0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.12 % Command : run_E %s %d THM 0.12/0.32 % Computer : n025.cluster.edu 0.12/0.32 % Model : x86_64 x86_64 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.32 % Memory : 8042.1875MB 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.32 % CPULimit : 1440 0.12/0.32 % WCLimit : 180 0.12/0.32 % DateTime : Thu Jul 4 06:18:09 EDT 2024 0.12/0.32 % CPUTime : 0.19/0.47 Running higher-order theorem proving 0.19/0.48 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p 0.40/0.56 # Version: 3.2.0-ho 0.40/0.56 # Preprocessing class: HSMSSLSSLLLCHFA. 0.40/0.56 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.40/0.56 # Starting new_ho_10 with 900s (5) cores 0.40/0.56 # Starting sh5l with 180s (1) cores 0.40/0.56 # Starting new_bool_1 with 180s (1) cores 0.40/0.56 # Starting new_bool_2 with 180s (1) cores 0.40/0.56 # new_bool_1 with pid 26495 completed with status 0 0.40/0.56 # Result found by new_bool_1 0.40/0.56 # Preprocessing class: HSMSSLSSLLLCHFA. 0.40/0.56 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.40/0.56 # Starting new_ho_10 with 900s (5) cores 0.40/0.56 # Starting sh5l with 180s (1) cores 0.40/0.56 # Starting new_bool_1 with 180s (1) cores 0.40/0.56 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.40/0.56 # Search class: HGHSM-FSLM31-SHFMMMBN 0.40/0.56 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 0.40/0.56 # Starting ho_unfolding_3 with 98s (1) cores 0.40/0.56 # ho_unfolding_3 with pid 26502 completed with status 0 0.40/0.56 # Result found by ho_unfolding_3 0.40/0.56 # Preprocessing class: HSMSSLSSLLLCHFA. 0.40/0.56 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.40/0.56 # Starting new_ho_10 with 900s (5) cores 0.40/0.56 # Starting sh5l with 180s (1) cores 0.40/0.56 # Starting new_bool_1 with 180s (1) cores 0.40/0.56 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.40/0.56 # Search class: HGHSM-FSLM31-SHFMMMBN 0.40/0.56 # Scheduled 6 strats onto 1 cores with 180 seconds (180 total) 0.40/0.56 # Starting ho_unfolding_3 with 98s (1) cores 0.40/0.56 # Preprocessing time : 0.005 s 0.40/0.56 # Presaturation interreduction done 0.40/0.56 0.40/0.56 # Proof found! 0.40/0.56 # SZS status Theorem 0.40/0.56 # SZS output start CNFRefutation 0.40/0.56 thf(decl_22, type, in: $i > $i > $o). 0.40/0.56 thf(decl_23, type, exu: ($i > $o) > $o). 0.40/0.56 thf(decl_24, type, setextAx: $o). 0.40/0.56 thf(decl_25, type, emptyset: $i). 0.40/0.56 thf(decl_26, type, emptysetAx: $o). 0.40/0.56 thf(decl_27, type, setadjoin: $i > $i > $i). 0.40/0.56 thf(decl_28, type, setadjoinAx: $o). 0.40/0.56 thf(decl_29, type, powerset: $i > $i). 0.40/0.56 thf(decl_30, type, powersetAx: $o). 0.40/0.56 thf(decl_31, type, setunion: $i > $i). 0.40/0.56 thf(decl_32, type, setunionAx: $o). 0.40/0.56 thf(decl_33, type, omega: $i). 0.40/0.56 thf(decl_34, type, omega0Ax: $o). 0.40/0.56 thf(decl_35, type, omegaSAx: $o). 0.40/0.56 thf(decl_36, type, omegaIndAx: $o). 0.40/0.56 thf(decl_37, type, replAx: $o). 0.40/0.56 thf(decl_38, type, foundationAx: $o). 0.40/0.56 thf(decl_39, type, wellorderingAx: $o). 0.40/0.56 thf(decl_40, type, descr: ($i > $o) > $i). 0.40/0.56 thf(decl_41, type, descrp: $o). 0.40/0.56 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.40/0.56 thf(decl_43, type, dsetconstrI: $o). 0.40/0.56 thf(decl_44, type, dsetconstrEL: $o). 0.40/0.56 thf(decl_45, type, dsetconstrER: $o). 0.40/0.56 thf(decl_46, type, exuE1: $o). 0.40/0.56 thf(decl_47, type, prop2set: $o > $i). 0.40/0.56 thf(decl_48, type, prop2setE: $o). 0.40/0.56 thf(decl_49, type, emptysetE: $o). 0.40/0.56 thf(decl_50, type, emptysetimpfalse: $o). 0.40/0.56 thf(decl_51, type, notinemptyset: $o). 0.40/0.56 thf(decl_52, type, exuE3e: $o). 0.40/0.56 thf(decl_53, type, setext: $o). 0.40/0.56 thf(decl_54, type, emptyI: $o). 0.40/0.56 thf(decl_55, type, noeltsimpempty: $o). 0.40/0.56 thf(decl_56, type, setbeta: $o). 0.40/0.56 thf(decl_57, type, nonempty: $i > $o). 0.40/0.56 thf(decl_58, type, nonemptyE1: $o). 0.40/0.56 thf(decl_59, type, nonemptyI: $o). 0.40/0.56 thf(decl_60, type, nonemptyI1: $o). 0.40/0.56 thf(decl_61, type, setadjoinIL: $o). 0.40/0.56 thf(decl_62, type, emptyinunitempty: $o). 0.40/0.56 thf(decl_63, type, setadjoinIR: $o). 0.40/0.56 thf(decl_64, type, setadjoinE: $o). 0.40/0.56 thf(decl_65, type, setadjoinOr: $o). 0.40/0.56 thf(decl_66, type, setoftrueEq: $o). 0.40/0.56 thf(decl_67, type, powersetI: $o). 0.40/0.56 thf(decl_68, type, emptyinPowerset: $o). 0.40/0.56 thf(decl_69, type, emptyInPowerset: $o). 0.40/0.56 thf(decl_70, type, powersetE: $o). 0.40/0.56 thf(decl_71, type, setunionI: $o). 0.40/0.56 thf(decl_72, type, setunionE: $o). 0.40/0.56 thf(decl_73, type, subPowSU: $o). 0.40/0.56 thf(decl_74, type, exuE2: $o). 0.40/0.56 thf(decl_75, type, nonemptyImpWitness: $o). 0.40/0.56 thf(decl_76, type, uniqinunit: $o). 0.40/0.56 thf(decl_77, type, notinsingleton: $o). 0.40/0.56 thf(decl_78, type, eqinunit: $o). 0.40/0.56 thf(decl_79, type, singletonsswitch: $o). 0.40/0.56 thf(decl_80, type, upairsetE: $o). 0.40/0.56 thf(decl_81, type, upairsetIL: $o). 0.40/0.56 thf(decl_82, type, upairsetIR: $o). 0.40/0.56 thf(decl_83, type, emptyE1: $o). 0.40/0.56 thf(decl_84, type, vacuousDall: $o). 0.40/0.56 thf(decl_85, type, quantDeMorgan1: $o). 0.40/0.56 thf(decl_86, type, quantDeMorgan2: $o). 0.40/0.56 thf(decl_87, type, quantDeMorgan3: $o). 0.40/0.56 thf(decl_88, type, quantDeMorgan4: $o). 0.40/0.56 thf(decl_89, type, prop2setI: $o). 0.40/0.56 thf(decl_91, type, prop2set2propI: $o). 0.40/0.56 thf(decl_92, type, notdexE: $o). 0.40/0.56 thf(decl_93, type, notdallE: $o). 0.40/0.56 thf(decl_94, type, exuI1: $o). 0.40/0.56 thf(decl_95, type, exuI3: $o). 0.40/0.56 thf(decl_96, type, exuI2: $o). 0.40/0.56 thf(decl_97, type, inCongP: $o). 0.40/0.56 thf(decl_98, type, in__Cong: $o). 0.40/0.56 thf(decl_99, type, exuE3u: $o). 0.40/0.56 thf(decl_100, type, exu__Cong: $o). 0.40/0.56 thf(decl_101, type, emptyset__Cong: $o). 0.40/0.56 thf(decl_102, type, setadjoin__Cong: $o). 0.40/0.56 thf(decl_103, type, powerset__Cong: $o). 0.40/0.56 thf(decl_104, type, setunion__Cong: $o). 0.40/0.56 thf(decl_105, type, omega__Cong: $o). 0.40/0.56 thf(decl_106, type, exuEu: $o). 0.40/0.56 thf(decl_107, type, descr__Cong: $o). 0.40/0.56 thf(decl_108, type, dsetconstr__Cong: $o). 0.40/0.56 thf(decl_109, type, subset: $i > $i > $o). 0.40/0.56 thf(decl_112, type, subsetI1: $o). 0.40/0.56 thf(decl_113, type, eqimpsubset2: $o). 0.40/0.56 thf(decl_114, type, eqimpsubset1: $o). 0.40/0.56 thf(decl_115, type, subsetI2: $o). 0.40/0.56 thf(decl_116, type, emptysetsubset: $o). 0.40/0.56 thf(decl_117, type, subsetE: $o). 0.40/0.56 thf(decl_118, type, epred1_0: $o). 0.40/0.56 thf(decl_119, type, esk1_2: $i > $i > $i). 0.40/0.56 thf(decl_120, type, esk2_2: $i > $i > $i). 0.40/0.56 thf(decl_121, type, esk3_2: $i > $i > $i). 0.40/0.56 thf(decl_122, type, esk4_1: $i > $i). 0.40/0.56 thf(decl_123, type, esk5_2: ($i > $i > $o) > $i > $i). 0.40/0.56 thf(decl_124, type, esk6_3: ($i > $i > $o) > $i > $i > $i). 0.40/0.56 thf(decl_125, type, esk7_2: ($i > $i > $o) > $i > $i). 0.40/0.56 thf(decl_126, type, esk8_3: ($i > $i > $o) > $i > $i > $i). 0.40/0.56 thf(decl_127, type, esk9_1: $i > $i). 0.40/0.56 thf(decl_128, type, esk10_2: ($i > $o) > $i > $i). 0.40/0.56 thf(decl_129, type, esk11_2: ($i > $o) > $i > $i). 0.40/0.56 thf(decl_130, type, esk12_1: ($i > $o) > $i). 0.40/0.56 thf(decl_131, type, esk13_2: ($i > $o) > $i > $i). 0.40/0.56 thf(decl_132, type, esk14_1: ($i > $o) > $i). 0.40/0.56 thf(decl_133, type, esk15_2: $i > $i > $i). 0.40/0.56 thf(decl_134, type, esk16_2: $i > $i > $i). 0.40/0.56 thf(decl_135, type, esk17_1: $i > $i). 0.40/0.56 thf(decl_136, type, esk18_1: $i > $i). 0.40/0.56 thf(decl_137, type, esk19_1: $i > $i). 0.40/0.56 thf(decl_138, type, esk20_2: $i > $i > $i). 0.40/0.56 thf(decl_139, type, esk21_3: $i > $i > $o > $i). 0.40/0.56 thf(decl_140, type, esk22_2: ($i > $o) > $i > $i). 0.40/0.56 thf(decl_141, type, esk23_1: ($i > $o) > $i). 0.40/0.56 thf(decl_142, type, esk24_1: $i > $i). 0.40/0.56 thf(decl_143, type, esk25_2: $i > ($i > $o) > $i). 0.40/0.56 thf(decl_144, type, esk26_2: $i > ($i > $o) > $i). 0.40/0.56 thf(decl_145, type, esk27_2: $i > ($i > $o) > $i). 0.40/0.56 thf(decl_146, type, esk28_2: $i > ($i > $o) > $i). 0.40/0.56 thf(decl_147, type, esk29_2: $i > ($i > $o) > $i). 0.40/0.56 thf(decl_148, type, esk30_2: $i > ($i > $o) > $i). 0.40/0.56 thf(decl_149, type, esk31_2: ($i > $o) > $i > $i). 0.40/0.56 thf(decl_150, type, esk32_1: ($i > $o) > $i). 0.40/0.56 thf(decl_151, type, esk33_1: ($i > $o) > $i). 0.40/0.56 thf(decl_152, type, esk34_1: ($i > $o) > $i). 0.40/0.56 thf(decl_153, type, esk35_1: ($i > $o) > $i). 0.40/0.56 thf(decl_154, type, esk36_2: ($i > $o) > $i > $i). 0.40/0.56 thf(decl_155, type, esk37_1: ($i > $o) > $i). 0.40/0.56 thf(decl_156, type, esk38_2: ($i > $o) > $i > $i). 0.40/0.56 thf(decl_157, type, esk39_2: ($i > $o) > ($i > $o) > $i). 0.40/0.56 thf(decl_158, type, esk40_2: ($i > $o) > ($i > $o) > $i). 0.40/0.56 thf(decl_159, type, esk41_3: ($i > $o) > ($i > $o) > $i > $i). 0.40/0.56 thf(decl_160, type, esk42_2: ($i > $o) > ($i > $o) > $i). 0.40/0.56 thf(decl_161, type, esk43_3: ($i > $o) > ($i > $o) > $i > $i). 0.40/0.56 thf(decl_162, type, esk44_2: ($i > $o) > ($i > $o) > $i). 0.40/0.56 thf(decl_163, type, esk45_2: ($i > $o) > $i > $i). 0.40/0.56 thf(decl_164, type, esk46_2: ($i > $o) > ($i > $o) > $i). 0.40/0.56 thf(decl_165, type, esk47_2: ($i > $o) > ($i > $o) > $i). 0.40/0.56 thf(decl_166, type, esk48_3: ($i > $o) > ($i > $o) > $i > $i). 0.40/0.56 thf(decl_167, type, esk49_3: ($i > $o) > ($i > $o) > $i > $i). 0.40/0.56 thf(decl_168, type, esk50_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.40/0.56 thf(decl_169, type, esk51_4: $i > $i > ($i > $o) > ($i > $o) > $i). 0.40/0.56 thf(decl_170, type, esk52_2: $i > $i > $i). 0.40/0.56 thf(decl_171, type, esk53_2: $i > $i > $i). 0.40/0.56 thf(decl_172, type, esk54_0: $i). 0.40/0.56 thf(decl_173, type, esk55_0: $i). 0.40/0.56 thf(decl_174, type, esk56_0: $i). 0.40/0.56 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', nonempty)). 0.40/0.56 thf(exuE2, axiom, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exuE2)). 0.40/0.56 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exu)). 0.40/0.56 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exuE3e)). 0.40/0.56 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exuE1)). 0.40/0.56 thf(descrp, axiom, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>(X1 @ (descr @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', descrp)). 0.40/0.56 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', replAx)). 0.40/0.56 thf(exuI1, axiom, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exuI1)). 0.40/0.56 thf(exuI3, axiom, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[X2:$i]:((X1 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exuI3)). 0.40/0.56 thf(exu__Cong, axiom, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[X2:$i]:((X1 @ X2))))<=>(exu @ (^[X2:$i]:((X17 @ X2)))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exu__Cong)). 0.40/0.56 thf(exuEu, axiom, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exuEu)). 0.40/0.56 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', descr__Cong)). 0.40/0.56 thf(exuE3u, axiom, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exuE3u)). 0.40/0.56 thf(exuI2, axiom, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[X2:$i]:((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', exuI2)). 0.40/0.56 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', nonemptyI)). 0.40/0.56 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', nonemptyI1)). 0.40/0.56 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', nonemptyE1)). 0.40/0.56 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', dsetconstrI)). 0.40/0.56 thf(emptyE1, axiom, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[X2:$i]:((X1 @ X2))))=(emptyset))=>~($true))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptyE1)). 0.40/0.56 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:$i]:((X17 @ X2)))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', dsetconstr__Cong)). 0.40/0.56 thf(nonemptyImpWitness, axiom, ((nonemptyImpWitness)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:(((in @ X2 @ X4)&($true)))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', nonemptyImpWitness)). 0.40/0.56 thf(setoftrueEq, axiom, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[X2:$i]:(($true))))=(X4)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setoftrueEq)). 0.40/0.56 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setbeta)). 0.40/0.56 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', dsetconstrER)). 0.40/0.56 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', dsetconstrEL)). 0.40/0.56 thf(subsetE2, conjecture, (((((powersetAx)=>((setunionAx)=>(((omegaSAx)=>((omegaIndAx)=>((((wellorderingAx)=>((((dsetconstrEL)=>((dsetconstrER)=>(((prop2setE)=>((emptysetE)=>(((notinemptyset)=>((((emptyI)=>(((setbeta)=>(((nonemptyI)=>(((((setadjoinIR)=>((((setoftrueEq)=>((powersetI)=>((emptyinPowerset)=>((emptyInPowerset)=>(((setunionI)=>((((exuE2)=>(((uniqinunit)=>((((singletonsswitch)=>((upairsetE)=>(((upairsetIR)=>((emptyE1)=>((((((quantDeMorgan4)=>(((((notdallE)=>((exuI1)=>((exuI3)=>((((in__Cong)=>(((exu__Cong)=>((emptyset__Cong)=>(((powerset__Cong)=>((setunion__Cong)=>(((exuEu)=>((descr__Cong)=>((dsetconstr__Cong)=>(((eqimpsubset2)=>((eqimpsubset1)=>(((emptysetsubset)=>((subsetE)=>![X4:$i, X5:$i, X2:$i]:(((~((in @ X2 @ X5))=>~((in @ X2 @ X4)))<=(subset @ X4 @ X5)))))<=(subsetI2))))<=(subsetI1)))))<=(omega__Cong))))<=(setadjoin__Cong))))<=(exuE3u)))<=(inCongP))<=(exuI2)))))<=(notdexE))<=(prop2set2propI))<=(prop2setI)))<=(quantDeMorgan3))<=(quantDeMorgan2))<=(quantDeMorgan1))<=(vacuousDall))))<=(upairsetIL))))<=(eqinunit))<=(notinsingleton)))<=(nonemptyImpWitness)))<=(subPowSU))<=(setunionE)))<=(powersetE))))))<=(setadjoinOr))<=(setadjoinE)))<=(emptyinunitempty))<=(setadjoinIL))<=(nonemptyI1)))<=(nonemptyE1)))<=(noeltsimpempty)))<=(setext))<=(exuE3e)))<=(emptysetimpfalse))))<=(exuE1))))<=(dsetconstrI))<=(descrp)))<=(foundationAx))<=(replAx))))<=(omega0Ax))))<=(setadjoinAx))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', subsetE2)). 0.40/0.56 thf(emptyInPowerset, axiom, ((emptyInPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptyInPowerset)). 0.40/0.56 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setextAx)). 0.40/0.56 thf(setadjoinIL, axiom, ((setadjoinIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setadjoinIL)). 0.40/0.56 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', noeltsimpempty)). 0.40/0.56 thf(uniqinunit, axiom, ((uniqinunit)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>((X2)=(X3))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', uniqinunit)). 0.40/0.56 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/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setext)). 0.40/0.56 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptysetimpfalse)). 0.40/0.56 thf(singletonsswitch, axiom, ((singletonsswitch)<=>![X2:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ emptyset))=>(in @ X3 @ (setadjoin @ X2 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', singletonsswitch)). 0.40/0.56 thf(upairsetE, axiom, ((upairsetE)<=>![X2:$i, X3:$i, X14:$i]:(((in @ X14 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))=>(((X14)=(X2))|((X14)=(X3)))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', upairsetE)). 0.40/0.56 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', foundationAx)). 0.40/0.56 thf(upairsetIR, axiom, ((upairsetIR)<=>![X2:$i, X3:$i]:((in @ X3 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', upairsetIR)). 0.40/0.56 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', omega0Ax)). 0.40/0.56 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setadjoinAx)). 0.40/0.56 thf(emptyinPowerset, axiom, ((emptyinPowerset)<=>![X4:$i]:((in @ emptyset @ (powerset @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptyinPowerset)). 0.40/0.56 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptysetAx)). 0.40/0.56 thf(quantDeMorgan4, axiom, ((quantDeMorgan4)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))=>~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', quantDeMorgan4)). 0.40/0.56 thf(subsetI2, axiom, ((subsetI2)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', subsetI2)). 0.40/0.56 thf(notdallE, axiom, ((notdallE)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', notdallE)). 0.40/0.56 thf(in__Cong, axiom, ((in__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X2:$i, X3:$i]:((((X2)=(X3))=>((in @ X2 @ X4)<=>(in @ X3 @ X5))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', in__Cong)). 0.40/0.56 thf(emptyset__Cong, axiom, ((emptyset__Cong)<=>((emptyset)=(emptyset))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptyset__Cong)). 0.40/0.56 thf(powerset__Cong, axiom, ((powerset__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((powerset @ X4)=(powerset @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', powerset__Cong)). 0.40/0.56 thf(setunion__Cong, axiom, ((setunion__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>((setunion @ X4)=(setunion @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setunion__Cong)). 0.40/0.56 thf(eqimpsubset2, axiom, ((eqimpsubset2)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X5 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', eqimpsubset2)). 0.40/0.56 thf(eqimpsubset1, axiom, ((eqimpsubset1)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', eqimpsubset1)). 0.40/0.56 thf(emptysetsubset, axiom, ((emptysetsubset)<=>![X4:$i]:((subset @ emptyset @ X4))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptysetsubset)). 0.40/0.56 thf(subsetE, axiom, ((subsetE)<=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>((in @ X2 @ X4)=>(in @ X2 @ X5))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', subsetE)). 0.40/0.56 thf(subsetI1, axiom, ((subsetI1)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(subset @ X4 @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', subsetI1)). 0.40/0.56 thf(omega__Cong, axiom, ((omega__Cong)<=>((omega)=(omega))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', omega__Cong)). 0.40/0.56 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/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setadjoin__Cong)). 0.40/0.56 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/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', inCongP)). 0.40/0.56 thf(notdexE, axiom, ((notdexE)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', notdexE)). 0.40/0.56 thf(prop2setI, axiom, ((prop2setI)<=>![X15:$o]:(((X15)=>(in @ emptyset @ (prop2set @ ((X15))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', prop2setI)). 0.40/0.56 thf(quantDeMorgan3, axiom, ((quantDeMorgan3)<=>![X4:$i, X1:$i > $o]:((~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))=>![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', quantDeMorgan3)). 0.40/0.56 thf(quantDeMorgan2, axiom, ((quantDeMorgan2)<=>![X4:$i, X1:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>~((X1 @ X2))))=>~(?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', quantDeMorgan2)). 0.40/0.56 thf(quantDeMorgan1, axiom, ((quantDeMorgan1)<=>![X4:$i, X1:$i > $o]:((~(![X2:$i]:(((in @ X2 @ X4)=>(X1 @ X2))))=>?[X2:$i]:(((in @ X2 @ X4)&~((X1 @ X2))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', quantDeMorgan1)). 0.40/0.56 thf(vacuousDall, axiom, ((vacuousDall)<=>![X1:$i > $o, X2:$i]:(((in @ X2 @ emptyset)=>(X1 @ X2)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', vacuousDall)). 0.40/0.56 thf(setunionI, axiom, ((setunionI)<=>![X4:$i, X2:$i, X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(in @ X2 @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setunionI)). 0.40/0.56 thf(upairsetIL, axiom, ((upairsetIL)<=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', upairsetIL)). 0.40/0.56 thf(eqinunit, axiom, ((eqinunit)<=>![X2:$i, X3:$i]:((((X2)=(X3))=>(in @ X2 @ (setadjoin @ X3 @ emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', eqinunit)). 0.40/0.56 thf(notinsingleton, axiom, ((notinsingleton)<=>![X2:$i, X3:$i]:((((X2)!=(X3))=>~((in @ X3 @ (setadjoin @ X2 @ emptyset)))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', notinsingleton)). 0.40/0.56 thf(subPowSU, axiom, ((subPowSU)<=>![X4:$i, X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ (powerset @ (setunion @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', subPowSU)). 0.40/0.56 thf(setunionE, axiom, ((setunionE)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))=>![X13:$o]:((![X5:$i]:(((in @ X2 @ X5)=>((in @ X5 @ X4)=>(X13))))=>(X13)))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setunionE)). 0.40/0.56 thf(powersetE, axiom, ((powersetE)<=>![X4:$i, X5:$i, X2:$i]:(((in @ X5 @ (powerset @ X4))=>((in @ X2 @ X5)=>(in @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', powersetE)). 0.40/0.56 thf(setadjoinOr, axiom, ((setadjoinOr)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setadjoinOr)). 0.40/0.56 thf(setadjoinE, axiom, ((setadjoinE)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))=>![X12:$o]:(((((X3)=(X2))=>(X12))=>(((in @ X3 @ X4)=>(X12))=>(X12))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setadjoinE)). 0.40/0.56 thf(emptyinunitempty, axiom, ((emptyinunitempty)<=>(in @ emptyset @ (setadjoin @ emptyset @ emptyset))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptyinunitempty)). 0.40/0.56 thf(powersetI, axiom, ((powersetI)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>(in @ X5 @ (powerset @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', powersetI)). 0.40/0.56 thf(setadjoinIR, axiom, ((setadjoinIR)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ X4)=>(in @ X3 @ (setadjoin @ X2 @ X4))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setadjoinIR)). 0.40/0.56 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptyI)). 0.40/0.56 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', notinemptyset)). 0.40/0.56 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X11:$o]:((X11))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', emptysetE)). 0.40/0.56 thf(prop2setE, axiom, ((prop2setE)<=>![X10:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X10))))=>(X10)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', prop2setE)). 0.40/0.56 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:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', wellorderingAx)). 0.40/0.56 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$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/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', omegaIndAx)). 0.40/0.56 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', omegaSAx)). 0.40/0.56 thf(setunionAx, axiom, ((setunionAx)<=>![X4:$i, X2:$i]:(((in @ X2 @ (setunion @ X4))<=>?[X5:$i]:(((in @ X2 @ X5)&(in @ X5 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', setunionAx)). 0.40/0.56 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox2/tmp/tmp.mj5jcpN1Fc/E---3.1_26357.p', powersetAx)). 0.40/0.56 thf(c_0_83, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.40/0.56 thf(c_0_84, plain, ((exuE2)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))))), inference(fof_simplification,[status(thm)],[exuE2])). 0.40/0.56 thf(c_0_85, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.40/0.56 thf(c_0_86, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.40/0.56 thf(c_0_87, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.40/0.56 thf(c_0_88, plain, ((descrp)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[descrp])). 0.40/0.56 thf(c_0_89, plain, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[Z0/* 3 */:$i]:((X6 @ X2 @ Z0))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.40/0.56 thf(c_0_90, plain, ((exuI1)<=>![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI1])). 0.40/0.56 thf(c_0_91, plain, ((exuI3)<=>![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exuI3])). 0.40/0.56 thf(c_0_92, plain, ((exu__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))<=>(exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))), inference(fof_simplification,[status(thm)],[exu__Cong])). 0.40/0.56 thf(c_0_93, plain, ((exuEu)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuEu])). 0.40/0.56 thf(c_0_94, plain, ((descr__Cong)<=>![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>((exu @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[descr__Cong])). 0.40/0.56 thf(c_0_95, plain, ((exuE3u)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))))), inference(fof_simplification,[status(thm)],[exuE3u])). 0.40/0.56 thf(c_0_96, plain, ((exuI2)<=>![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))), inference(fof_simplification,[status(thm)],[exuI2])). 0.40/0.56 thf(c_0_97, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.40/0.56 thf(c_0_98, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_83])). 0.40/0.56 thf(c_0_99, plain, ((exuE2)=(![X1:$i > $o]:(((?[X255:$i]:((((X1 @ X255))&![X256:$i]:((((X1 @ X256))=>((X255)=(X256)))))))=>?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2))))))))), inference(apply_def,[status(thm)],[c_0_84, c_0_85])). 0.40/0.56 thf(c_0_100, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_83])). 0.40/0.56 thf(c_0_101, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X253:$i]:((((X1 @ X253))&![X254:$i]:((((X1 @ X254))=>((X253)=(X254)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_86, c_0_85])). 0.40/0.56 thf(c_0_102, plain, ((exuE1)=(![X1:$i > $o]:(((?[X251:$i]:((((X1 @ X251))&![X252:$i]:((((X1 @ X252))=>((X251)=(X252)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_87, c_0_85])). 0.40/0.56 thf(c_0_103, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.40/0.56 thf(c_0_104, plain, ((descrp)=(![X1:$i > $o]:(((?[X249:$i]:((((X1 @ X249))&![X250:$i]:((((X1 @ X250))=>((X249)=(X250)))))))=>(X1 @ (descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(apply_def,[status(thm)],[c_0_88, c_0_85])). 0.40/0.56 thf(c_0_105, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X247:$i]:((((X6 @ X2 @ X247))&![X248:$i]:((((X6 @ X2 @ X248))=>((X247)=(X248)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_89, c_0_85])). 0.40/0.56 thf(c_0_106, plain, ((emptyE1)<=>![X4:$i, X1:$i > $o]:((?[X2:$i]:(((in @ X2 @ X4)&(X1 @ X2)))=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(emptyset))=>~($true))))), inference(fof_simplification,[status(thm)],[emptyE1])). 0.40/0.56 thf(c_0_107, plain, ((exuI1)=(![X1:$i > $o]:((?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))=>(?[X257:$i]:((((X1 @ X257))&![X258:$i]:((((X1 @ X258))=>((X257)=(X258))))))))))), inference(apply_def,[status(thm)],[c_0_90, c_0_85])). 0.40/0.56 thf(c_0_108, plain, ((exuI3)=(![X1:$i > $o]:((?[X2:$i]:((X1 @ X2))=>(![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3)))))=>(?[X259:$i]:((((X1 @ X259))&![X260:$i]:((((X1 @ X260))=>((X259)=(X260)))))))))))), inference(apply_def,[status(thm)],[c_0_91, c_0_85])). 0.40/0.56 thf(c_0_109, plain, ((exu__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X265:$i]:((((X1 @ X265))&![X266:$i]:((((X1 @ X266))=>((X265)=(X266)))))))<=>(?[X267:$i]:((((X17 @ X267))&![X268:$i]:((((X17 @ X268))=>((X267)=(X268)))))))))))), inference(apply_def,[status(thm)],[c_0_92, c_0_85])). 0.40/0.56 thf(c_0_110, plain, ((exuEu)=(![X1:$i > $o]:(((?[X269:$i]:((((X1 @ X269))&![X270:$i]:((((X1 @ X270))=>((X269)=(X270)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_93, c_0_85])). 0.40/0.56 thf(c_0_111, plain, ((descr__Cong)=(![X1:$i > $o, X17:$i > $o]:((![X2:$i, X3:$i]:((((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3))))=>((?[X271:$i]:((((X1 @ X271))&![X272:$i]:((((X1 @ X272))=>((X271)=(X272)))))))=>((?[X273:$i]:((((X17 @ X273))&![X274:$i]:((((X17 @ X274))=>((X273)=(X274)))))))=>((descr @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(descr @ (^[Z0/* 3 */:$i]:((X17 @ Z0))))))))))), inference(apply_def,[status(thm)],[c_0_94, c_0_85])). 0.40/0.56 thf(c_0_112, plain, ((dsetconstr__Cong)<=>![X4:$i, X5:$i]:((((X4)=(X5))=>![X1:$i > $o, X17:$i > $o]:((![X2:$i]:(((in @ X2 @ X4)=>![X3:$i]:(((in @ X3 @ X5)=>(((X2)=(X3))=>((X1 @ X2)<=>(X17 @ X3)))))))=>((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=(dsetconstr @ X5 @ (^[Z0/* 3 */:$i]:((X17 @ Z0)))))))))), inference(fof_simplification,[status(thm)],[dsetconstr__Cong])). 0.40/0.56 thf(c_0_113, plain, ((exuE3u)=(![X1:$i > $o]:(((?[X263:$i]:((((X1 @ X263))&![X264:$i]:((((X1 @ X264))=>((X263)=(X264)))))))=>![X2:$i, X3:$i]:(((X1 @ X2)=>((X1 @ X3)=>((X2)=(X3))))))))), inference(apply_def,[status(thm)],[c_0_95, c_0_85])). 0.40/0.56 thf(c_0_114, plain, ((exuI2)=(![X1:$i > $o]:((?[X2:$i]:(![X3:$i]:(((X1 @ X3)<=>((X3)=(X2)))))=>(?[X261:$i]:((((X1 @ X261))&![X262:$i]:((((X1 @ X262))=>((X261)=(X262))))))))))), inference(apply_def,[status(thm)],[c_0_96, c_0_85])). 0.40/0.56 thf(c_0_115, axiom, ((nonemptyImpWitness)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:(((in @ X2 @ X4)&($true))))))), inference(apply_def,[status(thm)],[nonemptyImpWitness, c_0_83])). 0.40/0.56 thf(c_0_116, plain, ((setoftrueEq)<=>![X4:$i]:(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:(($true))))=(X4)))), inference(fof_simplification,[status(thm)],[setoftrueEq])). 0.40/0.56 thf(c_0_117, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_97, c_0_83])). 0.40/0.56 thf(c_0_118, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.40/0.56 thf(c_0_119, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.40/0.56 thf(c_0_120, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.40/0.56 thf(c_0_121, plain, ((epred1_0)<=>![X285:$i]:(?[X286:$i]:((((![X287:$i]:(((in @ X287 @ X286)=>![X288:$i]:(((in @ X288 @ X287)=>(in @ X288 @ X285)))))&![X289:$i, X290:$i]:((((in @ X289 @ X285)&(in @ X290 @ X285))=>(![X291:$i]:(((in @ X291 @ X286)=>((in @ X289 @ X291)<=>(in @ X290 @ X291))))=>((X289)=(X290))))))&![X292:$i, X293:$i]:((((in @ X292 @ X286)&(in @ X293 @ X286))=>(![X294:$i]:(((in @ X294 @ X292)=>(in @ X294 @ X293)))|![X295:$i]:(((in @ X295 @ X293)=>(in @ X295 @ X292)))))))&![X296:$i]:(((![X297:$i]:(((in @ X297 @ X296)=>(in @ X297 @ X285)))&?[X298:$i]:((in @ X298 @ X296)))=>?[X299:$i, X300:$i]:(((((in @ X299 @ X286)&(in @ X300 @ X296))&~(?[X301:$i]:(((in @ X301 @ X299)&(in @ X301 @ X296)))))&![X302:$i]:(((in @ X302 @ X286)=>(![X303:$i]:(((in @ X303 @ X302)=>(in @ X303 @ X299)))|(in @ X300 @ X302)))))))))))), introduced(definition)). 0.40/0.56 thf(c_0_122, negated_conjecture, ~((![X525:$i, X526:$i]:((![X527:$i]:(((in @ X527 @ X525)<=>(in @ X527 @ X526)))=>((X525)=(X526))))=>(![X524:$i]:(~(in @ X524 @ emptyset))=>(![X521:$i, X522:$i, X523:$i]:(((in @ X523 @ (setadjoin @ X521 @ X522))<=>(((X523)=(X521))|(in @ X523 @ X522))))=>(![X275:$i, X276:$i]:(((in @ X276 @ (powerset @ X275))<=>![X277:$i]:(((in @ X277 @ X276)=>(in @ X277 @ X275)))))=>(![X278:$i, X279:$i]:(((in @ X279 @ (setunion @ X278))<=>?[X280:$i]:(((in @ X279 @ X280)&(in @ X280 @ X278)))))=>((in @ emptyset @ omega)=>(![X281:$i]:(((in @ X281 @ omega)=>(in @ (setadjoin @ X281 @ X281) @ omega)))=>(![X282:$i]:((((in @ emptyset @ X282)&![X283:$i]:((((in @ X283 @ omega)&(in @ X283 @ X282))=>(in @ (setadjoin @ X283 @ X283) @ X282))))=>![X284:$i]:(((in @ X284 @ omega)=>(in @ X284 @ X282)))))=>(![X513:$i > $i > $o, X514:$i]:((![X515:$i]:(((in @ X515 @ X514)=>?[X516:$i]:(((X513 @ X515 @ X516)&![X517:$i]:(((X513 @ X515 @ X517)=>((X516)=(X517))))))))=>?[X518:$i]:(![X519:$i]:(((in @ X519 @ X518)<=>?[X520:$i]:(((in @ X520 @ X514)&(X513 @ X520 @ X519))))))))=>(![X509:$i]:((?[X510:$i]:((in @ X510 @ X509))=>?[X511:$i]:(((in @ X511 @ X509)&~(?[X512:$i]:(((in @ X512 @ X511)&(in @ X512 @ X509))))))))=>((epred1_0)=>(![X506:$i > $o]:((?[X507:$i]:(((X506 @ X507)&![X508:$i]:(((X506 @ X508)=>((X507)=(X508))))))=>(X506 @ (descr @ (^[Z0/* 17 */:$i]:(X506 @ Z0))))))=>(![X503:$i, X504:$i > $o, X505:$i]:(((in @ X505 @ X503)=>((X504 @ X505)=>(in @ X505 @ (dsetconstr @ X503 @ X504)))))=>(![X304:$i, X305:$i > $o, X306:$i]:(((in @ X306 @ (dsetconstr @ X304 @ X305))=>(in @ X306 @ X304)))=>(![X307:$i, X308:$i > $o, X309:$i]:(((in @ X309 @ (dsetconstr @ X307 @ X308))=>(X308 @ X309)))=>(![X498:$i > $o]:((?[X499:$i]:(((X498 @ X499)&![X500:$i]:(((X498 @ X500)=>((X499)=(X500))))))=>?[X501:$i]:(((X498 @ X501)&![X502:$i]:(((X498 @ X502)=>((X501)=(X502))))))))=>(![X310:$o, X311:$i]:(((in @ X311 @ (prop2set @ ((X310))))=>(X310)))=>(![X312:$i]:(((in @ X312 @ emptyset)=>![X313:$o]:((X313))))=>(![X497:$i]:(((in @ X497 @ emptyset)=>~($true)))=>(![X314:$i]:(~(in @ X314 @ emptyset))=>(![X493:$i > $o]:((?[X494:$i]:(((X493 @ X494)&![X495:$i]:(((X493 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$o]:((?[X336:$i]:(((X335 @ X336)&![X337:$i]:(((X335 @ X337)=>((X336)=(X337))))))=>?[X338:$i]:(![X339:$i]:(((X335 @ X339)<=>((X339)=(X338)))))))=>(![X463:$i]:((((X463)!=(emptyset))=>?[X464:$i]:(((in @ X464 @ X463)&$true))))=>(![X340:$i, X341:$i]:(((in @ X340 @ (setadjoin @ X341 @ emptyset))=>((X340)=(X341))))=>(![X461:$i, X462:$i]:((((X461)!=(X462))=>~(in @ X462 @ (setadjoin @ X461 @ emptyset))))=>(![X459:$i, X460:$i]:((((X459)=(X460))=>(in @ X459 @ (setadjoin @ X460 @ emptyset))))=>(![X342:$i, X343:$i]:(((in @ X342 @ (setadjoin @ X343 @ emptyset))=>(in @ X343 @ (setadjoin @ X342 @ emptyset))))=>(![X344:$i, X345:$i, X346:$i]:(((in @ X346 @ (setadjoin @ X344 @ (setadjoin @ X345 @ emptyset)))=>(((X346)=(X344))|((X346)=(X345)))))=>(![X457:$i, X458:$i]:((in @ X457 @ (setadjoin @ X457 @ (setadjoin @ X458 @ emptyset))))=>(![X347:$i, X348:$i]:((in @ X348 @ (setadjoin @ X347 @ (setadjoin @ X348 @ emptyset))))=>(![X349:$i, X350:$i > $o]:((?[X351:$i]:(((in @ X351 @ X349)&(X350 @ 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X356)&~((X357 @ X359))))))=>(![X360:$i > $o]:((?[X361:$i]:(((X360 @ X361)&![X362:$i]:(((X360 @ X362)=>((X361)=(X362))))))=>?[X363:$i]:(((X360 @ X363)&![X364:$i]:(((X360 @ X364)=>((X363)=(X364))))))))=>(![X365:$i > $o]:((?[X366:$i]:((X365 @ X366))=>(![X367:$i, X368:$i]:(((X365 @ X367)=>((X365 @ X368)=>((X367)=(X368)))))=>?[X369:$i]:(((X365 @ X369)&![X370:$i]:(((X365 @ X370)=>((X369)=(X370)))))))))=>(![X433:$i > $o]:((?[X434:$i]:(![X435:$i]:(((X433 @ X435)<=>((X435)=(X434)))))=>?[X436:$i]:(((X433 @ X436)&![X437:$i]:(((X433 @ X437)=>((X436)=(X437))))))))=>(![X429:$i, X430:$i]:((((X429)=(X430))=>![X431:$i, X432:$i]:((((X431)=(X432))=>((in @ X431 @ X429)=>(in @ X432 @ X430))))))=>(![X371:$i, X372:$i]:((((X371)=(X372))=>![X373:$i, X374:$i]:((((X373)=(X374))=>((in @ X373 @ X371)<=>(in @ X374 @ X372))))))=>(![X424:$i > $o]:((?[X425:$i]:(((X424 @ X425)&![X426:$i]:(((X424 @ X426)=>((X425)=(X426))))))=>![X427:$i, X428:$i]:(((X424 @ X427)=>((X424 @ X428)=>((X427)=(X428)))))))=>(![X375:$i > $o, X376:$i > $o]:((![X377:$i, X378:$i]:((((X377)=(X378))=>((X375 @ X377)<=>(X376 @ X378))))=>(?[X379:$i]:(((X375 @ X379)&![X380:$i]:(((X375 @ X380)=>((X379)=(X380))))))<=>?[X381:$i]:(((X376 @ X381)&![X382:$i]:(((X376 @ X382)=>((X381)=(X382)))))))))=>(((emptyset)=(emptyset))=>(![X420:$i, X421:$i]:((((X420)=(X421))=>![X422:$i, X423:$i]:((((X422)=(X423))=>((setadjoin @ X420 @ X422)=(setadjoin @ X421 @ X423))))))=>(![X383:$i, X384:$i]:((((X383)=(X384))=>((powerset @ X383)=(powerset @ X384))))=>(![X385:$i, X386:$i]:((((X385)=(X386))=>((setunion @ X385)=(setunion @ X386))))=>(((omega)=(omega))=>(![X387:$i > $o]:((?[X388:$i]:(((X387 @ X388)&![X389:$i]:(((X387 @ X389)=>((X388)=(X389))))))=>![X390:$i, X391:$i]:(((X387 @ X390)=>((X387 @ X391)=>((X390)=(X391)))))))=>(![X392:$i > $o, X393:$i > $o]:((![X394:$i, X395:$i]:((((X394)=(X395))=>((X392 @ X394)<=>(X393 @ X395))))=>(?[X396:$i]:(((X392 @ X396)&![X397:$i]:(((X392 @ X397)=>((X396)=(X397))))))=>(?[X398:$i]:(((X393 @ X398)&![X399:$i]:(((X393 @ X399)=>((X398)=(X399))))))=>((descr @ X392)=(descr @ X393))))))=>(![X400:$i, X401:$i]:((((X400)=(X401))=>![X402:$i > $o, X403:$i > $o]:((![X404:$i]:(((in @ X404 @ X400)=>![X405:$i]:(((in @ X405 @ X401)=>(((X404)=(X405))=>((X402 @ X404)<=>(X403 @ X405)))))))=>((dsetconstr @ X400 @ X402)=(dsetconstr @ X401 @ X403))))))=>(![X417:$i, X418:$i]:((![X419:$i]:(((in @ X419 @ X417)=>(in @ X419 @ X418)))=>(subset @ X417 @ X418)))=>(![X406:$i, X407:$i]:((((X406)=(X407))=>(subset @ X407 @ X406)))=>(![X408:$i, X409:$i]:((((X408)=(X409))=>(subset @ X408 @ X409)))=>(![X414:$i, X415:$i]:((![X416:$i]:(((in @ X416 @ X414)=>(in @ X416 @ X415)))=>(subset @ X414 @ X415)))=>(![X410:$i]:((subset @ emptyset @ X410))=>(![X411:$i, X412:$i, X413:$i]:(((subset @ X411 @ X412)=>((in @ X413 @ X411)=>(in @ X413 @ X412))))=>![X4:$i, X5:$i, X2:$i]:(((subset @ X4 @ X5)=>(~(in @ X2 @ X5)=>~(in @ X2 @ 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(assume_negation,[status(cth)],[subsetE2]), emptyInPowerset]), setextAx]), setadjoinIL]), c_0_98]), c_0_99]), c_0_100]), noeltsimpempty]), uniqinunit]), setext]), c_0_101]), emptysetimpfalse]), singletonsswitch]), c_0_102]), c_0_103]), upairsetE]), c_0_104]), foundationAx]), c_0_105]), upairsetIR]), omega0Ax]), setadjoinAx]), emptyinPowerset]), emptysetAx]), c_0_106]), quantDeMorgan4]), subsetI2]), notdallE]), c_0_107]), c_0_108]), in__Cong]), c_0_109]), emptyset__Cong]), powerset__Cong]), setunion__Cong]), c_0_110]), c_0_111]), c_0_112]), eqimpsubset2]), eqimpsubset1]), emptysetsubset]), subsetE]), subsetI1]), omega__Cong]), setadjoin__Cong]), c_0_113]), inCongP]), c_0_114]), notdexE]), prop2setI]), quantDeMorgan3]), quantDeMorgan2]), quantDeMorgan1]), vacuousDall]), setunionI]), upairsetIL]), eqinunit]), notinsingleton]), c_0_115]), subPowSU]), setunionE]), powersetE]), setadjoinOr]), setadjoinE]), emptyinunitempty]), powersetI]), c_0_116]), setadjoinIR]), c_0_117]), c_0_118]), emptyI]), notinemptyset]), emptysetE]), prop2setE]), c_0_119]), c_0_120]), wellorderingAx]), omegaIndAx]), omegaSAx]), setunionAx]), powersetAx])])]), c_0_121])). 0.40/0.56 thf(c_0_123, negated_conjecture, ![X528:$i, X529:$i, X531:$i, X532:$i, X533:$i, X534:$i, X535:$i, X536:$i, X537:$i, X538:$i, X539:$i, X541:$i, X542:$i, X544:$i, X545:$i, X546:$i, X547:$i, X548:$i, X550:$i, X551:$i > $i > $o, X552:$i, X554:$i, X557:$i, X559:$i, X560:$i, X561:$i, X562:$i, X564:$i, X565:$i > $o, X566:$i, X568:$i, X569:$i > $o, X570:$i, X571:$i, X572:$i > $o, X573:$i, X574:$i, X575:$i > $o, X576:$i, X577:$i > $o, X578:$i, X581:$i, X582:$o, X583:$i, X584:$i, X585:$o, X586:$i, X587:$i, X588:$i > $o, X589:$i, X592:$i, X593:$i, X596:$i, X598:$i, X600:$i, X601:$i > $o, X602:$i, X603:$i, X605:$i, X606:$i > $o, X607:$i, X608:$i, X609:$i, X610:$i, X611:$i, X612:$i, X613:$i, X614:$i, X615:$i, X616:$i, X617:$i, X618:$o, X619:$i, X620:$i, X621:$i, X622:$i, X623:$i, X624:$i, X626:$i, X627:$i, X628:$i, X629:$i, X630:$i, X631:$i, X632:$i, X633:$i, X634:$i, X635:$i, X636:$o, X638:$i, X639:$i, X640:$i > $o, X641:$i, X644:$i, X645:$i, X646:$i, X648:$i, X649:$i, X650:$i, X651:$i, X652:$i, X653:$i, X654:$i, X655:$i, X656:$i, X657:$i, X658:$i, X659:$i, X660:$i, X661:$i, X662:$i, X663:$i, X664:$i > $o, X665:$i, X666:$i > $o, X667:$i, X668:$i, X669:$i > $o, X670:$i, X672:$i, X673:$i > $o, X675:$i, X676:$i, X677:$i > $o, X679:$i, X680:$i, X681:$i > $o, X682:$i, X684:$o, X685:$i, X686:$i > $o, X688:$i, X689:$i, X690:$i > $o, X691:$i, X693:$i > $o, X694:$i, X697:$i, X698:$i > $o, X699:$i, X703:$i, X704:$i > $o, X705:$i, X708:$i, X709:$i, X710:$i, X711:$i, X712:$i, X713:$i, X714:$i, X715:$i, X716:$i, X717:$i > $o, X718:$i, X720:$i, X721:$i, X722:$i > $o, X723:$i > $o, X726:$i, X729:$i, X730:$i, X733:$i, X734:$i, X735:$i, X736:$i, X737:$i, X738:$i, X739:$i, X740:$i, X741:$i, X742:$i > $o, X743:$i, X745:$i, X746:$i, X747:$i > $o, X748:$i > $o, X751:$i, X753:$i, X755:$i, X756:$i, X757:$i > $o, X758:$i > $o, X761:$i, X762:$i, X764:$i, X765:$i, X766:$i, 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X757)=(dsetconstr @ X756 @ X758))|((X755)!=(X756)))&(((in @ (esk51_4 @ X755 @ X756 @ X757 @ X758) @ X756)|((dsetconstr @ X755 @ X757)=(dsetconstr @ X756 @ X758))|((X755)!=(X756)))&((((esk50_4 @ X755 @ X756 @ X757 @ X758)=(esk51_4 @ X755 @ X756 @ X757 @ X758))|((dsetconstr @ X755 @ X757)=(dsetconstr @ X756 @ X758))|((X755)!=(X756)))&((~(X757 @ (esk50_4 @ X755 @ X756 @ X757 @ X758))|~(X758 @ (esk51_4 @ X755 @ X756 @ X757 @ X758))|((dsetconstr @ X755 @ X757)=(dsetconstr @ X756 @ X758))|((X755)!=(X756)))&((X757 @ (esk50_4 @ X755 @ X756 @ X757 @ X758))|(X758 @ (esk51_4 @ X755 @ X756 @ X757 @ X758))|((dsetconstr @ X755 @ X757)=(dsetconstr @ X756 @ X758))|((X755)!=(X756)))))))&((((in @ (esk52_2 @ X761 @ X762) @ X761)|(subset @ X761 @ X762))&(~(in @ (esk52_2 @ X761 @ X762) @ X762)|(subset @ X761 @ X762)))&((((X764)!=(X765))|(subset @ X765 @ X764))&((((X766)!=(X767))|(subset @ X766 @ X767))&((((in @ (esk53_2 @ X768 @ X769) @ X768)|(subset @ X768 @ X769))&(~(in @ (esk53_2 @ X768 @ X769) @ X769)|(subset @ X768 @ X769)))&((subset @ emptyset @ X771)&((~(subset @ X772 @ X773)|(~(in @ X774 @ X772)|(in @ X774 @ X773)))&((subset @ esk54_0 @ esk55_0)&(~(in @ esk56_0 @ esk55_0)&(in @ esk56_0 @ esk54_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_122])])])])])])])). 0.40/0.56 thf(c_0_124, negated_conjecture, ![X4:$i, X3:$i, X2:$i]:(((in @ X4 @ X3)|~((subset @ X2 @ X3))|~((in @ X4 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_123])). 0.40/0.56 thf(c_0_125, negated_conjecture, (in @ esk56_0 @ esk54_0), inference(split_conjunct,[status(thm)],[c_0_123])). 0.40/0.56 thf(c_0_126, negated_conjecture, ![X2:$i]:(((in @ esk56_0 @ X2)|~((subset @ esk54_0 @ X2)))), inference(spm,[status(thm)],[c_0_124, c_0_125])). 0.40/0.56 thf(c_0_127, negated_conjecture, (subset @ esk54_0 @ esk55_0), inference(split_conjunct,[status(thm)],[c_0_123])). 0.40/0.56 thf(c_0_128, negated_conjecture, ~((in @ esk56_0 @ esk55_0)), inference(split_conjunct,[status(thm)],[c_0_123])). 0.40/0.56 thf(c_0_129, negated_conjecture, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_127]), c_0_128]), ['proof']). 0.40/0.56 # SZS output end CNFRefutation 0.40/0.56 # Parsed axioms : 180 0.40/0.56 # Removed by relevancy pruning/SinE : 97 0.40/0.56 # Initial clauses : 194 0.40/0.56 # Removed in clause preprocessing : 13 0.40/0.56 # Initial clauses in saturation : 181 0.40/0.56 # Processed clauses : 266 0.40/0.56 # ...of these trivial : 3 0.40/0.56 # ...subsumed : 17 0.40/0.56 # ...remaining for further processing : 246 0.40/0.56 # Other redundant clauses eliminated : 13 0.40/0.56 # Clauses deleted for lack of memory : 0 0.40/0.56 # Backward-subsumed : 0 0.40/0.56 # Backward-rewritten : 3 0.40/0.56 # Generated clauses : 168 0.40/0.56 # ...of the previous two non-redundant : 142 0.40/0.56 # ...aggressively subsumed : 0 0.40/0.56 # Contextual simplify-reflections : 0 0.40/0.56 # Paramodulations : 142 0.40/0.56 # Factorizations : 0 0.40/0.56 # NegExts : 0 0.40/0.56 # Equation resolutions : 13 0.40/0.56 # Disequality decompositions : 0 0.40/0.56 # Total rewrite steps : 39 0.40/0.56 # ...of those cached : 25 0.40/0.56 # Propositional unsat checks : 0 0.40/0.56 # Propositional check models : 0 0.40/0.56 # Propositional check unsatisfiable : 0 0.40/0.56 # Propositional clauses : 0 0.40/0.56 # Propositional clauses after purity: 0 0.40/0.56 # Propositional unsat core size : 0 0.40/0.56 # Propositional preprocessing time : 0.000 0.40/0.56 # Propositional encoding time : 0.000 0.40/0.56 # Propositional solver time : 0.000 0.40/0.56 # Success case prop preproc time : 0.000 0.40/0.56 # Success case prop encoding time : 0.000 0.40/0.56 # Success case prop solver time : 0.000 0.40/0.56 # Current number of processed clauses : 70 0.40/0.56 # Positive orientable unit clauses : 17 0.40/0.56 # Positive unorientable unit clauses: 0 0.40/0.56 # Negative unit clauses : 2 0.40/0.56 # Non-unit-clauses : 51 0.40/0.56 # Current number of unprocessed clauses: 218 0.40/0.56 # ...number of literals in the above : 706 0.40/0.56 # Current number of archived formulas : 0 0.40/0.56 # Current number of archived clauses : 164 0.40/0.56 # Clause-clause subsumption calls (NU) : 5975 0.40/0.56 # Rec. Clause-clause subsumption calls : 1804 0.40/0.56 # Non-unit clause-clause subsumptions : 12 0.40/0.56 # Unit Clause-clause subsumption calls : 21 0.40/0.56 # Rewrite failures with RHS unbound : 0 0.40/0.56 # BW rewrite match attempts : 7 0.40/0.56 # BW rewrite match successes : 3 0.40/0.56 # Condensation attempts : 266 0.40/0.56 # Condensation successes : 3 0.40/0.56 # Termbank termtop insertions : 32772 0.40/0.56 # Search garbage collected termcells : 9540 0.40/0.56 0.40/0.56 # ------------------------------------------------- 0.40/0.56 # User time : 0.046 s 0.40/0.56 # System time : 0.014 s 0.40/0.56 # Total time : 0.060 s 0.40/0.56 # Maximum resident set size: 4492 pages 0.40/0.56 0.40/0.56 # ------------------------------------------------- 0.40/0.56 # User time : 0.051 s 0.40/0.56 # System time : 0.018 s 0.40/0.56 # Total time : 0.068 s 0.40/0.56 # Maximum resident set size: 2148 pages 0.40/0.56 % E---3.1 exiting 0.40/0.57 % E exiting 0.40/0.57 EOF