0.00/0.05	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.07	% Command  : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.18/0.44	% Computer : n021.cluster.edu
0.18/0.44	% Model    : x86_64 x86_64
0.18/0.44	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.18/0.44	% Memory   : 8046.5625MB
0.18/0.44	% OS       : Linux 6.8.0-71-generic
0.18/0.44	% CPULimit : 1440
0.18/0.44	% WCLimit  : 180
0.18/0.44	% DateTime : Mon Jul 27 14:27:38 UTC 2026
0.18/0.44	% CPUTime  : 
0.18/0.44	Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM
0.18/0.50	Running higher-order theorem proving
0.26/0.57	Running: /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.2fwxYblIuK/E---3.1_853989.p
0.33/1.03	% Version: 3.5.1-ho
0.33/1.03	% Preprocessing class: HSLMSMSSLLLCHSA.
0.33/1.03	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
0.33/1.03	% Starting lpo1_fix with 540s (3) cores
0.33/1.03	% Starting full_lambda_9 with 180s (1) cores
0.33/1.03	% Starting almost_fo_4 with 180s (1) cores
0.33/1.03	% Starting new_ho_9 with 180s (1) cores
0.33/1.03	% Starting pre_casc_4 with 180s (1) cores
0.33/1.03	% Starting ho_unfolding_6 with 180s (1) cores
0.33/1.03	% full_lambda_9 with pid 854005 completed with status 0
0.33/1.03	% Result found by full_lambda_9
0.33/1.03	% Preprocessing class: HSLMSMSSLLLCHSA.
0.33/1.03	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
0.33/1.03	% Starting lpo1_fix with 540s (3) cores
0.33/1.03	% Starting full_lambda_9 with 180s (1) cores
0.33/1.03	% (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
0.33/1.03	% SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
0.33/1.03	% Search class: HGHSM-FSLM32-DHSMMSBN
0.33/1.03	% partial match(1): HGHSM-FSLM32-MHSMMSBN
0.33/1.03	% Scheduled 12 strats onto 1 cores with 180 seconds (180 total)
0.33/1.03	% Starting SubtermCWHack with 17s (1) cores
0.33/1.03	% SubtermCWHack with pid 854014 completed with status 0
0.33/1.03	% Result found by SubtermCWHack
0.33/1.03	% Preprocessing class: HSLMSMSSLLLCHSA.
0.33/1.03	% Scheduled 6 strats onto 8 cores with 180 seconds (1440 total)
0.33/1.03	% Starting lpo1_fix with 540s (3) cores
0.33/1.03	% Starting full_lambda_9 with 180s (1) cores
0.33/1.03	% (lift_lambdas = 1, lambda_to_forall = 0,unroll_only_formulas = 1, sine = GSinE(CountFormulas,hypos,4,,3,20000,3.0,true))
0.33/1.03	% SinE strategy is GSinE(CountFormulas,hypos,4,,3,20000,3.0,true)
0.33/1.03	% Search class: HGHSM-FSLM32-DHSMMSBN
0.33/1.03	% partial match(1): HGHSM-FSLM32-MHSMMSBN
0.33/1.03	% Scheduled 12 strats onto 1 cores with 180 seconds (180 total)
0.33/1.03	% Starting SubtermCWHack with 17s (1) cores
0.33/1.03	% Preprocessing time       : 0.007 s
0.33/1.03	
0.33/1.03	% Proof found!
0.33/1.03	% SZS status Theorem
0.33/1.03	% SZS output start CNFRefutation
0.33/1.03	thf(decl_23, type, is_of: $i > ($i > $o) > $o).
0.33/1.03	thf(decl_24, type, all_of: ($i > $o) > ($i > $o) > $o).
0.33/1.03	thf(decl_26, type, in: $i > $i > $o).
0.33/1.03	thf(decl_48, type, ordsucc: $i > $i).
0.33/1.03	thf(decl_78, type, e_is: $i > $i > $i > $o).
0.33/1.03	thf(decl_124, type, nat: $i).
0.33/1.03	thf(decl_125, type, n_is: $i > $i > $o).
0.33/1.03	thf(decl_131, type, n_1: $i).
0.33/1.03	thf(decl_143, type, n_pl: $i > $i > $i).
0.33/1.03	thf(decl_156, type, esk1_0: $i).
0.33/1.03	thf(decl_157, type, esk2_0: $i).
0.33/1.03	thf(decl_158, type, esk3_0: $i).
0.33/1.03	thf(decl_171, type, epred5_1: $i > $i > $o).
0.33/1.03	thf(decl_174, type, epred8_2: $i > $i > $i > $o).
0.33/1.03	thf(def_all_of, axiom, ((all_of)=(^[X3:$i > $o, X2:$i > $o]:(![X4:$i]:((((is_of @ X4 @ X3))=>((X2 @ X4))))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', def_all_of)).
0.33/1.03	thf(def_is_of, axiom, ((is_of)=(^[X1:$i, X2:$i > $o]:((X2 @ X1)))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', def_is_of)).
0.33/1.03	thf(def_e_is, axiom, ((e_is)=(^[X1:$i, X60:$i, X61:$i]:(((X60)=(X61))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', def_e_is)).
0.33/1.03	thf(def_n_is, axiom, ((n_is)=(^[Z0:$i, Z1:$i]:(((Z0)=(Z1))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', def_n_is)).
0.33/1.03	thf(satz20b, conjecture, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X271:$i]:((in @ X271 @ nat))) @ (^[X272:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ nat))) @ (^[X4:$i]:((((n_is @ X1 @ X272))<=((n_is @ (n_pl @ X1 @ X4) @ (n_pl @ X272 @ X4))))))))))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', satz20b)).
0.33/1.03	thf(satz4f, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X217:$i]:((in @ X217 @ nat))) @ (^[X218:$i]:((n_is @ (ordsucc @ (n_pl @ X1 @ X218)) @ (n_pl @ X1 @ (ordsucc @ X218))))))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', satz4f)).
0.33/1.03	thf(satz4e, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((n_is @ (ordsucc @ X1) @ (n_pl @ X1 @ n_1))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', satz4e)).
0.33/1.03	thf(satz4h, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X245:$i]:((in @ X245 @ nat))) @ (^[X246:$i]:((n_is @ (ordsucc @ (n_pl @ X1 @ X246)) @ (n_pl @ (ordsucc @ X1) @ X246)))))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', satz4h)).
0.33/1.03	thf(satz4g, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((n_is @ (ordsucc @ X1) @ (n_pl @ n_1 @ X1))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', satz4g)).
0.33/1.03	thf(satz5, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X233:$i]:((in @ X233 @ nat))) @ (^[X234:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ nat))) @ (^[X4:$i]:((n_is @ (n_pl @ (n_pl @ X1 @ X234) @ X4) @ (n_pl @ X1 @ (n_pl @ X234 @ X4)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', satz5)).
0.33/1.03	thf(n_1_p, axiom, (is_of @ n_1 @ (^[X1:$i]:((in @ X1 @ nat)))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', n_1_p)).
0.33/1.03	thf(satz6, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X283:$i]:((in @ X283 @ nat))) @ (^[X284:$i]:((n_is @ (n_pl @ X1 @ X284) @ (n_pl @ X284 @ X1)))))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', satz6)).
0.33/1.03	thf(satz8a, axiom, (all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X207:$i]:((in @ X207 @ nat))) @ (^[X208:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ nat))) @ (^[X4:$i]:((((n_is @ (n_pl @ X1 @ X208) @ (n_pl @ X1 @ X4)))=>((n_is @ X208 @ X4)))))))))))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', satz8a)).
0.33/1.03	thf(ordsucc_inj, axiom, ![X1:$i, X158:$i]:((((ordsucc @ X1)=(ordsucc @ X158))=>((X1)=(X158)))), file('/export/starexec/sandbox/tmp/tmp.2fwxYblIuK/E---3.1_853989.p', ordsucc_inj)).
0.33/1.03	thf(c_0_14, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:(((((Z0 @ X4)))=>((Z1 @ X4))))))), inference(fof_simplification,[status(thm)],[def_all_of])).
0.33/1.03	thf(c_0_15, plain, ((is_of)=(^[Z0:$i, Z1:$i > $o]:((Z1 @ Z0)))), inference(fof_simplification,[status(thm)],[def_is_of])).
0.33/1.03	thf(c_0_16, plain, ((e_is)=(^[Z0:$i, Z1:$i, Z2:$i]:(((Z1)=(Z2))))), inference(fof_simplification,[status(thm)],[def_e_is])).
0.33/1.03	thf(c_0_17, plain, ((all_of)=(^[Z0:$i > $o, Z1:$i > $o]:(![X4:$i]:(((((Z0 @ X4)))=>((Z1 @ X4))))))), inference(apply_def,[status(thm)],[c_0_14, c_0_15])).
0.33/1.03	thf(c_0_18, axiom, ((n_is)=(^[Z0:$i, Z1:$i]:(((Z0)=(Z1))))), inference(apply_def,[status(thm)],[def_n_is, c_0_16])).
0.33/1.03	thf(c_0_19, negated_conjecture, ~((all_of @ (^[X1:$i]:((in @ X1 @ nat))) @ (^[X1:$i]:((all_of @ (^[X271:$i]:((in @ X271 @ nat))) @ (^[X272:$i]:((all_of @ (^[X4:$i]:((in @ X4 @ nat))) @ (^[X4:$i]:((((n_is @ X1 @ X272))<=((n_is @ (n_pl @ X1 @ X4) @ (n_pl @ X272 @ X4)))))))))))))), inference(assume_negation,[status(cth)],[satz20b])).
0.33/1.03	thf(c_0_20, plain, ![X375:$i]:(((in @ X375 @ nat)=>![X374:$i]:(((in @ X374 @ nat)=>((ordsucc @ (n_pl @ X375 @ X374))=(n_pl @ X375 @ (ordsucc @ X374))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4f]), c_0_17]), c_0_18])).
0.33/1.03	thf(c_0_21, negated_conjecture, ~(![X368:$i]:(((in @ X368 @ nat)=>![X367:$i]:(((in @ X367 @ nat)=>![X366:$i]:(((in @ X366 @ nat)=>(((n_pl @ X368 @ X366)=(n_pl @ X367 @ X366))=>((X368)=(X367)))))))))), inference(fof_simplification,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_19]), c_0_17]), c_0_18])])).
0.33/1.03	thf(c_0_22, plain, ![X910:$i, X911:$i]:(((~(epred5_1 @ X911 @ X910)|((X911)=(ordsucc @ X910)))&(((X911)!=(ordsucc @ X910))|(epred5_1 @ X911 @ X910)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
0.33/1.03	thf(c_0_23, plain, ![X535:$i, X536:$i]:((~(in @ X535 @ nat)|(~(in @ X536 @ nat)|((ordsucc @ (n_pl @ X535 @ X536))=(n_pl @ X535 @ (ordsucc @ X536)))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])])).
0.33/1.03	thf(c_0_24, negated_conjecture, ((in @ esk1_0 @ nat)&((in @ esk2_0 @ nat)&((in @ esk3_0 @ nat)&(((n_pl @ esk1_0 @ esk3_0)=(n_pl @ esk2_0 @ esk3_0))&((esk1_0)!=(esk2_0)))))), inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])).
0.33/1.03	thf(c_0_25, plain, ![X1:$i, X4:$i]:(((epred5_1 @ X1 @ X4)|((X1)!=(ordsucc @ X4)))), inference(split_conjunct,[status(thm)],[c_0_22])).
0.33/1.03	thf(c_0_26, plain, ![X1:$i, X4:$i]:((((ordsucc @ (n_pl @ X1 @ X4))=(n_pl @ X1 @ (ordsucc @ X4)))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_23])).
0.33/1.03	thf(c_0_27, negated_conjecture, ((n_pl @ esk1_0 @ esk3_0)=(n_pl @ esk2_0 @ esk3_0)), inference(split_conjunct,[status(thm)],[c_0_24])).
0.33/1.03	thf(c_0_28, negated_conjecture, (in @ esk3_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_24])).
0.33/1.03	thf(c_0_29, negated_conjecture, (in @ esk2_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_24])).
0.33/1.03	thf(c_0_30, plain, ![X1:$i]:((epred5_1 @ (ordsucc @ X1) @ X1)), inference(er,[status(thm)],[c_0_25])).
0.33/1.03	thf(c_0_31, negated_conjecture, ((ordsucc @ (n_pl @ esk1_0 @ esk3_0))=(n_pl @ esk2_0 @ (ordsucc @ esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_27]), c_0_28]), c_0_29])])).
0.33/1.03	thf(c_0_32, negated_conjecture, (in @ esk1_0 @ nat), inference(split_conjunct,[status(thm)],[c_0_24])).
0.33/1.03	thf(c_0_33, plain, ![X408:$i]:(((in @ X408 @ nat)=>((ordsucc @ X408)=(n_pl @ X408 @ n_1)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4e]), c_0_17]), c_0_18])).
0.33/1.03	thf(c_0_34, plain, ![X385:$i]:(((in @ X385 @ nat)=>![X384:$i]:(((in @ X384 @ nat)=>((ordsucc @ (n_pl @ X385 @ X384))=(n_pl @ (ordsucc @ X385) @ X384)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4h]), c_0_17]), c_0_18])).
0.33/1.03	thf(c_0_35, plain, ![X407:$i]:(((in @ X407 @ nat)=>((ordsucc @ X407)=(n_pl @ n_1 @ X407)))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz4g]), c_0_17]), c_0_18])).
0.33/1.03	thf(c_0_36, plain, (epred5_1 @ (n_pl @ esk2_0 @ (ordsucc @ esk3_0)) @ (n_pl @ esk1_0 @ esk3_0)), inference(spm,[status(thm)],[c_0_30, c_0_31])).
0.33/1.03	thf(c_0_37, negated_conjecture, ((n_pl @ esk2_0 @ (ordsucc @ esk3_0))=(n_pl @ esk1_0 @ (ordsucc @ esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_31]), c_0_28]), c_0_32])])).
0.33/1.03	thf(c_0_38, plain, ![X569:$i]:((~(in @ X569 @ nat)|((ordsucc @ X569)=(n_pl @ X569 @ n_1)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_33])])])).
0.33/1.03	thf(c_0_39, plain, ![X545:$i, X546:$i]:((~(in @ X545 @ nat)|(~(in @ X546 @ nat)|((ordsucc @ (n_pl @ X545 @ X546))=(n_pl @ (ordsucc @ X545) @ X546))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_34])])])])).
0.33/1.03	thf(c_0_40, plain, ![X568:$i]:((~(in @ X568 @ nat)|((ordsucc @ X568)=(n_pl @ n_1 @ X568)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_35])])])).
0.33/1.03	thf(c_0_41, plain, (epred5_1 @ (n_pl @ esk1_0 @ (ordsucc @ esk3_0)) @ (n_pl @ esk1_0 @ esk3_0)), inference(rw,[status(thm)],[c_0_36, c_0_37])).
0.33/1.03	thf(c_0_42, plain, ![X1:$i]:((((ordsucc @ X1)=(n_pl @ X1 @ n_1))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_38])).
0.33/1.03	thf(c_0_43, plain, ![X1:$i, X4:$i]:((((ordsucc @ (n_pl @ X1 @ X4))=(n_pl @ (ordsucc @ X1) @ X4))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_39])).
0.33/1.03	thf(c_0_44, plain, ![X1:$i]:((((ordsucc @ X1)=(n_pl @ n_1 @ X1))|~((in @ X1 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_40])).
0.33/1.03	thf(c_0_45, plain, ![X1:$i, X4:$i]:((((X1)=(ordsucc @ X4))|~((epred5_1 @ X1 @ X4)))), inference(split_conjunct,[status(thm)],[c_0_22])).
0.33/1.03	thf(c_0_46, plain, (epred5_1 @ (n_pl @ esk1_0 @ (n_pl @ esk3_0 @ n_1)) @ (n_pl @ esk1_0 @ esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_42]), c_0_28])])).
0.33/1.03	thf(c_0_47, negated_conjecture, ((n_pl @ (ordsucc @ esk2_0) @ esk3_0)=(n_pl @ esk1_0 @ (ordsucc @ esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43, c_0_27]), c_0_31]), c_0_37]), c_0_28]), c_0_29])])).
0.33/1.03	thf(c_0_48, plain, (epred5_1 @ (n_pl @ esk1_0 @ (n_pl @ n_1 @ esk3_0)) @ (n_pl @ esk1_0 @ esk3_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41, c_0_44]), c_0_28])])).
0.33/1.03	thf(c_0_49, plain, ((n_pl @ esk1_0 @ (ordsucc @ esk3_0))=(n_pl @ esk1_0 @ (n_pl @ esk3_0 @ n_1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_46]), c_0_31]), c_0_37])).
0.33/1.03	thf(c_0_50, plain, ![X378:$i]:(((in @ X378 @ nat)=>![X377:$i]:(((in @ X377 @ nat)=>![X376:$i]:(((in @ X376 @ nat)=>((n_pl @ (n_pl @ X378 @ X377) @ X376)=(n_pl @ X378 @ (n_pl @ X377 @ X376))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz5]), c_0_17]), c_0_18])).
0.33/1.03	thf(c_0_51, negated_conjecture, ((n_pl @ (n_pl @ n_1 @ esk2_0) @ esk3_0)=(n_pl @ esk1_0 @ (ordsucc @ esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_44]), c_0_29])])).
0.33/1.03	thf(c_0_52, plain, ((n_pl @ esk1_0 @ (n_pl @ esk3_0 @ n_1))=(n_pl @ esk1_0 @ (n_pl @ n_1 @ esk3_0))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_48]), c_0_31]), c_0_37]), c_0_49])).
0.33/1.03	thf(c_0_53, plain, ![X537:$i, X538:$i, X539:$i]:((~(in @ X537 @ nat)|(~(in @ X538 @ nat)|(~(in @ X539 @ nat)|((n_pl @ (n_pl @ X537 @ X538) @ X539)=(n_pl @ X537 @ (n_pl @ X538 @ X539))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])])).
0.33/1.03	thf(c_0_54, plain, (in @ n_1 @ nat), inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[n_1_p]), c_0_15])).
0.33/1.03	thf(c_0_55, plain, ![X392:$i]:(((in @ X392 @ nat)=>![X391:$i]:(((in @ X391 @ nat)=>((n_pl @ X392 @ X391)=(n_pl @ X391 @ X392)))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz6]), c_0_17]), c_0_18])).
0.33/1.03	thf(c_0_56, plain, ![X903:$i, X904:$i, X905:$i]:(((~(epred8_2 @ X905 @ X904 @ X903)|((X904)=(n_pl @ X905 @ X903)))&(((X904)!=(n_pl @ X905 @ X903))|(epred8_2 @ X905 @ X904 @ X903)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])).
0.33/1.03	thf(c_0_57, negated_conjecture, ((ordsucc @ (n_pl @ esk1_0 @ esk3_0))=(n_pl @ esk1_0 @ (ordsucc @ esk3_0))), inference(rw,[status(thm)],[c_0_31, c_0_37])).
0.33/1.03	thf(c_0_58, negated_conjecture, ((n_pl @ (n_pl @ n_1 @ esk2_0) @ esk3_0)=(n_pl @ esk1_0 @ (n_pl @ n_1 @ esk3_0))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51, c_0_49]), c_0_52])).
0.33/1.03	thf(c_0_59, plain, ![X1:$i, X4:$i, X5:$i]:((((n_pl @ (n_pl @ X1 @ X4) @ X5)=(n_pl @ X1 @ (n_pl @ X4 @ X5)))|~((in @ X1 @ nat))|~((in @ X4 @ nat))|~((in @ X5 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_53])).
0.33/1.03	thf(c_0_60, plain, (in @ n_1 @ nat), inference(split_conjunct,[status(thm)],[c_0_54])).
0.33/1.03	thf(c_0_61, plain, ![X552:$i, X553:$i]:((~(in @ X552 @ nat)|(~(in @ X553 @ nat)|((n_pl @ X552 @ X553)=(n_pl @ X553 @ X552))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])])).
0.33/1.03	thf(c_0_62, plain, ![X1:$i, X4:$i, X5:$i]:(((epred8_2 @ X4 @ X1 @ X5)|((X1)!=(n_pl @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_56])).
0.33/1.03	thf(c_0_63, negated_conjecture, ((ordsucc @ (n_pl @ esk1_0 @ esk3_0))=(n_pl @ esk1_0 @ (n_pl @ n_1 @ esk3_0))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57, c_0_49]), c_0_52])).
0.33/1.03	thf(c_0_64, negated_conjecture, ((n_pl @ esk1_0 @ (n_pl @ n_1 @ esk3_0))=(n_pl @ n_1 @ (n_pl @ esk1_0 @ esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58, c_0_59]), c_0_27]), c_0_28]), c_0_29]), c_0_60])])).
0.33/1.03	thf(c_0_65, plain, ![X1:$i, X4:$i]:((((n_pl @ X1 @ X4)=(n_pl @ X4 @ X1))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(split_conjunct,[status(thm)],[c_0_61])).
0.33/1.03	thf(c_0_66, plain, ![X1:$i, X4:$i]:((epred8_2 @ X1 @ (n_pl @ X1 @ X4) @ X4)), inference(er,[status(thm)],[c_0_62])).
0.33/1.03	thf(c_0_67, negated_conjecture, ((ordsucc @ (n_pl @ esk1_0 @ esk3_0))=(n_pl @ n_1 @ (n_pl @ esk1_0 @ esk3_0))), inference(rw,[status(thm)],[c_0_63, c_0_64])).
0.33/1.03	thf(c_0_68, plain, ![X1:$i, X4:$i]:((((ordsucc @ (n_pl @ X1 @ X4))=(n_pl @ X4 @ (ordsucc @ X1)))|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(spm,[status(thm)],[c_0_26, c_0_65])).
0.33/1.03	thf(c_0_69, plain, ![X373:$i]:(((in @ X373 @ nat)=>![X372:$i]:(((in @ X372 @ nat)=>![X371:$i]:(((in @ X371 @ nat)=>(((n_pl @ X373 @ X372)=(n_pl @ X373 @ X371))=>((X372)=(X371))))))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[satz8a]), c_0_17]), c_0_18])).
0.33/1.03	thf(c_0_70, plain, ![X1:$i, X4:$i]:(((epred8_2 @ X1 @ (n_pl @ X4 @ X1) @ X4)|~((in @ X1 @ nat))|~((in @ X4 @ nat)))), inference(spm,[status(thm)],[c_0_66, c_0_65])).
0.33/1.03	thf(c_0_71, plain, ![X625:$i, X626:$i]:((((ordsucc @ X625)!=(ordsucc @ X626))|((X625)=(X626)))), inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ordsucc_inj])])])).
0.33/1.03	thf(c_0_72, plain, ![X4:$i, X1:$i]:(((epred5_1 @ (n_pl @ X1 @ (ordsucc @ X4)) @ (n_pl @ X1 @ X4))|~((in @ X4 @ nat))|~((in @ X1 @ nat)))), inference(spm,[status(thm)],[c_0_30, c_0_26])).
0.33/1.03	thf(c_0_73, negated_conjecture, ((n_pl @ esk3_0 @ (ordsucc @ esk1_0))=(n_pl @ n_1 @ (n_pl @ esk1_0 @ esk3_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_68]), c_0_32]), c_0_28])])).
0.33/1.03	thf(c_0_74, plain, ![X532:$i, X533:$i, X534:$i]:((~(in @ X532 @ nat)|(~(in @ X533 @ nat)|(~(in @ X534 @ nat)|(((n_pl @ X532 @ X533)!=(n_pl @ X532 @ X534))|((X533)=(X534))))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_69])])])])).
0.33/1.03	thf(c_0_75, plain, ![X1:$i, X4:$i, X5:$i]:((((X4)=(n_pl @ X1 @ X5))|~((epred8_2 @ X1 @ X4 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_56])).
0.33/1.03	thf(c_0_76, negated_conjecture, (epred8_2 @ esk3_0 @ (n_pl @ esk1_0 @ esk3_0) @ esk2_0), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_27]), c_0_28]), c_0_29])])).
0.33/1.03	thf(c_0_77, plain, ![X1:$i, X4:$i]:((((X1)=(X4))|((ordsucc @ X1)!=(ordsucc @ X4)))), inference(split_conjunct,[status(thm)],[c_0_71])).
0.33/1.03	thf(c_0_78, plain, (epred5_1 @ (n_pl @ n_1 @ (n_pl @ esk1_0 @ esk3_0)) @ (n_pl @ esk3_0 @ esk1_0)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72, c_0_73]), c_0_32]), c_0_28])])).
0.33/1.03	thf(c_0_79, plain, ![X1:$i, X4:$i, X5:$i]:((((X4)=(X5))|~((in @ X1 @ nat))|~((in @ X4 @ nat))|~((in @ X5 @ nat))|((n_pl @ X1 @ X4)!=(n_pl @ X1 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_74])).
0.33/1.03	thf(c_0_80, plain, ((n_pl @ esk3_0 @ esk2_0)=(n_pl @ esk1_0 @ esk3_0)), inference(spm,[status(thm)],[c_0_75, c_0_76])).
0.33/1.03	thf(c_0_81, negated_conjecture, ![X1:$i]:((((X1)=(n_pl @ esk1_0 @ esk3_0))|((ordsucc @ X1)!=(n_pl @ n_1 @ (n_pl @ esk1_0 @ esk3_0))))), inference(spm,[status(thm)],[c_0_77, c_0_67])).
0.33/1.03	thf(c_0_82, plain, ((ordsucc @ (n_pl @ esk3_0 @ esk1_0))=(n_pl @ n_1 @ (n_pl @ esk1_0 @ esk3_0))), inference(spm,[status(thm)],[c_0_45, c_0_78])).
0.33/1.03	thf(c_0_83, plain, ![X1:$i]:((((esk2_0)=(X1))|((n_pl @ esk3_0 @ X1)!=(n_pl @ esk1_0 @ esk3_0))|~((in @ X1 @ nat)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79, c_0_80]), c_0_29]), c_0_28])])).
0.33/1.03	thf(c_0_84, negated_conjecture, ((n_pl @ esk3_0 @ esk1_0)=(n_pl @ esk1_0 @ esk3_0)), inference(spm,[status(thm)],[c_0_81, c_0_82])).
0.33/1.03	thf(c_0_85, negated_conjecture, ((esk1_0)!=(esk2_0)), inference(split_conjunct,[status(thm)],[c_0_24])).
0.33/1.03	thf(c_0_86, plain, ($false), inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_84]), c_0_32])]), c_0_85]), ['proof']).
0.33/1.03	% SZS output end CNFRefutation
0.33/1.03	% Parsed axioms                        : 384
0.33/1.03	% Removed by relevancy pruning/SinE    : 264
0.33/1.03	% Initial clauses                      : 325
0.33/1.03	% Removed in clause preprocessing      : 171
0.33/1.03	% Initial clauses in saturation        : 154
0.33/1.03	% Processed clauses                    : 1692
0.33/1.03	% ...of these trivial                  : 95
0.33/1.03	% ...subsumed                          : 773
0.33/1.03	% ...remaining for further processing  : 824
0.33/1.03	% Other redundant clauses eliminated   : 82
0.33/1.03	% Clauses deleted for lack of memory   : 0
0.33/1.03	% Backward-subsumed                    : 2
0.33/1.03	% Backward-rewritten                   : 60
0.33/1.03	% Generated clauses                    : 6505
0.33/1.03	% ...of the previous two non-redundant : 6106
0.33/1.03	% ...aggressively subsumed             : 0
0.33/1.03	% Contextual simplify-reflections      : 2
0.33/1.03	% Paramodulations                      : 6405
0.33/1.03	% Factorizations                       : 2
0.33/1.03	% NegExts                              : 0
0.33/1.03	% Equation resolutions                 : 88
0.33/1.03	% Disequality decompositions           : 0
0.33/1.03	% Total rewrite steps                  : 3192
0.33/1.03	% ...of those cached                   : 3081
0.33/1.03	% Propositional unsat checks           : 0
0.33/1.03	%    Propositional check models        : 0
0.33/1.03	%    Propositional check unsatisfiable : 0
0.33/1.03	%    Propositional clauses             : 0
0.33/1.03	%    Propositional clauses after purity: 0
0.33/1.03	%    Propositional unsat core size     : 0
0.33/1.03	%    Propositional preprocessing time  : 0.000
0.33/1.03	%    Propositional encoding time       : 0.000
0.33/1.03	%    Propositional solver time         : 0.000
0.33/1.03	%    Success case prop preproc time    : 0.000
0.33/1.03	%    Success case prop encoding time   : 0.000
0.33/1.03	%    Success case prop solver time     : 0.000
0.33/1.03	% Current number of processed clauses  : 750
0.33/1.03	%    Positive orientable unit clauses  : 80
0.33/1.03	%    Positive unorientable unit clauses: 0
0.33/1.03	%    Negative unit clauses             : 387
0.33/1.03	%    Non-unit-clauses                  : 283
0.33/1.03	% Current number of unprocessed clauses: 4471
0.33/1.03	% ...number of literals in the above   : 13588
0.33/1.03	% Current number of archived formulas  : 0
0.33/1.03	% Current number of archived clauses   : 62
0.33/1.03	% Clause-clause subsumption calls (NU) : 12922
0.33/1.03	% Rec. Clause-clause subsumption calls : 8703
0.33/1.03	% Non-unit clause-clause subsumptions  : 473
0.33/1.03	% Unit Clause-clause subsumption calls : 41049
0.33/1.03	% Rewrite failures with RHS unbound    : 0
0.33/1.03	% BW rewrite match attempts            : 49
0.33/1.03	% BW rewrite match successes           : 8
0.33/1.03	% Condensation attempts                : 0
0.33/1.03	% Condensation successes               : 0
0.33/1.03	% Termbank termtop insertions          : 146653
0.33/1.03	% Search garbage collected termcells   : 15037
0.33/1.03	
0.33/1.03	% -------------------------------------------------
0.33/1.03	% User time                : 0.323 s
0.33/1.03	% System time              : 0.035 s
0.33/1.03	% Total time               : 0.358 s
0.33/1.03	% Maximum resident set size: 6304 pages
0.33/1.03	
0.33/1.03	% -------------------------------------------------
0.33/1.03	% User time                : 0.333 s
0.33/1.03	% System time              : 0.043 s
0.33/1.03	% Total time               : 0.375 s
0.33/1.03	% Maximum resident set size: 5376 pages
0.33/1.03	% E exiting
0.33/1.04	EOF