TSTP Solution File: SEU669^1 by E---3.1.00
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : E---3.1.00
% Problem : SEU669^1 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:28:59 EDT 2024
% Result : Timeout 1.20s 300.11s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU669^1 : TPTP v8.2.0. Released v3.7.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun May 19 18:09:08 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.18/0.47 Running higher-order theorem proving
% 0.18/0.47 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.20/300.11 # Version: 3.1.0-ho
% 1.20/300.11 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.20/300.11 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/300.11 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.20/300.11 # Starting pre_casc_3 with 300s (1) cores
% 1.20/300.11 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.20/300.11 # Starting full_lambda_10 with 300s (1) cores
% 1.20/300.11 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.20/300.11 # ehoh_best_nonlift_rwall with pid 3974 completed with status 0
% 1.20/300.11 # Result found by ehoh_best_nonlift_rwall
% 1.20/300.11 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.20/300.11 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/300.11 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.20/300.11 # Starting pre_casc_3 with 300s (1) cores
% 1.20/300.11 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.20/300.11 # Starting full_lambda_10 with 300s (1) cores
% 1.20/300.11 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.20/300.11 # No SInE strategy applied
% 1.20/300.11 # Search class: HGHSM-FSLM31-DHSMMSBN
% 1.20/300.11 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 1.20/300.11 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.20/300.11 # Starting new_ho_10_cnf2 with 174s (1) cores
% 1.20/300.11 # new_ho_10_cnf2 with pid 3977 completed with status 0
% 1.20/300.11 # Result found by new_ho_10_cnf2
% 1.20/300.11 # Preprocessing class: HSLMSLSSLLLCHSA.
% 1.20/300.11 # Scheduled 5 strats onto 8 cores with 300 seconds (2400 total)
% 1.20/300.11 # Starting ho_unfolding_5 with 1200s (4) cores
% 1.20/300.11 # Starting pre_casc_3 with 300s (1) cores
% 1.20/300.11 # Starting new_ho_10_cnf2 with 300s (1) cores
% 1.20/300.11 # Starting full_lambda_10 with 300s (1) cores
% 1.20/300.11 # Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 1.20/300.11 # No SInE strategy applied
% 1.20/300.11 # Search class: HGHSM-FSLM31-DHSMMSBN
% 1.20/300.11 # partial match(1): HGHSM-FSLM31-MHSMMSBN
% 1.20/300.11 # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 1.20/300.11 # Starting new_ho_10_cnf2 with 174s (1) cores
% 1.20/300.11 # Preprocessing time : 0.007 s
% 1.20/300.11 # Presaturation interreduction done
% 1.20/300.11
% 1.20/300.11 # Proof found!
% 1.20/300.11 # SZS status Theorem
% 1.20/300.11 # SZS output start CNFRefutation
% 1.20/300.11 thf(decl_22, type, in: $i > $i > $o).
% 1.20/300.11 thf(decl_23, type, exu: ($i > $o) > $o).
% 1.20/300.11 thf(decl_24, type, setextAx: $o).
% 1.20/300.11 thf(decl_25, type, emptyset: $i).
% 1.20/300.11 thf(decl_26, type, emptysetAx: $o).
% 1.20/300.11 thf(decl_27, type, setadjoin: $i > $i > $i).
% 1.20/300.11 thf(decl_28, type, setadjoinAx: $o).
% 1.20/300.11 thf(decl_29, type, powerset: $i > $i).
% 1.20/300.11 thf(decl_30, type, powersetAx: $o).
% 1.20/300.11 thf(decl_31, type, setunion: $i > $i).
% 1.20/300.11 thf(decl_32, type, setunionAx: $o).
% 1.20/300.11 thf(decl_33, type, omega: $i).
% 1.20/300.11 thf(decl_34, type, omega0Ax: $o).
% 1.20/300.11 thf(decl_35, type, omegaSAx: $o).
% 1.20/300.11 thf(decl_36, type, omegaIndAx: $o).
% 1.20/300.11 thf(decl_37, type, replAx: $o).
% 1.20/300.11 thf(decl_38, type, foundationAx: $o).
% 1.20/300.11 thf(decl_39, type, wellorderingAx: $o).
% 1.20/300.11 thf(decl_40, type, descr: ($i > $o) > $i).
% 1.20/300.11 thf(decl_41, type, descrp: $o).
% 1.20/300.11 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_43, type, dsetconstrI: $o).
% 1.20/300.11 thf(decl_44, type, dsetconstrEL: $o).
% 1.20/300.11 thf(decl_45, type, dsetconstrER: $o).
% 1.20/300.11 thf(decl_46, type, exuE1: $o).
% 1.20/300.11 thf(decl_47, type, prop2set: $o > $i).
% 1.20/300.11 thf(decl_48, type, prop2setE: $o).
% 1.20/300.11 thf(decl_49, type, emptysetE: $o).
% 1.20/300.11 thf(decl_50, type, emptysetimpfalse: $o).
% 1.20/300.11 thf(decl_51, type, notinemptyset: $o).
% 1.20/300.11 thf(decl_52, type, exuE3e: $o).
% 1.20/300.11 thf(decl_53, type, setext: $o).
% 1.20/300.11 thf(decl_54, type, emptyI: $o).
% 1.20/300.11 thf(decl_55, type, noeltsimpempty: $o).
% 1.20/300.11 thf(decl_56, type, setbeta: $o).
% 1.20/300.11 thf(decl_57, type, nonempty: $i > $o).
% 1.20/300.11 thf(decl_58, type, nonemptyE1: $o).
% 1.20/300.11 thf(decl_59, type, nonemptyI: $o).
% 1.20/300.11 thf(decl_60, type, nonemptyI1: $o).
% 1.20/300.11 thf(decl_61, type, setadjoinIL: $o).
% 1.20/300.11 thf(decl_62, type, emptyinunitempty: $o).
% 1.20/300.11 thf(decl_63, type, setadjoinIR: $o).
% 1.20/300.11 thf(decl_64, type, setadjoinE: $o).
% 1.20/300.11 thf(decl_65, type, setadjoinOr: $o).
% 1.20/300.11 thf(decl_66, type, setoftrueEq: $o).
% 1.20/300.11 thf(decl_67, type, powersetI: $o).
% 1.20/300.11 thf(decl_68, type, emptyinPowerset: $o).
% 1.20/300.11 thf(decl_69, type, emptyInPowerset: $o).
% 1.20/300.11 thf(decl_70, type, powersetE: $o).
% 1.20/300.11 thf(decl_71, type, setunionI: $o).
% 1.20/300.11 thf(decl_72, type, setunionE: $o).
% 1.20/300.11 thf(decl_73, type, subPowSU: $o).
% 1.20/300.11 thf(decl_74, type, exuE2: $o).
% 1.20/300.11 thf(decl_75, type, nonemptyImpWitness: $o).
% 1.20/300.11 thf(decl_76, type, uniqinunit: $o).
% 1.20/300.11 thf(decl_77, type, notinsingleton: $o).
% 1.20/300.11 thf(decl_78, type, eqinunit: $o).
% 1.20/300.11 thf(decl_79, type, singletonsswitch: $o).
% 1.20/300.11 thf(decl_80, type, upairsetE: $o).
% 1.20/300.11 thf(decl_81, type, upairsetIL: $o).
% 1.20/300.11 thf(decl_82, type, upairsetIR: $o).
% 1.20/300.11 thf(decl_83, type, emptyE1: $o).
% 1.20/300.11 thf(decl_84, type, vacuousDall: $o).
% 1.20/300.11 thf(decl_85, type, quantDeMorgan1: $o).
% 1.20/300.11 thf(decl_86, type, quantDeMorgan2: $o).
% 1.20/300.11 thf(decl_87, type, quantDeMorgan3: $o).
% 1.20/300.11 thf(decl_88, type, quantDeMorgan4: $o).
% 1.20/300.11 thf(decl_89, type, prop2setI: $o).
% 1.20/300.11 thf(decl_90, type, set2prop: $i > $o).
% 1.20/300.11 thf(decl_91, type, prop2set2propI: $o).
% 1.20/300.11 thf(decl_92, type, notdexE: $o).
% 1.20/300.11 thf(decl_93, type, notdallE: $o).
% 1.20/300.11 thf(decl_94, type, exuI1: $o).
% 1.20/300.11 thf(decl_95, type, exuI3: $o).
% 1.20/300.11 thf(decl_96, type, exuI2: $o).
% 1.20/300.11 thf(decl_97, type, inCongP: $o).
% 1.20/300.11 thf(decl_98, type, in__Cong: $o).
% 1.20/300.11 thf(decl_99, type, exuE3u: $o).
% 1.20/300.11 thf(decl_100, type, exu__Cong: $o).
% 1.20/300.11 thf(decl_101, type, emptyset__Cong: $o).
% 1.20/300.11 thf(decl_102, type, setadjoin__Cong: $o).
% 1.20/300.11 thf(decl_103, type, powerset__Cong: $o).
% 1.20/300.11 thf(decl_104, type, setunion__Cong: $o).
% 1.20/300.11 thf(decl_105, type, omega__Cong: $o).
% 1.20/300.11 thf(decl_106, type, exuEu: $o).
% 1.20/300.11 thf(decl_107, type, descr__Cong: $o).
% 1.20/300.11 thf(decl_108, type, dsetconstr__Cong: $o).
% 1.20/300.11 thf(decl_109, type, subset: $i > $i > $o).
% 1.20/300.11 thf(decl_112, type, subsetI1: $o).
% 1.20/300.11 thf(decl_113, type, eqimpsubset2: $o).
% 1.20/300.11 thf(decl_114, type, eqimpsubset1: $o).
% 1.20/300.11 thf(decl_115, type, subsetI2: $o).
% 1.20/300.11 thf(decl_116, type, emptysetsubset: $o).
% 1.20/300.11 thf(decl_117, type, subsetE: $o).
% 1.20/300.11 thf(decl_118, type, subsetE2: $o).
% 1.20/300.11 thf(decl_119, type, notsubsetI: $o).
% 1.20/300.11 thf(decl_120, type, notequalI1: $o).
% 1.20/300.11 thf(decl_121, type, notequalI2: $o).
% 1.20/300.11 thf(decl_122, type, subsetRefl: $o).
% 1.20/300.11 thf(decl_123, type, subsetTrans: $o).
% 1.20/300.11 thf(decl_124, type, setadjoinSub: $o).
% 1.20/300.11 thf(decl_125, type, setadjoinSub2: $o).
% 1.20/300.11 thf(decl_126, type, subset2powerset: $o).
% 1.20/300.11 thf(decl_127, type, setextsub: $o).
% 1.20/300.11 thf(decl_128, type, subsetemptysetimpeq: $o).
% 1.20/300.11 thf(decl_129, type, powersetI1: $o).
% 1.20/300.11 thf(decl_130, type, powersetE1: $o).
% 1.20/300.11 thf(decl_131, type, inPowerset: $o).
% 1.20/300.11 thf(decl_132, type, powersetsubset: $o).
% 1.20/300.11 thf(decl_133, type, sepInPowerset: $o).
% 1.20/300.11 thf(decl_134, type, sepSubset: $o).
% 1.20/300.11 thf(decl_135, type, binunion: $i > $i > $i).
% 1.20/300.11 thf(decl_136, type, binunionIL: $o).
% 1.20/300.11 thf(decl_137, type, upairset2IR: $o).
% 1.20/300.11 thf(decl_138, type, binunionIR: $o).
% 1.20/300.11 thf(decl_139, type, binunionEcases: $o).
% 1.20/300.11 thf(decl_140, type, binunionE: $o).
% 1.20/300.11 thf(decl_141, type, binunionLsub: $o).
% 1.20/300.11 thf(decl_142, type, binunionRsub: $o).
% 1.20/300.11 thf(decl_143, type, binintersect: $i > $i > $i).
% 1.20/300.11 thf(decl_144, type, binintersectI: $o).
% 1.20/300.11 thf(decl_145, type, binintersectSubset5: $o).
% 1.20/300.11 thf(decl_146, type, binintersectEL: $o).
% 1.20/300.11 thf(decl_147, type, binintersectLsub: $o).
% 1.20/300.11 thf(decl_148, type, binintersectSubset2: $o).
% 1.20/300.11 thf(decl_149, type, binintersectSubset3: $o).
% 1.20/300.11 thf(decl_150, type, binintersectER: $o).
% 1.20/300.11 thf(decl_151, type, disjointsetsI1: $o).
% 1.20/300.11 thf(decl_152, type, binintersectRsub: $o).
% 1.20/300.11 thf(decl_153, type, binintersectSubset4: $o).
% 1.20/300.11 thf(decl_154, type, binintersectSubset1: $o).
% 1.20/300.11 thf(decl_155, type, bs114d: $o).
% 1.20/300.11 thf(decl_157, type, setminus: $i > $i > $i).
% 1.20/300.11 thf(decl_158, type, setminusI: $o).
% 1.20/300.11 thf(decl_159, type, setminusEL: $o).
% 1.20/300.11 thf(decl_160, type, setminusER: $o).
% 1.20/300.11 thf(decl_161, type, setminusSubset2: $o).
% 1.20/300.11 thf(decl_162, type, setminusERneg: $o).
% 1.20/300.11 thf(decl_163, type, setminusELneg: $o).
% 1.20/300.11 thf(decl_164, type, setminusILneg: $o).
% 1.20/300.11 thf(decl_165, type, setminusIRneg: $o).
% 1.20/300.11 thf(decl_166, type, setminusLsub: $o).
% 1.20/300.11 thf(decl_167, type, setminusSubset1: $o).
% 1.20/300.11 thf(decl_168, type, symdiff: $i > $i > $i).
% 1.20/300.11 thf(decl_169, type, symdiffE: $o).
% 1.20/300.11 thf(decl_170, type, symdiffI1: $o).
% 1.20/300.11 thf(decl_171, type, symdiffI2: $o).
% 1.20/300.11 thf(decl_172, type, symdiffIneg1: $o).
% 1.20/300.11 thf(decl_173, type, symdiffIneg2: $o).
% 1.20/300.11 thf(decl_174, type, iskpair: $i > $o).
% 1.20/300.11 thf(decl_175, type, secondinupair: $o).
% 1.20/300.11 thf(decl_176, type, setukpairIL: $o).
% 1.20/300.11 thf(decl_177, type, setukpairIR: $o).
% 1.20/300.11 thf(decl_178, type, kpairiskpair: $o).
% 1.20/300.11 thf(decl_179, type, kpair: $i > $i > $i).
% 1.20/300.11 thf(decl_180, type, kpairp: $o).
% 1.20/300.11 thf(decl_181, type, cartprod: $i > $i > $i).
% 1.20/300.11 thf(decl_182, type, singletonsubset: $o).
% 1.20/300.11 thf(decl_183, type, singletoninpowerset: $o).
% 1.20/300.11 thf(decl_184, type, singletoninpowunion: $o).
% 1.20/300.11 thf(decl_185, type, upairset2E: $o).
% 1.20/300.11 thf(decl_186, type, upairsubunion: $o).
% 1.20/300.11 thf(decl_187, type, upairinpowunion: $o).
% 1.20/300.11 thf(decl_188, type, ubforcartprodlem1: $o).
% 1.20/300.11 thf(decl_189, type, ubforcartprodlem2: $o).
% 1.20/300.11 thf(decl_190, type, ubforcartprodlem3: $o).
% 1.20/300.11 thf(decl_191, type, cartprodpairin: $o).
% 1.20/300.11 thf(decl_192, type, cartprodmempair1: $o).
% 1.20/300.11 thf(decl_193, type, cartprodmempair: $o).
% 1.20/300.11 thf(decl_194, type, setunionE2: $o).
% 1.20/300.11 thf(decl_195, type, setunionsingleton1: $o).
% 1.20/300.11 thf(decl_196, type, setunionsingleton2: $o).
% 1.20/300.11 thf(decl_197, type, setunionsingleton: $o).
% 1.20/300.11 thf(decl_198, type, singleton: $i > $o).
% 1.20/300.11 thf(decl_199, type, singletonprop: $o).
% 1.20/300.11 thf(decl_200, type, ex1: $i > ($i > $o) > $o).
% 1.20/300.11 thf(decl_201, type, ex1E1: $o).
% 1.20/300.11 thf(decl_202, type, ex1I: $o).
% 1.20/300.11 thf(decl_203, type, ex1I2: $o).
% 1.20/300.11 thf(decl_204, type, singletonsuniq: $o).
% 1.20/300.11 thf(decl_209, type, setukpairinjL1: $o).
% 1.20/300.11 thf(decl_210, type, kfstsingleton: $o).
% 1.20/300.11 thf(decl_211, type, theprop: $o).
% 1.20/300.11 thf(decl_212, type, kfst: $i > $i).
% 1.20/300.11 thf(decl_213, type, kfstpairEq: $o).
% 1.20/300.11 thf(decl_214, type, cartprodfstin: $o).
% 1.20/300.11 thf(decl_215, type, setukpairinjL2: $o).
% 1.20/300.11 thf(decl_216, type, setukpairinjL: $o).
% 1.20/300.11 thf(decl_217, type, setukpairinjR11: $o).
% 1.20/300.11 thf(decl_218, type, setukpairinjR12: $o).
% 1.20/300.11 thf(decl_219, type, setukpairinjR1: $o).
% 1.20/300.11 thf(decl_220, type, upairequniteq: $o).
% 1.20/300.11 thf(decl_221, type, setukpairinjR2: $o).
% 1.20/300.11 thf(decl_222, type, setukpairinjR: $o).
% 1.20/300.11 thf(decl_223, type, ksndsingleton: $o).
% 1.20/300.11 thf(decl_224, type, ksnd: $i > $i).
% 1.20/300.11 thf(decl_225, type, ksndpairEq: $o).
% 1.20/300.11 thf(decl_226, type, kpairsurjEq: $o).
% 1.20/300.11 thf(decl_227, type, cartprodsndin: $o).
% 1.20/300.11 thf(decl_228, type, cartprodpairmemEL: $o).
% 1.20/300.11 thf(decl_229, type, cartprodpairmemER: $o).
% 1.20/300.11 thf(decl_230, type, cartprodmempaircEq: $o).
% 1.20/300.11 thf(decl_231, type, cartprodfstpairEq: $o).
% 1.20/300.11 thf(decl_232, type, cartprodsndpairEq: $o).
% 1.20/300.11 thf(decl_233, type, cartprodpairsurjEq: $o).
% 1.20/300.11 thf(decl_234, type, breln: $i > $i > $i > $o).
% 1.20/300.11 thf(decl_235, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 1.20/300.11 thf(decl_236, type, dpsetconstrI: $o).
% 1.20/300.11 thf(decl_237, type, dpsetconstrSub: $o).
% 1.20/300.11 thf(decl_238, type, setOfPairsIsBReln: $o).
% 1.20/300.11 thf(decl_239, type, dpsetconstrERa: $o).
% 1.20/300.11 thf(decl_240, type, epred1_0: $o).
% 1.20/300.11 thf(decl_241, type, esk1_2: $i > $i > $i).
% 1.20/300.11 thf(decl_242, type, esk2_2: $i > $i > $i).
% 1.20/300.11 thf(decl_243, type, esk3_2: $i > $i > $i).
% 1.20/300.11 thf(decl_244, type, esk4_1: $i > $i).
% 1.20/300.11 thf(decl_245, type, esk5_2: ($i > $i > $o) > $i > $i).
% 1.20/300.11 thf(decl_246, type, esk6_3: ($i > $i > $o) > $i > $i > $i).
% 1.20/300.11 thf(decl_247, type, esk7_2: ($i > $i > $o) > $i > $i).
% 1.20/300.11 thf(decl_248, type, esk8_3: ($i > $i > $o) > $i > $i > $i).
% 1.20/300.11 thf(decl_249, type, esk9_1: $i > $i).
% 1.20/300.11 thf(decl_250, type, esk10_2: ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_251, type, esk11_2: ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_252, type, esk12_1: ($i > $o) > $i).
% 1.20/300.11 thf(decl_253, type, esk13_2: ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_254, type, esk14_1: ($i > $o) > $i).
% 1.20/300.11 thf(decl_255, type, esk15_2: $i > $i > $i).
% 1.20/300.11 thf(decl_256, type, esk16_2: $i > $i > $i).
% 1.20/300.11 thf(decl_257, type, esk17_1: $i > $i).
% 1.20/300.11 thf(decl_258, type, esk18_1: $i > $i).
% 1.20/300.11 thf(decl_259, type, esk19_1: $i > $i).
% 1.20/300.11 thf(decl_260, type, esk20_2: $i > $i > $i).
% 1.20/300.11 thf(decl_261, type, esk21_3: $i > $i > $o > $i).
% 1.20/300.11 thf(decl_262, type, esk22_2: ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_263, type, esk23_1: ($i > $o) > $i).
% 1.20/300.11 thf(decl_264, type, esk24_1: $i > $i).
% 1.20/300.11 thf(decl_265, type, esk25_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_266, type, esk26_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_267, type, esk27_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_268, type, esk28_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_269, type, esk29_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_270, type, esk30_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_271, type, esk31_2: ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_272, type, esk32_1: ($i > $o) > $i).
% 1.20/300.11 thf(decl_273, type, esk33_1: ($i > $o) > $i).
% 1.20/300.11 thf(decl_274, type, esk34_1: ($i > $o) > $i).
% 1.20/300.11 thf(decl_275, type, esk35_1: ($i > $o) > $i).
% 1.20/300.11 thf(decl_276, type, esk36_2: ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_277, type, esk37_1: ($i > $o) > $i).
% 1.20/300.11 thf(decl_278, type, esk38_2: ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_279, type, esk39_2: ($i > $o) > ($i > $o) > $i).
% 1.20/300.11 thf(decl_280, type, esk40_2: ($i > $o) > ($i > $o) > $i).
% 1.20/300.11 thf(decl_281, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_282, type, esk42_2: ($i > $o) > ($i > $o) > $i).
% 1.20/300.11 thf(decl_283, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_284, type, esk44_2: ($i > $o) > ($i > $o) > $i).
% 1.20/300.11 thf(decl_285, type, esk45_2: ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_286, type, esk46_2: ($i > $o) > ($i > $o) > $i).
% 1.20/300.11 thf(decl_287, type, esk47_2: ($i > $o) > ($i > $o) > $i).
% 1.20/300.11 thf(decl_288, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_289, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_290, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.20/300.11 thf(decl_291, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i).
% 1.20/300.11 thf(decl_292, type, esk52_2: $i > $i > $i).
% 1.20/300.11 thf(decl_293, type, esk53_2: $i > $i > $i).
% 1.20/300.11 thf(decl_294, type, esk54_2: $i > $i > $i).
% 1.20/300.11 thf(decl_295, type, esk55_3: $i > $i > $i > $i).
% 1.20/300.11 thf(decl_296, type, esk56_3: $i > $i > $i > $i).
% 1.20/300.11 thf(decl_297, type, esk57_2: $i > $i > $i).
% 1.20/300.11 thf(decl_298, type, esk58_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_299, type, esk59_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_300, type, esk60_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_301, type, esk61_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_302, type, esk62_3: $i > ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_303, type, esk63_3: $i > ($i > $o) > $i > $i).
% 1.20/300.11 thf(decl_304, type, esk64_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_305, type, esk65_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_306, type, esk66_2: $i > ($i > $o) > $i).
% 1.20/300.11 thf(decl_307, type, esk67_1: $i > $i).
% 1.20/300.11 thf(decl_308, type, esk68_1: $i > $i).
% 1.20/300.11 thf(decl_309, type, esk69_0: $i).
% 1.20/300.11 thf(decl_310, type, esk70_0: $i).
% 1.20/300.11 thf(decl_311, type, epred2_0: $i > $i > $o).
% 1.20/300.11 thf(decl_312, type, esk71_0: $i).
% 1.20/300.11 thf(decl_313, type, esk72_0: $i).
% 1.20/300.11 thf(decl_319, type, esk78_0: $i).
% 1.20/300.11 thf(decl_320, type, esk79_0: $i).
% 1.20/300.11 thf(ex1, axiom, ((ex1)=(^[X4:$i, X1:$i > $o]:((singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1)).
% 1.20/300.11 thf(singleton, axiom, ((singleton)=(^[X4:$i]:(?[X2:$i]:(((in @ X2 @ X4)&((X4)=(setadjoin @ X2 @ emptyset))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singleton)).
% 1.20/300.11 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', replAx)).
% 1.20/300.11 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu)).
% 1.20/300.11 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descrp)).
% 1.20/300.11 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE1)).
% 1.20/300.11 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3e)).
% 1.20/300.11 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonempty)).
% 1.20/300.11 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI)).
% 1.20/300.11 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE2)).
% 1.20/300.11 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI1)).
% 1.20/300.11 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI3)).
% 1.20/300.11 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuI2)).
% 1.20/300.11 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuE3u)).
% 1.20/300.11 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exu__Cong)).
% 1.20/300.11 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', exuEu)).
% 1.20/300.11 thf(descr__Cong, axiom, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))=>((exu @ (^[X2:$i]:((X17 @ X2))))=>((descr @ (^[X2:$i]:((X1 @ X2))))=(descr @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', descr__Cong)).
% 1.20/300.11 thf(singletonprop, axiom, ((singletonprop)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(singleton @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonprop)).
% 1.20/300.11 thf(ex1E1, axiom, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1E1)).
% 1.20/300.11 thf(ex1I, axiom, ((ex1I)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(ex1 @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I)).
% 1.20/300.11 thf(ex1I2, axiom, ((ex1I2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))=>(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(ex1 @ X4 @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ex1I2)).
% 1.20/300.11 thf(kfstsingleton, axiom, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:((in @ (setadjoin @ X2 @ emptyset) @ X18)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstsingleton)).
% 1.20/300.11 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[X2:$i]:(((X18)=(kpair @ (kfst @ X18) @ X2))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndsingleton)).
% 1.20/300.11 thf(dpsetconstrI, axiom, ((dpsetconstrI)<=>![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X23 @ X14 @ X18))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrI)).
% 1.20/300.11 thf(dpsetconstr, axiom, ((dpsetconstr)=(^[X4:$i, X5:$i, X22:$i > $i > $o]:(dsetconstr @ (cartprod @ X4 @ X5) @ (^[X18:$i]:(?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:((((in @ X3 @ X5)&(X22 @ X2 @ X3))&((X18)=(kpair @ X2 @ X3))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstr)).
% 1.20/300.11 thf(dpsetconstrSub, axiom, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X24 @ X2 @ X3)))) @ (cartprod @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrSub)).
% 1.20/300.11 thf(setOfPairsIsBReln, axiom, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X25:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[X2:$i, X3:$i]:((X25 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setOfPairsIsBReln)).
% 1.20/300.11 thf(breln, axiom, ((breln)=(^[X4:$i, X5:$i, X7:$i]:((subset @ X7 @ (cartprod @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', breln)).
% 1.20/300.11 thf(dpsetconstrERa, axiom, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X26 @ X14 @ X18)))))=>(X26 @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrERa)).
% 1.20/300.11 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrI)).
% 1.20/300.11 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrEL)).
% 1.20/300.11 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstrER)).
% 1.20/300.11 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setbeta)).
% 1.20/300.11 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyE1)).
% 1.20/300.11 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyI1)).
% 1.20/300.11 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setoftrueEq)).
% 1.20/300.11 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', nonemptyImpWitness)).
% 1.20/300.11 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyE1)).
% 1.20/300.11 thf(dsetconstr__Cong, axiom, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(dsetconstr @ X5 @ (^[X2:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dsetconstr__Cong)).
% 1.20/300.11 thf(sepInPowerset, axiom, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepInPowerset)).
% 1.20/300.11 thf(sepSubset, axiom, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2)))) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', sepSubset)).
% 1.20/300.11 thf(theprop, axiom, ((theprop)<=>![X21:$i]:(((singleton @ X21)=>(in @ (setunion @ X21) @ X21)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', theprop)).
% 1.20/300.11 thf(dpsetconstrEL1, conjecture, ((setextAx)=>((emptysetAx)=>((setadjoinAx)=>((powersetAx)=>((setunionAx)=>((omega0Ax)=>((omegaSAx)=>((omegaIndAx)=>((replAx)=>((foundationAx)=>((wellorderingAx)=>((descrp)=>((dsetconstrI)=>((dsetconstrEL)=>((dsetconstrER)=>((exuE1)=>((prop2setE)=>((emptysetE)=>((emptysetimpfalse)=>((notinemptyset)=>((exuE3e)=>((setext)=>((emptyI)=>((noeltsimpempty)=>((setbeta)=>((nonemptyE1)=>((nonemptyI)=>((nonemptyI1)=>((setadjoinIL)=>((emptyinunitempty)=>((setadjoinIR)=>((setadjoinE)=>((setadjoinOr)=>((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>((powersetE)=>((setunionI)=>((setunionE)=>((subPowSU)=>((exuE2)=>((nonemptyImpWitness)=>((uniqinunit)=>((notinsingleton)=>((eqinunit)=>((singletonsswitch)=>((upairsetE)=>((upairsetIL)=>((upairsetIR)=>((emptyE1)=>((vacuousDall)=>((quantDeMorgan1)=>((quantDeMorgan2)=>((quantDeMorgan3)=>((quantDeMorgan4)=>((prop2setI)=>((prop2set2propI)=>((notdexE)=>((notdallE)=>((exuI1)=>((exuI3)=>((exuI2)=>((inCongP)=>((in__Cong)=>((exuE3u)=>((exu__Cong)=>((emptyset__Cong)=>((setadjoin__Cong)=>((powerset__Cong)=>((setunion__Cong)=>((omega__Cong)=>((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>((subsetI1)=>((eqimpsubset2)=>((eqimpsubset1)=>((subsetI2)=>((emptysetsubset)=>((subsetE)=>((subsetE2)=>((notsubsetI)=>((notequalI1)=>((notequalI2)=>((subsetRefl)=>((subsetTrans)=>((setadjoinSub)=>((setadjoinSub2)=>((subset2powerset)=>((setextsub)=>((subsetemptysetimpeq)=>((powersetI1)=>((powersetE1)=>((inPowerset)=>((powersetsubset)=>((sepInPowerset)=>((sepSubset)=>((binunionIL)=>((upairset2IR)=>((binunionIR)=>((binunionEcases)=>((binunionE)=>((binunionLsub)=>((binunionRsub)=>((binintersectI)=>((binintersectSubset5)=>((binintersectEL)=>((binintersectLsub)=>((binintersectSubset2)=>((binintersectSubset3)=>((binintersectER)=>((disjointsetsI1)=>((binintersectRsub)=>((binintersectSubset4)=>((binintersectSubset1)=>((bs114d)=>((setminusI)=>((setminusEL)=>((setminusER)=>((setminusSubset2)=>((setminusERneg)=>((setminusELneg)=>((setminusILneg)=>((setminusIRneg)=>((setminusLsub)=>((setminusSubset1)=>((symdiffE)=>((symdiffI1)=>((symdiffI2)=>((symdiffIneg1)=>((symdiffIneg2)=>((secondinupair)=>((setukpairIL)=>((setukpairIR)=>((kpairiskpair)=>((kpairp)=>((singletonsubset)=>((singletoninpowerset)=>((singletoninpowunion)=>((upairset2E)=>((upairsubunion)=>((upairinpowunion)=>((ubforcartprodlem1)=>((ubforcartprodlem2)=>((ubforcartprodlem3)=>((cartprodpairin)=>((cartprodmempair1)=>((cartprodmempair)=>((setunionE2)=>((setunionsingleton1)=>((setunionsingleton2)=>((setunionsingleton)=>((singletonprop)=>((ex1E1)=>((ex1I)=>((ex1I2)=>((singletonsuniq)=>((setukpairinjL1)=>((kfstsingleton)=>((theprop)=>((kfstpairEq)=>((cartprodfstin)=>((setukpairinjL2)=>((setukpairinjL)=>((setukpairinjR11)=>((setukpairinjR12)=>((setukpairinjR1)=>((upairequniteq)=>((setukpairinjR2)=>((setukpairinjR)=>((ksndsingleton)=>((ksndpairEq)=>((kpairsurjEq)=>((cartprodsndin)=>((cartprodpairmemEL)=>((cartprodpairmemER)=>((cartprodmempaircEq)=>((cartprodfstpairEq)=>((cartprodsndpairEq)=>((cartprodpairsurjEq)=>((dpsetconstrI)=>((dpsetconstrSub)=>((setOfPairsIsBReln)=>((dpsetconstrERa)=>![X4:$i, X5:$i, X27:$i > $i > $o, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[X14:$i, X18:$i]:((X27 @ X14 @ X18)))))=>(in @ X2 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', dpsetconstrEL1)).
% 1.20/300.11 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextAx)).
% 1.20/300.11 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetAx)).
% 1.20/300.11 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinAx)).
% 1.20/300.11 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetAx)).
% 1.20/300.11 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionAx)).
% 1.20/300.11 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega0Ax)).
% 1.20/300.11 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaSAx)).
% 1.20/300.11 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omegaIndAx)).
% 1.20/300.11 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', foundationAx)).
% 1.20/300.11 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', wellorderingAx)).
% 1.20/300.11 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setE)).
% 1.20/300.11 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetE)).
% 1.20/300.11 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetimpfalse)).
% 1.20/300.11 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinemptyset)).
% 1.20/300.11 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setext)).
% 1.20/300.11 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyI)).
% 1.20/300.11 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', noeltsimpempty)).
% 1.20/300.11 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIL)).
% 1.20/300.11 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinunitempty)).
% 1.20/300.11 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinIR)).
% 1.20/300.11 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinE)).
% 1.20/300.11 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinOr)).
% 1.20/300.11 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI)).
% 1.20/300.11 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyinPowerset)).
% 1.20/300.11 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyInPowerset)).
% 1.20/300.11 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE)).
% 1.20/300.11 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionI)).
% 1.20/300.11 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE)).
% 1.20/300.11 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subPowSU)).
% 1.20/300.11 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', uniqinunit)).
% 1.20/300.11 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notinsingleton)).
% 1.20/300.11 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqinunit)).
% 1.20/300.11 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsswitch)).
% 1.20/300.11 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetE)).
% 1.20/300.11 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIL)).
% 1.20/300.11 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsetIR)).
% 1.20/300.11 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', vacuousDall)).
% 1.20/300.11 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan1)).
% 1.20/300.11 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan2)).
% 1.20/300.11 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan3)).
% 1.20/300.11 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', quantDeMorgan4)).
% 1.20/300.11 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2setI)).
% 1.20/300.11 thf(prop2set2propI, axiom, ((prop2set2propI)<=>![X16:$o]:(((X16)=>(set2prop @ (prop2set @ ((X16))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', prop2set2propI)).
% 1.20/300.11 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdexE)).
% 1.20/300.11 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notdallE)).
% 1.20/300.11 thf(inCongP, axiom, ((inCongP)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inCongP)).
% 1.20/300.11 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', in__Cong)).
% 1.20/300.11 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptyset__Cong)).
% 1.20/300.11 thf(setadjoin__Cong, axiom, ((setadjoin__Cong)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>![X14:$i, X18:$i]:((((X14)=(X18))=>((setadjoin @ X2 @ X14)=(setadjoin @ X3 @ X18))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoin__Cong)).
% 1.20/300.11 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powerset__Cong)).
% 1.20/300.11 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunion__Cong)).
% 1.20/300.11 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', omega__Cong)).
% 1.20/300.11 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI1)).
% 1.20/300.11 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset2)).
% 1.20/300.11 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', eqimpsubset1)).
% 1.20/300.11 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetI2)).
% 1.20/300.11 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', emptysetsubset)).
% 1.20/300.11 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE)).
% 1.20/300.11 thf(subsetE2, axiom, ((subsetE2)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetE2)).
% 1.20/300.11 thf(notsubsetI, axiom, ((notsubsetI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>~((subset @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notsubsetI)).
% 1.20/300.11 thf(notequalI1, axiom, ((notequalI1)<=>![X4:$i, X5:$i]:((~((subset @ X4 @ X5))=>((X4)!=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI1)).
% 1.20/300.11 thf(notequalI2, axiom, ((notequalI2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>((X4)!=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', notequalI2)).
% 1.20/300.11 thf(subsetRefl, axiom, ((subsetRefl)<=>![X4:$i]:((subset @ X4 @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetRefl)).
% 1.20/300.11 thf(subsetTrans, axiom, ((subsetTrans)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X7)=>(subset @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetTrans)).
% 1.20/300.11 thf(setadjoinSub, axiom, ((setadjoinSub)<=>![X2:$i, X4:$i]:((subset @ X4 @ (setadjoin @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub)).
% 1.20/300.11 thf(setadjoinSub2, axiom, ((setadjoinSub2)<=>![X4:$i, X2:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ X4 @ (setadjoin @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setadjoinSub2)).
% 1.20/300.11 thf(subset2powerset, axiom, ((subset2powerset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(in @ X4 @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subset2powerset)).
% 1.20/300.11 thf(setextsub, axiom, ((setextsub)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((subset @ X5 @ X4)=>((X4)=(X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setextsub)).
% 1.20/300.11 thf(subsetemptysetimpeq, axiom, ((subsetemptysetimpeq)<=>![X4:$i]:(((subset @ X4 @ emptyset)=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', subsetemptysetimpeq)).
% 1.20/300.11 thf(powersetI1, axiom, ((powersetI1)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetI1)).
% 1.20/300.11 thf(powersetE1, axiom, ((powersetE1)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetE1)).
% 1.20/300.11 thf(inPowerset, axiom, ((inPowerset)<=>![X4:$i]:((in @ X4 @ (powerset @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', inPowerset)).
% 1.20/300.11 thf(powersetsubset, axiom, ((powersetsubset)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>(subset @ (powerset @ X4) @ (powerset @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', powersetsubset)).
% 1.20/300.11 thf(binunionIL, axiom, ((binunionIL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIL)).
% 1.20/300.11 thf(upairset2IR, axiom, ((upairset2IR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2IR)).
% 1.20/300.11 thf(binunionIR, axiom, ((binunionIR)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ (binunion @ X4 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionIR)).
% 1.20/300.11 thf(binunionEcases, axiom, ((binunionEcases)<=>![X4:$i, X5:$i, X2:$i, X19:$o]:(((in @ X2 @ (binunion @ X4 @ X5))=>(((in @ X2 @ X4)=>(X19))=>(((in @ X2 @ X5)=>(X19))=>(X19)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionEcases)).
% 1.20/300.11 thf(binunionE, axiom, ((binunionE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binunion @ X4 @ X5))=>((in @ X2 @ X4)|(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionE)).
% 1.20/300.11 thf(binunionLsub, axiom, ((binunionLsub)<=>![X4:$i, X5:$i]:((subset @ X4 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionLsub)).
% 1.20/300.11 thf(binunionRsub, axiom, ((binunionRsub)<=>![X4:$i, X5:$i]:((subset @ X5 @ (binunion @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binunionRsub)).
% 1.20/300.11 thf(binintersectI, axiom, ((binintersectI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>(in @ X2 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectI)).
% 1.20/300.11 thf(binintersectSubset5, axiom, ((binintersectSubset5)<=>![X4:$i, X5:$i, X7:$i]:(((subset @ X7 @ X4)=>((subset @ X7 @ X5)=>(subset @ X7 @ (binintersect @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset5)).
% 1.20/300.11 thf(binintersectEL, axiom, ((binintersectEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectEL)).
% 1.20/300.11 thf(binintersectLsub, axiom, ((binintersectLsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectLsub)).
% 1.20/300.11 thf(binintersectSubset2, axiom, ((binintersectSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((binintersect @ X4 @ X5)=(X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset2)).
% 1.20/300.11 thf(binintersectSubset3, axiom, ((binintersectSubset3)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset3)).
% 1.20/300.11 thf(binintersectER, axiom, ((binintersectER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (binintersect @ X4 @ X5))=>(in @ X2 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectER)).
% 1.20/300.11 thf(disjointsetsI1, axiom, ((disjointsetsI1)<=>![X4:$i, X5:$i]:((~(?[X2:$i]:(((in @ X2 @ X4)&(in @ X2 @ X5))))=>((binintersect @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', disjointsetsI1)).
% 1.20/300.11 thf(binintersectRsub, axiom, ((binintersectRsub)<=>![X4:$i, X5:$i]:((subset @ (binintersect @ X4 @ X5) @ X5))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectRsub)).
% 1.20/300.11 thf(binintersectSubset4, axiom, ((binintersectSubset4)<=>![X4:$i, X5:$i]:(((subset @ X5 @ X4)=>((binintersect @ X4 @ X5)=(X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset4)).
% 1.20/300.11 thf(binintersectSubset1, axiom, ((binintersectSubset1)<=>![X4:$i, X5:$i]:((((binintersect @ X4 @ X5)=(X4))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', binintersectSubset1)).
% 1.20/300.11 thf(bs114d, axiom, ((bs114d)<=>![X4:$i, X5:$i, X7:$i]:(((binintersect @ X4 @ (binunion @ X5 @ X7))=(binunion @ (binintersect @ X4 @ X5) @ (binintersect @ X4 @ X7))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', bs114d)).
% 1.20/300.11 thf(setminusI, axiom, ((setminusI)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusI)).
% 1.20/300.11 thf(setminusEL, axiom, ((setminusEL)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusEL)).
% 1.20/300.11 thf(setminusER, axiom, ((setminusER)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (setminus @ X4 @ X5))=>~((in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusER)).
% 1.20/300.11 thf(setminusSubset2, axiom, ((setminusSubset2)<=>![X4:$i, X5:$i]:(((subset @ X4 @ X5)=>((setminus @ X4 @ X5)=(emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset2)).
% 1.20/300.11 thf(setminusERneg, axiom, ((setminusERneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusERneg)).
% 1.20/300.11 thf(setminusELneg, axiom, ((setminusELneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ (setminus @ X4 @ X5)))=>(~((in @ X2 @ X5))=>~((in @ X2 @ X4)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusELneg)).
% 1.20/300.11 thf(setminusILneg, axiom, ((setminusILneg)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusILneg)).
% 1.20/300.11 thf(setminusIRneg, axiom, ((setminusIRneg)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X5)=>~((in @ X2 @ (setminus @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusIRneg)).
% 1.20/300.11 thf(setminusLsub, axiom, ((setminusLsub)<=>![X4:$i, X5:$i]:((subset @ (setminus @ X4 @ X5) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusLsub)).
% 1.20/300.11 thf(setminusSubset1, axiom, ((setminusSubset1)<=>![X4:$i, X5:$i]:((((setminus @ X4 @ X5)=(emptyset))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setminusSubset1)).
% 1.20/300.11 thf(symdiffE, axiom, ((symdiffE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ (symdiff @ X4 @ X5))=>![X20:$o]:((((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(X20)))=>((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(X20)))=>(X20))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffE)).
% 1.20/300.11 thf(symdiffI1, axiom, ((symdiffI1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(~((in @ X2 @ X5))=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI1)).
% 1.20/300.11 thf(symdiffI2, axiom, ((symdiffI2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ (symdiff @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffI2)).
% 1.20/300.11 thf(symdiffIneg1, axiom, ((symdiffIneg1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ X5)=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg1)).
% 1.20/300.11 thf(symdiffIneg2, axiom, ((symdiffIneg2)<=>![X4:$i, X5:$i, X2:$i]:((~((in @ X2 @ X4))=>(~((in @ X2 @ X5))=>~((in @ X2 @ (symdiff @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', symdiffIneg2)).
% 1.20/300.11 thf(secondinupair, axiom, ((secondinupair)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', secondinupair)).
% 1.20/300.11 thf(setukpairIL, axiom, ((setukpairIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIL)).
% 1.20/300.11 thf(setukpairIR, axiom, ((setukpairIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairIR)).
% 1.20/300.11 thf(kpairiskpair, axiom, ((kpairiskpair)<=>![X2:$i, X3:$i]:((iskpair @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairiskpair)).
% 1.20/300.11 thf(kpairp, axiom, ((kpairp)<=>![X2:$i, X3:$i]:((iskpair @ (kpair @ X2 @ X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairp)).
% 1.20/300.11 thf(singletonsubset, axiom, ((singletonsubset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(subset @ (setadjoin @ X2 @ emptyset) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsubset)).
% 1.20/300.11 thf(singletoninpowerset, axiom, ((singletoninpowerset)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ X4))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowerset)).
% 1.20/300.11 thf(singletoninpowunion, axiom, ((singletoninpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ (setadjoin @ X2 @ emptyset) @ (powerset @ (binunion @ X4 @ X5)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletoninpowunion)).
% 1.20/300.11 thf(upairset2E, axiom, ((upairset2E)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairset2E)).
% 1.20/300.11 thf(upairsubunion, axiom, ((upairsubunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (binunion @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairsubunion)).
% 1.20/300.11 thf(upairinpowunion, axiom, ((upairinpowunion)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairinpowunion)).
% 1.20/300.11 thf(ubforcartprodlem1, axiom, ((ubforcartprodlem1)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(subset @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (binunion @ X4 @ X5)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem1)).
% 1.20/300.11 thf(ubforcartprodlem2, axiom, ((ubforcartprodlem2)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem2)).
% 1.20/300.11 thf(ubforcartprodlem3, axiom, ((ubforcartprodlem3)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (powerset @ (powerset @ (binunion @ X4 @ X5))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ubforcartprodlem3)).
% 1.20/300.11 thf(cartprodpairin, axiom, ((cartprodpairin)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairin)).
% 1.20/300.11 thf(cartprodmempair1, axiom, ((cartprodmempair1)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>?[X2:$i]:(((in @ X2 @ X4)&?[X3:$i]:(((in @ X3 @ X5)&((X18)=(kpair @ X2 @ X3))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair1)).
% 1.20/300.11 thf(cartprodmempair, axiom, ((cartprodmempair)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(iskpair @ X18)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempair)).
% 1.20/300.11 thf(setunionE2, axiom, ((setunionE2)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>?[X21:$i]:(((in @ X21 @ X4)&(in @ X2 @ X21)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionE2)).
% 1.20/300.11 thf(setunionsingleton1, axiom, ((setunionsingleton1)<=>![X4:$i]:((subset @ (setunion @ (setadjoin @ X4 @ emptyset)) @ X4))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton1)).
% 1.20/300.11 thf(setunionsingleton2, axiom, ((setunionsingleton2)<=>![X4:$i]:((subset @ X4 @ (setunion @ (setadjoin @ X4 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton2)).
% 1.20/300.11 thf(setunionsingleton, axiom, ((setunionsingleton)<=>![X2:$i]:(((setunion @ (setadjoin @ X2 @ emptyset))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setunionsingleton)).
% 1.20/300.11 thf(singletonsuniq, axiom, ((singletonsuniq)<=>![X2:$i, X3:$i]:((((setadjoin @ X2 @ emptyset)=(setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', singletonsuniq)).
% 1.20/300.11 thf(setukpairinjL1, axiom, ((setukpairinjL1)<=>![X2:$i, X3:$i, X14:$i]:(((in @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL1)).
% 1.20/300.11 thf(kfstpairEq, axiom, ((kfstpairEq)<=>![X2:$i, X3:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kfstpairEq)).
% 1.20/300.11 thf(cartprodfstin, axiom, ((cartprodfstin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (kfst @ X18) @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstin)).
% 1.20/300.11 thf(setukpairinjL2, axiom, ((setukpairinjL2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL2)).
% 1.20/300.11 thf(setukpairinjL, axiom, ((setukpairinjL)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X2)=(X14))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjL)).
% 1.20/300.11 thf(setukpairinjR11, axiom, ((setukpairinjR11)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR11)).
% 1.20/300.11 thf(setukpairinjR12, axiom, ((setukpairinjR12)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR12)).
% 1.20/300.11 thf(setukpairinjR1, axiom, ((setukpairinjR1)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>(((X14)=(X18))=>((X3)=(X18)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR1)).
% 1.20/300.11 thf(upairequniteq, axiom, ((upairequniteq)<=>![X2:$i, X3:$i, X14:$i]:((((setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))=(setadjoin @ X14 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', upairequniteq)).
% 1.20/300.11 thf(setukpairinjR2, axiom, ((setukpairinjR2)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X14 @ emptyset) @ (setadjoin @ (setadjoin @ X14 @ (setadjoin @ X18 @ emptyset)) @ emptyset)))=>((X3)=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR2)).
% 1.20/300.11 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X2:$i, X3:$i, X14:$i, X18:$i]:((((kpair @ X2 @ X3)=(kpair @ X14 @ X18))=>((X3)=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', setukpairinjR)).
% 1.20/300.11 thf(ksndpairEq, axiom, ((ksndpairEq)<=>![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', ksndpairEq)).
% 1.20/300.11 thf(kpairsurjEq, axiom, ((kpairsurjEq)<=>![X18:$i]:(((iskpair @ X18)=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', kpairsurjEq)).
% 1.20/300.11 thf(cartprodsndin, axiom, ((cartprodsndin)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>(in @ (ksnd @ X18) @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndin)).
% 1.20/300.11 thf(cartprodpairmemEL, axiom, ((cartprodpairmemEL)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemEL)).
% 1.20/300.11 thf(cartprodpairmemER, axiom, ((cartprodpairmemER)<=>![X4:$i, X5:$i, X2:$i, X3:$i]:(((in @ (kpair @ X2 @ X3) @ (cartprod @ X4 @ X5))=>(in @ X3 @ X5)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairmemER)).
% 1.20/300.11 thf(cartprodmempaircEq, axiom, ((cartprodmempaircEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kpair @ X2 @ X3)=(kpair @ X2 @ X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodmempaircEq)).
% 1.20/300.11 thf(cartprodfstpairEq, axiom, ((cartprodfstpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((kfst @ (kpair @ X2 @ X3))=(X2))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodfstpairEq)).
% 1.20/300.11 thf(cartprodsndpairEq, axiom, ((cartprodsndpairEq)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((ksnd @ (kpair @ X2 @ X3))=(X3))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodsndpairEq)).
% 1.20/300.11 thf(cartprodpairsurjEq, axiom, ((cartprodpairsurjEq)<=>![X4:$i, X5:$i, X18:$i]:(((in @ X18 @ (cartprod @ X4 @ X5))=>((kpair @ (kfst @ X18) @ (ksnd @ X18))=(X18))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p', cartprodpairsurjEq)).
% 1.20/300.11 thf(c_0_192, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X576:$i]:(((in @ X576 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X576 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[ex1])).
% 1.20/300.11 thf(c_0_193, plain, ((singleton)=(^[Z0/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&((Z0)=(setadjoin @ X2 @ emptyset))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 1.20/300.11 thf(c_0_194, 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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])).
% 1.20/300.11 thf(c_0_195, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])).
% 1.20/300.11 thf(c_0_196, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])).
% 1.20/300.11 thf(c_0_197, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])).
% 1.20/300.11 thf(c_0_198, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])).
% 1.20/300.11 thf(c_0_199, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])).
% 1.20/300.11 thf(c_0_200, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])).
% 1.20/300.11 thf(c_0_201, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])).
% 1.20/300.11 thf(c_0_202, 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])).
% 1.20/300.11 thf(c_0_203, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])).
% 1.20/300.11 thf(c_0_204, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])).
% 1.20/300.11 thf(c_0_205, 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])).
% 1.20/300.11 thf(c_0_206, 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 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])).
% 1.20/300.11 thf(c_0_207, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])).
% 1.20/300.11 thf(c_0_208, 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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])).
% 1.20/300.11 thf(c_0_209, plain, ((singletonprop)<=>![X4:$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 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[singletonprop])).
% 1.20/300.11 thf(c_0_210, plain, ((ex1E1)<=>![X4:$i, X1:$i > $o]:(((ex1 @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))))), inference(fof_simplification,[status(thm)],[ex1E1])).
% 1.20/300.11 thf(c_0_211, plain, ((ex1)=(^[Z0/* 19 */:$i, Z1:$i > $o]:((?[X576:$i]:(((in @ X576 @ (dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2)))))&((dsetconstr @ Z0 @ (^[Z2/* 3 */:$i]:((Z1 @ Z2))))=(setadjoin @ X576 @ emptyset)))))))), inference(apply_def,[status(thm)],[c_0_192, c_0_193])).
% 1.20/300.11 thf(c_0_212, 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])).
% 1.20/300.11 thf(c_0_213, 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 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[ex1I2])).
% 1.20/300.11 thf(c_0_214, plain, ((kfstsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))))), inference(fof_simplification,[status(thm)],[kfstsingleton])).
% 1.20/300.11 thf(c_0_215, plain, ((ksndsingleton)<=>![X18:$i]:(((iskpair @ X18)=>(singleton @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 1.20/300.11 thf(c_0_216, plain, ((dpsetconstrI)<=>![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X23 @ Z0 @ Z1))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstrI])).
% 1.20/300.11 thf(c_0_217, plain, ((dpsetconstr)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i > $i > $o]:(dsetconstr @ (cartprod @ Z0 @ Z1) @ (^[Z3/* 5 */:$i]:(?[X2:$i]:(((in @ X2 @ Z0)&?[X3:$i]:((((in @ X3 @ Z1)&(Z2 @ X2 @ X3))&((Z3)=(kpair @ X2 @ X3))))))))))), inference(fof_simplification,[status(thm)],[dpsetconstr])).
% 1.20/300.11 thf(c_0_218, plain, ((dpsetconstrSub)<=>![X4:$i, X5:$i, X24:$i > $i > $o]:((subset @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X24 @ Z0 @ Z1)))) @ (cartprod @ X4 @ X5)))), inference(fof_simplification,[status(thm)],[dpsetconstrSub])).
% 1.20/300.11 thf(c_0_219, plain, ((setOfPairsIsBReln)<=>![X4:$i, X5:$i, X25:$i > $i > $o]:((breln @ X4 @ X5 @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X25 @ Z0 @ Z1))))))), inference(fof_simplification,[status(thm)],[setOfPairsIsBReln])).
% 1.20/300.11 thf(c_0_220, plain, ((breln)=(^[Z0/* 19 */:$i, Z1:$i, Z2:$i]:((subset @ Z2 @ (cartprod @ Z0 @ Z1))))), inference(fof_simplification,[status(thm)],[breln])).
% 1.20/300.11 thf(c_0_221, plain, ((dpsetconstrERa)<=>![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dpsetconstr @ X4 @ X5 @ (^[Z0/* 19 */:$i, Z1:$i]:((X26 @ Z0 @ Z1)))))=>(X26 @ X2 @ X3))))))), inference(fof_simplification,[status(thm)],[dpsetconstrERa])).
% 1.20/300.11 thf(c_0_222, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X547:$i]:((((X6 @ X2 @ X547))&![X548:$i]:((((X6 @ X2 @ X548))=>((X547)=(X548)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_194, c_0_195])).
% 1.20/300.11 thf(c_0_223, plain, ((descrp)=(![X1:$i > $o]:(((?[X549:$i]:((((X1 @ X549))&![X550:$i]:((((X1 @ X550))=>((X549)=(X550)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_196, c_0_195])).
% 1.20/300.11 thf(c_0_224, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])).
% 1.20/300.11 thf(c_0_225, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])).
% 1.20/300.11 thf(c_0_226, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 1.20/300.11 thf(c_0_227, plain, ((exuE1)=(![X1:$i > $o]:(((?[X551:$i]:((((X1 @ X551))&![X552:$i]:((((X1 @ X552))=>((X551)=(X552)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_197, c_0_195])).
% 1.20/300.11 thf(c_0_228, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X553:$i]:((((X1 @ X553))&![X554:$i]:((((X1 @ X554))=>((X553)=(X554)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_198, c_0_195])).
% 1.20/300.11 thf(c_0_229, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])).
% 1.20/300.11 thf(c_0_230, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_199])).
% 1.20/300.11 thf(c_0_231, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_200, c_0_199])).
% 1.20/300.11 thf(c_0_232, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_199])).
% 1.20/300.11 thf(c_0_233, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])).
% 1.20/300.11 thf(c_0_234, plain, ((exuE2)=(![X1:$i > $o]:(((?[X555:$i]:((((X1 @ X555))&![X556:$i]:((((X1 @ X556))=>((X555)=(X556)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_201, c_0_195])).
% 1.20/300.11 thf(c_0_235, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_199])).
% 1.20/300.11 thf(c_0_236, 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])).
% 1.20/300.11 thf(c_0_237, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X557:$i]:((((X1 @ X557))&![X558:$i]:((((X1 @ X558))=>((X557)=(X558))))))))))), inference(apply_def,[status(thm)],[c_0_202, c_0_195])).
% 1.20/300.11 thf(c_0_238, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X559:$i]:((((X1 @ X559))&![X560:$i]:((((X1 @ X560))=>((X559)=(X560)))))))))))), inference(apply_def,[status(thm)],[c_0_203, c_0_195])).
% 1.20/300.11 thf(c_0_239, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X561:$i]:((((X1 @ X561))&![X562:$i]:((((X1 @ X562))=>((X561)=(X562))))))))))), inference(apply_def,[status(thm)],[c_0_204, c_0_195])).
% 1.20/300.11 thf(c_0_240, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X563:$i]:((((X1 @ X563))&![X564:$i]:((((X1 @ X564))=>((X563)=(X564)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_205, c_0_195])).
% 1.20/300.11 thf(c_0_241, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X565:$i]:((((X1 @ X565))&![X566:$i]:((((X1 @ X566))=>((X565)=(X566)))))))<=>(?[X567:$i]:((((X17 @ X567))&![X568:$i]:((((X17 @ X568))=>((X567)=(X568)))))))))))), inference(apply_def,[status(thm)],[c_0_206, c_0_195])).
% 1.20/300.11 thf(c_0_242, plain, ((exuEu)=(![X1:$i > $o]:(((?[X569:$i]:((((X1 @ X569))&![X570:$i]:((((X1 @ X570))=>((X569)=(X570)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_207, c_0_195])).
% 1.20/300.11 thf(c_0_243, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X571:$i]:((((X1 @ X571))&![X572:$i]:((((X1 @ X572))=>((X571)=(X572)))))))=>((?[X573:$i]:((((X17 @ X573))&![X574:$i]:((((X17 @ X574))=>((X573)=(X574)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_208, c_0_195])).
% 1.20/300.11 thf(c_0_244, plain, ((dsetconstr__Cong)<=>![X4:$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 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])).
% 1.20/300.11 thf(c_0_245, plain, ((sepInPowerset)<=>![X4:$i, X1:$i > $o]:((in @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ (powerset @ X4)))), inference(fof_simplification,[status(thm)],[sepInPowerset])).
% 1.20/300.11 thf(c_0_246, plain, ((sepSubset)<=>![X4:$i, X1:$i > $o]:((subset @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))) @ X4))), inference(fof_simplification,[status(thm)],[sepSubset])).
% 1.20/300.11 thf(c_0_247, 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)))=>(?[X575:$i]:(((in @ X575 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(setadjoin @ X575 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_209, c_0_193])).
% 1.20/300.11 thf(c_0_248, plain, ((ex1E1)=(![X4:$i, X1:$i > $o]:(((?[X577:$i]:(((in @ X577 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X577 @ emptyset)))))=>?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), inference(apply_def,[status(thm)],[c_0_210, c_0_211])).
% 1.20/300.11 thf(c_0_249, plain, ((ex1I)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(![X3:$i]:(((in @ X3 @ X4)=>((X1 @ X3)=>((X3)=(X2)))))=>(?[X578:$i]:(((in @ X578 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X578 @ emptyset))))))))))), inference(apply_def,[status(thm)],[c_0_212, c_0_211])).
% 1.20/300.11 thf(c_0_250, 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)))=>(?[X579:$i]:(((in @ X579 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0))))))&((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(((X1 @ Z0)))))=(setadjoin @ X579 @ emptyset)))))))))), inference(apply_def,[status(thm)],[c_0_213, c_0_211])).
% 1.20/300.11 thf(c_0_251, plain, ((kfstsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X580:$i]:(((in @ X580 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18)))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X18))))=(setadjoin @ X580 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_214, c_0_193])).
% 1.20/300.11 thf(c_0_252, axiom, ((theprop)=(![X21:$i]:(((?[X581:$i]:(((in @ X581 @ X21)&((X21)=(setadjoin @ X581 @ emptyset)))))=>(in @ (setunion @ X21) @ X21))))), inference(apply_def,[status(thm)],[theprop, c_0_193])).
% 1.20/300.11 thf(c_0_253, plain, ((ksndsingleton)=(![X18:$i]:(((iskpair @ X18)=>(?[X582:$i]:(((in @ X582 @ (dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0))))))&((dsetconstr @ (setunion @ X18) @ (^[Z0/* 3 */:$i]:(((X18)=(kpair @ (kfst @ X18) @ Z0)))))=(setadjoin @ X582 @ emptyset))))))))), inference(apply_def,[status(thm)],[c_0_215, c_0_193])).
% 1.20/300.11 thf(c_0_254, plain, ((dpsetconstrI)=(![X4:$i, X5:$i, X23:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((X23 @ X2 @ X3)=>(in @ (kpair @ X2 @ X3) @ (dsetconstr @ (cartprod @ X4 @ X5) @ (^[Z0/* 5 */:$i]:(?[X583:$i]:(((in @ X583 @ X4)&?[X584:$i]:((((in @ X584 @ X5)&((X23 @ X583 @ X584)))&((Z0)=(kpair @ X583 @ X584))))))))))))))))), inference(apply_def,[status(thm)],[c_0_216, c_0_217])).
% 1.20/300.11 thf(c_0_255, plain, ((dpsetconstrSub)=(![X4:$i, X5:$i, X24:$i > $i > $o]:((subset @ (dsetconstr @ (cartprod @ X4 @ X5) @ (^[Z0/* 5 */:$i]:(?[X585:$i]:(((in @ X585 @ X4)&?[X586:$i]:((((in @ X586 @ X5)&((X24 @ X585 @ X586)))&((Z0)=(kpair @ X585 @ X586))))))))) @ (cartprod @ X4 @ X5))))), inference(apply_def,[status(thm)],[c_0_218, c_0_217])).
% 1.20/300.11 thf(c_0_256, plain, ((setOfPairsIsBReln)=(![X4:$i, X5:$i, X25:$i > $i > $o]:(((subset @ (dsetconstr @ (cartprod @ X4 @ X5) @ (^[Z0/* 5 */:$i]:(?[X587:$i]:(((in @ X587 @ X4)&?[X588:$i]:((((in @ X588 @ X5)&((X25 @ X587 @ X588)))&((Z0)=(kpair @ X587 @ X588))))))))) @ (cartprod @ X4 @ X5)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_219, c_0_220]), c_0_217])).
% 1.20/300.11 thf(c_0_257, plain, ((dpsetconstrERa)=(![X4:$i, X5:$i, X26:$i > $i > $o, X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>((in @ (kpair @ X2 @ X3) @ (dsetconstr @ (cartprod @ X4 @ X5) @ (^[Z0/* 5 */:$i]:(?[X589:$i]:(((in @ X589 @ X4)&?[X590:$i]:((((in @ X590 @ X5)&((X26 @ X589 @ X590)))&((Z0)=(kpair @ X589 @ X590))))))))))=>(X26 @ X2 @ X3)))))))), inference(apply_def,[status(thm)],[c_0_221, c_0_217])).
% 1.20/300.11 thf(c_0_258, plain, ((epred1_0)<=>![X620:$i]:(?[X621:$i]:((((![X622:$i]:(((in @ X622 @ X621)=>![X623:$i]:(((in @ X623 @ X622)=>(in @ X623 @ X620)))))&![X624:$i, X625:$i]:((((in @ X624 @ X620)&(in @ X625 @ X620))=>(![X626:$i]:(((in @ X626 @ X621)=>((in @ X624 @ X626)<=>(in @ X625 @ X626))))=>((X624)=(X625))))))&![X627:$i, X628:$i]:((((in @ X627 @ X621)&(in @ X628 @ X621))=>(![X629:$i]:(((in @ X629 @ X627)=>(in @ X629 @ X628)))|![X630:$i]:(((in @ X630 @ X628)=>(in @ X630 @ X627)))))))&![X631:$i]:(((![X632:$i]:(((in @ X632 @ X631)=>(in @ X632 @ X620)))&?[X633:$i]:((in @ X633 @ X631)))=>?[X634:$i, X635:$i]:(((((in @ X634 @ X621)&(in @ X635 @ X631))&~(?[X636:$i]:(((in @ X636 @ X634)&(in @ X636 @ X631)))))&![X637:$i]:(((in @ X637 @ X621)=>(![X638:$i]:(((in @ X638 @ X637)=>(in @ X638 @ X634)))|(in @ X635 @ X637)))))))))))), introduced(definition)).
% 1.20/300.11 thf(c_0_259, negated_conjecture, ~((![X591:$i, X592:$i]:((![X593:$i]:(((in @ X593 @ X591)<=>(in @ X593 @ X592)))=>((X591)=(X592))))=>(![X594:$i]:(~(in @ X594 @ emptyset))=>(![X595:$i, X596:$i, X597:$i]:(((in @ X597 @ (setadjoin @ X595 @ X596))<=>(((X597)=(X595))|(in @ X597 @ X596))))=>(![X598:$i, X599:$i]:(((in @ X599 @ (powerset @ X598))<=>![X600:$i]:(((in @ X600 @ X599)=>(in @ X600 @ X598)))))=>(![X601:$i, X602:$i]:(((in @ X602 @ (setunion @ X601))<=>?[X603:$i]:(((in @ X602 @ X603)&(in @ X603 @ X601)))))=>((in @ emptyset @ omega)=>(![X604:$i]:(((in @ X604 @ omega)=>(in @ (setadjoin @ X604 @ X604) @ omega)))=>(![X605:$i]:((((in @ emptyset @ X605)&![X606:$i]:((((in @ X606 @ omega)&(in @ X606 @ X605))=>(in @ (setadjoin @ X606 @ X606) @ X605))))=>![X607:$i]:(((in @ X607 @ omega)=>(in @ X607 @ X605)))))=>(![X608:$i > $i > $o, X609:$i]:((![X610:$i]:(((in @ X610 @ X609)=>?[X611:$i]:(((X608 @ X610 @ X611)&![X612:$i]:(((X608 @ X610 @ X612)=>((X611)=(X612))))))))=>?[X613:$i]:(![X614:$i]:(((in @ X614 @ X613)<=>?[X615:$i]:(((in @ X615 @ X609)&(X608 @ X615 @ X614))))))))=>(![X616:$i]:((?[X617:$i]:((in @ X617 @ X616))=>?[X618:$i]:(((in @ X618 @ X616)&~(?[X619:$i]:(((in @ X619 @ X618)&(in @ X619 @ X616))))))))=>((epred1_0)=>(![X639:$i > $o]:((?[X640:$i]:(((X639 @ X640)&![X641:$i]:(((X639 @ X641)=>((X640)=(X641))))))=>(X639 @ (descr @ (^[Z0/* 17 */:$i]:(X639 @ Z0))))))=>(![X642:$i, X643:$i > $o, X644:$i]:(((in @ X644 @ X642)=>((X643 @ X644)=>(in @ X644 @ (dsetconstr @ X642 @ X643)))))=>(![X645:$i, X646:$i > $o, X647:$i]:(((in @ X647 @ (dsetconstr @ X645 @ X646))=>(in @ X647 @ X645)))=>(![X648:$i, X649:$i > $o, X650:$i]:(((in @ X650 @ (dsetconstr @ X648 @ X649))=>(X649 @ X650)))=>(![X651:$i > $o]:((?[X652:$i]:(((X651 @ X652)&![X653:$i]:(((X651 @ X653)=>((X652)=(X653))))))=>?[X654:$i]:(((X651 @ X654)&![X655:$i]:(((X651 @ X655)=>((X654)=(X655))))))))=>(![X656:$o, X657:$i]:(((in @ X657 @ (prop2set @ ((X656))))=>(X656)))=>(![X658:$i]:(((in @ X658 @ emptyset)=>![X659:$o]:((X659))))=>(![X660:$i]:(((in @ X660 @ emptyset)=>~($true)))=>(![X661:$i]:(~(in @ X661 @ emptyset))=>(![X662:$i > $o]:((?[X663:$i]:(((X662 @ X663)&![X664:$i]:(((X662 @ X664)=>((X663)=(X664))))))=>?[X665:$i]:((X662 @ X665))))=>(![X666:$i, X667:$i]:((![X668:$i]:(((in @ X668 @ X666)=>(in @ X668 @ X667)))=>(![X669:$i]:(((in @ X669 @ X667)=>(in @ X669 @ X666)))=>((X666)=(X667)))))=>(![X670:$i]:((![X671:$i]:(~(in @ X671 @ X670))=>((X670)=(emptyset))))=>(![X672:$i]:((![X673:$i]:(~(in @ X673 @ X672))=>((X672)=(emptyset))))=>(![X674:$i, X675:$i > $o, X676:$i]:(((in @ X676 @ X674)=>((in @ X676 @ (dsetconstr @ X674 @ X675))<=>(X675 @ X676))))=>(![X677:$i]:((((X677)!=(emptyset))=>?[X678:$i]:((in @ X678 @ X677))))=>(![X679:$i, X680:$i > $o, X681:$i]:(((in @ X681 @ X679)=>((X680 @ X681)=>((dsetconstr @ X679 @ X680)!=(emptyset)))))=>(![X682:$i]:((?[X683:$i]:((in @ X683 @ X682))=>((X682)!=(emptyset))))=>(![X684:$i, X685:$i]:((in @ X684 @ (setadjoin @ X684 @ X685)))=>((in @ emptyset @ (setadjoin @ emptyset @ emptyset))=>(![X686:$i, X687:$i, X688:$i]:(((in @ X688 @ X687)=>(in @ X688 @ (setadjoin @ X686 @ X687))))=>(![X689:$i, X690:$i, X691:$i]:(((in @ X691 @ (setadjoin @ X689 @ X690))=>![X692:$o]:(((((X691)=(X689))=>(X692))=>(((in @ X691 @ X690)=>(X692))=>(X692))))))=>(![X693:$i, X694:$i, X695:$i]:(((in @ X695 @ (setadjoin @ X693 @ X694))=>(((X695)=(X693))|(in @ X695 @ X694))))=>(![X696:$i]:(((dsetconstr @ X696 @ (^[Z0/* 1 */:$i]:($true)))=(X696)))=>(![X697:$i, X698:$i]:((![X699:$i]:(((in @ X699 @ X698)=>(in @ X699 @ X697)))=>(in @ X698 @ (powerset @ X697))))=>(![X700:$i]:((in @ emptyset @ (powerset @ X700)))=>(![X701:$i]:((in @ emptyset @ (powerset @ X701)))=>(![X702:$i, X703:$i, X704:$i]:(((in @ X703 @ (powerset @ X702))=>((in @ X704 @ X703)=>(in @ X704 @ X702))))=>(![X705:$i, X706:$i, X707:$i]:(((in @ X706 @ X707)=>((in @ X707 @ X705)=>(in @ X706 @ (setunion @ X705)))))=>(![X708:$i, X709:$i]:(((in @ X709 @ (setunion @ X708))=>![X710:$o]:((![X711:$i]:(((in @ X709 @ X711)=>((in @ X711 @ X708)=>(X710))))=>(X710)))))=>(![X712:$i, X713:$i]:(((in @ X713 @ X712)=>(in @ X713 @ (powerset @ (setunion @ X712)))))=>(![X714:$i > $o]:((?[X715:$i]:(((X714 @ X715)&![X716:$i]:(((X714 @ X716)=>((X715)=(X716))))))=>?[X717:$i]:(![X718:$i]:(((X714 @ X718)<=>((X718)=(X717)))))))=>(![X719:$i]:((((X719)!=(emptyset))=>?[X720:$i]:(((in @ X720 @ X719)&$true))))=>(![X721:$i, X722:$i]:(((in @ X721 @ (setadjoin @ X722 @ emptyset))=>((X721)=(X722))))=>(![X723:$i, X724:$i]:((((X723)!=(X724))=>~(in @ X724 @ (setadjoin @ X723 @ emptyset))))=>(![X725:$i, X726:$i]:((((X725)=(X726))=>(in @ X725 @ (setadjoin @ X726 @ emptyset))))=>(![X727:$i, X728:$i]:(((in @ X727 @ (setadjoin @ X728 @ emptyset))=>(in @ X728 @ (setadjoin @ X727 @ emptyset))))=>(![X729:$i, X730:$i, X731:$i]:(((in @ X731 @ (setadjoin @ X729 @ (setadjoin @ X730 @ emptyset)))=>(((X731)=(X729))|((X731)=(X730)))))=>(![X732:$i, X733:$i]:((in @ X732 @ (setadjoin @ X732 @ (setadjoin @ X733 @ emptyset))))=>(![X734:$i, X735:$i]:((in @ X735 @ (setadjoin @ X734 @ (setadjoin @ X735 @ emptyset))))=>(![X736:$i, X737:$i > $o]:((?[X738:$i]:(((in @ X738 @ X736)&(X737 @ X738)))=>(((dsetconstr @ X736 @ X737)=(emptyset))=>~($true))))=>(![X739:$i > $o, X740:$i]:(((in @ X740 @ emptyset)=>(X739 @ X740)))=>(![X741:$i, X742:$i > $o]:((~(![X743:$i]:(((in @ X743 @ X741)=>(X742 @ X743))))=>?[X744:$i]:(((in @ X744 @ X741)&~((X742 @ X744))))))=>(![X745:$i, X746:$i > $o]:((![X747:$i]:(((in @ X747 @ X745)=>~((X746 @ X747))))=>~(?[X748:$i]:(((in @ X748 @ X745)&(X746 @ X748))))))=>(![X749:$i, X750:$i > $o]:((~(?[X751:$i]:(((in @ X751 @ X749)&(X750 @ X751))))=>![X752:$i]:(((in @ X752 @ X749)=>~((X750 @ X752))))))=>(![X753:$i, X754:$i > $o]:((?[X755:$i]:(((in @ X755 @ X753)&~((X754 @ X755))))=>~(![X756:$i]:(((in @ X756 @ X753)=>(X754 @ X756))))))=>(![X757:$o]:(((X757)=>(in @ emptyset @ (prop2set @ ((X757))))))=>(![X758:$o]:(((X758)=>(set2prop @ (prop2set @ ((X758))))))=>(![X759:$i, X760:$i > $o]:((~(?[X761:$i]:(((in @ X761 @ X759)&(X760 @ X761))))=>![X762:$i]:(((in @ X762 @ X759)=>~((X760 @ X762))))))=>(![X763:$i, X764:$i > $o]:((~(![X765:$i]:(((in @ X765 @ X763)=>(X764 @ X765))))=>?[X766:$i]:(((in @ X766 @ X763)&~((X764 @ X766))))))=>(![X767:$i > $o]:((?[X768:$i]:(((X767 @ X768)&![X769:$i]:(((X767 @ X769)=>((X768)=(X769))))))=>?[X770:$i]:(((X767 @ X770)&![X771:$i]:(((X767 @ X771)=>((X770)=(X771))))))))=>(![X772:$i > $o]:((?[X773:$i]:((X772 @ X773))=>(![X774:$i, X775:$i]:(((X772 @ X774)=>((X772 @ X775)=>((X774)=(X775)))))=>?[X776:$i]:(((X772 @ X776)&![X777:$i]:(((X772 @ X777)=>((X776)=(X777)))))))))=>(![X778:$i > $o]:((?[X779:$i]:(![X780:$i]:(((X778 @ X780)<=>((X780)=(X779)))))=>?[X781:$i]:(((X778 @ X781)&![X782:$i]:(((X778 @ X782)=>((X781)=(X782))))))))=>(![X783:$i, X784:$i]:((((X783)=(X784))=>![X785:$i, X786:$i]:((((X785)=(X786))=>((in @ X785 @ X783)=>(in @ X786 @ X784))))))=>(![X787:$i, X788:$i]:((((X787)=(X788))=>![X789:$i, X790:$i]:((((X789)=(X790))=>((in @ X789 @ X787)<=>(in @ X790 @ X788))))))=>(![X791:$i > $o]:((?[X792:$i]:(((X791 @ X792)&![X793:$i]:(((X791 @ X793)=>((X792)=(X793))))))=>![X794:$i, X795:$i]:(((X791 @ X794)=>((X791 @ X795)=>((X794)=(X795)))))))=>(![X796:$i > $o, X797:$i > $o]:((![X798:$i, X799:$i]:((((X798)=(X799))=>((X796 @ X798)<=>(X797 @ X799))))=>(?[X800:$i]:(((X796 @ X800)&![X801:$i]:(((X796 @ X801)=>((X800)=(X801))))))<=>?[X802:$i]:(((X797 @ X802)&![X803:$i]:(((X797 @ X803)=>((X802)=(X803)))))))))=>(((emptyset)=(emptyset))=>(![X804:$i, X805:$i]:((((X804)=(X805))=>![X806:$i, X807:$i]:((((X806)=(X807))=>((setadjoin @ X804 @ X806)=(setadjoin @ X805 @ X807))))))=>(![X808:$i, X809:$i]:((((X808)=(X809))=>((powerset @ X808)=(powerset @ X809))))=>(![X810:$i, X811:$i]:((((X810)=(X811))=>((setunion @ X810)=(setunion @ X811))))=>(((omega)=(omega))=>(![X812:$i > $o]:((?[X813:$i]:(((X812 @ X813)&![X814:$i]:(((X812 @ X814)=>((X813)=(X814))))))=>![X815:$i, X816:$i]:(((X812 @ X815)=>((X812 @ X816)=>((X815)=(X816)))))))=>(![X817:$i > $o, X818:$i > $o]:((![X819:$i, X820:$i]:((((X819)=(X820))=>((X817 @ X819)<=>(X818 @ X820))))=>(?[X821:$i]:(((X817 @ X821)&![X822:$i]:(((X817 @ X822)=>((X821)=(X822))))))=>(?[X823:$i]:(((X818 @ X823)&![X824:$i]:(((X818 @ X824)=>((X823)=(X824))))))=>((descr @ X817)=(descr @ X818))))))=>(![X825:$i, X826:$i]:((((X825)=(X826))=>![X827:$i > $o, X828:$i > $o]:((![X829:$i]:(((in @ X829 @ X825)=>![X830:$i]:(((in @ X830 @ X826)=>(((X829)=(X830))=>((X827 @ X829)<=>(X828 @ X830)))))))=>((dsetconstr @ X825 @ X827)=(dsetconstr @ X826 @ X828))))))=>(![X831:$i, X832:$i]:((![X833:$i]:(((in @ X833 @ X831)=>(in @ X833 @ X832)))=>(subset @ X831 @ X832)))=>(![X834:$i, X835:$i]:((((X834)=(X835))=>(subset @ X835 @ X834)))=>(![X836:$i, X837:$i]:((((X836)=(X837))=>(subset @ X836 @ X837)))=>(![X838:$i, X839:$i]:((![X840:$i]:(((in @ X840 @ X838)=>(in @ X840 @ X839)))=>(subset @ X838 @ X839)))=>(![X841:$i]:((subset @ emptyset @ X841))=>(![X842:$i, X843:$i, 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X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fool_unroll,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[dpsetconstrEL1])]), setextAx]), emptysetAx]), setadjoinAx]), powersetAx]), setunionAx]), omega0Ax]), omegaSAx]), omegaIndAx]), c_0_222]), foundationAx]), wellorderingAx]), c_0_223]), c_0_224]), c_0_225]), c_0_226]), c_0_227]), prop2setE]), emptysetE]), emptysetimpfalse]), notinemptyset]), c_0_228]), setext]), emptyI]), noeltsimpempty]), c_0_229]), c_0_230]), c_0_231]), c_0_232]), setadjoinIL]), emptyinunitempty]), setadjoinIR]), setadjoinE]), setadjoinOr]), c_0_233]), powersetI]), emptyinPowerset]), emptyInPowerset]), powersetE]), setunionI]), setunionE]), subPowSU]), c_0_234]), c_0_235]), uniqinunit]), notinsingleton]), eqinunit]), singletonsswitch]), upairsetE]), upairsetIL]), upairsetIR]), c_0_236]), vacuousDall]), quantDeMorgan1]), quantDeMorgan2]), quantDeMorgan3]), quantDeMorgan4]), prop2setI]), prop2set2propI]), notdexE]), notdallE]), c_0_237]), c_0_238]), c_0_239]), inCongP]), in__Cong]), c_0_240]), c_0_241]), emptyset__Cong]), setadjoin__Cong]), powerset__Cong]), setunion__Cong]), omega__Cong]), c_0_242]), c_0_243]), c_0_244]), subsetI1]), eqimpsubset2]), eqimpsubset1]), subsetI2]), emptysetsubset]), subsetE]), subsetE2]), notsubsetI]), notequalI1]), notequalI2]), subsetRefl]), subsetTrans]), setadjoinSub]), setadjoinSub2]), subset2powerset]), setextsub]), subsetemptysetimpeq]), powersetI1]), powersetE1]), inPowerset]), powersetsubset]), c_0_245]), c_0_246]), 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_247]), c_0_248]), c_0_249]), c_0_250]), singletonsuniq]), setukpairinjL1]), c_0_251]), c_0_252]), kfstpairEq]), cartprodfstin]), setukpairinjL2]), setukpairinjL]), setukpairinjR11]), setukpairinjR12]), setukpairinjR1]), upairequniteq]), setukpairinjR2]), setukpairinjR]), c_0_253]), ksndpairEq]), kpairsurjEq]), cartprodsndin]), cartprodpairmemEL]), cartprodpairmemER]), cartprodmempaircEq]), cartprodfstpairEq]), cartprodsndpairEq]), cartprodpairsurjEq]), c_0_217]), c_0_254]), c_0_255]), c_0_256]), c_0_257])])]), c_0_258])).
% 1.20/300.11 thf(c_0_260, negated_conjecture, ![X1150:$i, X1151:$i, X1153:$i, X1154:$i, X1155:$i, X1156:$i, X1157:$i, X1158:$i, X1159:$i, X1160:$i, X1161:$i, X1163:$i, X1164:$i, X1166:$i, X1167:$i, X1168:$i, X1169:$i, X1170:$i, X1172:$i, X1173:$i > $i > $o, X1174:$i, X1176:$i, X1179:$i, X1181:$i, X1182:$i, X1183:$i, X1184:$i, X1186:$i, X1187:$i > $o, X1188:$i, X1190:$i, X1191:$i > $o, X1192:$i, X1193:$i, X1194:$i > $o, X1195:$i, X1196:$i, X1197:$i > $o, X1198:$i, X1199:$i > $o, X1200:$i, X1203:$i, X1204:$o, X1205:$i, X1206:$i, X1207:$o, X1208:$i, X1209:$i, X1210:$i > $o, X1211:$i, X1214:$i, X1215:$i, X1218:$i, X1220:$i, X1222:$i, X1223:$i > $o, X1224:$i, X1225:$i, X1227:$i, X1228:$i > $o, X1229:$i, X1230:$i, X1231:$i, X1232:$i, X1233:$i, X1234:$i, X1235:$i, X1236:$i, X1237:$i, X1238:$i, X1239:$i, X1240:$o, X1241:$i, X1242:$i, X1243:$i, X1244:$i, X1245:$i, X1246:$i, X1248:$i, X1249:$i, X1250:$i, X1251:$i, X1252:$i, X1253:$i, X1254:$i, X1255:$i, X1256:$i, X1257:$i, X1258:$o, X1260:$i, X1261:$i, X1262:$i > $o, X1263:$i, X1266:$i, X1267:$i, X1268:$i, X1270:$i, X1271:$i, X1272:$i, X1273:$i, X1274:$i, X1275:$i, X1276:$i, X1277:$i, X1278:$i, X1279:$i, X1280:$i, X1281:$i, X1282:$i, X1283:$i, X1284:$i, X1285:$i, X1286:$i > $o, X1287:$i, X1288:$i > $o, X1289:$i, X1290:$i, X1291:$i > $o, X1292:$i, X1294:$i, X1295:$i > $o, X1297:$i, X1298:$i, X1299:$i > $o, X1301:$i, X1302:$i, X1303:$i > $o, X1304:$i, X1306:$o, X1307:$o, X1308:$i, X1309:$i > $o, X1311:$i, X1312:$i, X1313:$i > $o, X1314:$i, X1316:$i > $o, X1317:$i, X1320:$i, X1321:$i > $o, X1322:$i, X1326:$i, X1327:$i > $o, X1328:$i, X1331:$i, X1332:$i, X1333:$i, X1334:$i, X1335:$i, X1336:$i, X1337:$i, X1338:$i, X1339:$i, X1340:$i > $o, X1341:$i, X1343:$i, X1344:$i, X1345:$i > $o, X1346:$i > $o, X1349:$i, X1352:$i, X1353:$i, X1356:$i, X1357:$i, X1358:$i, X1359:$i, X1360:$i, X1361:$i, X1362:$i, X1363:$i, X1364:$i, X1365:$i > $o, X1366:$i, X1368:$i, X1369:$i, X1370:$i > $o, X1371:$i > $o, X1374:$i, X1376:$i, X1378:$i, X1379:$i, X1380:$i > $o, X1381:$i > $o, X1384:$i, X1385:$i, X1387:$i, X1388:$i, X1389:$i, X1390:$i, X1391:$i, X1392:$i, X1394:$i, X1395:$i, X1396:$i, X1397:$i, X1398:$i, X1399:$i, X1400:$i, X1401:$i, X1402:$i, X1403:$i, X1404:$i, X1405:$i, X1406:$i, X1407:$i, X1408:$i, X1409:$i, X1410:$i, X1411:$i, X1412:$i, X1413:$i, X1414:$i, X1415:$i, X1416:$i, X1417:$i, X1418:$i, X1419:$i, X1420:$i, X1421:$i, X1422:$i, X1423:$i, X1424:$i, X1425:$i, X1426:$i, X1427:$i, X1428:$i, X1429:$i, X1430:$i, X1431:$i > $o, X1432:$i, X1433:$i > $o, X1434:$i, X1435:$i, X1436:$i, X1437:$i, X1438:$i, X1439:$i, X1440:$i, X1441:$i, X1442:$i, X1443:$i, X1444:$i, X1445:$o, X1446:$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:$i, X1466:$i, X1467:$i, X1468:$i, X1469:$i, X1470:$i, X1471:$i, X1472:$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:$i, X1513:$o, X1514:$i, X1515:$i, X1516:$i, X1517:$i, X1518:$i, X1519:$i, X1520:$i, X1521:$i, X1522:$i, X1523:$i, X1524:$i, X1525:$i, X1526:$i, X1527:$i, X1528:$i, X1529:$i, X1530:$i, X1531:$i, X1532:$i, X1533:$i, X1534:$i, X1535:$i, X1536:$i, X1537:$i, X1538:$i, X1539:$i, X1540:$i, X1541:$i, X1542:$i, X1543:$i, X1544:$i, X1545:$i, X1546:$i, X1547:$i, X1548:$i, X1549:$i, X1550:$i, X1551:$i, X1552:$i, X1553:$i, X1554:$i, X1555:$i, X1556:$i, X1557:$i, X1558:$i, X1559:$i, X1560:$i, X1561:$i, X1562:$i, X1563:$i, X1564:$i, X1565:$i, X1566:$i, X1567:$i, X1568:$i, X1569:$i, X1570:$i, X1571:$i, X1572:$i, X1575:$i, X1576:$i, X1577:$i, X1578:$i, X1579:$i, X1581:$i, X1582:$i, X1583:$i, X1584:$i, X1585:$i > $o, X1588:$i, X1590:$i, X1591:$i > $o, X1592:$i, X1594:$i, X1595:$i > $o, X1596:$i, X1599:$i, X1600:$i > $o, X1603:$i, X1605:$i, X1606:$i, X1607:$i, X1608:$i, X1609:$i, X1610:$i, X1612:$i, X1613:$i, X1614:$i, X1615:$i, X1616:$i, X1617:$i, X1618:$i, X1619:$i, X1620:$i, X1621:$i, X1622:$i, X1623:$i, X1624:$i, X1625:$i, X1626:$i, X1627:$i, X1628:$i, X1629:$i, X1630:$i, X1631:$i, X1632:$i, X1633:$i, X1634:$i, X1635:$i, X1636:$i, X1637:$i, X1638:$i, X1639:$i, X1640:$i, X1641:$i, X1642:$i, X1643:$i, X1644:$i, X1645:$i, X1646:$i, X1648:$i, X1649:$i, X1650:$i, X1651:$i, X1652:$i, X1653:$i, X1654:$i, X1655:$i, X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i, X1663:$i, X1664:$i, X1665:$i, X1666:$i, X1667:$i, X1668:$i, X1669:$i, X1670:$i, X1671:$i, X1672:$i, X1673:$i, X1674:$i, X1675:$i, X1676:$i, X1677:$i, X1678:$i, X1679:$i > $i > $o, X1680:$i, X1681:$i, X1682:$i, X1683:$i, X1684:$i > $i > $o, X1685:$i, X1686:$i, X1687:$i > $i > $o, X1688:$i, X1689:$i, X1690:$i > $i > $o, X1691:$i, X1692:$i]:((((~(in @ (esk1_2 @ X1150 @ X1151) @ X1150)|~(in @ (esk1_2 @ X1150 @ X1151) @ X1151)|((X1150)=(X1151)))&((in @ (esk1_2 @ X1150 @ X1151) @ X1150)|(in @ (esk1_2 @ X1150 @ X1151) @ X1151)|((X1150)=(X1151))))&(~(in @ X1153 @ emptyset)&(((~(in @ X1156 @ (setadjoin @ X1154 @ X1155))|(((X1156)=(X1154))|(in @ X1156 @ X1155)))&((((X1156)!=(X1154))|(in @ X1156 @ (setadjoin @ X1154 @ X1155)))&(~(in @ X1156 @ X1155)|(in @ X1156 @ (setadjoin @ X1154 @ X1155)))))&(((~(in @ X1158 @ (powerset @ X1157))|(~(in @ X1159 @ X1158)|(in @ X1159 @ X1157)))&(((in @ (esk2_2 @ X1160 @ X1161) @ X1161)|(in @ X1161 @ (powerset @ X1160)))&(~(in @ (esk2_2 @ X1160 @ X1161) @ X1160)|(in @ X1161 @ (powerset @ X1160)))))&(((((in @ X1164 @ (esk3_2 @ X1163 @ X1164))|~(in @ X1164 @ (setunion @ X1163)))&((in @ (esk3_2 @ X1163 @ X1164) @ X1163)|~(in @ X1164 @ (setunion @ X1163))))&(~(in @ X1167 @ X1168)|~(in @ X1168 @ X1166)|(in @ X1167 @ (setunion @ X1166))))&((in @ emptyset @ omega)&((~(in @ X1169 @ omega)|(in @ (setadjoin @ X1169 @ X1169) @ omega))&(((((in @ (esk4_1 @ X1170) @ omega)|~(in @ emptyset @ X1170)|(~(in @ X1172 @ omega)|(in @ X1172 @ X1170)))&((in @ (esk4_1 @ X1170) @ X1170)|~(in @ emptyset @ X1170)|(~(in @ X1172 @ omega)|(in @ X1172 @ X1170))))&(~(in @ (setadjoin @ (esk4_1 @ X1170) @ (esk4_1 @ X1170)) @ X1170)|~(in @ emptyset @ X1170)|(~(in @ X1172 @ omega)|(in @ X1172 @ X1170))))&((((((in @ (esk8_3 @ X1173 @ X1174 @ X1179) @ X1174)|~(in @ X1179 @ (esk7_2 @ X1173 @ X1174))|(in @ (esk5_2 @ X1173 @ X1174) @ X1174))&((X1173 @ (esk8_3 @ X1173 @ X1174 @ X1179) @ X1179)|~(in @ X1179 @ (esk7_2 @ X1173 @ X1174))|(in @ (esk5_2 @ X1173 @ X1174) @ X1174)))&(~(in @ X1182 @ X1174)|~(X1173 @ X1182 @ X1181)|(in @ X1181 @ (esk7_2 @ X1173 @ X1174))|(in @ (esk5_2 @ X1173 @ X1174) @ X1174)))&(((((in @ (esk8_3 @ X1173 @ X1174 @ X1179) @ X1174)|~(in @ X1179 @ (esk7_2 @ X1173 @ X1174))|((X1173 @ (esk5_2 @ X1173 @ X1174) @ (esk6_3 @ X1173 @ X1174 @ X1176))|~(X1173 @ (esk5_2 @ X1173 @ X1174) 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X1595 @ X1596) @ (dsetconstr @ X1594 @ X1595))|(in @ (esk62_3 @ X1594 @ X1595 @ X1596) @ X1594)|~(X1595 @ X1596)|~(in @ X1596 @ X1594))&(((dsetconstr @ X1594 @ X1595)=(setadjoin @ (esk63_3 @ X1594 @ X1595 @ X1596) @ emptyset))|(in @ (esk62_3 @ X1594 @ X1595 @ X1596) @ X1594)|~(X1595 @ X1596)|~(in @ X1596 @ X1594)))&((((in @ (esk63_3 @ X1594 @ X1595 @ X1596) @ (dsetconstr @ X1594 @ X1595))|(X1595 @ (esk62_3 @ X1594 @ X1595 @ X1596))|~(X1595 @ X1596)|~(in @ X1596 @ X1594))&(((dsetconstr @ X1594 @ X1595)=(setadjoin @ (esk63_3 @ X1594 @ X1595 @ X1596) @ emptyset))|(X1595 @ (esk62_3 @ X1594 @ X1595 @ X1596))|~(X1595 @ X1596)|~(in @ X1596 @ X1594)))&(((in @ (esk63_3 @ X1594 @ X1595 @ X1596) @ (dsetconstr @ X1594 @ X1595))|((esk62_3 @ X1594 @ X1595 @ X1596)!=(X1596))|~(X1595 @ X1596)|~(in @ X1596 @ X1594))&(((dsetconstr @ X1594 @ X1595)=(setadjoin @ (esk63_3 @ X1594 @ X1595 @ X1596) @ emptyset))|((esk62_3 @ X1594 @ X1595 @ X1596)!=(X1596))|~(X1595 @ X1596)|~(in @ X1596 @ X1594)))))&(((((in @ (esk66_2 @ X1599 @ X1600) @ (dsetconstr @ X1599 @ X1600))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|(in @ (esk64_2 @ X1599 @ X1600) @ X1599))&(((dsetconstr @ X1599 @ X1600)=(setadjoin @ (esk66_2 @ X1599 @ X1600) @ emptyset))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|(in @ (esk64_2 @ X1599 @ X1600) @ X1599)))&((((in @ (esk66_2 @ X1599 @ X1600) @ (dsetconstr @ X1599 @ X1600))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|(in @ (esk65_2 @ X1599 @ X1600) @ X1599))&(((dsetconstr @ X1599 @ X1600)=(setadjoin @ (esk66_2 @ X1599 @ X1600) @ emptyset))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|(in @ (esk65_2 @ X1599 @ X1600) @ X1599)))&((((in @ (esk66_2 @ X1599 @ X1600) @ (dsetconstr @ X1599 @ X1600))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|(X1600 @ (esk64_2 @ X1599 @ X1600)))&(((dsetconstr @ X1599 @ X1600)=(setadjoin @ (esk66_2 @ X1599 @ X1600) @ emptyset))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|(X1600 @ (esk64_2 @ X1599 @ X1600))))&((((in @ (esk66_2 @ X1599 @ X1600) @ (dsetconstr @ X1599 @ X1600))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|(X1600 @ (esk65_2 @ X1599 @ X1600)))&(((dsetconstr @ X1599 @ X1600)=(setadjoin @ (esk66_2 @ X1599 @ X1600) @ emptyset))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|(X1600 @ (esk65_2 @ X1599 @ X1600))))&(((in @ (esk66_2 @ X1599 @ X1600) @ (dsetconstr @ X1599 @ X1600))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|((esk64_2 @ X1599 @ X1600)!=(esk65_2 @ X1599 @ X1600)))&(((dsetconstr @ X1599 @ X1600)=(setadjoin @ (esk66_2 @ X1599 @ X1600) @ emptyset))|(~(in @ X1603 @ X1599)|~(X1600 @ X1603))|((esk64_2 @ X1599 @ X1600)!=(esk65_2 @ X1599 @ X1600))))))))&((((setadjoin @ X1605 @ emptyset)!=(setadjoin @ X1606 @ emptyset))|((X1605)=(X1606)))&((~(in @ (setadjoin @ X1609 @ emptyset) @ (setadjoin @ (setadjoin @ X1607 @ emptyset) @ (setadjoin @ (setadjoin @ X1607 @ (setadjoin @ X1608 @ emptyset)) @ emptyset)))|((X1607)=(X1609)))&((((in @ (esk67_1 @ X1610) @ (dsetconstr @ (setunion @ X1610) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1610)))))|~(iskpair @ X1610))&(((dsetconstr @ (setunion @ X1610) @ (^[Z0/* 3 */:$i]:((in @ (setadjoin @ Z0 @ emptyset) @ X1610))))=(setadjoin @ (esk67_1 @ X1610) @ emptyset))|~(iskpair @ X1610)))&((~(in @ X1613 @ X1612)|((X1612)!=(setadjoin @ X1613 @ emptyset))|(in @ (setunion @ X1612) @ X1612))&(((kfst @ (kpair @ X1614 @ X1615))=(X1614))&((~(in @ X1618 @ (cartprod @ X1616 @ X1617))|(in @ (kfst @ X1618) @ X1616))&((((setadjoin @ (setadjoin @ X1619 @ emptyset) @ (setadjoin @ (setadjoin @ X1619 @ (setadjoin @ X1620 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1621 @ emptyset) @ (setadjoin @ (setadjoin @ X1621 @ (setadjoin @ X1622 @ emptyset)) @ emptyset)))|((X1619)=(X1621)))&((((kpair @ X1623 @ X1624)!=(kpair @ X1625 @ X1626))|((X1623)=(X1625)))&((((X1627)!=(X1628))|((setadjoin @ X1627 @ (setadjoin @ X1628 @ emptyset))=(setadjoin @ X1627 @ emptyset)))&((((X1629)!=(X1630))|((setadjoin @ (setadjoin @ X1629 @ emptyset) @ (setadjoin @ (setadjoin @ X1629 @ (setadjoin @ X1630 @ emptyset)) @ emptyset))=(setadjoin @ (setadjoin @ X1629 @ emptyset) @ emptyset)))&((((setadjoin @ (setadjoin @ X1631 @ emptyset) @ (setadjoin @ (setadjoin @ X1631 @ (setadjoin @ X1632 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1633 @ emptyset) @ (setadjoin @ (setadjoin @ X1633 @ (setadjoin @ X1634 @ emptyset)) @ emptyset)))|(((X1633)!=(X1634))|((X1632)=(X1634))))&((((setadjoin @ X1635 @ (setadjoin @ X1636 @ emptyset))!=(setadjoin @ X1637 @ emptyset))|((X1635)=(X1636)))&((((setadjoin @ (setadjoin @ X1638 @ emptyset) @ (setadjoin @ (setadjoin @ X1638 @ (setadjoin @ X1639 @ emptyset)) @ emptyset))!=(setadjoin @ (setadjoin @ X1640 @ emptyset) @ (setadjoin @ (setadjoin @ X1640 @ (setadjoin @ X1641 @ emptyset)) @ emptyset)))|((X1639)=(X1641)))&((((kpair @ X1642 @ X1643)!=(kpair @ X1644 @ X1645))|((X1643)=(X1645)))&((((in @ (esk68_1 @ X1646) @ (dsetconstr @ (setunion @ X1646) @ (^[Z0/* 3 */:$i]:(((X1646)=(kpair @ (kfst @ X1646) @ Z0))))))|~(iskpair @ X1646))&(((dsetconstr @ (setunion @ X1646) @ (^[Z0/* 3 */:$i]:(((X1646)=(kpair @ (kfst @ X1646) @ Z0)))))=(setadjoin @ (esk68_1 @ X1646) @ emptyset))|~(iskpair @ X1646)))&(((ksnd @ (kpair @ X1648 @ X1649))=(X1649))&((~(iskpair @ X1650)|((kpair @ (kfst @ X1650) @ (ksnd @ X1650))=(X1650)))&((~(in @ X1653 @ (cartprod @ X1651 @ X1652))|(in @ (ksnd @ X1653) @ X1652))&((~(in @ (kpair @ X1656 @ X1657) @ (cartprod @ X1654 @ X1655))|(in @ X1656 @ X1654))&((~(in @ (kpair @ X1660 @ X1661) @ (cartprod @ X1658 @ X1659))|(in @ X1661 @ X1659))&((~(in @ X1664 @ X1662)|(~(in @ X1665 @ X1663)|((kpair @ X1664 @ X1665)=(kpair @ X1664 @ X1665))))&((~(in @ X1668 @ X1666)|(~(in @ X1669 @ X1667)|((kfst @ (kpair @ X1668 @ X1669))=(X1668))))&((~(in @ X1672 @ X1670)|(~(in @ X1673 @ X1671)|((ksnd @ (kpair @ X1672 @ X1673))=(X1673))))&((~(in @ X1676 @ (cartprod @ X1674 @ X1675))|((kpair @ (kfst @ X1676) @ (ksnd @ X1676))=(X1676)))&((~(in @ X1680 @ X1677)|(~(in @ X1681 @ X1678)|(~(X1679 @ X1680 @ X1681)|(in @ (kpair @ X1680 @ X1681) @ (dsetconstr @ (cartprod @ X1677 @ X1678) @ (^[Z0/* 5 */:$i]:(?[X1129:$i]:(((in @ X1129 @ X1677)&?[X1130:$i]:((((in @ X1130 @ X1678)&X1679 @ X1129 @ X1130)&((Z0)=(kpair @ X1129 @ X1130)))))))))))))&((subset @ (dsetconstr @ (cartprod @ X1682 @ X1683) @ (^[Z0/* 5 */:$i]:(?[X1134:$i]:(((in @ X1134 @ X1682)&?[X1135:$i]:((((in @ X1135 @ X1683)&X1684 @ X1134 @ X1135)&((Z0)=(kpair @ X1134 @ X1135))))))))) @ (cartprod @ X1682 @ X1683))&((subset @ (dsetconstr @ (cartprod @ X1685 @ X1686) @ (^[Z0/* 5 */:$i]:(?[X1139:$i]:(((in @ X1139 @ X1685)&?[X1140:$i]:((((in @ X1140 @ X1686)&X1687 @ X1139 @ X1140)&((Z0)=(kpair @ X1139 @ X1140))))))))) @ (cartprod @ X1685 @ X1686))&((~(in @ X1691 @ X1688)|(~(in @ X1692 @ X1689)|(~(in @ (kpair @ X1691 @ X1692) @ (dsetconstr @ (cartprod @ X1688 @ X1689) @ (^[Z0/* 5 */:$i]:(?[X1146:$i]:(((in @ X1146 @ X1688)&?[X1147:$i]:((((in @ X1147 @ X1689)&X1690 @ X1146 @ X1147)&((Z0)=(kpair @ X1146 @ X1147))))))))))|(X1690 @ X1691 @ X1692))))&((in @ (kpair @ esk71_0 @ esk72_0) @ (dsetconstr @ (cartprod @ esk69_0 @ esk70_0) @ (^[Z0/* 5 */:$i]:(?[X1148:$i]:(((in @ X1148 @ esk69_0)&?[X1149:$i]:((((in @ X1149 @ esk70_0)&epred2_0 @ X1148 @ X1149)&((Z0)=(kpair @ X1148 @ X1149))))))))))&~(in @ esk71_0 @ esk69_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_259])])])])])])])).
% 1.20/300.11 thf(c_0_261, negated_conjecture, ![X3:$i, X2:$i, X1:$i > $o]:(((X1 @ X2)|~((in @ X2 @ (dsetconstr @ X3 @ X1))))), inference(split_conjunct,[status(thm)],[c_0_260])).
% 1.20/300.11 thf(c_0_262, negated_conjecture, (in @ (kpair @ esk71_0 @ esk72_0) @ (dsetconstr @ (cartprod @ esk69_0 @ esk70_0) @ (^[Z0/* 5 */:$i]:(?[X1721:$i]:(((in @ X1721 @ esk69_0)&?[X1722:$i]:((((in @ X1722 @ esk70_0)&(epred2_0 @ X1721 @ X1722))&((Z0)=(kpair @ X1721 @ X1722)))))))))), inference(split_conjunct,[status(thm)],[c_0_260])).
% 1.20/300.11 thf(c_0_263, negated_conjecture, ?[X1723:$i]:(((in @ X1723 @ esk69_0)&?[X1724:$i]:((((in @ X1724 @ esk70_0)&(epred2_0 @ X1723 @ X1724))&((kpair @ esk71_0 @ esk72_0)=(kpair @ X1723 @ X1724)))))), inference(spm,[status(thm)],[c_0_261, c_0_262])).
% 1.20/300.11 thf(c_0_264, negated_conjecture, ![X2:$i, X3:$i]:(((ksnd @ (kpair @ X2 @ X3))=(X3))), inference(split_conjunct,[status(thm)],[c_0_260])).
% 1.20/300.11 thf(c_0_265, negated_conjecture, ((kpair @ esk71_0 @ esk72_0)=(kpair @ esk78_0 @ esk79_0)), inference(dynamic_cnf,[status(thm)],[c_0_263])).
% 1.20/300.11 thf(c_0_266, negated_conjecture, ((esk72_0)=(esk79_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_264, c_0_265]), c_0_264])).
% 1.20/300.11 thf(c_0_267, negated_conjecture, ![X3:$i, X2:$i]:(((kfst @ (kpair @ X2 @ X3))=(X2))), inference(split_conjunct,[status(thm)],[c_0_260])).
% 1.20/300.11 thf(c_0_268, negated_conjecture, ((kpair @ esk71_0 @ esk79_0)=(kpair @ esk78_0 @ esk79_0)), inference(rw,[status(thm)],[c_0_265, c_0_266])).
% 1.20/300.11 thf(c_0_269, negated_conjecture, ~((in @ esk71_0 @ esk69_0)), inference(split_conjunct,[status(thm)],[c_0_260])).
% 1.20/300.11 thf(c_0_270, negated_conjecture, ((esk71_0)=(esk78_0)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_267, c_0_268]), c_0_267])).
% 1.20/300.11 thf(c_0_271, negated_conjecture, (in @ esk78_0 @ esk69_0), inference(dynamic_cnf,[status(thm)],[c_0_263])).
% 1.20/300.11 thf(c_0_272, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_269, c_0_270]), c_0_271])]), ['proof']).
% 1.20/300.11 # SZS output end CNFRefutation
% 1.20/300.11 # Parsed axioms : 410
% 1.20/300.11 # Removed by relevancy pruning/SinE : 0
% 1.20/300.11 # Initial clauses : 556
% 1.20/300.11 # Removed in clause preprocessing : 243
% 1.20/300.11 # Initial clauses in saturation : 313
% 1.20/300.11 # Processed clauses : 434
% 1.20/300.11 # ...of these trivial : 9
% 1.20/300.11 # ...subsumed : 39
% 1.20/300.11 # ...remaining for further processing : 386
% 1.20/300.11 # Other redundant clauses eliminated : 25
% 1.20/300.11 # Clauses deleted for lack of memory : 0
% 1.20/300.11 # Backward-subsumed : 0
% 1.20/300.11 # Backward-rewritten : 7
% 1.20/300.11 # Generated clauses : 241
% 1.20/300.11 # ...of the previous two non-redundant : 166
% 1.20/300.11 # ...aggressively subsumed : 0
% 1.20/300.11 # Contextual simplify-reflections : 0
% 1.20/300.11 # Paramodulations : 209
% 1.20/300.11 # Factorizations : 0
% 1.20/300.11 # NegExts : 0
% 1.20/300.11 # Equation resolutions : 28
% 1.20/300.11 # Disequality decompositions : 0
% 1.20/300.11 # Total rewrite steps : 102
% 1.20/300.11 # ...of those cached : 62
% 1.20/300.11 # Propositional unsat checks : 0
% 1.20/300.11 # Propositional check models : 0
% 1.20/300.11 # Propositional check unsatisfiable : 0
% 1.20/300.11 # Propositional clauses : 0
% 1.20/300.11 # Propositional clauses after purity: 0
% 1.20/300.11 # Propositional unsat core size : 0
% 1.20/300.11 # Propositional preprocessing time : 0.000
% 1.20/300.11 # Propositional encoding time : 0.000
% 1.20/300.11 # Propositional solver time : 0.000
% 1.20/300.11 # Success case prop preproc time : 0.000
% 1.20/300.11 # Success case prop encoding time : 0.000
% 1.20/300.11 # Success case prop solver time : 0.000
% 1.20/300.11 # Current number of processed clauses : 92
% 1.20/300.11 # Positive orientable unit clauses : 41
% 1.20/300.11 # Positive unorientable unit clauses: 0
% 1.20/300.11 # Negative unit clauses : 1
% 1.20/300.11 # Non-unit-clauses : 50
% 1.20/300.11 # Current number of unprocessed clauses: 312
% 1.20/300.11 # ...number of literals in the above : 954
% 1.20/300.11 # Current number of archived formulas : 0
% 1.20/300.11 # Current number of archived clauses : 278
% 1.20/300.11 # Clause-clause subsumption calls (NU) : 13843
% 1.20/300.11 # Rec. Clause-clause subsumption calls : 5889
% 1.20/300.11 # Non-unit clause-clause subsumptions : 29
% 1.20/300.11 # Unit Clause-clause subsumption calls : 130
% 1.20/300.11 # Rewrite failures with RHS unbound : 0
% 1.20/300.11 # BW rewrite match attempts : 20
% 1.20/300.11 # BW rewrite match successes : 5
% 1.20/300.11 # Condensation attempts : 434
% 1.20/300.11 # Condensation successes : 6
% 1.20/300.11 # Termbank termtop insertions : 57262
% 1.20/300.11 # Search garbage collected termcells : 18328
% 1.20/300.11
% 1.20/300.11 # -------------------------------------------------
% 1.20/300.11 # User time : 0.126 s
% 1.20/300.11 # System time : 0.017 s
% 1.20/300.11 # Total time : 0.143 s
% 1.20/300.11 # Maximum resident set size: 6060 pages
% 1.20/300.11
% 1.20/300.11 # -------------------------------------------------
% 1.20/300.11 # User time : 0.139 s
% 1.20/300.11 # System time : 0.021 s
% 1.20/300.11 # Total time : 0.160 s
% 1.20/300.11 # Maximum resident set size: 2208 pages
% 1.20/300.11 % E---3.1 exiting
% 1.20/300.11 % E exiting
%------------------------------------------------------------------------------