0.03/0.13 % Problem : Vampire---4.8_25398 : TPTP v0.0.0. Released v0.0.0. 0.03/0.14 % Command : run_E %s %d THM 0.15/0.35 % Computer : n019.cluster.edu 0.15/0.35 % Model : x86_64 x86_64 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.35 % Memory : 8042.1875MB 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.35 % CPULimit : 1440 0.15/0.35 % WCLimit : 180 0.15/0.35 % DateTime : Mon Jul 3 12:58:49 EDT 2023 0.15/0.36 % CPUTime : 0.22/0.49 Running higher-order theorem provingRunning: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398 0.22/0.49 # Version: 3.1pre001-ho 0.22/0.51 # Preprocessing class: HSMSSLSSMLLCHFA. 0.22/0.51 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.22/0.51 # Starting new_ho_10 with 900s (5) cores 0.22/0.51 # Starting sh5l with 180s (1) cores 0.22/0.51 # Starting new_bool_1 with 180s (1) cores 0.22/0.51 # Starting new_bool_2 with 180s (1) cores 0.22/0.51 # new_bool_2 with pid 25582 completed with status 0 0.22/0.51 # Result found by new_bool_2 0.22/0.51 # Preprocessing class: HSMSSLSSMLLCHFA. 0.22/0.51 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.22/0.51 # Starting new_ho_10 with 900s (5) cores 0.22/0.51 # Starting sh5l with 180s (1) cores 0.22/0.51 # Starting new_bool_1 with 180s (1) cores 0.22/0.51 # Starting new_bool_2 with 180s (1) cores 0.22/0.51 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.22/0.51 # Search class: HGHSF-FFMS31-SHFSMSBN 0.22/0.51 # partial match(1): HGHSM-FFMS31-SHFSMSBN 0.22/0.51 # Scheduled 5 strats onto 1 cores with 180 seconds (180 total) 0.22/0.51 # Starting new_ho_10 with 109s (1) cores 0.22/0.51 # new_ho_10 with pid 25584 completed with status 0 0.22/0.51 # Result found by new_ho_10 0.22/0.51 # Preprocessing class: HSMSSLSSMLLCHFA. 0.22/0.51 # Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.22/0.51 # Starting new_ho_10 with 900s (5) cores 0.22/0.51 # Starting sh5l with 180s (1) cores 0.22/0.51 # Starting new_bool_1 with 180s (1) cores 0.22/0.51 # Starting new_bool_2 with 180s (1) cores 0.22/0.51 # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0) 0.22/0.51 # Search class: HGHSF-FFMS31-SHFSMSBN 0.22/0.51 # partial match(1): HGHSM-FFMS31-SHFSMSBN 0.22/0.51 # Scheduled 5 strats onto 1 cores with 180 seconds (180 total) 0.22/0.51 # Starting new_ho_10 with 109s (1) cores 0.22/0.51 # Preprocessing time : 0.004 s 0.22/0.51 # Presaturation interreduction done 0.22/0.51 0.22/0.51 # Proof found! 0.22/0.51 # SZS status Theorem 0.22/0.51 # SZS output start CNFRefutation 0.22/0.51 thf(decl_22, type, in: $i > $i > $o). 0.22/0.51 thf(decl_23, type, exu: ($i > $o) > $o). 0.22/0.51 thf(decl_24, type, setextAx: $o). 0.22/0.51 thf(decl_25, type, emptyset: $i). 0.22/0.51 thf(decl_26, type, emptysetAx: $o). 0.22/0.51 thf(decl_27, type, setadjoin: $i > $i > $i). 0.22/0.51 thf(decl_28, type, setadjoinAx: $o). 0.22/0.51 thf(decl_29, type, powerset: $i > $i). 0.22/0.51 thf(decl_30, type, powersetAx: $o). 0.22/0.51 thf(decl_32, type, setunionAx: $o). 0.22/0.51 thf(decl_33, type, omega: $i). 0.22/0.51 thf(decl_34, type, omega0Ax: $o). 0.22/0.51 thf(decl_35, type, omegaSAx: $o). 0.22/0.51 thf(decl_36, type, omegaIndAx: $o). 0.22/0.51 thf(decl_37, type, replAx: $o). 0.22/0.51 thf(decl_38, type, foundationAx: $o). 0.22/0.51 thf(decl_39, type, wellorderingAx: $o). 0.22/0.51 thf(decl_41, type, descrp: $o). 0.22/0.51 thf(decl_42, type, dsetconstr: $i > ($i > $o) > $i). 0.22/0.51 thf(decl_43, type, dsetconstrI: $o). 0.22/0.51 thf(decl_44, type, dsetconstrEL: $o). 0.22/0.51 thf(decl_45, type, dsetconstrER: $o). 0.22/0.51 thf(decl_46, type, exuE1: $o). 0.22/0.51 thf(decl_47, type, prop2set: $o > $i). 0.22/0.51 thf(decl_48, type, prop2setE: $o). 0.22/0.51 thf(decl_49, type, emptysetE: $o). 0.22/0.51 thf(decl_50, type, emptysetimpfalse: $o). 0.22/0.51 thf(decl_51, type, notinemptyset: $o). 0.22/0.51 thf(decl_52, type, exuE3e: $o). 0.22/0.51 thf(decl_53, type, setext: $o). 0.22/0.51 thf(decl_54, type, emptyI: $o). 0.22/0.51 thf(decl_55, type, noeltsimpempty: $o). 0.22/0.51 thf(decl_56, type, setbeta: $o). 0.22/0.51 thf(decl_57, type, nonempty: $i > $o). 0.22/0.51 thf(decl_58, type, nonemptyE1: $o). 0.22/0.51 thf(decl_59, type, nonemptyI: $o). 0.22/0.51 thf(decl_60, type, nonemptyI1: $o). 0.22/0.51 thf(decl_61, type, epred1_0: $o). 0.22/0.51 thf(decl_62, type, esk1_2: $i > $i > $i). 0.22/0.51 thf(decl_63, type, esk2_2: $i > $i > $i). 0.22/0.51 thf(decl_64, type, esk3_1: $i > $i). 0.22/0.51 thf(decl_65, type, esk4_2: ($i > $i > $o) > $i > $i). 0.22/0.51 thf(decl_66, type, esk5_3: ($i > $i > $o) > $i > $i > $i). 0.22/0.51 thf(decl_67, type, esk6_2: ($i > $i > $o) > $i > $i). 0.22/0.51 thf(decl_68, type, esk7_3: ($i > $i > $o) > $i > $i > $i). 0.22/0.51 thf(decl_69, type, esk8_1: $i > $i). 0.22/0.51 thf(decl_70, type, esk9_2: ($i > $o) > $i > $i). 0.22/0.51 thf(decl_71, type, esk10_1: ($i > $o) > $i). 0.22/0.51 thf(decl_72, type, esk11_2: ($i > $o) > $i > $i). 0.22/0.51 thf(decl_73, type, esk12_1: ($i > $o) > $i). 0.22/0.51 thf(decl_74, type, esk13_2: $i > $i > $i). 0.22/0.51 thf(decl_75, type, esk14_2: $i > $i > $i). 0.22/0.51 thf(decl_76, type, esk15_1: $i > $i). 0.22/0.51 thf(decl_77, type, esk16_1: $i > $i). 0.22/0.51 thf(decl_78, type, esk17_1: $i > $i). 0.22/0.51 thf(decl_79, type, esk18_0: $i). 0.22/0.51 thf(decl_80, type, esk19_0: $i). 0.22/0.51 thf(nonempty, axiom, ((nonempty)=(^[X2:$i]:(((X2)!=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', nonempty)). 0.22/0.51 thf(exuE3e, axiom, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:((X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', exuE3e)). 0.22/0.51 thf(exu, axiom, ((exu)=(^[X1:$i > $o]:(?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', exu)). 0.22/0.51 thf(replAx, axiom, ((replAx)<=>![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(exu @ (^[X3:$i]:((X6 @ X2 @ X3))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', replAx)). 0.22/0.51 thf(exuE1, axiom, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[X2:$i]:((X1 @ X2))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', exuE1)). 0.22/0.51 thf(prop2set, axiom, ((prop2set)=(^[X10:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[X2:$i]:((X10)))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', prop2set)). 0.22/0.51 thf(nonemptyI, axiom, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', nonemptyI)). 0.22/0.51 thf(nonemptyE1, axiom, ((nonemptyE1)<=>![X4:$i]:(((nonempty @ X4)=>?[X2:$i]:((in @ X2 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', nonemptyE1)). 0.22/0.51 thf(setbeta, axiom, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))<=>(X1 @ X2))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', setbeta)). 0.22/0.51 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(X1 @ X2)))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', dsetconstrER)). 0.22/0.51 thf(dsetconstrEL, axiom, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3)))))=>(in @ X2 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', dsetconstrEL)). 0.22/0.51 thf(dsetconstrI, axiom, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[X3:$i]:((X1 @ X3))))))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', dsetconstrI)). 0.22/0.51 thf(prop2setE, axiom, ((prop2setE)<=>![X11:$o, X2:$i]:(((in @ X2 @ (prop2set @ ((X11))))=>(X11)))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', prop2setE)). 0.22/0.51 thf(nonemptyI1, axiom, ((nonemptyI1)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(nonempty @ X4)))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', nonemptyI1)). 0.22/0.51 thf(setadjoinIL, conjecture, ((((setadjoinAx)=>((((omega0Ax)=>(((omegaIndAx)=>((replAx)=>((foundationAx)=>(((((((exuE1)=>((prop2setE)=>((emptysetE)=>(((notinemptyset)=>(((setext)=>(((noeltsimpempty)=>((((nonemptyI)=>(![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))<=(nonemptyI1)))<=(nonemptyE1))<=(setbeta)))<=(emptyI)))<=(exuE3e)))<=(emptysetimpfalse)))))<=(dsetconstrER))<=(dsetconstrEL))<=(dsetconstrI))<=(descrp))<=(wellorderingAx)))))<=(omegaSAx)))<=(setunionAx))<=(powersetAx)))<=(emptysetAx))<=(setextAx)), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', setadjoinIL)). 0.22/0.51 thf(setextAx, axiom, ((setextAx)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)<=>(in @ X2 @ X5)))=>((X4)=(X5))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', setextAx)). 0.22/0.51 thf(emptyI, axiom, ((emptyI)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', emptyI)). 0.22/0.51 thf(emptysetimpfalse, axiom, ((emptysetimpfalse)<=>![X2:$i]:(((in @ X2 @ emptyset)=>~($true)))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', emptysetimpfalse)). 0.22/0.51 thf(setadjoinAx, axiom, ((setadjoinAx)<=>![X2:$i, X4:$i, X3:$i]:(((in @ X3 @ (setadjoin @ X2 @ X4))<=>(((X3)=(X2))|(in @ X3 @ X4))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', setadjoinAx)). 0.22/0.51 thf(wellorderingAx, axiom, ((wellorderingAx)<=>![X4:$i]:(?[X5:$i]:((((![X7:$i]:(((in @ X7 @ X5)=>![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))))&![X2:$i, X3:$i]:((((in @ X2 @ X4)&(in @ X3 @ X4))=>(![X7:$i]:(((in @ X7 @ X5)=>((in @ X2 @ X7)<=>(in @ X3 @ X7))))=>((X2)=(X3))))))&![X7:$i, X8:$i]:((((in @ X7 @ X5)&(in @ X8 @ X5))=>(![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X8)))|![X2:$i]:(((in @ X2 @ X8)=>(in @ X2 @ X7)))))))&![X7:$i]:(((![X2:$i]:(((in @ X2 @ X7)=>(in @ X2 @ X4)))&?[X2:$i]:((in @ X2 @ X7)))=>?[X8:$i, X2:$i]:(((((in @ X8 @ X5)&(in @ X2 @ X7))&~(?[X3:$i]:(((in @ X3 @ X8)&(in @ X3 @ X7)))))&![X9:$i]:(((in @ X9 @ X5)=>(![X3:$i]:(((in @ X3 @ X9)=>(in @ X3 @ X8)))|(in @ X2 @ X9)))))))))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', wellorderingAx)). 0.22/0.51 thf(omega0Ax, axiom, ((omega0Ax)<=>(in @ emptyset @ omega)), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', omega0Ax)). 0.22/0.51 thf(omegaSAx, axiom, ((omegaSAx)<=>![X2:$i]:(((in @ X2 @ omega)=>(in @ (setadjoin @ X2 @ X2) @ omega)))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', omegaSAx)). 0.22/0.51 thf(powersetAx, axiom, ((powersetAx)<=>![X4:$i, X5:$i]:(((in @ X5 @ (powerset @ X4))<=>![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', powersetAx)). 0.22/0.51 thf(emptysetAx, axiom, ((emptysetAx)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', emptysetAx)). 0.22/0.51 thf(omegaIndAx, axiom, ((omegaIndAx)<=>![X4:$i]:((((in @ emptyset @ X4)&![X2:$i]:((((in @ X2 @ omega)&(in @ X2 @ X4))=>(in @ (setadjoin @ X2 @ X2) @ X4))))=>![X2:$i]:(((in @ X2 @ omega)=>(in @ X2 @ X4)))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', omegaIndAx)). 0.22/0.51 thf(foundationAx, axiom, ((foundationAx)<=>![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>?[X5:$i]:(((in @ X5 @ X4)&~(?[X2:$i]:(((in @ X2 @ X5)&(in @ X2 @ X4))))))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', foundationAx)). 0.22/0.51 thf(emptysetE, axiom, ((emptysetE)<=>![X2:$i]:(((in @ X2 @ emptyset)=>![X12:$o]:((X12))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', emptysetE)). 0.22/0.51 thf(notinemptyset, axiom, ((notinemptyset)<=>![X2:$i]:(~((in @ X2 @ emptyset)))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', notinemptyset)). 0.22/0.51 thf(setext, axiom, ((setext)<=>![X4:$i, X5:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(in @ X2 @ X5)))=>(![X2:$i]:(((in @ X2 @ X5)=>(in @ X2 @ X4)))=>((X4)=(X5)))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', setext)). 0.22/0.51 thf(noeltsimpempty, axiom, ((noeltsimpempty)<=>![X4:$i]:((![X2:$i]:(~((in @ X2 @ X4)))=>((X4)=(emptyset))))), file('/export/starexec/sandbox/tmp/tmp.bNB9BaWkJU/Vampire---4.8_25398', noeltsimpempty)). 0.22/0.51 thf(c_0_30, plain, ((nonempty)=(^[Z0/* 4 */:$i]:(((Z0)!=(emptyset))))), inference(fof_simplification,[status(thm)],[nonempty])). 0.22/0.51 thf(c_0_31, plain, ((exuE3e)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:((X1 @ X2))))), inference(fof_simplification,[status(thm)],[exuE3e])). 0.22/0.51 thf(c_0_32, plain, ((exu)=(^[Z0/* 5 */:$i > $o]:(?[X2:$i]:(((Z0 @ X2)&![X3:$i]:(((Z0 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exu])). 0.22/0.51 thf(c_0_33, plain, ((replAx)<=>![X6:$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:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2))))))))), inference(fof_simplification,[status(thm)],[replAx])). 0.22/0.51 thf(c_0_34, plain, ((exuE1)<=>![X1:$i > $o]:(((exu @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3))))))))), inference(fof_simplification,[status(thm)],[exuE1])). 0.22/0.51 thf(c_0_35, plain, ((prop2set)=(^[Z0/* 42 */:$o]:(dsetconstr @ (powerset @ emptyset) @ (^[Z1/* 3 */:$i]:((Z0)))))), inference(fof_simplification,[status(thm)],[prop2set])). 0.22/0.51 thf(c_0_36, plain, ((nonemptyI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(nonempty @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[nonemptyI])). 0.22/0.51 thf(c_0_37, axiom, ((nonemptyE1)=(![X4:$i]:(((((X4)!=(emptyset)))=>?[X2:$i]:((in @ X2 @ X4)))))), inference(apply_def,[status(thm)],[nonemptyE1, c_0_30])). 0.22/0.51 thf(c_0_38, plain, ((setbeta)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))<=>(X1 @ X2))))), inference(fof_simplification,[status(thm)],[setbeta])). 0.22/0.51 thf(c_0_39, plain, ((exuE3e)=(![X1:$i > $o]:(((?[X100:$i]:((((X1 @ X100))&![X101:$i]:((((X1 @ X101))=>((X100)=(X101)))))))=>?[X2:$i]:((X1 @ X2)))))), inference(apply_def,[status(thm)],[c_0_31, c_0_32])). 0.22/0.51 thf(c_0_40, plain, ((dsetconstrER)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(X1 @ X2)))), inference(fof_simplification,[status(thm)],[dsetconstrER])). 0.22/0.51 thf(c_0_41, plain, ((dsetconstrEL)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0)))))=>(in @ X2 @ X4)))), inference(fof_simplification,[status(thm)],[dsetconstrEL])). 0.22/0.51 thf(c_0_42, plain, ((dsetconstrI)<=>![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(in @ X2 @ (dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))))))), inference(fof_simplification,[status(thm)],[dsetconstrI])). 0.22/0.51 thf(c_0_43, plain, ((replAx)=(![X6:$i > $i > $o, X4:$i]:((![X2:$i]:(((in @ X2 @ X4)=>(?[X96:$i]:((((X6 @ X2 @ X96))&![X97:$i]:((((X6 @ X2 @ X97))=>((X96)=(X97)))))))))=>?[X5:$i]:(![X2:$i]:(((in @ X2 @ X5)<=>?[X3:$i]:(((in @ X3 @ X4)&(X6 @ X3 @ X2)))))))))), inference(apply_def,[status(thm)],[c_0_33, c_0_32])). 0.22/0.51 thf(c_0_44, plain, ((exuE1)=(![X1:$i > $o]:(((?[X98:$i]:((((X1 @ X98))&![X99:$i]:((((X1 @ X99))=>((X98)=(X99)))))))=>?[X2:$i]:(((X1 @ X2)&![X3:$i]:(((X1 @ X3)=>((X2)=(X3)))))))))), inference(apply_def,[status(thm)],[c_0_34, c_0_32])). 0.22/0.51 thf(c_0_45, axiom, ((prop2setE)=(![X11:$o, X2:$i]:(((in @ X2 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:(((X11))))))=>(X11))))), inference(apply_def,[status(thm)],[prop2setE, c_0_35])). 0.22/0.51 thf(c_0_46, plain, ((nonemptyI)=(![X4:$i, X1:$i > $o, X2:$i]:(((in @ X2 @ X4)=>((X1 @ X2)=>(((dsetconstr @ X4 @ (^[Z0/* 3 */:$i]:((X1 @ Z0))))!=(emptyset)))))))), inference(apply_def,[status(thm)],[c_0_36, c_0_30])). 0.22/0.51 thf(c_0_47, axiom, ((nonemptyI1)=(![X4:$i]:((?[X2:$i]:((in @ X2 @ X4))=>(((X4)!=(emptyset))))))), inference(apply_def,[status(thm)],[nonemptyI1, c_0_30])). 0.22/0.51 thf(c_0_48, plain, ((epred1_0)<=>![X162:$i]:(?[X163:$i]:((((![X164:$i]:(((in @ X164 @ X163)=>![X165:$i]:(((in @ X165 @ X164)=>(in @ X165 @ X162)))))&![X166:$i, X167:$i]:((((in @ X166 @ X162)&(in @ X167 @ X162))=>(![X168:$i]:(((in @ X168 @ X163)=>((in @ X166 @ X168)<=>(in @ X167 @ X168))))=>((X166)=(X167))))))&![X169:$i, X170:$i]:((((in @ X169 @ X163)&(in @ X170 @ X163))=>(![X171:$i]:(((in @ X171 @ X169)=>(in @ X171 @ X170)))|![X172:$i]:(((in @ X172 @ X170)=>(in @ X172 @ X169)))))))&![X173:$i]:(((![X174:$i]:(((in @ X174 @ X173)=>(in @ X174 @ X162)))&?[X175:$i]:((in @ X175 @ X173)))=>?[X176:$i, X177:$i]:(((((in @ X176 @ X163)&(in @ X177 @ X173))&~(?[X178:$i]:(((in @ X178 @ X176)&(in @ X178 @ X173)))))&![X179:$i]:(((in @ X179 @ X163)=>(![X180:$i]:(((in @ X180 @ X179)=>(in @ X180 @ X176)))|(in @ X177 @ X179)))))))))))), introduced(definition)). 0.22/0.51 thf(c_0_49, negated_conjecture, ~((![X186:$i, X187:$i]:((![X188:$i]:(((in @ X188 @ X186)<=>(in @ X188 @ X187)))=>((X186)=(X187))))=>(![X185:$i]:(~(in @ X185 @ emptyset))=>(![X102:$i, X103:$i, X104:$i]:(((in @ X104 @ (setadjoin @ X102 @ X103))<=>(((X104)=(X102))|(in @ X104 @ X103))))=>(![X182:$i, X183:$i]:(((in @ X183 @ (powerset @ X182))<=>![X184:$i]:(((in @ X184 @ X183)=>(in @ X184 @ X182)))))=>((setunionAx)=>((in @ emptyset @ omega)=>(![X181:$i]:(((in @ X181 @ omega)=>(in @ (setadjoin @ X181 @ X181) @ omega)))=>(![X105:$i]:((((in @ emptyset @ X105)&![X106:$i]:((((in @ X106 @ omega)&(in @ X106 @ X105))=>(in @ (setadjoin @ X106 @ X106) @ X105))))=>![X107:$i]:(((in @ X107 @ omega)=>(in @ X107 @ X105)))))=>(![X108:$i > $i > $o, X109:$i]:((![X110:$i]:(((in @ X110 @ X109)=>?[X111:$i]:(((X108 @ X110 @ X111)&![X112:$i]:(((X108 @ X110 @ X112)=>((X111)=(X112))))))))=>?[X113:$i]:(![X114:$i]:(((in @ X114 @ X113)<=>?[X115:$i]:(((in @ X115 @ X109)&(X108 @ X115 @ X114))))))))=>(![X116:$i]:((?[X117:$i]:((in @ X117 @ X116))=>?[X118:$i]:(((in @ X118 @ X116)&~(?[X119:$i]:(((in @ X119 @ X118)&(in @ X119 @ X116))))))))=>((epred1_0)=>((descrp)=>(![X159:$i, X160:$i > $o, X161:$i]:(((in @ X161 @ X159)=>((X160 @ X161)=>(in @ X161 @ (dsetconstr @ X159 @ (^[Z0/* 3 */:$i]:((X160 @ Z0))))))))=>(![X156:$i, X157:$i > $o, X158:$i]:(((in @ X158 @ (dsetconstr @ X156 @ (^[Z0/* 3 */:$i]:((X157 @ Z0)))))=>(in @ X158 @ X156)))=>(![X153:$i, X154:$i > $o, X155:$i]:(((in @ X155 @ (dsetconstr @ X153 @ (^[Z0/* 3 */:$i]:((X154 @ Z0)))))=>(X154 @ X155)))=>(![X120:$i > $o]:((?[X121:$i]:(((X120 @ X121)&![X122:$i]:(((X120 @ X122)=>((X121)=(X122))))))=>?[X123:$i]:(((X120 @ X123)&![X124:$i]:(((X120 @ X124)=>((X123)=(X124))))))))=>(![X125:$o, X126:$i]:(((in @ X126 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:((X125)))))=>(X125)))=>(![X127:$i]:(((in @ X127 @ emptyset)=>![X128:$o]:((X128))))=>(![X152:$i]:(~(in @ X152 @ emptyset))=>(![X129:$i]:(~(in @ X129 @ emptyset))=>(![X148:$i > $o]:((?[X149:$i]:(((X148 @ X149)&![X150:$i]:(((X148 @ X150)=>((X149)=(X150))))))=>?[X151:$i]:((X148 @ X151))))=>(![X130:$i, X131:$i]:((![X132:$i]:(((in @ X132 @ X130)=>(in @ X132 @ X131)))=>(![X133:$i]:(((in @ X133 @ X131)=>(in @ X133 @ X130)))=>((X130)=(X131)))))=>(![X146:$i]:((![X147:$i]:(~(in @ X147 @ X146))=>((X146)=(emptyset))))=>(![X134:$i]:((![X135:$i]:(~(in @ X135 @ X134))=>((X134)=(emptyset))))=>(![X143:$i, X144:$i > $o, X145:$i]:(((in @ X145 @ X143)=>((in @ X145 @ (dsetconstr @ X143 @ (^[Z0/* 3 */:$i]:((X144 @ Z0)))))<=>(X144 @ X145))))=>(![X141:$i]:((((X141)!=(emptyset))=>?[X142:$i]:((in @ X142 @ X141))))=>(![X136:$i, X137:$i > $o, X138:$i]:(((in @ X138 @ X136)=>((X137 @ X138)=>((dsetconstr @ X136 @ (^[Z0/* 3 */:$i]:((X137 @ Z0))))!=(emptyset)))))=>(![X139:$i]:((?[X140:$i]:((in @ X140 @ X139))=>((X139)!=(emptyset))))=>![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3)))))))))))))))))))))))))))))))), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(assume_negation,[status(cth)],[setadjoinIL]), setextAx]), c_0_37]), c_0_38]), emptyI]), c_0_39]), emptysetimpfalse]), c_0_40]), c_0_41]), setadjoinAx]), c_0_42]), wellorderingAx]), omega0Ax]), omegaSAx]), powersetAx]), emptysetAx]), omegaIndAx]), c_0_43]), foundationAx]), c_0_44]), c_0_45]), emptysetE]), notinemptyset]), setext]), noeltsimpempty]), c_0_46]), c_0_47])]), c_0_48])). 0.22/0.51 thf(c_0_50, negated_conjecture, ![X189:$i, X190:$i, X192:$i, X193:$i, X194:$i, X195:$i, X196:$i, X197:$i, X198:$i, X199:$i, X200:$i, X202:$i, X203:$i, X205:$i, X206:$i > $i > $o, X207:$i, X209:$i, X212:$i, X214:$i, X215:$i, X216:$i, X217:$i, X219:$i, X220:$i, X221:$i > $o, X222:$i, X223:$i, X224:$i > $o, X225:$i, X226:$i, X227:$i > $o, X228:$i, X229:$i > $o, X230:$i, X233:$i, X234:$o, X235:$i, X236:$i, X237:$o, X238:$i, X239:$i, X240:$i > $o, X241:$i, X244:$i, X245:$i, X248:$i, X250:$i, X252:$i, X253:$i > $o, X254:$i, X255:$i, X257:$i, X258:$i > $o, X259:$i, X260:$i, X261:$i]:((((~(in @ (esk1_2 @ X189 @ X190) @ X189)|~(in @ (esk1_2 @ X189 @ X190) @ X190)|((X189)=(X190)))&((in @ (esk1_2 @ X189 @ X190) @ X189)|(in @ (esk1_2 @ X189 @ X190) @ X190)|((X189)=(X190))))&(~(in @ X192 @ emptyset)&(((~(in @ X195 @ (setadjoin @ X193 @ X194))|(((X195)=(X193))|(in @ X195 @ X194)))&((((X195)!=(X193))|(in @ X195 @ (setadjoin @ X193 @ X194)))&(~(in @ X195 @ X194)|(in @ X195 @ (setadjoin @ X193 @ X194)))))&(((~(in @ X197 @ (powerset @ X196))|(~(in @ X198 @ X197)|(in @ X198 @ X196)))&(((in @ (esk2_2 @ X199 @ X200) @ X200)|(in @ X200 @ (powerset @ X199)))&(~(in @ (esk2_2 @ X199 @ X200) @ X199)|(in @ X200 @ (powerset @ X199)))))&((setunionAx)&((in @ emptyset @ omega)&((~(in @ X202 @ omega)|(in @ (setadjoin @ X202 @ X202) @ omega))&(((((in @ (esk3_1 @ X203) @ omega)|~(in @ emptyset @ X203)|(~(in @ X205 @ omega)|(in @ X205 @ X203)))&((in @ (esk3_1 @ X203) @ X203)|~(in @ emptyset @ X203)|(~(in @ X205 @ omega)|(in @ X205 @ X203))))&(~(in @ (setadjoin @ (esk3_1 @ X203) @ (esk3_1 @ X203)) @ X203)|~(in @ emptyset @ X203)|(~(in @ X205 @ omega)|(in @ X205 @ X203))))&((((((in @ (esk7_3 @ X206 @ X207 @ X212) @ X207)|~(in @ X212 @ (esk6_2 @ X206 @ X207))|(in @ (esk4_2 @ X206 @ X207) @ X207))&((X206 @ (esk7_3 @ X206 @ X207 @ X212) @ X212)|~(in @ X212 @ (esk6_2 @ X206 @ X207))|(in @ (esk4_2 @ X206 @ X207) @ X207)))&(~(in @ X215 @ X207)|~(X206 @ X215 @ X214)|(in @ X214 @ (esk6_2 @ X206 @ X207))|(in @ (esk4_2 @ X206 @ X207) @ X207)))&(((((in @ (esk7_3 @ X206 @ X207 @ X212) @ X207)|~(in @ X212 @ (esk6_2 @ X206 @ X207))|((X206 @ (esk4_2 @ X206 @ X207) @ (esk5_3 @ X206 @ X207 @ X209))|~(X206 @ (esk4_2 @ X206 @ X207) @ X209)))&((X206 @ (esk7_3 @ X206 @ X207 @ X212) @ X212)|~(in @ X212 @ (esk6_2 @ X206 @ X207))|((X206 @ (esk4_2 @ X206 @ X207) @ (esk5_3 @ X206 @ X207 @ X209))|~(X206 @ (esk4_2 @ X206 @ X207) @ X209))))&(~(in @ X215 @ X207)|~(X206 @ X215 @ X214)|(in @ X214 @ (esk6_2 @ X206 @ X207))|((X206 @ (esk4_2 @ X206 @ X207) @ (esk5_3 @ X206 @ X207 @ X209))|~(X206 @ (esk4_2 @ X206 @ X207) @ X209))))&((((in @ (esk7_3 @ X206 @ X207 @ X212) @ X207)|~(in @ X212 @ (esk6_2 @ X206 @ X207))|(((X209)!=(esk5_3 @ X206 @ X207 @ X209))|~(X206 @ (esk4_2 @ X206 @ X207) @ X209)))&((X206 @ (esk7_3 @ X206 @ X207 @ X212) @ X212)|~(in @ X212 @ (esk6_2 @ X206 @ X207))|(((X209)!=(esk5_3 @ X206 @ X207 @ X209))|~(X206 @ (esk4_2 @ X206 @ X207) @ X209))))&(~(in @ X215 @ X207)|~(X206 @ X215 @ X214)|(in @ X214 @ (esk6_2 @ X206 @ X207))|(((X209)!=(esk5_3 @ X206 @ X207 @ X209))|~(X206 @ (esk4_2 @ X206 @ X207) @ X209))))))&((((in @ (esk8_1 @ X216) @ X216)|~(in @ X217 @ X216))&(~(in @ X219 @ (esk8_1 @ X216))|~(in @ X219 @ X216)|~(in @ X217 @ X216)))&((epred1_0)&((descrp)&((~(in @ X222 @ X220)|(~(X221 @ X222)|(in @ X222 @ (dsetconstr @ X220 @ (^[Z0/* 3 */:$i]:((X221 @ Z0)))))))&((~(in @ X225 @ (dsetconstr @ X223 @ (^[Z0/* 3 */:$i]:((X224 @ Z0)))))|(in @ X225 @ X223))&((~(in @ X228 @ (dsetconstr @ X226 @ (^[Z0/* 3 */:$i]:((X227 @ Z0)))))|(X227 @ X228))&(((((X229 @ (esk10_1 @ X229))|((X229 @ (esk9_2 @ X229 @ X230))|~(X229 @ X230)))&(~(X229 @ X233)|((esk10_1 @ X229)=(X233))|((X229 @ (esk9_2 @ X229 @ X230))|~(X229 @ X230))))&(((X229 @ (esk10_1 @ X229))|(((X230)!=(esk9_2 @ X229 @ X230))|~(X229 @ X230)))&(~(X229 @ X233)|((esk10_1 @ X229)=(X233))|(((X230)!=(esk9_2 @ X229 @ X230))|~(X229 @ X230)))))&((~(in @ X235 @ (dsetconstr @ (powerset @ emptyset) @ (^[Z0/* 3 */:$i]:((X234)))))|(X234))&((~(in @ X236 @ emptyset)|(X237))&(~(in @ X238 @ emptyset)&(~(in @ X239 @ emptyset)&((((X240 @ (esk11_2 @ X240 @ X241))|~(X240 @ X241)|(X240 @ (esk12_1 @ X240)))&(((X241)!=(esk11_2 @ X240 @ X241))|~(X240 @ X241)|(X240 @ (esk12_1 @ X240))))&(((((in @ (esk14_2 @ X244 @ X245) @ X245)|((X244)=(X245))|(in @ (esk13_2 @ X244 @ X245) @ X244))&(~(in @ (esk14_2 @ X244 @ X245) @ X244)|((X244)=(X245))|(in @ (esk13_2 @ X244 @ X245) @ X244)))&(((in @ (esk14_2 @ X244 @ X245) @ X245)|((X244)=(X245))|~(in @ (esk13_2 @ X244 @ X245) @ X245))&(~(in @ (esk14_2 @ X244 @ X245) @ X244)|((X244)=(X245))|~(in @ (esk13_2 @ X244 @ X245) @ X245))))&(((in @ (esk15_1 @ X248) @ X248)|((X248)=(emptyset)))&(((in @ (esk16_1 @ X250) @ X250)|((X250)=(emptyset)))&(((~(in @ X254 @ (dsetconstr @ X252 @ (^[Z0/* 3 */:$i]:((X253 @ Z0)))))|(X253 @ X254)|~(in @ X254 @ X252))&(~(X253 @ X254)|(in @ X254 @ (dsetconstr @ X252 @ (^[Z0/* 3 */:$i]:((X253 @ Z0)))))|~(in @ X254 @ X252)))&((((X255)=(emptyset))|(in @ (esk17_1 @ X255) @ X255))&((~(in @ X259 @ X257)|(~(X258 @ X259)|((dsetconstr @ X257 @ (^[Z0/* 3 */:$i]:((X258 @ Z0))))!=(emptyset))))&((~(in @ X261 @ X260)|((X260)!=(emptyset)))&~(in @ esk18_0 @ (setadjoin @ esk18_0 @ esk19_0))))))))))))))))))))))))))))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])])])])). 0.22/0.51 thf(c_0_51, negated_conjecture, ![X2:$i, X4:$i, X3:$i]:(((in @ X2 @ (setadjoin @ X3 @ X4))|((X2)!=(X3)))), inference(split_conjunct,[status(thm)],[c_0_50])). 0.22/0.51 thf(c_0_52, negated_conjecture, ~((in @ esk18_0 @ (setadjoin @ esk18_0 @ esk19_0))), inference(split_conjunct,[status(thm)],[c_0_50])). 0.22/0.51 thf(c_0_53, negated_conjecture, ![X2:$i, X3:$i]:((in @ X2 @ (setadjoin @ X2 @ X3))), inference(er,[status(thm)],[c_0_51])). 0.22/0.51 thf(c_0_54, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])]), ['proof']). 0.22/0.51 # SZS output end CNFRefutation 0.22/0.51 # Parsed axioms : 71 0.22/0.51 # Removed by relevancy pruning/SinE : 41 0.22/0.51 # Initial clauses : 66 0.22/0.51 # Removed in clause preprocessing : 0 0.22/0.51 # Initial clauses in saturation : 66 0.22/0.51 # Processed clauses : 22 0.22/0.51 # ...of these trivial : 0 0.22/0.51 # ...subsumed : 4 0.22/0.51 # ...remaining for further processing : 18 0.22/0.51 # Other redundant clauses eliminated : 2 0.22/0.51 # Clauses deleted for lack of memory : 0 0.22/0.51 # Backward-subsumed : 0 0.22/0.51 # Backward-rewritten : 1 0.22/0.51 # Generated clauses : 2 0.22/0.51 # ...of the previous two non-redundant : 2 0.22/0.51 # ...aggressively subsumed : 0 0.22/0.51 # Contextual simplify-reflections : 0 0.22/0.51 # Paramodulations : 0 0.22/0.51 # Factorizations : 0 0.22/0.51 # NegExts : 0 0.22/0.51 # Equation resolutions : 2 0.22/0.51 # Total rewrite steps : 1 0.22/0.51 # Propositional unsat checks : 0 0.22/0.51 # Propositional check models : 0 0.22/0.51 # Propositional check unsatisfiable : 0 0.22/0.51 # Propositional clauses : 0 0.22/0.51 # Propositional clauses after purity: 0 0.22/0.51 # Propositional unsat core size : 0 0.22/0.51 # Propositional preprocessing time : 0.000 0.22/0.51 # Propositional encoding time : 0.000 0.22/0.51 # Propositional solver time : 0.000 0.22/0.51 # Success case prop preproc time : 0.000 0.22/0.51 # Success case prop encoding time : 0.000 0.22/0.51 # Success case prop solver time : 0.000 0.22/0.51 # Current number of processed clauses : 15 0.22/0.51 # Positive orientable unit clauses : 5 0.22/0.51 # Positive unorientable unit clauses: 0 0.22/0.51 # Negative unit clauses : 2 0.22/0.51 # Non-unit-clauses : 8 0.22/0.51 # Current number of unprocessed clauses: 46 0.22/0.51 # ...number of literals in the above : 179 0.22/0.51 # Current number of archived formulas : 0 0.22/0.51 # Current number of archived clauses : 1 0.22/0.51 # Clause-clause subsumption calls (NU) : 9 0.22/0.51 # Rec. Clause-clause subsumption calls : 9 0.22/0.51 # Non-unit clause-clause subsumptions : 0 0.22/0.51 # Unit Clause-clause subsumption calls : 7 0.22/0.51 # Rewrite failures with RHS unbound : 0 0.22/0.51 # BW rewrite match attempts : 1 0.22/0.51 # BW rewrite match successes : 1 0.22/0.51 # Condensation attempts : 22 0.22/0.51 # Condensation successes : 0 0.22/0.51 # Termbank termtop insertions : 7196 0.22/0.51 0.22/0.51 # ------------------------------------------------- 0.22/0.51 # User time : 0.010 s 0.22/0.51 # System time : 0.005 s 0.22/0.51 # Total time : 0.015 s 0.22/0.51 # Maximum resident set size: 2568 pages 0.22/0.51 0.22/0.51 # ------------------------------------------------- 0.22/0.51 # User time : 0.013 s 0.22/0.51 # System time : 0.007 s 0.22/0.51 # Total time : 0.020 s 0.22/0.51 # Maximum resident set size: 1800 pages 0.22/0.52 % E---3.1 exiting 0.22/0.52 EOF