%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SEU656^2 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:24:54 AM UTC 2026
% Result : Theorem 0.08s 0.14s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU656^2 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.09 % Computer : n012.cluster.edu
% 0.00/0.09 % Model : x86_64 x86_64
% 0.00/0.09 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.09 % Memory : 8046.5625MB
% 0.00/0.09 % OS : Linux 6.8.0-71-generic
% 0.00/0.09 % CPULimit : 300
% 0.00/0.09 % WCLimit : 300
% 0.00/0.09 % DateTime : Tue Sep 29 14:03:03 UTC 2026
% 0.00/0.09 % CPUTime :
% 0.00/0.10 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.12 Running higher-order theorem proving
% 0.08/0.12 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/tmp/tmp.TPvxPLAEid/E---3.1_152838.p
% 0.08/0.14 % Version: 3.5.1-ho
% 0.08/0.14 % Preprocessing class: HSSSSLSSMLMNSFA.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % Starting sh5l with 300s (1) cores
% 0.08/0.14 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.14 % Starting new_bool_2 with 300s (1) cores
% 0.08/0.14 % new_ho_10 with pid 152851 completed with status 0
% 0.08/0.14 % Result found by new_ho_10
% 0.08/0.14 % Preprocessing class: HSSSSLSSMLMNSFA.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HHUSM-FFSF21-MSFSMFBN
% 0.08/0.14 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.14 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.14 % Starting new_ho_10 with 901s (1) cores
% 0.08/0.14 % Starting sh5l with 151s (1) cores
% 0.08/0.14 % Starting new_bool_1 with 151s (1) cores
% 0.08/0.14 % Starting new_bool_2 with 146s (1) cores
% 0.08/0.14 % sh5l with pid 152860 completed with status 0
% 0.08/0.14 % Result found by sh5l
% 0.08/0.14 % Preprocessing class: HSSSSLSSMLMNSFA.
% 0.08/0.14 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.14 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.14 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.14 % No SInE strategy applied
% 0.08/0.14 % Search class: HHUSM-FFSF21-MSFSMFBN
% 0.08/0.14 % Scheduled 5 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.14 % Starting SubtermCWHack with 151s (1) cores
% 0.08/0.14 % Starting new_ho_10 with 901s (1) cores
% 0.08/0.14 % Starting sh5l with 151s (1) cores
% 0.08/0.14 % Preprocessing time : 0.001 s
% 0.08/0.14 % Presaturation interreduction done
% 0.08/0.14
% 0.08/0.14 % Proof found!
% 0.08/0.14 % SZS status Theorem
% 0.08/0.14 % SZS output start CNFRefutation
% 0.08/0.14 thf(decl_23, type, in: $i > $i > $o).
% 0.08/0.14 thf(decl_24, type, emptyset: $i).
% 0.08/0.14 thf(decl_25, type, setadjoin: $i > $i > $i).
% 0.08/0.14 thf(decl_26, type, setunion: $i > $i).
% 0.08/0.14 thf(decl_27, type, dsetconstr: $i > ($i > $o) > $i).
% 0.08/0.14 thf(decl_28, type, dsetconstrER: $o).
% 0.08/0.14 thf(decl_29, type, iskpair: $i > $o).
% 0.08/0.14 thf(decl_30, type, kpair: $i > $i > $i).
% 0.08/0.14 thf(decl_31, type, kpairp: $o).
% 0.08/0.14 thf(decl_32, type, singleton: $i > $o).
% 0.08/0.14 thf(decl_33, type, theprop: $o).
% 0.08/0.14 thf(decl_34, type, kfst: $i > $i).
% 0.08/0.14 thf(decl_35, type, setukpairinjR: $o).
% 0.08/0.14 thf(decl_36, type, ksndsingleton: $o).
% 0.08/0.14 thf(decl_37, type, ksnd: $i > $i).
% 0.08/0.14 thf(decl_38, type, esk1_2: $i > $i > $i).
% 0.08/0.14 thf(decl_39, type, esk2_2: $i > $i > $i).
% 0.08/0.14 thf(decl_40, type, esk3_1: $i > $i).
% 0.08/0.14 thf(decl_41, type, esk4_0: $i).
% 0.08/0.14 thf(decl_42, type, esk5_0: $i).
% 0.08/0.14 thf(decl_43, type, epred1_1: $i > $i > $o).
% 0.08/0.14 thf(iskpair, axiom, ((iskpair)=(^[X1:$i]:(?[X3:$i]:((((in @ X3 @ (setunion @ X1)))&(?[X4:$i]:((((in @ X4 @ (setunion @ X1)))&(((X1)=(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset)))))))))))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', iskpair)).
% 0.08/0.14 thf(singleton, axiom, ((singleton)=(^[X1:$i]:(?[X3:$i]:((((in @ X3 @ X1))&(((X1)=(setadjoin @ X3 @ emptyset)))))))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', singleton)).
% 0.08/0.14 thf(ksndsingleton, axiom, ((ksndsingleton)<=>![X7:$i]:(((iskpair @ X7)=>(singleton @ (dsetconstr @ (setunion @ X7) @ (^[X3:$i]:(((X7)=(kpair @ (kfst @ X7) @ X3))))))))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', ksndsingleton)).
% 0.08/0.14 thf(ksndpairEq, conjecture, ((dsetconstrER)=>((kpairp)=>((theprop)=>((setukpairinjR)=>((ksndsingleton)=>![X3:$i, X4:$i]:(((ksnd @ (kpair @ X3 @ X4))=(X4)))))))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', ksndpairEq)).
% 0.08/0.14 thf(dsetconstrER, axiom, ((dsetconstrER)<=>![X1:$i, X2:$i > $o, X3:$i]:(((in @ X3 @ (dsetconstr @ X1 @ (^[X4:$i]:((X2 @ X4)))))=>(X2 @ X3)))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', dsetconstrER)).
% 0.08/0.14 thf(kpairp, axiom, ((kpairp)<=>![X3:$i, X4:$i]:((iskpair @ (kpair @ X3 @ X4)))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', kpairp)).
% 0.08/0.14 thf(theprop, axiom, ((theprop)<=>![X5:$i]:(((singleton @ X5)=>(in @ (setunion @ X5) @ X5)))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', theprop)).
% 0.08/0.14 thf(setukpairinjR, axiom, ((setukpairinjR)<=>![X3:$i, X4:$i, X6:$i, X7:$i]:((((kpair @ X3 @ X4)=(kpair @ X6 @ X7))=>((X4)=(X7))))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', setukpairinjR)).
% 0.08/0.14 thf(kpair, axiom, ((kpair)=(^[X3:$i, X4:$i]:(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset)))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', kpair)).
% 0.08/0.14 thf(ksnd, axiom, ((ksnd)=(^[X7:$i]:(setunion @ (dsetconstr @ (setunion @ X7) @ (^[X3:$i]:(((X7)=(kpair @ (kfst @ X7) @ X3)))))))), file('/export/starexec/sandbox2/tmp/tmp.TPvxPLAEid/E---3.1_152838.p', ksnd)).
% 0.08/0.14 thf(c_0_10, plain, ((iskpair)=(^[Z0:$i]:(?[X3:$i]:((((in @ X3 @ (setunion @ Z0)))&(?[X4:$i]:((((in @ X4 @ (setunion @ Z0)))&(((Z0)=(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset)))))))))))), inference(fof_simplification,[status(thm)],[iskpair])).
% 0.08/0.14 thf(c_0_11, plain, ((singleton)=(^[Z0:$i]:(?[X3:$i]:((((in @ X3 @ Z0))&(((Z0)=(setadjoin @ X3 @ emptyset)))))))), inference(fof_simplification,[status(thm)],[singleton])).
% 0.08/0.14 thf(c_0_12, plain, ((ksndsingleton)<=>![X7:$i]:(((iskpair @ X7)=>(singleton @ (dsetconstr @ (setunion @ X7) @ (^[Z0:$i]:(((X7)=(kpair @ (kfst @ X7) @ Z0))))))))), inference(fof_simplification,[status(thm)],[ksndsingleton])).
% 0.08/0.14 thf(c_0_13, negated_conjecture, ~(((dsetconstrER)=>((kpairp)=>((theprop)=>((setukpairinjR)=>((ksndsingleton)=>![X3:$i, X4:$i]:(((ksnd @ (kpair @ X3 @ X4))=(X4))))))))), inference(assume_negation,[status(cth)],[ksndpairEq])).
% 0.08/0.14 thf(c_0_14, plain, ((dsetconstrER)<=>![X1:$i, X2:$i > $o, X3:$i]:(((in @ X3 @ (dsetconstr @ X1 @ (^[Z0:$i]:((X2 @ Z0)))))=>(X2 @ X3)))), inference(fof_simplification,[status(thm)],[dsetconstrER])).
% 0.08/0.14 thf(c_0_15, axiom, ((kpairp)=(![X3:$i, X4:$i]:((?[X21:$i]:((((in @ X21 @ (setunion @ (kpair @ X3 @ X4))))&(?[X22:$i]:((((in @ X22 @ (setunion @ (kpair @ X3 @ X4))))&(((kpair @ X3 @ X4)=(setadjoin @ (setadjoin @ X21 @ emptyset) @ (setadjoin @ (setadjoin @ X21 @ (setadjoin @ X22 @ emptyset)) @ emptyset))))))))))))), inference(apply_def,[status(thm)],[kpairp, c_0_10])).
% 0.08/0.14 thf(c_0_16, axiom, ((theprop)=(![X5:$i]:((((?[X23:$i]:((((in @ X23 @ X5))&(((X5)=(setadjoin @ X23 @ emptyset)))))))=>((in @ (setunion @ X5) @ X5)))))), inference(apply_def,[status(thm)],[theprop, c_0_11])).
% 0.08/0.14 thf(c_0_17, plain, ((ksndsingleton)=(![X7:$i]:((((?[X24:$i]:((((in @ X24 @ (setunion @ X7)))&(?[X25:$i]:((((in @ X25 @ (setunion @ X7)))&(((X7)=(setadjoin @ (setadjoin @ X24 @ emptyset) @ (setadjoin @ (setadjoin @ X24 @ (setadjoin @ X25 @ emptyset)) @ emptyset)))))))))))=>((?[X26:$i]:((((in @ X26 @ (dsetconstr @ (setunion @ X7) @ (^[Z0:$i]:(((X7)=(kpair @ (kfst @ X7) @ Z0)))))))&(((dsetconstr @ (setunion @ X7) @ (^[Z0:$i]:(((X7)=(kpair @ (kfst @ X7) @ Z0)))))=(setadjoin @ X26 @ emptyset))))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[c_0_12, c_0_10]), c_0_11])).
% 0.08/0.14 thf(c_0_18, negated_conjecture, ~((![X27:$i, X28:$i > $o, X29:$i]:(((in @ X29 @ (dsetconstr @ X27 @ X28))=>(X28 @ X29)))=>(![X30:$i, X31:$i]:(?[X32:$i]:(((in @ X32 @ (setunion @ (kpair @ X30 @ X31)))&?[X33:$i]:(((in @ X33 @ (setunion @ (kpair @ X30 @ X31)))&((kpair @ X30 @ X31)=(setadjoin @ (setadjoin @ X32 @ emptyset) @ (setadjoin @ (setadjoin @ X32 @ (setadjoin @ X33 @ emptyset)) @ emptyset))))))))=>(![X34:$i]:((?[X35:$i]:(((in @ X35 @ X34)&((X34)=(setadjoin @ X35 @ emptyset))))=>(in @ (setunion @ X34) @ X34)))=>(![X36:$i, X37:$i, X38:$i, X39:$i]:((((kpair @ X36 @ X37)=(kpair @ X38 @ X39))=>((X37)=(X39))))=>(![X40:$i]:((?[X41:$i]:(((in @ X41 @ (setunion @ X40))&?[X42:$i]:(((in @ X42 @ (setunion @ X40))&((X40)=(setadjoin @ (setadjoin @ X41 @ emptyset) @ (setadjoin @ (setadjoin @ X41 @ (setadjoin @ X42 @ emptyset)) @ emptyset)))))))=>?[X43:$i]:(((in @ X43 @ (dsetconstr @ (setunion @ X40) @ (^[Z0:$i]:(((X40)=(kpair @ (kfst @ X40) @ Z0))))))&((dsetconstr @ (setunion @ X40) @ (^[Z0:$i]:(((X40)=(kpair @ (kfst @ X40) @ Z0)))))=(setadjoin @ X43 @ emptyset))))))=>![X3:$i, X4:$i]:(((ksnd @ (kpair @ X3 @ X4))=(X4))))))))), 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)],[c_0_13, c_0_14]), c_0_15]), c_0_16]), setukpairinjR]), c_0_17])])).
% 0.08/0.14 thf(c_0_19, plain, ![X44:$i, X45:$i]:(((kpair @ X44 @ X45)=(setadjoin @ (setadjoin @ X44 @ emptyset) @ (setadjoin @ (setadjoin @ X44 @ (setadjoin @ X45 @ emptyset)) @ emptyset)))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[kpair])])).
% 0.08/0.14 thf(c_0_20, negated_conjecture, ![X50:$i, X51:$i > $o, X52:$i, X53:$i, X54:$i, X57:$i, X58:$i, X59:$i, X60:$i, X61:$i, X62:$i, X63:$i, X64:$i, X65:$i]:(((~(in @ X52 @ (dsetconstr @ X50 @ X51))|(X51 @ X52))&(((in @ (esk1_2 @ X53 @ X54) @ (setunion @ (kpair @ X53 @ X54)))&((in @ (esk2_2 @ X53 @ X54) @ (setunion @ (kpair @ X53 @ X54)))&((kpair @ X53 @ X54)=(setadjoin @ (setadjoin @ (esk1_2 @ X53 @ X54) @ emptyset) @ (setadjoin @ (setadjoin @ (esk1_2 @ X53 @ X54) @ (setadjoin @ (esk2_2 @ X53 @ X54) @ emptyset)) @ emptyset)))))&((~(in @ X58 @ X57)|((X57)!=(setadjoin @ X58 @ emptyset))|(in @ (setunion @ X57) @ X57))&((((kpair @ X59 @ X60)!=(kpair @ X61 @ X62))|((X60)=(X62)))&((((in @ (esk3_1 @ X63) @ (dsetconstr @ (setunion @ X63) @ (^[Z0:$i]:(((X63)=(kpair @ (kfst @ X63) @ Z0))))))|(~(in @ X64 @ (setunion @ X63))|(~(in @ X65 @ (setunion @ X63))|((X63)!=(setadjoin @ (setadjoin @ X64 @ emptyset) @ (setadjoin @ (setadjoin @ X64 @ (setadjoin @ X65 @ emptyset)) @ emptyset))))))&(((dsetconstr @ (setunion @ X63) @ (^[Z0:$i]:(((X63)=(kpair @ (kfst @ X63) @ Z0)))))=(setadjoin @ (esk3_1 @ X63) @ emptyset))|(~(in @ X64 @ (setunion @ X63))|(~(in @ X65 @ (setunion @ X63))|((X63)!=(setadjoin @ (setadjoin @ X64 @ emptyset) @ (setadjoin @ (setadjoin @ X64 @ (setadjoin @ X65 @ emptyset)) @ emptyset)))))))&((ksnd @ (kpair @ esk4_0 @ esk5_0))!=(esk5_0)))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_18])])])])])])).
% 0.08/0.14 thf(c_0_21, plain, ![X47:$i, X48:$i]:(((kpair @ X47 @ X48)=(setadjoin @ (setadjoin @ X47 @ emptyset) @ (setadjoin @ (setadjoin @ X47 @ (setadjoin @ X48 @ emptyset)) @ emptyset)))), inference(variable_rename,[status(thm)],[c_0_19])).
% 0.08/0.14 thf(c_0_22, negated_conjecture, ![X1:$i, X3:$i]:(((kpair @ X1 @ X3)=(setadjoin @ (setadjoin @ (esk1_2 @ X1 @ X3) @ emptyset) @ (setadjoin @ (setadjoin @ (esk1_2 @ X1 @ X3) @ (setadjoin @ (esk2_2 @ X1 @ X3) @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.08/0.14 thf(c_0_23, plain, ![X1:$i, X3:$i]:(((kpair @ X1 @ X3)=(setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_21])).
% 0.08/0.14 thf(c_0_24, negated_conjecture, ![X1:$i, X3:$i, X4:$i, X5:$i]:((((X3)=(X5))|((kpair @ X1 @ X3)!=(kpair @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.08/0.14 thf(c_0_25, negated_conjecture, ![X1:$i, X3:$i]:(((kpair @ (esk1_2 @ X1 @ X3) @ (esk2_2 @ X1 @ X3))=(kpair @ X1 @ X3))), inference(rw,[status(thm)],[c_0_22, c_0_23])).
% 0.08/0.14 thf(c_0_26, plain, ![X69:$i, X1:$i]:(((epred1_1 @ X1 @ X69)<=>((X1)=(kpair @ (kfst @ X1) @ X69)))), introduced(definition)).
% 0.08/0.14 thf(c_0_27, negated_conjecture, ![X1:$i, X3:$i, X5:$i, X4:$i]:((((X1)=(esk2_2 @ X3 @ X4))|((kpair @ X5 @ X1)!=(kpair @ X3 @ X4)))), inference(spm,[status(thm)],[c_0_24, c_0_25])).
% 0.08/0.14 thf(c_0_28, negated_conjecture, ![X1:$i, X3:$i, X4:$i]:((((dsetconstr @ (setunion @ X1) @ (epred1_1 @ X1))=(setadjoin @ (esk3_1 @ X1) @ emptyset))|~((in @ X3 @ (setunion @ X1)))|~((in @ X4 @ (setunion @ X1)))|((X1)!=(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20]), c_0_26])).
% 0.08/0.14 thf(c_0_29, negated_conjecture, ![X1:$i, X3:$i]:((in @ (esk2_2 @ X1 @ X3) @ (setunion @ (kpair @ X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.08/0.14 thf(c_0_30, negated_conjecture, ![X1:$i, X3:$i]:(((esk2_2 @ X1 @ X3)=(X3))), inference(er,[status(thm)],[c_0_27])).
% 0.08/0.14 thf(c_0_31, plain, ![X46:$i]:(((ksnd @ X46)=(setunion @ (dsetconstr @ (setunion @ X46) @ (^[Z0:$i]:(((X46)=(kpair @ (kfst @ X46) @ Z0)))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[ksnd])])).
% 0.08/0.14 thf(c_0_32, negated_conjecture, ![X1:$i, X3:$i]:((((dsetconstr @ (setunion @ (kpair @ X1 @ X3)) @ (epred1_1 @ (kpair @ X1 @ X3)))=(setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))|~((in @ X3 @ (setunion @ (kpair @ X1 @ X3))))|~((in @ X1 @ (setunion @ (kpair @ X1 @ X3)))))), inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_23])])).
% 0.08/0.14 thf(c_0_33, negated_conjecture, ![X3:$i, X1:$i]:((in @ X1 @ (setunion @ (kpair @ X3 @ X1)))), inference(rw,[status(thm)],[c_0_29, c_0_30])).
% 0.08/0.14 thf(c_0_34, plain, ![X49:$i]:(((ksnd @ X49)=(setunion @ (dsetconstr @ (setunion @ X49) @ (^[Z0:$i]:(((X49)=(kpair @ (kfst @ X49) @ Z0)))))))), inference(variable_rename,[status(thm)],[c_0_31])).
% 0.08/0.14 thf(c_0_35, negated_conjecture, ![X1:$i, X3:$i, X4:$i]:(((((in @ (esk3_1 @ X1) @ (dsetconstr @ (setunion @ X1) @ (epred1_1 @ X1))))=(($true)))|~((in @ X3 @ (setunion @ X1)))|~((in @ X4 @ (setunion @ X1)))|((X1)!=(setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X4 @ emptyset)) @ emptyset))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_20]), c_0_26])).
% 0.08/0.14 thf(c_0_36, negated_conjecture, ![X1:$i, X3:$i]:((((dsetconstr @ (setunion @ (kpair @ X1 @ X3)) @ (epred1_1 @ (kpair @ X1 @ X3)))=(setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))|~((in @ X1 @ (setunion @ (kpair @ X1 @ X3)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])).
% 0.08/0.14 thf(c_0_37, negated_conjecture, ![X1:$i, X3:$i]:(((kpair @ (esk1_2 @ X1 @ X3) @ X3)=(kpair @ X1 @ X3))), inference(rw,[status(thm)],[c_0_25, c_0_30])).
% 0.08/0.14 thf(c_0_38, negated_conjecture, ![X1:$i, X3:$i]:((in @ (esk1_2 @ X1 @ X3) @ (setunion @ (kpair @ X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.08/0.14 thf(c_0_39, plain, ![X1:$i]:(((ksnd @ X1)=(setunion @ (dsetconstr @ (setunion @ X1) @ (epred1_1 @ X1))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_34]), c_0_26])).
% 0.08/0.14 thf(c_0_40, negated_conjecture, ![X1:$i, X3:$i]:(((in @ (esk3_1 @ (kpair @ X1 @ X3)) @ (dsetconstr @ (setunion @ (kpair @ X1 @ X3)) @ (epred1_1 @ (kpair @ X1 @ X3))))|~((in @ X3 @ (setunion @ (kpair @ X1 @ X3))))|~((in @ X1 @ (setunion @ (kpair @ X1 @ X3)))))), inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[c_0_35]), c_0_23])])).
% 0.08/0.14 thf(c_0_41, negated_conjecture, ![X1:$i, X3:$i, X2:$i > $o]:(((X2 @ X1)|~((in @ X1 @ (dsetconstr @ X3 @ X2))))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.08/0.14 thf(c_0_42, negated_conjecture, ![X1:$i, X3:$i]:(((dsetconstr @ (setunion @ (kpair @ X1 @ X3)) @ (epred1_1 @ (kpair @ X1 @ X3)))=(setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36, c_0_37]), c_0_38])])).
% 0.08/0.14 thf(c_0_43, negated_conjecture, ![X3:$i, X1:$i]:(((in @ (setunion @ X3) @ X3)|~((in @ X1 @ X3))|((X3)!=(setadjoin @ X1 @ emptyset)))), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.08/0.14 thf(c_0_44, negated_conjecture, ![X1:$i, X3:$i]:((((setunion @ (setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))=(ksnd @ (kpair @ X1 @ X3)))|~((in @ X1 @ (setunion @ (kpair @ X1 @ X3)))))), inference(spm,[status(thm)],[c_0_39, c_0_36])).
% 0.08/0.14 thf(c_0_45, negated_conjecture, ![X1:$i, X3:$i]:(((in @ (esk3_1 @ (kpair @ X1 @ X3)) @ (dsetconstr @ (setunion @ (kpair @ X1 @ X3)) @ (epred1_1 @ (kpair @ X1 @ X3))))|~((in @ X1 @ (setunion @ (kpair @ X1 @ X3)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_40, c_0_33])])).
% 0.08/0.14 thf(c_0_46, plain, ![X72:$i, X73:$i]:(((~(epred1_1 @ X73 @ X72)|((X73)=(kpair @ (kfst @ X73) @ X72)))&(((X73)!=(kpair @ (kfst @ X73) @ X72))|(epred1_1 @ X73 @ X72)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
% 0.08/0.14 thf(c_0_47, negated_conjecture, ![X1:$i, X4:$i, X3:$i]:(((epred1_1 @ (kpair @ X1 @ X3) @ X4)|~((in @ X4 @ (setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))))), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 0.08/0.14 thf(c_0_48, negated_conjecture, ![X1:$i]:(((in @ (setunion @ (setadjoin @ X1 @ emptyset)) @ (setadjoin @ X1 @ emptyset))|~((in @ X1 @ (setadjoin @ X1 @ emptyset))))), inference(er,[status(thm)],[c_0_43])).
% 0.08/0.14 thf(c_0_49, negated_conjecture, ![X1:$i, X3:$i]:(((setunion @ (setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))=(ksnd @ (kpair @ X1 @ X3)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_37]), c_0_38])])).
% 0.08/0.14 thf(c_0_50, negated_conjecture, ![X1:$i, X3:$i]:(((in @ (esk3_1 @ (kpair @ X1 @ X3)) @ (setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))|~((in @ X1 @ (setunion @ (kpair @ X1 @ X3)))))), inference(rw,[status(thm)],[c_0_45, c_0_42])).
% 0.08/0.14 thf(c_0_51, plain, ![X1:$i, X3:$i]:((((X1)=(kpair @ (kfst @ X1) @ X3))|~((epred1_1 @ X1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_46])).
% 0.08/0.14 thf(c_0_52, negated_conjecture, ![X1:$i, X3:$i]:(((epred1_1 @ (kpair @ X1 @ X3) @ (ksnd @ (kpair @ X1 @ X3)))|~((in @ (esk3_1 @ (kpair @ X1 @ X3)) @ (setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49])).
% 0.08/0.14 thf(c_0_53, negated_conjecture, ![X1:$i, X3:$i]:((in @ (esk3_1 @ (kpair @ X1 @ X3)) @ (setadjoin @ (esk3_1 @ (kpair @ X1 @ X3)) @ emptyset))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50, c_0_37]), c_0_38])])).
% 0.08/0.14 thf(c_0_54, negated_conjecture, ![X1:$i, X4:$i, X3:$i]:((((X1)=(X3))|~((epred1_1 @ (kpair @ X4 @ X1) @ X3)))), inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_24, c_0_51])])).
% 0.08/0.14 thf(c_0_55, negated_conjecture, ![X1:$i, X3:$i]:((epred1_1 @ (kpair @ X1 @ X3) @ (ksnd @ (kpair @ X1 @ X3)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 0.08/0.14 thf(c_0_56, negated_conjecture, ((ksnd @ (kpair @ esk4_0 @ esk5_0))!=(esk5_0)), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.08/0.14 thf(c_0_57, negated_conjecture, ![X1:$i, X3:$i]:(((ksnd @ (kpair @ X1 @ X3))=(X3))), inference(spm,[status(thm)],[c_0_54, c_0_55])).
% 0.08/0.14 thf(c_0_58, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])]), ['proof']).
% 0.08/0.14 % SZS output end CNFRefutation
% 0.08/0.14 % Parsed axioms : 25
% 0.08/0.14 % Removed by relevancy pruning/SinE : 0
% 0.08/0.14 % Initial clauses : 28
% 0.08/0.14 % Removed in clause preprocessing : 15
% 0.08/0.14 % Initial clauses in saturation : 13
% 0.08/0.14 % Processed clauses : 79
% 0.08/0.14 % ...of these trivial : 0
% 0.08/0.14 % ...subsumed : 15
% 0.08/0.14 % ...remaining for further processing : 64
% 0.08/0.14 % Other redundant clauses eliminated : 7
% 0.08/0.14 % Clauses deleted for lack of memory : 0
% 0.08/0.14 % Backward-subsumed : 4
% 0.08/0.14 % Backward-rewritten : 11
% 0.08/0.14 % Generated clauses : 132
% 0.08/0.14 % ...of the previous two non-redundant : 117
% 0.08/0.14 % ...aggressively subsumed : 0
% 0.08/0.14 % Contextual simplify-reflections : 0
% 0.08/0.14 % Paramodulations : 123
% 0.08/0.14 % Factorizations : 0
% 0.08/0.14 % NegExts : 0
% 0.08/0.14 % Equation resolutions : 9
% 0.08/0.14 % Disequality decompositions : 0
% 0.08/0.14 % Total rewrite steps : 42
% 0.08/0.14 % ...of those cached : 26
% 0.08/0.14 % Propositional unsat checks : 0
% 0.08/0.14 % Propositional check models : 0
% 0.08/0.14 % Propositional check unsatisfiable : 0
% 0.08/0.14 % Propositional clauses : 0
% 0.08/0.14 % Propositional clauses after purity: 0
% 0.08/0.14 % Propositional unsat core size : 0
% 0.08/0.14 % Propositional preprocessing time : 0.000
% 0.08/0.14 % Propositional encoding time : 0.000
% 0.08/0.14 % Propositional solver time : 0.000
% 0.08/0.14 % Success case prop preproc time : 0.000
% 0.08/0.14 % Success case prop encoding time : 0.000
% 0.08/0.14 % Success case prop solver time : 0.000
% 0.08/0.14 % Current number of processed clauses : 33
% 0.08/0.14 % Positive orientable unit clauses : 12
% 0.08/0.14 % Positive unorientable unit clauses: 0
% 0.08/0.14 % Negative unit clauses : 0
% 0.08/0.14 % Non-unit-clauses : 21
% 0.08/0.14 % Current number of unprocessed clauses: 44
% 0.08/0.14 % ...number of literals in the above : 80
% 0.08/0.14 % Current number of archived formulas : 0
% 0.08/0.14 % Current number of archived clauses : 28
% 0.08/0.14 % Clause-clause subsumption calls (NU) : 142
% 0.08/0.14 % Rec. Clause-clause subsumption calls : 136
% 0.08/0.14 % Non-unit clause-clause subsumptions : 18
% 0.08/0.14 % Unit Clause-clause subsumption calls : 9
% 0.08/0.14 % Rewrite failures with RHS unbound : 0
% 0.08/0.14 % BW rewrite match attempts : 9
% 0.08/0.14 % BW rewrite match successes : 8
% 0.08/0.14 % Condensation attempts : 81
% 0.08/0.14 % Condensation successes : 1
% 0.08/0.14 % Termbank termtop insertions : 6665
% 0.08/0.14 % Search garbage collected termcells : 546
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.005 s
% 0.08/0.14 % System time : 0.003 s
% 0.08/0.14 % Total time : 0.008 s
% 0.08/0.14 % Maximum resident set size: 3648 pages
% 0.08/0.14
% 0.08/0.14 % -------------------------------------------------
% 0.08/0.14 % User time : 0.024 s
% 0.08/0.14 % System time : 0.011 s
% 0.08/0.14 % Total time : 0.036 s
% 0.08/0.14 % Maximum resident set size: 4864 pages
% 0.08/0.14 % E exiting
%------------------------------------------------------------------------------