TSTP Solution File: ITP125^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP125^1 : TPTP v8.1.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 00:29:12 EDT 2022
% Result : Theorem 47.06s 47.04s
% Output : Proof 47.06s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP125^1 : TPTP v8.1.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 4 01:18:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 47.06/47.04 % SZS status Theorem
% 47.06/47.04 % Mode: mode485:USE_SINE=true:SINE_TOLERANCE=1.2:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=4.:SINE_DEPTH=0
% 47.06/47.04 % Inferences: 441
% 47.06/47.04 % SZS output start Proof
% 47.06/47.04 thf(conj_0,conjecture,((ord_less_nat @ k) @ (plen_P694648887list_a @ pi))).
% 47.06/47.04 thf(h0,negated_conjecture,(~(((ord_less_nat @ k) @ (plen_P694648887list_a @ pi)))),inference(assume_negation,[status(cth)],[conj_0])).
% 47.06/47.04 thf(pax136, axiom, (p136=>![X25:nat, X22:nat, X23:nat]:(ford_less_nat @ X25 @ X22=>ford_less_nat @ X25 @ (fplus_plus_nat @ X22 @ X23))), file('<stdin>', pax136)).
% 47.06/47.04 thf(pax2, axiom, (p2=>ford_less_nat @ fk @ (fmonito1457594016ress_a @ fsigma @ fphi_1 @ (fplen_P694648887list_a @ fpi))), file('<stdin>', pax2)).
% 47.06/47.04 thf(pax147, axiom, (p147=>![X25:nat, X22:nat]:(ford_less_eq_nat @ X25 @ X22=>~(![X23:nat]:~((X22)=(fplus_plus_nat @ X25 @ X23))))), file('<stdin>', pax147)).
% 47.06/47.04 thf(pax18, axiom, (p18=>![X170:trace_1367752404list_a, X171:formula_a, X172:nat]:ford_less_eq_nat @ (fmonito1457594016ress_a @ X170 @ X171 @ X172) @ X172), file('<stdin>', pax18)).
% 47.06/47.04 thf(ax1057, axiom, p136, file('<stdin>', ax1057)).
% 47.06/47.04 thf(ax1191, axiom, p2, file('<stdin>', ax1191)).
% 47.06/47.04 thf(ax1046, axiom, p147, file('<stdin>', ax1046)).
% 47.06/47.04 thf(ax1175, axiom, p18, file('<stdin>', ax1175)).
% 47.06/47.04 thf(nax1, axiom, (p1<=ford_less_nat @ fk @ (fplen_P694648887list_a @ fpi)), file('<stdin>', nax1)).
% 47.06/47.04 thf(ax1192, axiom, ~(p1), file('<stdin>', ax1192)).
% 47.06/47.04 thf(c_0_10, plain, ![X3295:nat, X3296:nat, X3297:nat]:(~p136|(~ford_less_nat @ X3295 @ X3296|ford_less_nat @ X3295 @ (fplus_plus_nat @ X3296 @ X3297))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax136])])])).
% 47.06/47.04 thf(c_0_11, plain, (~p2|ford_less_nat @ fk @ (fmonito1457594016ress_a @ fsigma @ fphi_1 @ (fplen_P694648887list_a @ fpi))), inference(fof_nnf,[status(thm)],[pax2])).
% 47.06/47.04 thf(c_0_12, plain, ![X3235:nat, X3236:nat]:(~p147|(~ford_less_eq_nat @ X3235 @ X3236|(X3236)=(fplus_plus_nat @ X3235 @ (esk1531_2 @ X3235 @ X3236)))), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax147])])])])])).
% 47.06/47.04 thf(c_0_13, plain, ![X3905:trace_1367752404list_a, X3906:formula_a, X3907:nat]:(~p18|ford_less_eq_nat @ (fmonito1457594016ress_a @ X3905 @ X3906 @ X3907) @ X3907), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax18])])])).
% 47.06/47.04 thf(c_0_14, plain, ![X1:nat, X3:nat, X2:nat]:(ford_less_nat @ X1 @ (fplus_plus_nat @ X2 @ X3)|~p136|~ford_less_nat @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_10])).
% 47.06/47.04 thf(c_0_15, plain, p136, inference(split_conjunct,[status(thm)],[ax1057])).
% 47.06/47.04 thf(c_0_16, plain, (ford_less_nat @ fk @ (fmonito1457594016ress_a @ fsigma @ fphi_1 @ (fplen_P694648887list_a @ fpi))|~p2), inference(split_conjunct,[status(thm)],[c_0_11])).
% 47.06/47.04 thf(c_0_17, plain, p2, inference(split_conjunct,[status(thm)],[ax1191])).
% 47.06/47.04 thf(c_0_18, plain, ![X1:nat, X2:nat]:((X2)=(fplus_plus_nat @ X1 @ (esk1531_2 @ X1 @ X2))|~p147|~ford_less_eq_nat @ X1 @ X2), inference(split_conjunct,[status(thm)],[c_0_12])).
% 47.06/47.04 thf(c_0_19, plain, p147, inference(split_conjunct,[status(thm)],[ax1046])).
% 47.06/47.04 thf(c_0_20, plain, ![X20:formula_a, X16:trace_1367752404list_a, X1:nat]:(ford_less_eq_nat @ (fmonito1457594016ress_a @ X16 @ X20 @ X1) @ X1|~p18), inference(split_conjunct,[status(thm)],[c_0_13])).
% 47.06/47.04 thf(c_0_21, plain, p18, inference(split_conjunct,[status(thm)],[ax1175])).
% 47.06/47.04 thf(c_0_22, plain, (~ford_less_nat @ fk @ (fplen_P694648887list_a @ fpi)|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 47.06/47.04 thf(c_0_23, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1192])).
% 47.06/47.04 thf(c_0_24, plain, ![X1:nat, X3:nat, X2:nat]:(ford_less_nat @ X1 @ (fplus_plus_nat @ X2 @ X3)|~ford_less_nat @ X1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_14, c_0_15])])).
% 47.06/47.04 thf(c_0_25, plain, ford_less_nat @ fk @ (fmonito1457594016ress_a @ fsigma @ fphi_1 @ (fplen_P694648887list_a @ fpi)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 47.06/47.04 thf(c_0_26, plain, ![X1:nat, X2:nat]:((fplus_plus_nat @ X1 @ (esk1531_2 @ X1 @ X2))=(X2)|~ford_less_eq_nat @ X1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])])).
% 47.06/47.04 thf(c_0_27, plain, ![X20:formula_a, X16:trace_1367752404list_a, X1:nat]:ford_less_eq_nat @ (fmonito1457594016ress_a @ X16 @ X20 @ X1) @ X1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 47.06/47.04 thf(c_0_28, plain, (p1|~ford_less_nat @ fk @ (fplen_P694648887list_a @ fpi)), inference(split_conjunct,[status(thm)],[c_0_22])).
% 47.06/47.04 thf(c_0_29, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_23])).
% 47.06/47.04 thf(c_0_30, plain, ![X1:nat]:ford_less_nat @ fk @ (fplus_plus_nat @ (fmonito1457594016ress_a @ fsigma @ fphi_1 @ (fplen_P694648887list_a @ fpi)) @ X1), inference(spm,[status(thm)],[c_0_24, c_0_25])).
% 47.06/47.04 thf(c_0_31, plain, ![X20:formula_a, X16:trace_1367752404list_a, X1:nat]:(fplus_plus_nat @ (fmonito1457594016ress_a @ X16 @ X20 @ X1) @ (esk1531_2 @ (fmonito1457594016ress_a @ X16 @ X20 @ X1) @ X1))=(X1), inference(spm,[status(thm)],[c_0_26, c_0_27])).
% 47.06/47.04 thf(c_0_32, plain, ~ford_less_nat @ fk @ (fplen_P694648887list_a @ fpi), inference(sr,[status(thm)],[c_0_28, c_0_29])).
% 47.06/47.04 thf(c_0_33, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_31]), c_0_32]), ['proof']).
% 47.06/47.04 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 47.06/47.04 thf(0,theorem,((ord_less_nat @ k) @ (plen_P694648887list_a @ pi)),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 47.06/47.04 % SZS output end Proof
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