$i]:(((in @ X860 @ X859)=>(in @ X860 @ (binunion @ X858 @ X859))))=>(![X861:$i, X862:$i, X863:$i, X864:$o]:(((in @ X863 @ (binunion @ X861 @ X862))=>(((in @ X863 @ X861)=>(X864))=>(((in @ X863 @ X862)=>(X864))=>(X864)))))=>(![X865:$i, X866:$i, X867:$i]:(((in @ X867 @ (binunion @ X865 @ X866))=>((in @ X867 @ X865)|(in @ X867 @ X866))))=>(![X868:$i, X869:$i]:((subset @ X868 @ (binunion @ X868 @ X869)))=>(![X870:$i, X871:$i]:((subset @ X871 @ (binunion @ X870 @ X871)))=>(![X872:$i, X873:$i, X874:$i]:(((in @ X874 @ X872)=>((in @ X874 @ X873)=>(in @ X874 @ (binintersect @ X872 @ X873)))))=>(![X875:$i, X876:$i, X877:$i]:(((subset @ X877 @ X875)=>((subset @ X877 @ X876)=>(subset @ X877 @ (binintersect @ X875 @ X876)))))=>(![X878:$i, X879:$i, X880:$i]:(((in @ X880 @ (binintersect @ X878 @ X879))=>(in @ X880 @ X878)))=>(![X881:$i, X882:$i]:((subset @ (binintersect @ X881 @ X882) @ X881))=>(![X883:$i, X884:$i]:(((subset @ X883 @ X884)=>((binintersect @ X883 @ X884)=(X883))))=>(![X885:$i, X886:$i]:((((binintersect @ X885 @ X886)=(X886))=>(subset @ X886 @ X885)))=>(![X887:$i, X888:$i, X889:$i]:(((in @ X889 @ (binintersect @ X887 @ X888))=>(in @ X889 @ X888)))=>(![X890:$i, X891:$i]:((~(?[X892:$i]:(((in @ X892 @ X890)&(in @ X892 @ X891))))=>((binintersect @ X890 @ X891)=(emptyset))))=>(![X893:$i, X894:$i]:((subset @ (binintersect @ X893 @ X894) @ X894))=>(![X895:$i, X896:$i]:(((subset @ X896 @ X895)=>((binintersect @ X895 @ X896)=(X896))))=>(![X897:$i, X898:$i]:((((binintersect @ X897 @ X898)=(X897))=>(subset @ X897 @ X898)))=>(![X899:$i, X900:$i, X901:$i]:(((binintersect @ X899 @ (binunion @ X900 @ X901))=(binunion @ (binintersect @ X899 @ X900) @ (binintersect @ X899 @ X901))))=>(![X902:$i, X903:$i, X904:$i]:(((in @ X904 @ X902)=>(~(in @ X904 @ X903)=>(in @ X904 @ (setminus @ X902 @ X903)))))=>(![X905:$i, X906:$i, X907:$i]:(((in @ X907 @ (setminus @ X905 @ X906))=>(in @ X907 @ X905)))=>(![X908:$i, X909:$i, X910:$i]:(((in @ X910 @ (setminus @ X908 @ X909))=>~(in @ X910 @ X909)))=>(![X911:$i, X912:$i]:(((subset @ X911 @ X912)=>((setminus @ X911 @ X912)=(emptyset))))=>(![X913:$i, X914:$i, X915:$i]:((~(in @ X915 @ (setminus @ X913 @ X914))=>((in @ X915 @ X913)=>(in @ X915 @ X914))))=>(![X916:$i, X917:$i, X918:$i]:((~(in @ X918 @ (setminus @ X916 @ 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X942)=>(~(in @ X944 @ X943)=>~(in @ X944 @ (symdiff @ X942 @ X943)))))=>(![X945:$i, X946:$i]:((in @ X946 @ (setadjoin @ X945 @ (setadjoin @ X946 @ emptyset))))=>(![X947:$i, X948:$i]:((in @ X947 @ (setunion @ (setadjoin @ (setadjoin @ X947 @ emptyset) @ (setadjoin @ (setadjoin @ X947 @ (setadjoin @ X948 @ emptyset)) @ emptyset)))))=>(![X949:$i, X950:$i]:((in @ X950 @ (setunion @ (setadjoin @ (setadjoin @ X949 @ emptyset) @ (setadjoin @ (setadjoin @ X949 @ (setadjoin @ X950 @ emptyset)) @ emptyset)))))=>(![X951:$i, X952:$i]:((iskpair @ (setadjoin @ (setadjoin @ X951 @ emptyset) @ (setadjoin @ (setadjoin @ X951 @ (setadjoin @ X952 @ emptyset)) @ emptyset))))=>(![X953:$i, X954:$i]:((iskpair @ (kpair @ X953 @ X954)))=>(![X955:$i, X956:$i]:(((in @ X956 @ X955)=>(subset @ (setadjoin @ X956 @ emptyset) @ X955)))=>(![X957:$i, X958:$i]:(((in @ X958 @ X957)=>(in @ (setadjoin @ X958 @ emptyset) @ (powerset @ X957))))=>(![X959:$i, X960:$i, X961:$i]:(((in @ X961 @ X959)=>(in @ (setadjoin @ X961 @ emptyset) @ (powerset @ (binunion @ X959 @ X960)))))=>(![X962:$i, X963:$i, X964:$i]:(((in @ X964 @ (setadjoin @ X962 @ (setadjoin @ X963 @ emptyset)))=>(((X964)=(X962))|((X964)=(X963)))))=>(![X965:$i, X966:$i, X967:$i]:(((in @ X967 @ X965)=>![X968:$i]:(((in @ X968 @ X966)=>(subset @ (setadjoin @ X967 @ (setadjoin @ X968 @ emptyset)) @ (binunion @ X965 @ X966))))))=>(![X969:$i, X970:$i, X971:$i]:(((in @ X971 @ X969)=>![X972:$i]:(((in @ X972 @ X970)=>(in @ (setadjoin @ X971 @ (setadjoin @ X972 @ emptyset)) @ (powerset @ (binunion @ X969 @ X970)))))))=>(![X973:$i, X974:$i, X975:$i]:(((in @ X975 @ X973)=>![X976:$i]:(((in @ X976 @ X974)=>(subset @ (setadjoin @ (setadjoin @ X975 @ emptyset) @ (setadjoin @ (setadjoin @ X975 @ (setadjoin @ X976 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X973 @ X974)))))))=>(![X977:$i, X978:$i, X979:$i]:(((in @ X979 @ X977)=>![X980:$i]:(((in @ X980 @ X978)=>(in @ (setadjoin @ (setadjoin @ X979 @ emptyset) @ (setadjoin @ (setadjoin @ X979 @ (setadjoin @ X980 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X977 @ X978))))))))=>(![X981:$i, X982:$i, X983:$i]:(((in @ X983 @ X981)=>![X984:$i]:(((in @ X984 @ X982)=>(in @ (kpair @ X983 @ X984) @ (powerset @ (powerset @ (binunion @ X981 @ X982))))))))=>(![X985:$i, X986:$i, X987:$i]:(((in @ X987 @ X985)=>![X988:$i]:(((in @ X988 @ X986)=>(in @ (kpair @ X987 @ X988) @ (cartprod @ X985 @ X986))))))=>(![X989:$i, X990:$i, X991:$i]:(((in @ X991 @ (cartprod @ X989 @ X990))=>?[X992:$i]:(((in @ X992 @ X989)&?[X993:$i]:(((in @ X993 @ X990)&((X991)=(kpair @ X992 @ X993))))))))=>(![X994:$i, X995:$i, X996:$i]:(((in @ X996 @ (cartprod @ X994 @ X995))=>(iskpair @ X996)))=>(![X997:$i, X998:$i]:(((in @ X998 @ (setunion @ X997))=>?[X999:$i]:(((in @ X999 @ X997)&(in @ X998 @ X999)))))=>(![X1000:$i]:((subset @ (setunion @ (setadjoin @ X1000 @ emptyset)) @ X1000))=>(![X1001:$i]:((subset @ X1001 @ (setunion @ (setadjoin @ X1001 @ emptyset))))=>(![X1002:$i]:(((setunion @ (setadjoin @ X1002 @ emptyset))=(X1002)))=>(![X1003:$i, X1004:$i > $o]:((![X1005:$i]:(((in @ X1005 @ X1003)=>![X1006:$i]:(((in @ X1006 @ X1003)=>((X1004 @ X1005)=>((X1004 @ X1006)=>((X1005)=(X1006))))))))=>(?[X1007:$i]:(((in @ X1007 @ X1003)&(X1004 @ X1007)))=>?[X1008:$i]:(((in @ X1008 @ (dsetconstr @ X1003 @ X1004))&((dsetconstr @ X1003 @ X1004)=(setadjoin @ X1008 @ emptyset)))))))=>(![X1009:$i, X1010:$i > $o]:((?[X1011:$i]:(((in @ X1011 @ (dsetconstr @ X1009 @ X1010))&((dsetconstr @ X1009 @ X1010)=(setadjoin @ X1011 @ emptyset))))=>?[X1012:$i]:(((in @ X1012 @ X1009)&(X1010 @ X1012)))))=>(![X1013:$i, X1014:$i > $o, X1015:$i]:(((in @ X1015 @ X1013)=>((X1014 @ X1015)=>(![X1016:$i]:(((in @ X1016 @ X1013)=>((X1014 @ X1016)=>((X1016)=(X1015)))))=>?[X1017:$i]:(((in @ X1017 @ (dsetconstr @ X1013 @ X1014))&((dsetconstr @ X1013 @ X1014)=(setadjoin @ X1017 @ emptyset))))))))=>(![X1018:$i, X1019:$i > $o]:((![X1020:$i]:(((in @ X1020 @ X1018)=>![X1021:$i]:(((in @ X1021 @ X1018)=>((X1019 @ X1020)=>((X1019 @ X1021)=>((X1020)=(X1021))))))))=>(?[X1022:$i]:(((in @ X1022 @ X1018)&(X1019 @ X1022)))=>?[X1023:$i]:(((in @ X1023 @ (dsetconstr @ X1018 @ X1019))&((dsetconstr @ X1018 @ X1019)=(setadjoin @ X1023 @ emptyset)))))))=>(![X1024:$i, X1025:$i]:((((setadjoin @ X1024 @ emptyset)=(setadjoin @ X1025 @ emptyset))=>((X1024)=(X1025))))=>(![X1026:$i, X1027:$i, X1028:$i]:(((in @ (setadjoin @ X1028 @ emptyset) @ (setadjoin @ (setadjoin @ X1026 @ emptyset) @ (setadjoin @ (setadjoin @ X1026 @ (setadjoin @ X1027 @ emptyset)) @ emptyset)))=>((X1026)=(X1028))))=>(![X1029:$i]:(((iskpair @ X1029)=>?[X1030:$i]:(((in @ X1030 @ (dsetconstr @ (setunion @ X1029) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1029)))))&((dsetconstr @ (setunion @ X1029) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1029))))=(setadjoin @ X1030 @ emptyset))))))=>(![X1031:$i]:((?[X1032:$i]:(((in @ X1032 @ X1031)&((X1031)=(setadjoin @ X1032 @ emptyset))))=>(in @ (setunion @ X1031) @ X1031)))=>(![X1033:$i, X1034:$i]:(((kfst @ (kpair @ X1033 @ X1034))=(X1033)))=>(![X1035:$i, X1036:$i, X1037:$i]:(((in @ X1037 @ (cartprod @ X1035 @ X1036))=>(in @ (kfst @ X1037) @ X1035)))=>(![X1038:$i, X1039:$i, X1040:$i, X1041:$i]:((((setadjoin @ (setadjoin @ X1038 @ emptyset) @ (setadjoin @ (setadjoin @ X1038 @ (setadjoin @ X1039 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1040 @ emptyset) @ (setadjoin @ (setadjoin @ X1040 @ (setadjoin @ X1041 @ emptyset)) @ emptyset)))=>((X1038)=(X1040))))=>(![X1042:$i, X1043:$i, X1044:$i, X1045:$i]:((((kpair @ X1042 @ X1043)=(kpair @ X1044 @ X1045))=>((X1042)=(X1044))))=>(![X1046:$i, X1047:$i]:((((X1046)=(X1047))=>((setadjoin @ X1046 @ (setadjoin @ X1047 @ emptyset))=(setadjoin @ X1046 @ emptyset))))=>(![X1048:$i, X1049:$i]:((((X1048)=(X1049))=>((setadjoin @ (setadjoin @ X1048 @ emptyset) @ (setadjoin @ (setadjoin @ X1048 @ (setadjoin @ X1049 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1048 @ emptyset) @ emptyset))))=>(![X1050:$i, X1051:$i, X1052:$i, X1053:$i]:((((setadjoin @ (setadjoin @ X1050 @ emptyset) @ (setadjoin @ (setadjoin @ X1050 @ (setadjoin @ X1051 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1052 @ emptyset) @ (setadjoin @ (setadjoin @ X1052 @ (setadjoin @ X1053 @ emptyset)) @ emptyset)))=>(((X1052)=(X1053))=>((X1051)=(X1053)))))=>(![X1054:$i, X1055:$i, X1056:$i]:((((setadjoin @ X1054 @ (setadjoin @ X1055 @ emptyset))=(setadjoin @ X1056 @ emptyset))=>((X1054)=(X1055))))=>(![X1057:$i, X1058:$i, X1059:$i, X1060:$i]:((((setadjoin @ (setadjoin @ X1057 @ emptyset) @ (setadjoin @ (setadjoin @ X1057 @ (setadjoin @ X1058 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1059 @ emptyset) @ (setadjoin @ (setadjoin @ X1059 @ (setadjoin @ X1060 @ emptyset)) @ emptyset)))=>((X1058)=(X1060))))=>(![X1061:$i, X1062:$i, X1063:$i, X1064:$i]:((((kpair @ X1061 @ X1062)=(kpair @ X1063 @ X1064))=>((X1062)=(X1064))))=>(![X1065:$i]:(((iskpair @ X1065)=>?[X1066:$i]:(((in @ X1066 @ (dsetconstr @ (setunion @ X1065) @ (^[Z0/* 3 */:$i]:(((X1065)=(kpair @ (kfst @ X1065) @ Z0))))))&((dsetconstr @ (setunion @ X1065) @ (^[Z0/* 3 */:$i]:(((X1065)=(kpair @ (kfst @ X1065) @ Z0)))))=(setadjoin @ X1066 @ emptyset))))))=>(![X1067:$i, X1068:$i]:(((ksnd @ (kpair @ X1067 @ X1068))=(X1068)))=>(![X1069:$i]:(((iskpair @ X1069)=>((kpair @ (kfst @ X1069) @ (ksnd @ X1069))=(X1069))))=>(![X1070:$i, X1071:$i, X1072:$i]:(((in @ X1072 @ (cartprod @ X1070 @ X1071))=>(in @ (ksnd @ X1072) @ X1071)))=>(![X1073:$i, X1074:$i, X1075:$i, X1076:$i]:(((in @ (kpair @ X1075 @ X1076) @ (cartprod @ X1073 @ X1074))=>(in @ X1075 @ X1073)))=>(![X1077:$i, X1078:$i, X1079:$i, X1080:$i]:(((in @ (kpair @ X1079 @ X1080) @ (cartprod @ X1077 @ X1078))=>(in @ X1080 @ X1078)))=>(![X1081:$i, X1082:$i, X1083:$i]:(((in @ X1083 @ X1081)=>![X1084:$i]:(((in @ X1084 @ X1082)=>((kpair @ X1083 @ X1084)=(kpair @ X1083 @ X1084))))))=>(![X1085:$i, X1086:$i, X1087:$i]:(((in @ X1087 @ X1085)=>![X1088:$i]:(((in @ X1088 @ X1086)=>((kfst @ (kpair @ X1087 @ X1088))=(X1087))))))=>(![X1089:$i, X1090:$i, X1091:$i]:(((in @ X1091 @ X1089)=>![X1092:$i]:(((in @ X1092 @ X1090)=>((ksnd @ (kpair @ X1091 @ X1092))=(X1092))))))=>(![X1093:$i, X1094:$i, X1095:$i]:(((in @ X1095 @ (cartprod @ X1093 @ X1094))=>((kpair @ (kfst @ X1095) @ (ksnd @ X1095))=(X1095))))=>![X4:$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 @ X23))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 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(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[dpsetconstrI])]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_211]), foundationAx]), wellorderingAx]), c_0_212]), c_0_213]), c_0_214]), c_0_215]), c_0_216]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_217]), setext]), emptyI]), noeltsimpempty]), c_0_218]), c_0_219]), c_0_220]), c_0_221]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_222]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_223]), c_0_224]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_225]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_226]), c_0_227]), c_0_228]), inCongP]), in__Cong]), c_0_229]), c_0_230]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_231]), c_0_232]), c_0_233]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_234]), c_0_235]), 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_236]), c_0_237]), c_0_238]), c_0_239]), singletonsuniq]), setukpairinjL1]), c_0_240]), c_0_241]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_242]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq])])]), c_0_243])).
% 1.05/0.70 thf(c_0_245, plain, ![X1096:$i, X1097:$i, X1098:$i > $i > $o]:(((dpsetconstr @ X1096 @ X1097 @ X1098)=(dsetconstr @ (cartprod @ X1096 @ X1097) @ (^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ X1096)&?[X3:$i]:((((in @ X3 @ X1097)&X1098 @ X2 @ X3)&((Z0)=(kpair @ X2 @ X3))))))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[dpsetconstr])])).
% 1.05/0.70 thf(c_0_246, negated_conjecture, ![X1102:$i, X1103:$i, X1105:$i, X1106:$i, X1107:$i, X1108:$i, X1109:$i, X1110:$i, X1111:$i, X1112:$i, X1113:$i, X1115:$i, X1116:$i, X1118:$i, X1119:$i, X1120:$i, X1121:$i, X1122:$i, X1124:$i, X1125:$i > $i > $o, X1126:$i, X1128:$i, X1131:$i, X1133:$i, X1134:$i, X1135:$i, X1136:$i, X1138:$i, X1139:$i > $o, X1140:$i, X1142:$i, X1143:$i > $o, X1144:$i, X1145:$i, X1146:$i > $o, X1147:$i, X1148:$i, X1149:$i > $o, X1150:$i, X1151:$i > $o, X1152:$i, X1155:$i, X1156:$o, X1157:$i, X1158:$i, X1159:$o, X1160:$i, X1161:$i, X1162:$i > $o, X1163:$i, X1166:$i, X1167:$i, X1170:$i, X1172:$i, X1174:$i, X1175:$i > $o, X1176:$i, X1177:$i, X1179:$i, X1180:$i > $o, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1185:$i, X1186:$i, X1187:$i, X1188:$i, X1189:$i, X1190:$i, X1191:$i, X1192:$o, X1193:$i, X1194:$i, X1195:$i, X1196:$i, X1197:$i, X1198:$i, X1200:$i, X1201:$i, X1202:$i, X1203:$i, X1204:$i, X1205:$i, X1206:$i, X1207:$i, X1208:$i, X1209:$i, X1210:$o, X1212:$i, X1213:$i, X1214:$i > $o, X1215:$i, X1218:$i, X1219:$i, X1220:$i, X1222:$i, X1223:$i, X1224:$i, X1225:$i, X1226:$i, X1227:$i, X1228:$i, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i > $o, X1239:$i, X1240:$i > $o, X1241:$i, X1242:$i, X1243:$i > $o, X1244:$i, X1246:$i, X1247:$i > $o, X1249:$i, X1250:$i, X1251:$i > $o, X1253:$i, X1254:$i, X1255:$i > $o, X1256:$i, X1258:$o, X1259:$o, X1260:$i, X1261:$i > $o, X1263:$i, X1264:$i, X1265:$i > $o, X1266:$i, X1268:$i > $o, X1269:$i, X1272:$i, X1273:$i > $o, X1274:$i, X1278:$i, X1279:$i > $o, X1280:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i, X1287:$i, X1288:$i, X1289:$i, X1290:$i, X1291:$i, X1292:$i > $o, X1293:$i, X1295:$i, X1296:$i, X1297:$i > $o, X1298:$i > $o, X1301:$i, X1304:$i, X1305:$i, X1308:$i, X1309:$i, X1310:$i, X1311:$i, X1312:$i, X1313:$i, X1314:$i, X1315:$i, X1316:$i, X1317:$i > $o, X1318:$i, X1320:$i, X1321:$i, X1322:$i > $o, X1323:$i > $o, X1326:$i, X1328:$i, X1330:$i, X1331:$i, X1332:$i > $o, X1333:$i > $o, X1336:$i, X1337:$i, X1339:$i, X1340:$i, X1341:$i, X1342:$i, X1343:$i, X1344:$i, X1346:$i, X1347:$i, X1348:$i, X1349:$i, X1350:$i, X1351:$i, X1352:$i, X1353:$i, X1354:$i, X1355:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i, X1366:$i, X1367:$i, X1368:$i, X1369:$i, X1370:$i, X1371:$i, X1372:$i, X1373:$i, X1374:$i, X1375:$i, X1376:$i, X1377:$i, X1378:$i, X1379:$i, X1380:$i, X1381:$i, X1382:$i, X1383:$i > $o, X1384:$i, X1385:$i > $o, X1386:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1393:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$o, X1398:$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, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$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, X1458:$i, X1459:$i, X1460:$i, X1461:$i, X1462:$i, X1463:$i, X1464:$i, X1465:$o, 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:$i, X1499:$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:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i > $o, X1540:$i, X1542:$i, X1543:$i > $o, X1544:$i, X1546:$i, X1547:$i > $o, X1548:$i, X1551:$i, X1552:$i > $o, X1555:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1573:$i, X1574:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1580:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i, X1586:$i, X1587:$i, X1588:$i, X1589:$i, X1590:$i, X1591:$i, X1592:$i, X1593:$i, X1594:$i, X1595:$i, X1596:$i, X1597:$i, X1598:$i, X1600:$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]:((((~(in @ (esk1_2 @ X1102 @ X1103) @ X1102)|~(in @ (esk1_2 @ X1102 @ X1103) @ X1103)|((X1102)=(X1103)))&((in @ (esk1_2 @ X1102 @ X1103) @ X1102)|(in @ (esk1_2 @ X1102 @ X1103) @ X1103)|((X1102)=(X1103))))&(~(in @ X1105 @ emptyset)&(((~(in @ X1108 @ (setadjoin @ X1106 @ X1107))|(((X1108)=(X1106))|(in @ X1108 @ X1107)))&((((X1108)!=(X1106))|(in @ X1108 @ (setadjoin @ X1106 @ X1107)))&(~(in @ X1108 @ X1107)|(in @ X1108 @ (setadjoin @ X1106 @ X1107)))))&(((~(in @ X1110 @ (powerset @ X1109))|(~(in @ X1111 @ X1110)|(in @ X1111 @ X1109)))&(((in @ (esk2_2 @ X1112 @ X1113) @ X1113)|(in @ X1113 @ (powerset @ X1112)))&(~(in @ (esk2_2 @ X1112 @ X1113) @ X1112)|(in @ X1113 @ (powerset @ X1112)))))&(((((in @ X1116 @ (esk3_2 @ X1115 @ X1116))|~(in @ X1116 @ (setunion @ X1115)))&((in @ (esk3_2 @ X1115 @ X1116) @ X1115)|~(in @ X1116 @ (setunion @ X1115))))&(~(in @ X1119 @ X1120)|~(in @ X1120 @ X1118)|(in @ X1119 @ (setunion @ X1118))))&((in @ emptyset @ omega)&((~(in @ X1121 @ omega)|(in @ (setadjoin @ X1121 @ X1121) @ omega))&(((((in @ (esk4_1 @ X1122) @ omega)|~(in @ emptyset @ X1122)|(~(in @ X1124 @ omega)|(in @ X1124 @ X1122)))&((in @ (esk4_1 @ X1122) @ X1122)|~(in @ emptyset @ X1122)|(~(in @ X1124 @ omega)|(in @ X1124 @ X1122))))&(~(in @ (setadjoin @ (esk4_1 @ X1122) @ (esk4_1 @ X1122)) @ X1122)|~(in @ emptyset @ X1122)|(~(in @ X1124 @ omega)|(in @ X1124 @ X1122))))&((((((in @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1126)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|(in @ (esk5_2 @ X1125 @ X1126) @ X1126))&((X1125 @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1131)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|(in @ (esk5_2 @ X1125 @ X1126) @ X1126)))&(~(in @ X1134 @ X1126)|~(X1125 @ X1134 @ X1133)|(in @ X1133 @ (esk7_2 @ X1125 @ X1126))|(in @ (esk5_2 @ X1125 @ X1126) @ X1126)))&(((((in @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1126)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|((X1125 @ (esk5_2 @ X1125 @ X1126) @ (esk6_3 @ X1125 @ X1126 @ X1128))|~(X1125 @ (esk5_2 @ X1125 @ X1126) @ X1128)))&((X1125 @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1131)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|((X1125 @ (esk5_2 @ X1125 @ X1126) @ (esk6_3 @ X1125 @ X1126 @ X1128))|~(X1125 @ (esk5_2 @ X1125 @ X1126) @ X1128))))&(~(in @ X1134 @ X1126)|~(X1125 @ X1134 @ X1133)|(in @ X1133 @ (esk7_2 @ X1125 @ X1126))|((X1125 @ (esk5_2 @ X1125 @ X1126) @ (esk6_3 @ X1125 @ X1126 @ X1128))|~(X1125 @ (esk5_2 @ X1125 @ X1126) @ X1128))))&((((in @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1126)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|(((X1128)!=(esk6_3 @ X1125 @ X1126 @ X1128))|~(X1125 @ (esk5_2 @ X1125 @ X1126) @ X1128)))&((X1125 @ (esk8_3 @ X1125 @ X1126 @ X1131) @ X1131)|~(in @ X1131 @ (esk7_2 @ X1125 @ X1126))|(((X1128)!=(esk6_3 @ X1125 @ X1126 @ X1128))|~(X1125 @ (esk5_2 @ X1125 @ X1126) @ X1128))))&(~(in @ X1134 @ X1126)|~(X1125 @ X1134 @ X1133)|(in @ X1133 @ (esk7_2 @ X1125 @ X1126))|(((X1128)!=(esk6_3 @ X1125 @ X1126 @ X1128))|~(X1125 @ (esk5_2 @ X1125 @ X1126) @ X1128))))))&((((in @ (esk9_1 @ X1135) @ X1135)|~(in @ X1136 @ X1135))&(~(in @ X1138 @ (esk9_1 @ X1135))|~(in @ X1138 @ X1135)|~(in @ X1136 @ X1135)))&((epred1_0)&((((X1139 @ (esk10_2 @ X1139 @ X1140))|~(X1139 @ X1140)|(X1139 @ (descr @ X1139)))&(((X1140)!=(esk10_2 @ X1139 @ X1140))|~(X1139 @ X1140)|(X1139 @ (descr @ X1139))))&((~(in @ X1144 @ X1142)|(~(X1143 @ X1144)|(in @ X1144 @ (dsetconstr @ X1142 @ X1143))))&((~(in @ X1147 @ (dsetconstr @ X1145 @ X1146))|(in @ X1147 @ X1145))&((~(in @ X1150 @ (dsetconstr @ X1148 @ X1149))|(X1149 @ X1150))&(((((X1151 @ (esk12_1 @ X1151))|((X1151 @ (esk11_2 @ X1151 @ X1152))|~(X1151 @ X1152)))&(~(X1151 @ X1155)|((esk12_1 @ X1151)=(X1155))|((X1151 @ (esk11_2 @ X1151 @ X1152))|~(X1151 @ X1152))))&(((X1151 @ (esk12_1 @ X1151))|(((X1152)!=(esk11_2 @ X1151 @ X1152))|~(X1151 @ X1152)))&(~(X1151 @ X1155)|((esk12_1 @ X1151)=(X1155))|(((X1152)!=(esk11_2 @ X1151 @ X1152))|~(X1151 @ X1152)))))&((~(in @ X1157 @ (prop2set @ ((X1156))))|(X1156))&((~(in @ X1158 @ emptyset)|(X1159))&((~(in @ X1160 @ emptyset)|~($true))&(~(in @ X1161 @ emptyset)&((((X1162 @ (esk13_2 @ X1162 @ X1163))|~(X1162 @ X1163)|(X1162 @ (esk14_1 @ X1162)))&(((X1163)!=(esk13_2 @ X1162 @ X1163))|~(X1162 @ X1163)|(X1162 @ (esk14_1 @ X1162))))&(((((in @ (esk16_2 @ X1166 @ X1167) @ X1167)|((X1166)=(X1167))|(in @ (esk15_2 @ X1166 @ X1167) @ X1166))&(~(in @ (esk16_2 @ X1166 @ X1167) @ X1166)|((X1166)=(X1167))|(in @ (esk15_2 @ X1166 @ X1167) @ X1166)))&(((in @ (esk16_2 @ X1166 @ X1167) @ X1167)|((X1166)=(X1167))|~(in @ (esk15_2 @ X1166 @ X1167) @ X1167))&(~(in @ (esk16_2 @ X1166 @ X1167) @ X1166)|((X1166)=(X1167))|~(in @ (esk15_2 @ X1166 @ X1167) @ X1167))))&(((in @ (esk17_1 @ X1170) @ X1170)|((X1170)=(emptyset)))&(((in @ (esk18_1 @ X1172) @ X1172)|((X1172)=(emptyset)))&(((~(in @ X1176 @ (dsetconstr @ X1174 @ X1175))|(X1175 @ X1176)|~(in @ X1176 @ X1174))&(~(X1175 @ X1176)|(in @ X1176 @ (dsetconstr @ X1174 @ X1175))|~(in @ X1176 @ X1174)))&((((X1177)=(emptyset))|(in @ (esk19_1 @ X1177) @ X1177))&((~(in @ X1181 @ X1179)|(~(X1180 @ X1181)|((dsetconstr @ X1179 @ X1180)!=(emptyset))))&((~(in @ X1183 @ X1182)|((X1182)!=(emptyset)))&((in @ X1184 @ (setadjoin @ X1184 @ X1185))&((in @ emptyset @ (setadjoin @ emptyset @ emptyset))&((~(in @ X1188 @ X1187)|(in @ X1188 @ (setadjoin @ X1186 @ X1187)))&(((((in @ X1191 @ X1190)|(X1192)|((X1191)=(X1189))|~(in @ X1191 @ (setadjoin @ X1189 @ X1190)))&(~(X1192)|(X1192)|((X1191)=(X1189))|~(in @ X1191 @ (setadjoin @ X1189 @ X1190))))&(((in @ X1191 @ X1190)|(X1192)|~(X1192)|~(in @ X1191 @ (setadjoin @ X1189 @ X1190)))&(~(X1192)|(X1192)|~(X1192)|~(in @ X1191 @ (setadjoin @ X1189 @ X1190)))))&((~(in @ X1195 @ (setadjoin @ X1193 @ X1194))|(((X1195)=(X1193))|(in @ X1195 @ X1194)))&(((dsetconstr @ X1196 @ (^[Z0/* 1 */:$i]:($true)))=(X1196))&((((in @ (esk20_2 @ X1197 @ X1198) @ X1198)|(in @ X1198 @ (powerset @ X1197)))&(~(in @ (esk20_2 @ X1197 @ X1198) @ X1197)|(in @ X1198 @ (powerset @ X1197))))&((in @ emptyset @ (powerset @ X1200))&((in @ emptyset @ (powerset @ X1201))&((~(in @ X1203 @ (powerset @ X1202))|(~(in @ X1204 @ X1203)|(in @ X1204 @ X1202)))&((~(in @ X1206 @ X1207)|(~(in @ X1207 @ X1205)|(in @ X1206 @ (setunion @ X1205))))&((((in @ X1209 @ (esk21_3 @ X1208 @ X1209 @ X1210))|(X1210)|~(in @ X1209 @ (setunion @ X1208)))&(((in @ (esk21_3 @ X1208 @ X1209 @ X1210) @ X1208)|(X1210)|~(in @ X1209 @ (setunion @ X1208)))&(~(X1210)|(X1210)|~(in @ X1209 @ (setunion @ X1208)))))&((~(in @ X1213 @ X1212)|(in @ X1213 @ (powerset @ (setunion @ X1212))))&((((~(X1214 @ X1218)|((X1218)=(esk23_1 @ X1214))|((X1214 @ (esk22_2 @ X1214 @ X1215))|~(X1214 @ X1215)))&(((X1219)!=(esk23_1 @ X1214))|(X1214 @ X1219)|((X1214 @ (esk22_2 @ X1214 @ X1215))|~(X1214 @ X1215))))&((~(X1214 @ X1218)|((X1218)=(esk23_1 @ X1214))|(((X1215)!=(esk22_2 @ X1214 @ X1215))|~(X1214 @ X1215)))&(((X1219)!=(esk23_1 @ X1214))|(X1214 @ X1219)|(((X1215)!=(esk22_2 @ X1214 @ X1215))|~(X1214 @ X1215)))))&((((in @ (esk24_1 @ X1220) @ X1220)|((X1220)=(emptyset)))&(($true)|((X1220)=(emptyset))))&((~(in @ X1222 @ (setadjoin @ X1223 @ emptyset))|((X1222)=(X1223)))&((((X1224)=(X1225))|~(in @ X1225 @ (setadjoin @ X1224 @ emptyset)))&((((X1226)!=(X1227))|(in @ X1226 @ (setadjoin @ X1227 @ emptyset)))&((~(in @ X1228 @ (setadjoin @ X1229 @ emptyset))|(in @ X1229 @ (setadjoin @ X1228 @ emptyset)))&((~(in @ X1232 @ (setadjoin @ X1230 @ (setadjoin @ X1231 @ emptyset)))|(((X1232)=(X1230))|((X1232)=(X1231))))&((in @ X1233 @ (setadjoin @ X1233 @ (setadjoin @ X1234 @ emptyset)))&((in @ X1236 @ (setadjoin @ X1235 @ (setadjoin @ X1236 @ emptyset)))&((~(in @ X1239 @ X1237)|~(X1238 @ X1239)|(((dsetconstr @ X1237 @ X1238)!=(emptyset))|~($true)))&((~(in @ X1241 @ emptyset)|(X1240 @ X1241))&((((in @ (esk25_2 @ X1242 @ X1243) @ X1242)|(~(in @ X1244 @ X1242)|(X1243 @ X1244)))&(~(X1243 @ (esk25_2 @ X1242 @ X1243))|(~(in @ X1244 @ X1242)|(X1243 @ X1244))))&((((in @ (esk26_2 @ X1246 @ X1247) @ X1246)|(~(in @ X1249 @ X1246)|~(X1247 @ X1249)))&((X1247 @ (esk26_2 @ X1246 @ X1247))|(~(in @ X1249 @ X1246)|~(X1247 @ X1249))))&((((in @ (esk27_2 @ X1250 @ X1251) @ X1250)|(~(in @ X1253 @ X1250)|~(X1251 @ X1253)))&((X1251 @ (esk27_2 @ X1250 @ X1251))|(~(in @ X1253 @ X1250)|~(X1251 @ X1253))))&((((in 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X1395)))&(~(X1397)|(X1397)|~(X1397)|~(in @ X1396 @ (binunion @ X1394 @ X1395)))))&((~(in @ X1400 @ (binunion @ X1398 @ X1399))|((in @ X1400 @ X1398)|(in @ X1400 @ X1399)))&((subset @ X1401 @ (binunion @ X1401 @ X1402))&((subset @ X1404 @ (binunion @ X1403 @ X1404))&((~(in @ X1407 @ X1405)|(~(in @ X1407 @ X1406)|(in @ X1407 @ (binintersect @ X1405 @ X1406))))&((~(subset @ X1410 @ X1408)|(~(subset @ X1410 @ X1409)|(subset @ X1410 @ (binintersect @ X1408 @ X1409))))&((~(in @ X1413 @ (binintersect @ X1411 @ X1412))|(in @ X1413 @ X1411))&((subset @ (binintersect @ X1414 @ X1415) @ X1414)&((~(subset @ X1416 @ X1417)|((binintersect @ X1416 @ X1417)=(X1416)))&((((binintersect @ X1418 @ X1419)!=(X1419))|(subset @ X1419 @ X1418))&((~(in @ X1422 @ (binintersect @ X1420 @ X1421))|(in @ X1422 @ X1421))&((((in @ (esk54_2 @ X1423 @ X1424) @ X1423)|((binintersect @ X1423 @ X1424)=(emptyset)))&((in @ (esk54_2 @ X1423 @ X1424) @ X1424)|((binintersect @ X1423 @ X1424)=(emptyset))))&((subset @ (binintersect @ X1426 @ X1427) @ X1427)&((~(subset @ X1429 @ X1428)|((binintersect @ X1428 @ X1429)=(X1429)))&((((binintersect @ X1430 @ X1431)!=(X1430))|(subset @ X1430 @ X1431))&(((binintersect @ X1432 @ (binunion @ X1433 @ X1434))=(binunion @ (binintersect @ X1432 @ X1433) @ (binintersect @ X1432 @ X1434)))&((~(in @ X1437 @ X1435)|((in @ X1437 @ X1436)|(in @ X1437 @ (setminus @ X1435 @ X1436))))&((~(in @ X1440 @ (setminus @ X1438 @ X1439))|(in @ X1440 @ X1438))&((~(in @ X1443 @ (setminus @ X1441 @ X1442))|~(in @ X1443 @ X1442))&((~(subset @ X1444 @ X1445)|((setminus @ X1444 @ X1445)=(emptyset)))&(((in @ X1448 @ (setminus @ X1446 @ X1447))|(~(in @ X1448 @ X1446)|(in @ X1448 @ X1447)))&(((in @ X1451 @ (setminus @ X1449 @ X1450))|((in @ X1451 @ X1450)|~(in @ X1451 @ X1449)))&(((in @ X1454 @ X1452)|~(in @ X1454 @ (setminus @ X1452 @ X1453)))&((~(in @ X1457 @ X1456)|~(in @ X1457 @ (setminus @ X1455 @ X1456)))&((subset @ (setminus @ X1458 @ X1459) @ X1458)&((((setminus @ X1460 @ X1461)!=(emptyset))|(subset @ X1460 @ X1461))&((((~(in @ X1464 @ X1462)|(X1465)|(in @ X1464 @ X1462)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))&(((in @ X1464 @ X1463)|(X1465)|(in @ X1464 @ X1462)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))&(~(X1465)|(X1465)|(in @ X1464 @ X1462)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))))&(((~(in @ X1464 @ X1462)|(X1465)|~(in @ X1464 @ X1463)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))&(((in @ X1464 @ X1463)|(X1465)|~(in @ X1464 @ X1463)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))&(~(X1465)|(X1465)|~(in @ X1464 @ X1463)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))))&((~(in @ X1464 @ X1462)|(X1465)|~(X1465)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))&(((in @ X1464 @ X1463)|(X1465)|~(X1465)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))&(~(X1465)|(X1465)|~(X1465)|~(in @ X1464 @ (symdiff @ X1462 @ X1463)))))))&((~(in @ X1468 @ X1466)|((in @ X1468 @ X1467)|(in @ X1468 @ (symdiff @ X1466 @ X1467))))&(((in @ X1471 @ X1469)|(~(in @ X1471 @ X1470)|(in @ X1471 @ (symdiff @ X1469 @ X1470))))&((~(in @ X1474 @ X1472)|(~(in @ X1474 @ X1473)|~(in @ X1474 @ (symdiff @ X1472 @ X1473))))&(((in @ X1477 @ X1475)|((in @ X1477 @ X1476)|~(in @ X1477 @ (symdiff @ X1475 @ X1476))))&((in @ X1479 @ (setadjoin @ X1478 @ (setadjoin @ X1479 @ emptyset)))&((in @ X1480 @ (setunion @ (setadjoin @ (setadjoin @ X1480 @ emptyset) @ (setadjoin @ (setadjoin @ X1480 @ (setadjoin @ X1481 @ emptyset)) @ emptyset))))&((in @ X1483 @ (setunion @ (setadjoin @ (setadjoin @ X1482 @ emptyset) @ (setadjoin @ (setadjoin @ X1482 @ (setadjoin @ X1483 @ emptyset)) @ emptyset))))&((iskpair @ (setadjoin @ (setadjoin @ X1484 @ emptyset) @ (setadjoin @ (setadjoin @ X1484 @ (setadjoin @ X1485 @ emptyset)) @ emptyset)))&((iskpair @ (kpair @ X1486 @ X1487))&((~(in @ X1489 @ X1488)|(subset @ (setadjoin @ X1489 @ emptyset) @ X1488))&((~(in @ X1491 @ X1490)|(in @ (setadjoin @ X1491 @ emptyset) @ (powerset @ X1490)))&((~(in @ X1494 @ X1492)|(in @ (setadjoin @ X1494 @ emptyset) @ (powerset @ (binunion @ X1492 @ X1493))))&((~(in @ X1497 @ (setadjoin @ X1495 @ (setadjoin @ X1496 @ emptyset)))|(((X1497)=(X1495))|((X1497)=(X1496))))&((~(in @ X1500 @ X1498)|(~(in @ X1501 @ X1499)|(subset @ (setadjoin @ X1500 @ (setadjoin @ X1501 @ emptyset)) @ (binunion @ X1498 @ X1499))))&((~(in @ X1504 @ X1502)|(~(in @ X1505 @ X1503)|(in @ (setadjoin @ X1504 @ (setadjoin @ X1505 @ emptyset)) @ (powerset @ (binunion @ X1502 @ X1503)))))&((~(in @ X1508 @ X1506)|(~(in @ X1509 @ X1507)|(subset @ (setadjoin @ (setadjoin @ X1508 @ emptyset) @ (setadjoin @ (setadjoin @ X1508 @ (setadjoin @ X1509 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X1506 @ X1507)))))&((~(in @ X1512 @ X1510)|(~(in @ X1513 @ X1511)|(in @ (setadjoin @ (setadjoin @ X1512 @ emptyset) @ (setadjoin @ (setadjoin @ X1512 @ (setadjoin @ X1513 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X1510 @ X1511))))))&((~(in @ X1516 @ X1514)|(~(in @ X1517 @ X1515)|(in @ (kpair @ X1516 @ X1517) @ (powerset @ (powerset @ (binunion @ X1514 @ X1515))))))&((~(in @ X1520 @ X1518)|(~(in @ X1521 @ X1519)|(in @ (kpair @ X1520 @ X1521) @ (cartprod @ X1518 @ X1519))))&((((in @ (esk55_3 @ X1522 @ X1523 @ X1524) @ X1522)|~(in @ X1524 @ (cartprod @ X1522 @ X1523)))&(((in @ (esk56_3 @ X1522 @ X1523 @ X1524) @ X1523)|~(in @ X1524 @ (cartprod @ X1522 @ X1523)))&(((X1524)=(kpair @ (esk55_3 @ X1522 @ X1523 @ X1524) @ (esk56_3 @ X1522 @ X1523 @ X1524)))|~(in @ X1524 @ (cartprod @ X1522 @ X1523)))))&((~(in @ X1529 @ (cartprod @ X1527 @ X1528))|(iskpair @ X1529))&((((in @ (esk57_2 @ X1530 @ X1531) @ X1530)|~(in @ X1531 @ (setunion @ X1530)))&((in @ X1531 @ (esk57_2 @ X1530 @ X1531))|~(in @ X1531 @ (setunion @ X1530))))&((subset @ (setunion @ (setadjoin @ X1533 @ emptyset)) @ X1533)&((subset @ X1534 @ (setunion @ (setadjoin @ X1534 @ emptyset)))&(((setunion @ (setadjoin @ X1535 @ emptyset))=(X1535))&(((((in @ (esk60_2 @ X1536 @ X1537) @ (dsetconstr @ X1536 @ X1537))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|(in @ (esk58_2 @ X1536 @ X1537) @ X1536))&(((dsetconstr @ X1536 @ X1537)=(setadjoin @ (esk60_2 @ X1536 @ X1537) @ emptyset))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|(in @ (esk58_2 @ X1536 @ X1537) @ X1536)))&((((in @ (esk60_2 @ X1536 @ X1537) @ (dsetconstr @ X1536 @ X1537))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|(in @ (esk59_2 @ X1536 @ X1537) @ X1536))&(((dsetconstr @ X1536 @ X1537)=(setadjoin @ (esk60_2 @ X1536 @ X1537) @ emptyset))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|(in @ (esk59_2 @ X1536 @ X1537) @ X1536)))&((((in @ (esk60_2 @ X1536 @ X1537) @ (dsetconstr @ X1536 @ X1537))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|(X1537 @ (esk58_2 @ X1536 @ X1537)))&(((dsetconstr @ X1536 @ X1537)=(setadjoin @ (esk60_2 @ X1536 @ X1537) @ emptyset))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|(X1537 @ (esk58_2 @ X1536 @ X1537))))&((((in @ (esk60_2 @ X1536 @ X1537) @ (dsetconstr @ X1536 @ X1537))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|(X1537 @ (esk59_2 @ X1536 @ X1537)))&(((dsetconstr @ X1536 @ X1537)=(setadjoin @ (esk60_2 @ X1536 @ X1537) @ emptyset))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|(X1537 @ (esk59_2 @ X1536 @ X1537))))&(((in @ (esk60_2 @ X1536 @ X1537) @ (dsetconstr @ X1536 @ X1537))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|((esk58_2 @ X1536 @ X1537)!=(esk59_2 @ X1536 @ X1537)))&(((dsetconstr @ X1536 @ X1537)=(setadjoin @ (esk60_2 @ X1536 @ X1537) @ emptyset))|(~(in @ X1540 @ X1536)|~(X1537 @ X1540))|((esk58_2 @ X1536 @ X1537)!=(esk59_2 @ X1536 @ X1537))))))))&((((in @ (esk61_2 @ X1542 @ X1543) @ X1542)|(~(in @ X1544 @ (dsetconstr @ X1542 @ X1543))|((dsetconstr @ X1542 @ X1543)!=(setadjoin @ X1544 @ emptyset))))&((X1543 @ (esk61_2 @ X1542 @ X1543))|(~(in @ X1544 @ (dsetconstr @ X1542 @ X1543))|((dsetconstr @ X1542 @ X1543)!=(setadjoin @ X1544 @ emptyset)))))&(((((in @ (esk63_3 @ X1546 @ X1547 @ X1548) @ (dsetconstr @ X1546 @ X1547))|(in @ (esk62_3 @ X1546 @ X1547 @ X1548) @ X1546)|~(X1547 @ X1548)|~(in @ X1548 @ X1546))&(((dsetconstr @ X1546 @ X1547)=(setadjoin @ (esk63_3 @ X1546 @ X1547 @ X1548) @ emptyset))|(in @ (esk62_3 @ X1546 @ X1547 @ X1548) @ X1546)|~(X1547 @ X1548)|~(in @ X1548 @ X1546)))&((((in @ (esk63_3 @ X1546 @ X1547 @ X1548) @ (dsetconstr @ X1546 @ X1547))|(X1547 @ (esk62_3 @ X1546 @ X1547 @ X1548))|~(X1547 @ X1548)|~(in @ X1548 @ X1546))&(((dsetconstr @ X1546 @ X1547)=(setadjoin @ (esk63_3 @ X1546 @ X1547 @ X1548) @ emptyset))|(X1547 @ (esk62_3 @ X1546 @ X1547 @ X1548))|~(X1547 @ X1548)|~(in @ X1548 @ X1546)))&(((in @ (esk63_3 @ X1546 @ X1547 @ X1548) @ (dsetconstr @ X1546 @ X1547))|((esk62_3 @ X1546 @ X1547 @ X1548)!=(X1548))|~(X1547 @ X1548)|~(in @ X1548 @ X1546))&(((dsetconstr @ X1546 @ X1547)=(setadjoin @ (esk63_3 @ X1546 @ X1547 @ X1548) @ emptyset))|((esk62_3 @ X1546 @ X1547 @ X1548)!=(X1548))|~(X1547 @ X1548)|~(in @ X1548 @ X1546)))))&(((((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(in @ (esk64_2 @ X1551 @ X1552) @ X1551))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(in @ (esk64_2 @ X1551 @ X1552) @ X1551)))&((((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(in @ (esk65_2 @ X1551 @ X1552) @ X1551))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(in @ (esk65_2 @ X1551 @ X1552) @ X1551)))&((((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(X1552 @ (esk64_2 @ X1551 @ X1552)))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(X1552 @ (esk64_2 @ X1551 @ X1552))))&((((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(X1552 @ (esk65_2 @ X1551 @ X1552)))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|(X1552 @ (esk65_2 @ X1551 @ X1552))))&(((in @ (esk66_2 @ X1551 @ X1552) @ (dsetconstr @ X1551 @ X1552))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|((esk64_2 @ X1551 @ X1552)!=(esk65_2 @ X1551 @ X1552)))&(((dsetconstr @ X1551 @ X1552)=(setadjoin @ (esk66_2 @ X1551 @ X1552) @ emptyset))|(~(in @ X1555 @ X1551)|~(X1552 @ X1555))|((esk64_2 @ X1551 @ X1552)!=(esk65_2 @ X1551 @ X1552))))))))&((((setadjoin @ X1557 @ emptyset)!=(setadjoin @ X1558 @ emptyset))|((X1557)=(X1558)))&((~(in @ (setadjoin @ X1561 @ emptyset) @ (setadjoin @ (setadjoin @ X1559 @ emptyset) @ (setadjoin @ (setadjoin @ X1559 @ (setadjoin @ X1560 @ emptyset)) @ emptyset)))|((X1559)=(X1561)))&((((in @ (esk67_1 @ X1562) @ (dsetconstr @ (setunion @ X1562) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1562)))))|~(iskpair @ X1562))&(((dsetconstr @ (setunion @ X1562) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1562))))=(setadjoin @ (esk67_1 @ X1562) @ emptyset))|~(iskpair @ X1562)))&((~(in @ X1565 @ X1564)|((X1564)!=(setadjoin @ X1565 @ emptyset))|(in @ (setunion @ X1564) @ X1564))&(((kfst @ (kpair @ X1566 @ X1567))=(X1566))&((~(in @ X1570 @ (cartprod @ X1568 @ X1569))|(in @ (kfst @ X1570) @ X1568))&((((setadjoin @ (setadjoin @ X1571 @ emptyset) @ (setadjoin @ (setadjoin @ X1571 @ (setadjoin @ X1572 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1573 @ emptyset) @ (setadjoin @ (setadjoin @ X1573 @ (setadjoin @ X1574 @ emptyset)) @ emptyset)))|((X1571)=(X1573)))&((((kpair @ X1575 @ X1576)!=(kpair @ X1577 @ X1578))|((X1575)=(X1577)))&((((X1579)!=(X1580))|((setadjoin @ X1579 @ (setadjoin @ X1580 @ emptyset))=(setadjoin @ X1579 @ emptyset)))&((((X1581)!=(X1582))|((setadjoin @ (setadjoin @ X1581 @ emptyset) @ (setadjoin @ (setadjoin @ X1581 @ (setadjoin @ X1582 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1581 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1583 @ emptyset) @ (setadjoin @ (setadjoin @ X1583 @ (setadjoin @ X1584 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1585 @ emptyset) @ (setadjoin @ (setadjoin @ X1585 @ (setadjoin @ X1586 @ emptyset)) @ emptyset)))|(((X1585)!=(X1586))|((X1584)=(X1586))))&((((setadjoin @ X1587 @ (setadjoin @ X1588 @ emptyset))!=(setadjoin @ X1589 @ emptyset))|((X1587)=(X1588)))&((((setadjoin @ (setadjoin @ X1590 @ emptyset) @ (setadjoin @ (setadjoin @ X1590 @ (setadjoin @ X1591 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1592 @ emptyset) @ (setadjoin @ (setadjoin @ X1592 @ (setadjoin @ X1593 @ emptyset)) @ emptyset)))|((X1591)=(X1593)))&((((kpair @ X1594 @ X1595)!=(kpair @ X1596 @ X1597))|((X1595)=(X1597)))&((((in @ (esk68_1 @ X1598) @ (dsetconstr @ (setunion @ X1598) @ (^[Z0/* 3 */:$i]:(((X1598)=(kpair @ (kfst @ X1598) @ Z0))))))|~(iskpair @ X1598))&(((dsetconstr @ (setunion @ X1598) @ (^[Z0/* 3 */:$i]:(((X1598)=(kpair @ (kfst @ X1598) @ Z0)))))=(setadjoin @ (esk68_1 @ X1598) @ emptyset))|~(iskpair @ X1598)))&(((ksnd @ (kpair @ X1600 @ X1601))=(X1601))&((~(iskpair @ X1602)|((kpair @ (kfst @ X1602) @ (ksnd @ X1602))=(X1602)))&((~(in @ X1605 @ (cartprod @ X1603 @ X1604))|(in @ (ksnd @ X1605) @ X1604))&((~(in @ (kpair @ X1608 @ X1609) @ (cartprod @ X1606 @ X1607))|(in @ X1608 @ X1606))&((~(in @ (kpair @ X1612 @ X1613) @ (cartprod @ X1610 @ X1611))|(in @ X1613 @ X1611))&((~(in @ X1616 @ X1614)|(~(in @ X1617 @ X1615)|((kpair @ X1616 @ X1617)=(kpair @ X1616 @ X1617))))&((~(in @ X1620 @ X1618)|(~(in @ X1621 @ X1619)|((kfst @ (kpair @ X1620 @ X1621))=(X1620))))&((~(in @ X1624 @ X1622)|(~(in @ X1625 @ X1623)|((ksnd @ (kpair @ X1624 @ X1625))=(X1625))))&((~(in @ X1628 @ (cartprod @ X1626 @ X1627))|((kpair @ (kfst @ X1628) @ (ksnd @ X1628))=(X1628)))&((in @ esk71_0 @ esk69_0)&((in @ esk72_0 @ esk70_0)&((epred2_0 @ esk71_0 @ esk72_0)&~(in @ (kpair @ esk71_0 @ esk72_0) @ (dpsetconstr @ esk69_0 @ esk70_0 @ epred2_0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_244])])])])])])])).
% 1.05/0.70 thf(c_0_247, plain, ![X1099:$i, X1100:$i, X1101:$i > $i > $o]:(((dpsetconstr @ X1099 @ X1100 @ X1101)=(dsetconstr @ (cartprod @ X1099 @ X1100) @ (^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ X1099)&?[X3:$i]:((((in @ X3 @ X1100)&X1101 @ X2 @ X3)&((Z0)=(kpair @ X2 @ X3))))))))))), inference(variable_rename,[status(thm)],[c_0_245])).
% 1.05/0.70 thf(c_0_248, plain, ![X1655:$i, X2:$i, X3:$i, X6:$i > $i > $o]:(((epred3_3 @ X6 @ X3 @ X2 @ X1655)<=>?[X1653:$i]:(((in @ X1653 @ X2)&?[X1654:$i]:((((in @ X1654 @ X3)&(X6 @ X1653 @ X1654))&((X1655)=(kpair @ X1653 @ X1654)))))))), introduced(definition)).
% 1.05/0.70 thf(c_0_249, negated_conjecture, ~((in @ (kpair @ esk71_0 @ esk72_0) @ (dpsetconstr @ esk69_0 @ esk70_0 @ epred2_0))), inference(split_conjunct,[status(thm)],[c_0_246])).
% 1.05/0.70 thf(c_0_250, plain, ![X6:$i > $i > $o, X3:$i, X2:$i]:(((dpsetconstr @ X2 @ X3 @ X6)=(dsetconstr @ (cartprod @ X2 @ X3) @ (epred3_3 @ X6 @ X3 @ X2)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_247]), c_0_248])).
% 1.05/0.70 thf(c_0_251, plain, ![X1661:$i, X1662:$i, X1663:$i, X1664:$i > $i > $o, X1667:$i, X1668:$i]:(((((in @ (esk78_4 @ X1661 @ X1662 @ X1663 @ X1664) @ X1662)|~(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661))&((((in @ (esk79_4 @ X1661 @ X1662 @ X1663 @ X1664) @ X1663)|~(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661))&((X1664 @ (esk78_4 @ X1661 @ X1662 @ X1663 @ X1664) @ (esk79_4 @ X1661 @ X1662 @ X1663 @ X1664))|~(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661)))&(((X1661)=(kpair @ (esk78_4 @ X1661 @ X1662 @ X1663 @ X1664) @ (esk79_4 @ X1661 @ X1662 @ X1663 @ X1664)))|~(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661))))&(~(in @ X1667 @ X1662)|(~(in @ X1668 @ X1663)|~(X1664 @ X1667 @ X1668)|((X1661)!=(kpair @ X1667 @ X1668)))|(epred3_3 @ X1664 @ X1663 @ X1662 @ X1661)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])])])).
% 1.05/0.70 thf(c_0_252, negated_conjecture, ~((in @ (kpair @ esk71_0 @ esk72_0) @ (dsetconstr @ (cartprod @ esk69_0 @ esk70_0) @ (epred3_3 @ epred2_0 @ esk70_0 @ esk69_0)))), inference(rw,[status(thm)],[c_0_249, c_0_250])).
% 1.05/0.70 thf(c_0_253, negated_conjecture, ![X1:$i > $o, X2:$i, X3:$i]:(((in @ X2 @ (dsetconstr @ X3 @ X1))|~((X1 @ X2))|~((in @ X2 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_246])).
% 1.05/0.70 thf(c_0_254, plain, ![X3:$i, X2:$i, X6:$i > $i > $o, X7:$i, X5:$i, X4:$i]:(((epred3_3 @ X6 @ X5 @ X3 @ X7)|~((in @ X2 @ X3))|~((in @ X4 @ X5))|~((X6 @ X2 @ X4))|((X7)!=(kpair @ X2 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_251])).
% 1.05/0.70 thf(c_0_255, negated_conjecture, (~((in @ (kpair @ esk71_0 @ esk72_0) @ (cartprod @ esk69_0 @ esk70_0)))|~((epred3_3 @ epred2_0 @ esk70_0 @ esk69_0 @ (kpair @ esk71_0 @ esk72_0)))), inference(spm,[status(thm)],[c_0_252, c_0_253])).
% 1.05/0.70 thf(c_0_256, plain, ![X2:$i, X3:$i, X4:$i, X6:$i > $i > $o, X5:$i]:(((epred3_3 @ X6 @ X2 @ X3 @ (kpair @ X4 @ X5))|~((in @ X5 @ X2))|~((in @ X4 @ X3))|~((X6 @ X4 @ X5)))), inference(er,[status(thm)],[c_0_254])).
% 1.05/0.70 thf(c_0_257, negated_conjecture, (in @ esk72_0 @ esk70_0), inference(split_conjunct,[status(thm)],[c_0_246])).
% 1.05/0.70 thf(c_0_258, negated_conjecture, (in @ esk71_0 @ esk69_0), inference(split_conjunct,[status(thm)],[c_0_246])).
% 1.05/0.70 thf(c_0_259, negated_conjecture, (epred2_0 @ esk71_0 @ esk72_0), inference(split_conjunct,[status(thm)],[c_0_246])).
% 1.05/0.70 thf(c_0_260, negated_conjecture, ~((in @ (kpair @ esk71_0 @ esk72_0) @ (cartprod @ esk69_0 @ esk70_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_255, c_0_256]), c_0_257]), c_0_258]), c_0_259])])).
% 1.05/0.70 thf(c_0_261, negated_conjecture, ![X2:$i, X3:$i, X4:$i, X5:$i]:(((in @ (kpair @ X2 @ X4) @ (cartprod @ X3 @ X5))|~((in @ X2 @ X3))|~((in @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_246])).
% 1.05/0.70 thf(c_0_262, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_260, c_0_261]), c_0_257]), c_0_258])]), ['proof']).
% 1.05/0.70 # SZS output end CNFRefutation
% 1.05/0.70 # Parsed axioms : 402
% 1.05/0.70 # Removed by relevancy pruning/SinE : 0
% 1.05/0.70 # Initial clauses : 562
% 1.05/0.70 # Removed in clause preprocessing : 242
% 1.05/0.70 # Initial clauses in saturation : 320
% 1.05/0.70 # Processed clauses : 629
% 1.05/0.70 # ...of these trivial : 10
% 1.05/0.70 # ...subsumed : 82
% 1.05/0.70 # ...remaining for further processing : 537
% 1.05/0.70 # Other redundant clauses eliminated : 39
% 1.05/0.70 # Clauses deleted for lack of memory : 0
% 1.05/0.70 # Backward-subsumed : 4
% 1.05/0.70 # Backward-rewritten : 3
% 1.05/0.70 # Generated clauses : 3052
% 1.05/0.70 # ...of the previous two non-redundant : 2872
% 1.05/0.70 # ...aggressively subsumed : 0
% 1.05/0.70 # Contextual simplify-reflections : 0
% 1.05/0.70 # Paramodulations : 2995
% 1.05/0.70 # Factorizations : 0
% 1.05/0.70 # NegExts : 2
% 1.05/0.70 # Equation resolutions : 42
% 1.05/0.70 # Disequality decompositions : 0
% 1.05/0.70 # Total rewrite steps : 195
% 1.05/0.70 # ...of those cached : 131
% 1.05/0.70 # Propositional unsat checks : 0
% 1.05/0.70 # Propositional check models : 0
% 1.05/0.70 # Propositional check unsatisfiable : 0
% 1.05/0.70 # Propositional clauses : 0
% 1.05/0.70 # Propositional clauses after purity: 0
% 1.05/0.70 # Propositional unsat core size : 0
% 1.05/0.70 # Propositional preprocessing time : 0.000
% 1.05/0.70 # Propositional encoding time : 0.000
% 1.05/0.70 # Propositional solver time : 0.000
% 1.05/0.70 # Success case prop preproc time : 0.000
% 1.05/0.70 # Success case prop encoding time : 0.000
% 1.05/0.70 # Success case prop solver time : 0.000
% 1.05/0.70 # Current number of processed clauses : 235
% 1.05/0.70 # Positive orientable unit clauses : 45
% 1.05/0.70 # Positive unorientable unit clauses: 0
% 1.05/0.70 # Negative unit clauses : 7
% 1.05/0.70 # Non-unit-clauses : 183
% 1.05/0.70 # Current number of unprocessed clauses: 2830
% 1.05/0.70 # ...number of literals in the above : 9097
% 1.05/0.70 # Current number of archived formulas : 0
% 1.05/0.70 # Current number of archived clauses : 287
% 1.05/0.70 # Clause-clause subsumption calls (NU) : 17494
% 1.05/0.70 # Rec. Clause-clause subsumption calls : 8531
% 1.05/0.70 # Non-unit clause-clause subsumptions : 65
% 1.05/0.70 # Unit Clause-clause subsumption calls : 261
% 1.05/0.70 # Rewrite failures with RHS unbound : 0
% 1.05/0.70 # BW rewrite match attempts : 17
% 1.05/0.70 # BW rewrite match successes : 3
% 1.05/0.70 # Condensation attempts : 629
% 1.05/0.70 # Condensation successes : 6
% 1.05/0.70 # Termbank termtop insertions : 94469
% 1.05/0.70 # Search garbage collected termcells : 17966
% 1.05/0.70
% 1.05/0.70 # -------------------------------------------------
% 1.05/0.70 # User time : 0.159 s
% 1.05/0.70 # System time : 0.019 s
% 1.05/0.70 # Total time : 0.178 s
% 1.05/0.70 # Maximum resident set size: 5980 pages
% 1.05/0.70
% 1.05/0.70 # -------------------------------------------------
% 1.05/0.70 # User time : 0.497 s
% 1.05/0.70 # System time : 0.056 s
% 1.05/0.70 # Total time : 0.552 s
% 1.05/0.70 # Maximum resident set size: 2208 pages
% 1.05/0.70 % E---3.1 exiting
% 1.05/0.71 % E exiting
%------------------------------------------------------------------------------