0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.11	% Command    : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 240 THM
0.12/0.32	% Computer : n009.cluster.edu
0.12/0.32	% Model    : x86_64 x86_64
0.12/0.32	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.32	% Memory   : 8042.1875MB
0.12/0.32	% OS       : Linux 3.10.0-693.el7.x86_64
0.12/0.32	% CPULimit   : 1920
0.12/0.32	% WCLimit    : 240
0.12/0.32	% DateTime   : Wed Jul 30 02:10:34 EDT 2025
0.12/0.32	% CPUTime    : 
0.18/0.46	Running higher-order theorem proving
0.18/0.51	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=240 /export/starexec/sandbox2/tmp/tmp.PgLowky4a8/E---3.1_27519.p
1222.07/174.96	# Version: 3.0.0-ho
1222.07/174.96	# Preprocessing class: HSLSSMSSSSLNHHA.
1222.07/174.96	# Scheduled 4 strats onto 8 cores with 240 seconds (1920 total)
1222.07/174.96	# Starting full_lambda_1 with 960s (4) cores
1222.07/174.96	# Starting additional_ho_7 with 480s (2) cores
1222.07/174.96	# Starting full_lambda_3 with 240s (1) cores
1222.07/174.96	# Starting lpo8_s with 240s (1) cores
1222.07/174.96	# lpo8_s with pid 27600 completed with status 0
1222.07/174.96	# Result found by lpo8_s
1222.07/174.96	# Preprocessing class: HSLSSMSSSSLNHHA.
1222.07/174.96	# Scheduled 4 strats onto 8 cores with 240 seconds (1920 total)
1222.07/174.96	# Starting full_lambda_1 with 960s (4) cores
1222.07/174.96	# Starting additional_ho_7 with 480s (2) cores
1222.07/174.96	# Starting full_lambda_3 with 240s (1) cores
1222.07/174.96	# Starting lpo8_s with 240s (1) cores
1222.07/174.96	# SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
1222.07/174.96	# Search class: HGHSM-FSLS32-MHHFFSBN
1222.07/174.96	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
1222.07/174.96	# Starting pre_casc_4 with 130s (1) cores
1222.07/174.96	# pre_casc_4 with pid 27609 completed with status 8
1222.07/174.96	# Starting lpo8_s with 25s (1) cores
1222.07/174.96	# lpo8_s with pid 27648 completed with status 8
1222.07/174.96	# Starting ho_unfolding_6 with 22s (1) cores
1222.07/174.96	# ho_unfolding_6 with pid 27651 completed with status 0
1222.07/174.96	# Result found by ho_unfolding_6
1222.07/174.96	# Preprocessing class: HSLSSMSSSSLNHHA.
1222.07/174.96	# Scheduled 4 strats onto 8 cores with 240 seconds (1920 total)
1222.07/174.96	# Starting full_lambda_1 with 960s (4) cores
1222.07/174.96	# Starting additional_ho_7 with 480s (2) cores
1222.07/174.96	# Starting full_lambda_3 with 240s (1) cores
1222.07/174.96	# Starting lpo8_s with 240s (1) cores
1222.07/174.96	# SinE strategy is GSinE(CountFormulas,hypos,4.0,,6,20000,1.0)
1222.07/174.96	# Search class: HGHSM-FSLS32-MHHFFSBN
1222.07/174.96	# Scheduled 6 strats onto 1 cores with 240 seconds (240 total)
1222.07/174.96	# Starting pre_casc_4 with 130s (1) cores
1222.07/174.96	# pre_casc_4 with pid 27609 completed with status 8
1222.07/174.96	# Starting lpo8_s with 25s (1) cores
1222.07/174.96	# lpo8_s with pid 27648 completed with status 8
1222.07/174.96	# Starting ho_unfolding_6 with 22s (1) cores
1222.07/174.96	# Preprocessing time       : 0.009 s
1222.07/174.96	
1222.07/174.96	# Proof found!
1222.07/174.96	# SZS status Theorem
1222.07/174.96	# SZS output start CNFRefutation
1222.07/174.96	thf(decl_sort1, type, nat: $tType).
1222.07/174.96	thf(decl_sort2, type, set_nat_nat: $tType).
1222.07/174.96	thf(decl_37, type, finite570312790at_nat: set_nat_nat > $o).
1222.07/174.96	thf(decl_44, type, one_one_nat: nat).
1222.07/174.96	thf(decl_45, type, plus_plus_nat: nat > nat > nat).
1222.07/174.96	thf(decl_46, type, zero_zero_nat: nat).
1222.07/174.96	thf(decl_47, type, number1551313001itions: (nat > nat) > nat > $o).
1222.07/174.96	thf(decl_56, type, ord_less_eq_nat: nat > nat > $o).
1222.07/174.96	thf(decl_60, type, ord_le1415039317at_nat: set_nat_nat > set_nat_nat > $o).
1222.07/174.96	thf(decl_71, type, collect_nat_nat: ((nat > nat) > $o) > set_nat_nat).
1222.07/174.96	thf(decl_84, type, n: nat).
1222.07/174.96	thf(decl_97, type, esk13_2: ((nat > nat) > $o) > ((nat > nat) > $o) > nat > nat).
1222.07/174.96	thf(decl_202, type, epred1_0: (nat > nat) > $o).
1222.07/174.96	thf(decl_210, type, epred9_2: ((nat > nat) > $o) > ((nat > nat) > $o) > (nat > nat) > $o).
1222.07/174.96	thf(decl_222, type, epred21_0: (nat > nat) > $o).
1222.07/174.96	thf(decl_223, type, epred22_0: (nat > nat) > $o).
1222.07/174.96	thf(decl_270, type, esk124_1: (nat > nat) > nat).
1222.07/174.96	thf(decl_271, type, esk125_1: (nat > nat) > nat).
1222.07/174.96	thf(decl_272, type, esk126_1: (nat > nat) > nat).
1222.07/174.96	thf(decl_273, type, esk127_1: (nat > nat) > nat).
1222.07/174.96	thf(decl_284, type, esk138_2: ((nat > nat) > $o) > nat > nat).
1222.07/174.96	thf(conj_0, conjecture, (finite570312790at_nat @ (collect_nat_nat @ (^[X5:nat > nat]:((number1551313001itions @ X5 @ n))))), file('/export/starexec/sandbox2/tmp/tmp.PgLowky4a8/E---3.1_27519.p', conj_0)).
1222.07/174.96	thf(fact_5_finite__Collect__conjI, axiom, ![X292:(nat > nat) > $o, X293:(nat > nat) > $o]:(((finite570312790at_nat @ (collect_nat_nat @ (^[X19:nat > nat]:(((X292 @ X19)&(X293 @ X19))))))<=((finite570312790at_nat @ (collect_nat_nat @ X293))|(finite570312790at_nat @ (collect_nat_nat @ X292))))), file('/export/starexec/sandbox2/tmp/tmp.PgLowky4a8/E---3.1_27519.p', fact_5_finite__Collect__conjI)).
1222.07/174.96	thf(fact_0__092_060open_062finite_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062, axiom, (finite570312790at_nat @ (collect_nat_nat @ (^[X151:nat > nat]:((![X152:nat]:((ord_less_eq_nat @ (X151 @ X152) @ n))&![X153:nat]:((((X151 @ X153)=(zero_zero_nat))<=(ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X153)))))))), file('/export/starexec/sandbox2/tmp/tmp.PgLowky4a8/E---3.1_27519.p', fact_0__092_060open_062finite_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062)).
1222.07/174.96	thf(fact_251_Collect__mono__iff, axiom, ![X301:(nat > nat) > $o, X302:(nat > nat) > $o]:(((ord_le1415039317at_nat @ (collect_nat_nat @ X301) @ (collect_nat_nat @ X302))<=>![X19:nat > nat]:(((X301 @ X19)=>(X302 @ X19))))), file('/export/starexec/sandbox2/tmp/tmp.PgLowky4a8/E---3.1_27519.p', fact_251_Collect__mono__iff)).
1222.07/174.96	thf(fact_1__092_060open_062_123p_O_Ap_Apartitions_An_125_A_092_060subseteq_062_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062, axiom, (ord_le1415039317at_nat @ (collect_nat_nat @ (^[X5:nat > nat]:((number1551313001itions @ X5 @ n)))) @ (collect_nat_nat @ (^[X513:nat > nat]:((![X514:nat]:(((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X514)=>((X513 @ X514)=(zero_zero_nat))))&![X515:nat]:((ord_less_eq_nat @ (X513 @ X515) @ n))))))), file('/export/starexec/sandbox2/tmp/tmp.PgLowky4a8/E---3.1_27519.p', fact_1__092_060open_062_123p_O_Ap_Apartitions_An_125_A_092_060subseteq_062_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062)).
1222.07/174.96	thf(c_0_5, negated_conjecture, ~(finite570312790at_nat @ (collect_nat_nat @ (^[Z0/* 3 */:nat > nat]:((number1551313001itions @ Z0 @ n))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[conj_0])])])).
1222.07/174.96	thf(c_0_6, plain, ![X292:(nat > nat) > $o, X293:(nat > nat) > $o]:((((finite570312790at_nat @ (collect_nat_nat @ X293))|(finite570312790at_nat @ (collect_nat_nat @ X292)))=>(finite570312790at_nat @ (collect_nat_nat @ (^[Z0/* 8 */:nat > nat]:((X292 @ Z0&X293 @ Z0))))))), inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[fact_5_finite__Collect__conjI])])).
1222.07/174.96	thf(c_0_7, negated_conjecture, ~(finite570312790at_nat @ (collect_nat_nat @ (^[Z0/* 3 */:nat > nat]:((number1551313001itions @ Z0 @ n))))), inference(fof_nnf,[status(thm)],[c_0_5])).
1222.07/174.96	thf(c_0_8, plain, ![X2402:nat > nat]:(((epred1_0 @ X2402)<=>(number1551313001itions @ X2402 @ n))), introduced(definition)).
1222.07/174.96	thf(c_0_9, plain, ![X1529:(nat > nat) > $o, X1530:(nat > nat) > $o]:(((~(finite570312790at_nat @ (collect_nat_nat @ X1530))|(finite570312790at_nat @ (collect_nat_nat @ (^[Z0/* 8 */:nat > nat]:((X1529 @ Z0&X1530 @ Z0))))))&(~(finite570312790at_nat @ (collect_nat_nat @ X1529))|(finite570312790at_nat @ (collect_nat_nat @ (^[Z0/* 8 */:nat > nat]:((X1529 @ Z0&X1530 @ Z0)))))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])).
1222.07/174.96	thf(c_0_10, plain, ![X2418:nat > nat, X71:(nat > nat) > $o, X72:(nat > nat) > $o]:(((epred9_2 @ X72 @ X71 @ X2418)<=>((X71 @ X2418)&(X72 @ X2418)))), introduced(definition)).
1222.07/174.96	thf(c_0_11, negated_conjecture, ~((((finite570312790at_nat @ (collect_nat_nat @ epred1_0)))=(($true)))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_7]), c_0_8])).
1222.07/174.96	thf(c_0_12, plain, ![X72:(nat > nat) > $o, X71:(nat > nat) > $o]:(((((finite570312790at_nat @ (collect_nat_nat @ (epred9_2 @ X71 @ X72))))=(($true)))|~((finite570312790at_nat @ (collect_nat_nat @ X71))))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_9]), c_0_10])).
1222.07/174.96	thf(c_0_13, plain, (finite570312790at_nat @ (collect_nat_nat @ (^[Z0/* 8 */:nat > nat]:((![X152:nat]:((ord_less_eq_nat @ (Z0 @ X152) @ n))&![X153:nat]:((((Z0 @ X153)=(zero_zero_nat))<=(ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X153)))))))), inference(fof_simplification,[status(thm)],[fact_0__092_060open_062finite_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062])).
1222.07/174.96	thf(c_0_14, plain, ![X2455:nat > nat]:(((epred22_0 @ X2455)<=>(![X2453:nat]:((ord_less_eq_nat @ (X2455 @ X2453) @ n))&![X2454:nat]:((((X2455 @ X2454)=(zero_zero_nat))<=(ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X2454)))))), introduced(definition)).
1222.07/174.96	thf(c_0_15, plain, ![X2650:nat > nat, X2651:nat, X2652:nat]:((((~(ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X2651)|((X2650 @ X2651)=(zero_zero_nat))|~(epred21_0 @ X2650))&((ord_less_eq_nat @ (X2650 @ X2652) @ n)|~(epred21_0 @ X2650)))&(((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ (esk124_1 @ X2650))|~(ord_less_eq_nat @ (X2650 @ (esk125_1 @ X2650)) @ n)|(epred21_0 @ X2650))&(((X2650 @ (esk124_1 @ X2650))!=(zero_zero_nat))|~(ord_less_eq_nat @ (X2650 @ (esk125_1 @ X2650)) @ n)|(epred21_0 @ X2650))))), 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)],[])])])])])])).
1222.07/174.96	thf(c_0_16, plain, ![X2655:nat > nat, X2656:nat, X2657:nat, X2658:nat > nat]:(((((ord_less_eq_nat @ (X2655 @ X2656) @ n)|~(epred22_0 @ X2655))&(~(ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X2657)|((X2655 @ X2657)=(zero_zero_nat))|~(epred22_0 @ X2655)))&(((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ (esk127_1 @ X2658))|~(ord_less_eq_nat @ (X2658 @ (esk126_1 @ X2658)) @ n)|(epred22_0 @ X2658))&(((X2658 @ (esk127_1 @ X2658))!=(zero_zero_nat))|~(ord_less_eq_nat @ (X2658 @ (esk126_1 @ X2658)) @ n)|(epred22_0 @ X2658))))), 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)],[inference(fof_simplification,[status(thm)],[])])])])])])])])).
1222.07/174.96	thf(c_0_17, negated_conjecture, ~((finite570312790at_nat @ (collect_nat_nat @ epred1_0))), inference(cn,[status(thm)],[c_0_11])).
1222.07/174.96	thf(c_0_18, plain, ![X72:(nat > nat) > $o, X71:(nat > nat) > $o]:(((finite570312790at_nat @ (collect_nat_nat @ (epred9_2 @ X71 @ X72)))|~((finite570312790at_nat @ (collect_nat_nat @ X71))))), inference(cn,[status(thm)],[c_0_12])).
1222.07/174.96	thf(c_0_19, plain, (((finite570312790at_nat @ (collect_nat_nat @ epred22_0)))=(($true))), inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_13]), c_0_14])).
1222.07/174.96	thf(c_0_20, plain, ![X5:nat > nat]:(((epred21_0 @ X5)|((X5 @ (esk124_1 @ X5))!=(zero_zero_nat))|~((ord_less_eq_nat @ (X5 @ (esk125_1 @ X5)) @ n)))), inference(split_conjunct,[status(thm)],[c_0_15])).
1222.07/174.96	thf(c_0_21, plain, ![X8:nat, X5:nat > nat]:((((X5 @ X8)=(zero_zero_nat))|~((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X8))|~((epred22_0 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_16])).
1222.07/174.96	thf(c_0_22, plain, ![X8:nat, X5:nat > nat]:(((ord_less_eq_nat @ (X5 @ X8) @ n)|~((epred22_0 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_16])).
1222.07/174.96	thf(c_0_23, plain, ![X72:(nat > nat) > $o, X71:(nat > nat) > $o]:((((epred9_2 @ X71 @ X72)!=(epred1_0))|~((finite570312790at_nat @ (collect_nat_nat @ X71))))), inference(ext_sup,[status(thm)],[c_0_17, c_0_18])).
1222.07/174.96	thf(c_0_24, plain, (finite570312790at_nat @ (collect_nat_nat @ epred22_0)), inference(cn,[status(thm)],[c_0_19])).
1222.07/174.96	thf(c_0_25, plain, ![X1565:(nat > nat) > $o, X1566:(nat > nat) > $o, X1567:nat > nat, X1568:(nat > nat) > $o, X1569:(nat > nat) > $o]:(((~(ord_le1415039317at_nat @ (collect_nat_nat @ X1565) @ (collect_nat_nat @ X1566))|(~(X1565 @ X1567)|(X1566 @ X1567)))&(((X1568 @ (esk13_2 @ X1568 @ X1569))|(ord_le1415039317at_nat @ (collect_nat_nat @ X1568) @ (collect_nat_nat @ X1569)))&(~(X1569 @ (esk13_2 @ X1568 @ X1569))|(ord_le1415039317at_nat @ (collect_nat_nat @ X1568) @ (collect_nat_nat @ X1569)))))), 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)],[fact_251_Collect__mono__iff])])])])])])])).
1222.07/174.96	thf(c_0_26, plain, ![X5:nat > nat]:(((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ (esk124_1 @ X5))|(epred21_0 @ X5)|~((ord_less_eq_nat @ (X5 @ (esk125_1 @ X5)) @ n)))), inference(split_conjunct,[status(thm)],[c_0_15])).
1222.07/174.96	thf(c_0_27, plain, ![X5:nat > nat]:(((epred21_0 @ X5)|~((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ (esk124_1 @ X5)))|~((epred22_0 @ X5)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21]), c_0_22])).
1222.07/174.96	thf(c_0_28, plain, ![X2608:nat > nat, X2609:(nat > nat) > $o, X2610:(nat > nat) > $o]:(((((X2609 @ X2608)|~(epred9_2 @ X2610 @ X2609 @ X2608))&((X2610 @ X2608)|~(epred9_2 @ X2610 @ X2609 @ X2608)))&(~(X2609 @ X2608)|~(X2610 @ X2608)|(epred9_2 @ X2610 @ X2609 @ X2608)))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[])])])])).
1222.07/174.96	thf(c_0_29, plain, ![X71:(nat > nat) > $o]:(((epred9_2 @ epred22_0 @ X71)!=(epred1_0))), inference(spm,[status(thm)],[c_0_23, c_0_24])).
1222.07/174.96	thf(c_0_30, plain, ![X72:(nat > nat) > $o, X71:(nat > nat) > $o]:(((ord_le1415039317at_nat @ (collect_nat_nat @ X72) @ (collect_nat_nat @ X71))|~((X71 @ (esk13_2 @ X72 @ X71))))), inference(split_conjunct,[status(thm)],[c_0_25])).
1222.07/174.96	thf(c_0_31, plain, ![X5:nat > nat]:(((epred21_0 @ X5)|~((epred22_0 @ X5)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26, c_0_22]), c_0_27])).
1222.07/174.96	thf(c_0_32, plain, ![X72:(nat > nat) > $o, X71:(nat > nat) > $o, X5:nat > nat]:(((X71 @ X5)|~((epred9_2 @ X71 @ X72 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_28])).
1222.07/174.96	thf(c_0_33, plain, ![X71:(nat > nat) > $o, X72:(nat > nat) > $o]:(((X71 @ (esk13_2 @ X71 @ X72))|(ord_le1415039317at_nat @ (collect_nat_nat @ X71) @ (collect_nat_nat @ X72)))), inference(split_conjunct,[status(thm)],[c_0_25])).
1222.07/174.96	thf(c_0_34, plain, (ord_le1415039317at_nat @ (collect_nat_nat @ (^[Z0/* 3 */:nat > nat]:((number1551313001itions @ Z0 @ n)))) @ (collect_nat_nat @ (^[Z0/* 8 */:nat > nat]:((![X514:nat]:(((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X514)=>((Z0 @ X514)=(zero_zero_nat))))&![X515:nat]:((ord_less_eq_nat @ (Z0 @ X515) @ n))))))), inference(fof_simplification,[status(thm)],[fact_1__092_060open_062_123p_O_Ap_Apartitions_An_125_A_092_060subseteq_062_A_123f_O_A_I_092_060forall_062i_O_Af_Ai_A_092_060le_062_An_J_A_092_060and_062_A_I_092_060forall_062i_092_060ge_062n_A_L_A1_O_Af_Ai_A_061_A0_J_125_092_060close_062])).
1222.07/174.96	thf(c_0_35, plain, ![X2452:nat > nat]:(((epred21_0 @ X2452)<=>(![X2449:nat]:(((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X2449)=>((X2452 @ X2449)=(zero_zero_nat))))&![X2450:nat]:((ord_less_eq_nat @ (X2452 @ X2450) @ n))))), introduced(definition)).
1222.07/174.96	thf(c_0_36, plain, ![X71:(nat > nat) > $o]:(((epred9_2 @ epred22_0 @ X71 @ (esk138_2 @ X71))<~>(epred1_0 @ (esk138_2 @ X71)))), inference(neg_ext,[status(thm)],[c_0_29])).
1222.07/174.96	thf(c_0_37, plain, ![X71:(nat > nat) > $o]:(((ord_le1415039317at_nat @ (collect_nat_nat @ X71) @ (collect_nat_nat @ epred21_0))|~((epred22_0 @ (esk13_2 @ X71 @ epred21_0))))), inference(spm,[status(thm)],[c_0_30, c_0_31])).
1222.07/174.96	thf(c_0_38, plain, ![X71:(nat > nat) > $o, X72:(nat > nat) > $o, X185:(nat > nat) > $o]:(((ord_le1415039317at_nat @ (collect_nat_nat @ (epred9_2 @ X71 @ X72)) @ (collect_nat_nat @ X185))|(X71 @ (esk13_2 @ (epred9_2 @ X71 @ X72) @ X185)))), inference(spm,[status(thm)],[c_0_32, c_0_33])).
1222.07/174.96	thf(c_0_39, plain, (((ord_le1415039317at_nat @ (collect_nat_nat @ epred1_0) @ (collect_nat_nat @ epred21_0)))=(($true))), inference(lift_lambdas,[status(thm)],[inference(lift_lambdas,[status(thm)],[inference(split_conjunct,[status(thm)],[c_0_34]), c_0_35]), c_0_8])).
1222.07/174.96	thf(c_0_40, plain, ![X72:(nat > nat) > $o, X71:(nat > nat) > $o, X5:nat > nat]:(((X71 @ X5)|~((epred9_2 @ X72 @ X71 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_28])).
1222.07/174.96	thf(c_0_41, plain, ![X71:(nat > nat) > $o]:(((epred9_2 @ epred22_0 @ X71 @ (esk138_2 @ X71))|(epred1_0 @ (esk138_2 @ X71)))), inference(dynamic_cnf,[status(thm)],[c_0_36])).
1222.07/174.96	thf(c_0_42, plain, ![X5:nat > nat]:(((epred22_0 @ X5)|((X5 @ (esk127_1 @ X5))!=(zero_zero_nat))|~((ord_less_eq_nat @ (X5 @ (esk126_1 @ X5)) @ n)))), inference(split_conjunct,[status(thm)],[c_0_16])).
1222.07/174.96	thf(c_0_43, plain, ![X8:nat, X5:nat > nat]:((((X5 @ X8)=(zero_zero_nat))|~((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ X8))|~((epred21_0 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_15])).
1222.07/174.96	thf(c_0_44, plain, ![X8:nat, X5:nat > nat]:(((ord_less_eq_nat @ (X5 @ X8) @ n)|~((epred21_0 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_15])).
1222.07/174.96	thf(c_0_45, plain, ![X72:(nat > nat) > $o, X71:(nat > nat) > $o, X5:nat > nat]:(((X72 @ X5)|~((ord_le1415039317at_nat @ (collect_nat_nat @ X71) @ (collect_nat_nat @ X72)))|~((X71 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_25])).
1222.07/174.96	thf(c_0_46, plain, ![X71:(nat > nat) > $o]:((ord_le1415039317at_nat @ (collect_nat_nat @ (epred9_2 @ epred22_0 @ X71)) @ (collect_nat_nat @ epred21_0))), inference(spm,[status(thm)],[c_0_37, c_0_38])).
1222.07/174.96	thf(c_0_47, plain, (ord_le1415039317at_nat @ (collect_nat_nat @ epred1_0) @ (collect_nat_nat @ epred21_0)), inference(cn,[status(thm)],[c_0_39])).
1222.07/174.96	thf(c_0_48, plain, ![X71:(nat > nat) > $o]:((~((epred9_2 @ epred22_0 @ X71 @ (esk138_2 @ X71)))|~((epred1_0 @ (esk138_2 @ X71))))), inference(dynamic_cnf,[status(thm)],[c_0_36])).
1222.07/174.96	thf(c_0_49, plain, ![X72:(nat > nat) > $o, X71:(nat > nat) > $o, X5:nat > nat]:(((epred9_2 @ X72 @ X71 @ X5)|~((X71 @ X5))|~((X72 @ X5)))), inference(split_conjunct,[status(thm)],[c_0_28])).
1222.07/174.96	thf(c_0_50, plain, ![X71:(nat > nat) > $o]:(((epred1_0 @ (esk138_2 @ X71))|(X71 @ (esk138_2 @ X71)))), inference(spm,[status(thm)],[c_0_40, c_0_41])).
1222.07/174.96	thf(c_0_51, plain, ![X5:nat > nat]:(((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ (esk127_1 @ X5))|(epred22_0 @ X5)|~((ord_less_eq_nat @ (X5 @ (esk126_1 @ X5)) @ n)))), inference(split_conjunct,[status(thm)],[c_0_16])).
1222.07/174.96	thf(c_0_52, plain, ![X5:nat > nat]:(((epred22_0 @ X5)|~((ord_less_eq_nat @ (plus_plus_nat @ n @ one_one_nat) @ (esk127_1 @ X5)))|~((epred21_0 @ X5)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_44])).
1222.07/174.96	thf(c_0_53, plain, ![X71:(nat > nat) > $o, X5:nat > nat]:(((epred21_0 @ X5)|~((epred9_2 @ epred22_0 @ X71 @ X5)))), inference(spm,[status(thm)],[c_0_45, c_0_46])).
1222.07/174.96	thf(c_0_54, plain, ![X5:nat > nat]:(((epred21_0 @ X5)|~((epred1_0 @ X5)))), inference(spm,[status(thm)],[c_0_45, c_0_47])).
1222.07/174.96	thf(c_0_55, plain, ![X71:(nat > nat) > $o]:((~((epred1_0 @ (esk138_2 @ X71)))|~((epred22_0 @ (esk138_2 @ X71)))|~((X71 @ (esk138_2 @ X71))))), inference(spm,[status(thm)],[c_0_48, c_0_49])).
1222.07/174.96	thf(c_0_56, plain, (epred1_0 @ (esk138_2 @ epred1_0)), inference(ef,[status(thm)],[c_0_50])).
1222.07/174.96	thf(c_0_57, plain, ![X5:nat > nat]:(((epred22_0 @ X5)|~((epred21_0 @ X5)))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_44]), c_0_52])).
1222.07/174.96	thf(c_0_58, plain, ![X71:(nat > nat) > $o]:((epred21_0 @ (esk138_2 @ X71))), inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_53, c_0_41]), c_0_54])).
1222.07/174.96	thf(c_0_59, plain, ~((epred22_0 @ (esk138_2 @ epred1_0))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55, c_0_56]), c_0_56])])).
1222.07/174.96	thf(c_0_60, plain, ![X71:(nat > nat) > $o]:((epred22_0 @ (esk138_2 @ X71))), inference(spm,[status(thm)],[c_0_57, c_0_58])).
1222.07/174.96	thf(c_0_61, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_60])]), ['proof']).
1222.07/174.96	# SZS output end CNFRefutation
1222.07/174.96	# Parsed axioms                        : 429
1222.07/174.96	# Removed by relevancy pruning/SinE    : 119
1222.07/174.96	# Initial clauses                      : 789
1222.07/174.96	# Removed in clause preprocessing      : 17
1222.07/174.96	# Initial clauses in saturation        : 772
1222.07/174.96	# Processed clauses                    : 23748
1222.07/174.96	# ...of these trivial                  : 341
1222.07/174.96	# ...subsumed                          : 17104
1222.07/174.96	# ...remaining for further processing  : 6303
1222.07/174.96	# Other redundant clauses eliminated   : 4546
1222.07/174.96	# Clauses deleted for lack of memory   : 0
1222.07/174.96	# Backward-subsumed                    : 569
1222.07/174.96	# Backward-rewritten                   : 106
1222.07/174.96	# Generated clauses                    : 740618
1222.07/174.96	# ...of the previous two non-redundant : 712372
1222.07/174.96	# ...aggressively subsumed             : 0
1222.07/174.96	# Contextual simplify-reflections      : 85
1222.07/174.96	# Paramodulations                      : 733839
1222.07/174.96	# Factorizations                       : 1056
1222.07/174.96	# NegExts                              : 476
1222.07/174.96	# Equation resolutions                 : 4555
1222.07/174.96	# Disequality decompositions           : 0
1222.07/174.96	# Total rewrite steps                  : 66475
1222.07/174.96	# ...of those cached                   : 63005
1222.07/174.96	# Propositional unsat checks           : 1
1222.07/174.96	#    Propositional check models        : 0
1222.07/174.96	#    Propositional check unsatisfiable : 0
1222.07/174.96	#    Propositional clauses             : 0
1222.07/174.96	#    Propositional clauses after purity: 0
1222.07/174.96	#    Propositional unsat core size     : 0
1222.07/174.96	#    Propositional preprocessing time  : 0.000
1222.07/174.96	#    Propositional encoding time       : 0.674
1222.07/174.96	#    Propositional solver time         : 0.219
1222.07/174.96	#    Success case prop preproc time    : 0.000
1222.07/174.96	#    Success case prop encoding time   : 0.000
1222.07/174.96	#    Success case prop solver time     : 0.000
1222.07/174.96	# Current number of processed clauses  : 5539
1222.07/174.96	#    Positive orientable unit clauses  : 415
1222.07/174.96	#    Positive unorientable unit clauses: 3
1222.07/174.96	#    Negative unit clauses             : 333
1222.07/174.96	#    Non-unit-clauses                  : 4788
1222.07/174.96	# Current number of unprocessed clauses: 686738
1222.07/174.96	# ...number of literals in the above   : 2966283
1222.07/174.96	# Current number of archived formulas  : 0
1222.07/174.96	# Current number of archived clauses   : 698
1222.07/174.96	# Clause-clause subsumption calls (NU) : 4109882
1222.07/174.96	# Rec. Clause-clause subsumption calls : 2294297
1222.07/174.96	# Non-unit clause-clause subsumptions  : 6267
1222.07/174.96	# Unit Clause-clause subsumption calls : 261201
1222.07/174.96	# Rewrite failures with RHS unbound    : 0
1222.07/174.96	# BW rewrite match attempts            : 934
1222.07/174.96	# BW rewrite match successes           : 124
1222.07/174.96	# Condensation attempts                : 23748
1222.07/174.96	# Condensation successes               : 711
1222.07/174.96	# Termbank termtop insertions          : 51295337
1222.07/174.96	# Search garbage collected termcells   : 20271
1222.07/174.96	
1222.07/174.96	# -------------------------------------------------
1222.07/174.96	# User time                : 168.710 s
1222.07/174.96	# System time              : 2.970 s
1222.07/174.96	# Total time               : 171.680 s
1222.07/174.96	# Maximum resident set size: 7032 pages
1222.07/174.96	
1222.07/174.96	# -------------------------------------------------
1222.07/174.96	# User time                : 168.733 s
1222.07/174.96	# System time              : 2.975 s
1222.07/174.96	# Total time               : 171.707 s
1222.07/174.96	# Maximum resident set size: 2768 pages
1222.07/174.96	% E exiting
1222.07/174.96	% E exiting
1222.07/174.97	EOF