%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SYO330^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.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 08:42:46 AM UTC 2026
% Result : Theorem 0.53s 0.41s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO330^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n002.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 16:48:52 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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.PxqLNDTpiK/E---3.1_1538941.p
% 0.53/0.41 % Version: 3.5.1-ho
% 0.53/0.41 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.53/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.41 % Starting post_as_ho1 with 1500s (5) cores
% 0.53/0.41 % Starting post_as_ho12 with 300s (1) cores
% 0.53/0.41 % Starting new_ho_3 with 300s (1) cores
% 0.53/0.41 % Starting ehoh_best2_full_lfho with 300s (1) cores
% 0.53/0.41 % post_as_ho1 with pid 1538954 completed with status 0
% 0.53/0.41 % Result found by post_as_ho1
% 0.53/0.41 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.53/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.41 % Starting post_as_ho1 with 1500s (5) cores
% 0.53/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.53/0.41 % No SInE strategy applied
% 0.53/0.41 % Search class: HGUNF-FFSF21-SSSFFSBN
% 0.53/0.41 % partial match(1): HGUSF-FFSF21-SSSFFSBN
% 0.53/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.53/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.53/0.41 % Starting post_as_ho1 with 151s (1) cores
% 0.53/0.41 % Starting lpo8_s with 136s (1) cores
% 0.53/0.41 % Starting post_as_ho10 with 136s (1) cores
% 0.53/0.41 % Starting ehoh_best_nonlift_nonlambdatoforall with 136s (1) cores
% 0.53/0.41 % post_as_ho1 with pid 1538959 completed with status 10
% 0.53/0.41 % Starting ho_unfolding_6 with 136s (1) cores
% 0.53/0.41 % SubtermCWHack with pid 1538958 completed with status 10
% 0.53/0.41 % Starting post_as_ho12 with 669s (1) cores
% 0.53/0.41 % lpo8_s with pid 1538960 completed with status 10
% 0.53/0.41 % post_as_ho12 with pid 1538968 completed with status 0
% 0.53/0.41 % Result found by post_as_ho12
% 0.53/0.41 % Preprocessing class: HSMSSMSSSSSNSSA.
% 0.53/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.53/0.41 % Starting post_as_ho1 with 1500s (5) cores
% 0.53/0.41 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.53/0.41 % No SInE strategy applied
% 0.53/0.41 % Search class: HGUNF-FFSF21-SSSFFSBN
% 0.53/0.41 % partial match(1): HGUSF-FFSF21-SSSFFSBN
% 0.53/0.41 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.53/0.41 % Starting SubtermCWHack with 136s (1) cores
% 0.53/0.41 % Starting post_as_ho1 with 151s (1) cores
% 0.53/0.41 % Starting lpo8_s with 136s (1) cores
% 0.53/0.41 % Starting post_as_ho10 with 136s (1) cores
% 0.53/0.41 % Starting ehoh_best_nonlift_nonlambdatoforall with 136s (1) cores
% 0.53/0.41 % post_as_ho1 with pid 1538959 completed with status 10
% 0.53/0.41 % Starting ho_unfolding_6 with 136s (1) cores
% 0.53/0.41 % SubtermCWHack with pid 1538958 completed with status 10
% 0.53/0.41 % Starting post_as_ho12 with 669s (1) cores
% 0.53/0.41 % Preprocessing time : 0.001 s
% 0.53/0.41 % Presaturation interreduction done
% 0.53/0.41
% 0.53/0.41 % Proof found!
% 0.53/0.41 % SZS status Theorem
% 0.53/0.41 % SZS output start CNFRefutation
% 0.53/0.41 thf(decl_23, type, cNUMBER: $i > $o).
% 0.53/0.41 thf(decl_24, type, cODD: $i > $o).
% 0.53/0.41 thf(decl_25, type, cEVEN: $i > $o).
% 0.53/0.41 thf(decl_26, type, cS: $i > $i).
% 0.53/0.41 thf(decl_27, type, c0: $i).
% 0.53/0.41 thf(decl_28, type, epred1_0: $o).
% 0.53/0.41 thf(decl_29, type, esk1_0: $i).
% 0.53/0.41 thf(decl_30, type, esk2_2: ($i > $o) > ($i > $o) > $i).
% 0.53/0.41 thf(cEVEN_ODD_4, conjecture, (((((((cEVEN @ c0)&![X1:$i]:(((cEVEN @ X1)=>(cEVEN @ (cS @ (cS @ X1))))))&(cODD @ (cS @ c0)))&![X1:$i]:(((cODD @ X1)=>(cODD @ (cS @ (cS @ X1))))))&![X2:$i > $o, X3:$i > $o]:(((((X2 @ c0)&(X3 @ c0))&![X4:$i]:((((X2 @ X4)&(X3 @ X4))=>((X2 @ (cS @ X4))&(X3 @ (cS @ X4))))))=>![X4:$i]:(((X2 @ X4)&(X3 @ X4))))))&![X1:$i]:(((cNUMBER @ X1)<=>((cEVEN @ X1)|(cODD @ X1)))))=>![X1:$i]:((cNUMBER @ X1))), file('/export/starexec/sandbox2/tmp/tmp.PxqLNDTpiK/E---3.1_1538941.p', cEVEN_ODD_4)).
% 0.53/0.41 thf(c_0_1, plain, ((epred1_0)<=>((((((cEVEN @ c0)&![X1:$i]:(((cEVEN @ X1)=>(cEVEN @ (cS @ (cS @ X1))))))&(cODD @ (cS @ c0)))&![X1:$i]:(((cODD @ X1)=>(cODD @ (cS @ (cS @ X1))))))&![X2:$i > $o, X3:$i > $o]:(((((X2 @ c0)&(X3 @ c0))&![X4:$i]:((((X2 @ X4)&(X3 @ X4))=>((X2 @ (cS @ X4))&(X3 @ (cS @ X4))))))=>![X4:$i]:(((X2 @ X4)&(X3 @ X4))))))&![X1:$i]:(((cNUMBER @ X1)<=>((cEVEN @ X1)|(cODD @ X1)))))), introduced(definition)).
% 0.53/0.41 thf(c_0_2, negated_conjecture, ~((((((((cEVEN @ c0)&![X1:$i]:(((cEVEN @ X1)=>(cEVEN @ (cS @ (cS @ X1))))))&(cODD @ (cS @ c0)))&![X1:$i]:(((cODD @ X1)=>(cODD @ (cS @ (cS @ X1))))))&![X2:$i > $o, X3:$i > $o]:(((((X2 @ c0)&(X3 @ c0))&![X4:$i]:((((X2 @ X4)&(X3 @ X4))=>((X2 @ (cS @ X4))&(X3 @ (cS @ X4))))))=>![X4:$i]:(((X2 @ X4)&(X3 @ X4))))))&![X1:$i]:(((cNUMBER @ X1)<=>((cEVEN @ X1)|(cODD @ X1)))))=>![X1:$i]:((cNUMBER @ X1)))), inference(assume_negation,[status(cth)],[cEVEN_ODD_4])).
% 0.53/0.41 thf(c_0_3, plain, ((epred1_0)=>((((((cEVEN @ c0)&![X1:$i]:(((cEVEN @ X1)=>(cEVEN @ (cS @ (cS @ X1))))))&(cODD @ (cS @ c0)))&![X1:$i]:(((cODD @ X1)=>(cODD @ (cS @ (cS @ X1))))))&![X2:$i > $o, X3:$i > $o]:(((((X2 @ c0)&(X3 @ c0))&![X4:$i]:((((X2 @ X4)&(X3 @ X4))=>((X2 @ (cS @ X4))&(X3 @ (cS @ X4))))))=>![X4:$i]:(((X2 @ X4)&(X3 @ X4))))))&![X1:$i]:(((cNUMBER @ X1)<=>((cEVEN @ X1)|(cODD @ X1)))))), inference(split_equiv,[status(thm)],[c_0_1])).
% 0.53/0.41 thf(c_0_4, negated_conjecture, ~(((epred1_0)=>![X1:$i]:((cNUMBER @ X1)))), inference(apply_def,[status(thm)],[c_0_2, c_0_1])).
% 0.53/0.41 thf(c_0_5, plain, ![X14:$i, X15:$i, X16:$i > $o, X17:$i > $o, X19:$i, X20:$i, X21:$i]:((((((((cEVEN @ c0)|~(epred1_0))&(~(cEVEN @ X14)|(cEVEN @ (cS @ (cS @ X14)))|~(epred1_0)))&((cODD @ (cS @ c0))|~(epred1_0)))&(~(cODD @ X15)|(cODD @ (cS @ (cS @ X15)))|~(epred1_0)))&(((((X16 @ X19)|((X16 @ (esk2_2 @ X16 @ X17))|(~(X16 @ c0)|~(X17 @ c0)))|~(epred1_0))&((X17 @ X20)|((X16 @ (esk2_2 @ X16 @ X17))|(~(X16 @ c0)|~(X17 @ c0)))|~(epred1_0)))&(((X16 @ X19)|((X17 @ (esk2_2 @ X16 @ X17))|(~(X16 @ c0)|~(X17 @ c0)))|~(epred1_0))&((X17 @ X20)|((X17 @ (esk2_2 @ X16 @ X17))|(~(X16 @ c0)|~(X17 @ c0)))|~(epred1_0))))&(((X16 @ X19)|(~(X16 @ (cS @ (esk2_2 @ X16 @ X17)))|~(X17 @ (cS @ (esk2_2 @ X16 @ X17)))|(~(X16 @ c0)|~(X17 @ c0)))|~(epred1_0))&((X17 @ X20)|(~(X16 @ (cS @ (esk2_2 @ X16 @ X17)))|~(X17 @ (cS @ (esk2_2 @ X16 @ X17)))|(~(X16 @ c0)|~(X17 @ c0)))|~(epred1_0)))))&((~(cNUMBER @ X21)|((cEVEN @ X21)|(cODD @ X21))|~(epred1_0))&((~(cEVEN @ X21)|(cNUMBER @ X21)|~(epred1_0))&(~(cODD @ X21)|(cNUMBER @ X21)|~(epred1_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_3])])])])])])])).
% 0.53/0.41 thf(c_0_6, negated_conjecture, ((epred1_0)&~(cNUMBER @ esk1_0)), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])])).
% 0.53/0.41 thf(c_0_7, plain, ![X1:$i, X3:$i > $o, X2:$i > $o]:(((X2 @ X1)|(X2 @ (esk2_2 @ X3 @ X2))|~((X3 @ c0))|~((X2 @ c0))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_8, negated_conjecture, (epred1_0), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.53/0.41 thf(c_0_9, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cEVEN @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_10, plain, ![X1:$i, X3:$i > $o, X2:$i > $o]:(((X2 @ (esk2_2 @ X3 @ X2))|(X2 @ X1)|~((X3 @ c0))|~((X2 @ c0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_7, c_0_8])])).
% 0.53/0.41 thf(c_0_11, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cEVEN @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_8])])).
% 0.53/0.41 thf(c_0_12, plain, ((cEVEN @ c0)|~((epred1_0))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_13, plain, ![X1:$i, X3:$i > $o, X2:$i > $o]:(((X2 @ X1)|(X3 @ (esk2_2 @ X3 @ X2))|~((X3 @ c0))|~((X2 @ c0))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_14, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cODD @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_15, plain, ![X1:$i, X22:$i > $i, X2:$i > $o]:(((X2 @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (X22 @ Z0)))) @ X2))|(X2 @ X1)|~((cEVEN @ (X22 @ c0)))|~((X2 @ c0)))), inference(spm,[status(thm)],[c_0_10, c_0_11])).
% 0.53/0.41 thf(c_0_16, plain, (cEVEN @ c0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_8])])).
% 0.53/0.41 thf(c_0_17, plain, ![X1:$i, X2:$i > $o, X3:$i > $o]:(((X2 @ (esk2_2 @ X2 @ X3))|(X3 @ X1)|~((X2 @ c0))|~((X3 @ c0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_8])])).
% 0.53/0.41 thf(c_0_18, plain, ![X1:$i]:(((cNUMBER @ X1)|~((cODD @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_8])])).
% 0.53/0.41 thf(c_0_19, plain, ((cODD @ (cS @ c0))|~((epred1_0))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_20, plain, ![X1:$i, X2:$i > $o]:(((X2 @ (esk2_2 @ cNUMBER @ X2))|(X2 @ X1)|~((X2 @ c0)))), inference(spm,[status(thm)],[c_0_15, c_0_16])).
% 0.53/0.41 thf(c_0_21, plain, ![X1:$i, X22:$i > $i, X2:$i > $o]:(((cNUMBER @ (X22 @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (X22 @ Z0)))) @ X2)))|(X2 @ X1)|~((cODD @ (X22 @ c0)))|~((X2 @ c0)))), inference(spm,[status(thm)],[c_0_17, c_0_18])).
% 0.53/0.41 thf(c_0_22, plain, (cODD @ (cS @ c0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_8])])).
% 0.53/0.41 thf(c_0_23, plain, ![X1:$i, X22:$i > $i]:(((cNUMBER @ (X22 @ (esk2_2 @ cNUMBER @ (^[Z0:$i]:((cNUMBER @ (X22 @ Z0)))))))|(cNUMBER @ (X22 @ X1))|~((cEVEN @ (X22 @ c0))))), inference(spm,[status(thm)],[c_0_20, c_0_11])).
% 0.53/0.41 thf(c_0_24, plain, ![X1:$i, X2:$i > $o]:(((cNUMBER @ (cS @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ X2)))|(X2 @ X1)|~((X2 @ c0)))), inference(spm,[status(thm)],[c_0_21, c_0_22])).
% 0.53/0.41 thf(c_0_25, plain, (cNUMBER @ c0), inference(spm,[status(thm)],[c_0_23, c_0_16])).
% 0.53/0.41 thf(c_0_26, plain, ![X1:$i, X2:$i > $o, X3:$i > $o]:(((X2 @ X1)|~((X2 @ (cS @ (esk2_2 @ X2 @ X3))))|~((X3 @ (cS @ (esk2_2 @ X2 @ X3))))|~((X2 @ c0))|~((X3 @ c0))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_27, plain, ![X1:$i]:(((cNUMBER @ (cS @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER)))|(cNUMBER @ X1))), inference(spm,[status(thm)],[c_0_24, c_0_25])).
% 0.53/0.41 thf(c_0_28, plain, ![X1:$i, X22:$i > $i, X2:$i > $o]:(((X2 @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (X22 @ Z0)))) @ X2))|(X2 @ X1)|~((cODD @ (X22 @ c0)))|~((X2 @ c0)))), inference(spm,[status(thm)],[c_0_10, c_0_18])).
% 0.53/0.41 thf(c_0_29, plain, ![X1:$i, X3:$i > $o, X2:$i > $o]:(((X2 @ X1)|~((X3 @ (cS @ (esk2_2 @ X2 @ X3))))|~((X2 @ (cS @ (esk2_2 @ X2 @ X3))))|~((X3 @ c0))|~((X2 @ c0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_8])])).
% 0.53/0.41 thf(c_0_30, plain, (cNUMBER @ (cS @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER))), inference(ef,[status(thm)],[c_0_27])).
% 0.53/0.41 thf(c_0_31, plain, ![X1:$i, X2:$i > $o]:(((X2 @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ X2))|(X2 @ X1)|~((X2 @ c0)))), inference(spm,[status(thm)],[c_0_28, c_0_22])).
% 0.53/0.41 thf(c_0_32, plain, ![X1:$i]:(((cNUMBER @ (cS @ X1))|~((cNUMBER @ (cS @ (cS @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER)))))|~((cNUMBER @ (cS @ c0))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29, c_0_30]), c_0_25])])).
% 0.53/0.41 thf(c_0_33, plain, ![X1:$i]:(((cODD @ (cS @ (cS @ X1)))|~((cODD @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_34, plain, ![X1:$i]:(((cEVEN @ X1)|(cODD @ X1)|~((cNUMBER @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_35, plain, ![X1:$i]:(((cNUMBER @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER))|(cNUMBER @ X1))), inference(spm,[status(thm)],[c_0_31, c_0_25])).
% 0.53/0.41 thf(c_0_36, plain, ![X1:$i]:(((cEVEN @ (cS @ (cS @ X1)))|~((cEVEN @ X1))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_37, plain, ![X1:$i]:(((cNUMBER @ (cS @ X1))|~((cODD @ (cS @ (cS @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER)))))|~((cNUMBER @ (cS @ c0))))), inference(spm,[status(thm)],[c_0_32, c_0_18])).
% 0.53/0.41 thf(c_0_38, plain, ![X1:$i]:(((cODD @ (cS @ (cS @ X1)))|~((cODD @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_8])])).
% 0.53/0.41 thf(c_0_39, plain, ![X1:$i]:(((cEVEN @ X1)|(cODD @ X1)|~((cNUMBER @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_8])])).
% 0.53/0.41 thf(c_0_40, plain, (cNUMBER @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER)), inference(ef,[status(thm)],[c_0_35])).
% 0.53/0.41 thf(c_0_41, plain, ![X1:$i]:(((cNUMBER @ (cS @ X1))|~((cEVEN @ (cS @ (cS @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER)))))|~((cNUMBER @ (cS @ c0))))), inference(spm,[status(thm)],[c_0_32, c_0_11])).
% 0.53/0.41 thf(c_0_42, plain, ![X1:$i]:(((cEVEN @ (cS @ (cS @ X1)))|~((cEVEN @ X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_8])])).
% 0.53/0.41 thf(c_0_43, plain, ![X1:$i, X3:$i > $o, X2:$i > $o]:(((X2 @ X1)|~((X3 @ (cS @ (esk2_2 @ X3 @ X2))))|~((X2 @ (cS @ (esk2_2 @ X3 @ X2))))|~((X3 @ c0))|~((X2 @ c0))|~((epred1_0)))), inference(split_conjunct,[status(thm)],[c_0_5])).
% 0.53/0.41 thf(c_0_44, plain, ![X1:$i]:(((cNUMBER @ (cS @ X1))|~((cODD @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER)))|~((cNUMBER @ (cS @ c0))))), inference(spm,[status(thm)],[c_0_37, c_0_38])).
% 0.53/0.41 thf(c_0_45, plain, ((cEVEN @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER))|(cODD @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER))), inference(spm,[status(thm)],[c_0_39, c_0_40])).
% 0.53/0.41 thf(c_0_46, plain, ![X1:$i]:(((cNUMBER @ (cS @ X1))|~((cEVEN @ (esk2_2 @ (^[Z0:$i]:((cNUMBER @ (cS @ Z0)))) @ cNUMBER)))|~((cNUMBER @ (cS @ c0))))), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 0.53/0.41 thf(c_0_47, plain, ![X1:$i, X3:$i > $o, X2:$i > $o]:(((X2 @ X1)|~((X3 @ (cS @ (esk2_2 @ X3 @ X2))))|~((X2 @ (cS @ (esk2_2 @ X3 @ X2))))|~((X3 @ c0))|~((X2 @ c0)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_8])])).
% 0.53/0.41 thf(c_0_48, plain, ![X1:$i]:(((cNUMBER @ (cS @ X1))|~((cNUMBER @ (cS @ c0))))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44, c_0_45]), c_0_46])).
% 0.53/0.41 thf(c_0_49, plain, ![X1:$i, X2:$i > $o]:(((X2 @ X1)|~((X2 @ (cS @ (esk2_2 @ (^[Z0:$i]:(($true))) @ X2))))|~((X2 @ c0)))), inference(primitive_enumeration,[status(thm)],[c_0_47])).
% 0.53/0.41 thf(c_0_50, plain, ![X1:$i]:((cNUMBER @ (cS @ X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48, c_0_18]), c_0_22])])).
% 0.53/0.41 thf(c_0_51, negated_conjecture, ~((cNUMBER @ esk1_0)), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.53/0.41 thf(c_0_52, plain, ![X1:$i]:((cNUMBER @ X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49, c_0_50]), c_0_25])])).
% 0.53/0.41 thf(c_0_53, negated_conjecture, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_52])]), ['proof']).
% 0.53/0.41 % SZS output end CNFRefutation
% 0.53/0.41 % Parsed axioms : 6
% 0.53/0.41 % Removed by relevancy pruning/SinE : 0
% 0.53/0.41 % Initial clauses : 20
% 0.53/0.41 % Removed in clause preprocessing : 5
% 0.53/0.41 % Initial clauses in saturation : 15
% 0.53/0.41 % Processed clauses : 458
% 0.53/0.41 % ...of these trivial : 10
% 0.53/0.41 % ...subsumed : 153
% 0.53/0.41 % ...remaining for further processing : 295
% 0.53/0.41 % Other redundant clauses eliminated : 56
% 0.53/0.41 % Clauses deleted for lack of memory : 0
% 0.53/0.41 % Backward-subsumed : 81
% 0.53/0.41 % Backward-rewritten : 103
% 0.53/0.41 % Generated clauses : 3473
% 0.53/0.41 % ...of the previous two non-redundant : 2733
% 0.53/0.41 % ...aggressively subsumed : 0
% 0.53/0.41 % Contextual simplify-reflections : 4
% 0.53/0.41 % Paramodulations : 3186
% 0.53/0.41 % Factorizations : 76
% 0.53/0.41 % NegExts : 0
% 0.53/0.41 % Equation resolutions : 157
% 0.53/0.41 % Disequality decompositions : 0
% 0.53/0.41 % Total rewrite steps : 866
% 0.53/0.41 % ...of those cached : 777
% 0.53/0.41 % Propositional unsat checks : 0
% 0.53/0.41 % Propositional check models : 0
% 0.53/0.41 % Propositional check unsatisfiable : 0
% 0.53/0.41 % Propositional clauses : 0
% 0.53/0.41 % Propositional clauses after purity: 0
% 0.53/0.41 % Propositional unsat core size : 0
% 0.53/0.41 % Propositional preprocessing time : 0.000
% 0.53/0.41 % Propositional encoding time : 0.000
% 0.53/0.41 % Propositional solver time : 0.000
% 0.53/0.41 % Success case prop preproc time : 0.000
% 0.53/0.41 % Success case prop encoding time : 0.000
% 0.53/0.41 % Success case prop solver time : 0.000
% 0.53/0.41 % Current number of processed clauses : 96
% 0.53/0.41 % Positive orientable unit clauses : 17
% 0.53/0.41 % Positive unorientable unit clauses: 0
% 0.53/0.41 % Negative unit clauses : 2
% 0.53/0.41 % Non-unit-clauses : 77
% 0.53/0.41 % Current number of unprocessed clauses: 1569
% 0.53/0.41 % ...number of literals in the above : 5619
% 0.53/0.41 % Current number of archived formulas : 0
% 0.53/0.41 % Current number of archived clauses : 199
% 0.53/0.41 % Clause-clause subsumption calls (NU) : 2980
% 0.53/0.41 % Rec. Clause-clause subsumption calls : 2410
% 0.53/0.41 % Non-unit clause-clause subsumptions : 195
% 0.53/0.41 % Unit Clause-clause subsumption calls : 166
% 0.53/0.41 % Rewrite failures with RHS unbound : 0
% 0.53/0.41 % BW rewrite match attempts : 144
% 0.53/0.41 % BW rewrite match successes : 86
% 0.53/0.41 % Condensation attempts : 0
% 0.53/0.41 % Condensation successes : 0
% 0.53/0.41 % Termbank termtop insertions : 282731
% 0.53/0.41 % Search garbage collected termcells : 315
% 0.53/0.41
% 0.53/0.41 % -------------------------------------------------
% 0.53/0.41 % User time : 0.219 s
% 0.53/0.41 % System time : 0.021 s
% 0.53/0.41 % Total time : 0.240 s
% 0.53/0.41 % Maximum resident set size: 3584 pages
% 0.53/0.41
% 0.53/0.41 % -------------------------------------------------
% 0.53/0.41 % User time : 0.599 s
% 0.53/0.41 % System time : 0.051 s
% 0.53/0.41 % Total time : 0.649 s
% 0.53/0.41 % Maximum resident set size: 4864 pages
% 0.53/0.41 % E exiting
%------------------------------------------------------------------------------