TSTP Solution File: NUM741^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : NUM741^1 : TPTP v8.1.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n019.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 : Mon Jul 18 13:55:56 EDT 2022
% Result : Theorem 48.70s 48.76s
% Output : Proof 48.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : NUM741^1 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 01:32:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 48.70/48.76 % SZS status Theorem
% 48.70/48.76 % Mode: mode371
% 48.70/48.76 % Inferences: 2036
% 48.70/48.76 % SZS output start Proof
% 48.70/48.76 thf(satz50,conjecture,((less @ ((ts @ (num @ x)) @ (den @ z))) @ ((ts @ (num @ z)) @ (den @ x)))).
% 48.70/48.76 thf(h0,negated_conjecture,(~(((less @ ((ts @ (num @ x)) @ (den @ z))) @ ((ts @ (num @ z)) @ (den @ x))))),inference(assume_negation,[status(cth)],[satz50])).
% 48.70/48.76 thf(pax4, axiom, (p4=>![X1:nat, X2:nat, X3:nat]:(fless @ (fts @ X1 @ X3) @ (fts @ X2 @ X3)=>fless @ X1 @ X2)), file('<stdin>', pax4)).
% 48.70/48.76 thf(pax6, axiom, (p6=>![X1:nat, X2:nat]:(fts @ X1 @ X2)=(fts @ X2 @ X1)), file('<stdin>', pax6)).
% 48.70/48.76 thf(ax12, axiom, p4, file('<stdin>', ax12)).
% 48.70/48.76 thf(ax10, axiom, p6, file('<stdin>', ax10)).
% 48.70/48.76 thf(pax7, axiom, (p7=>![X1:nat, X2:nat, X3:nat]:(fts @ (fts @ X1 @ X2) @ X3)=(fts @ X1 @ (fts @ X2 @ X3))), file('<stdin>', pax7)).
% 48.70/48.76 thf(ax9, axiom, p7, file('<stdin>', ax9)).
% 48.70/48.76 thf(pax5, axiom, (p5=>![X1:nat, X2:nat, X3:nat, X4:nat]:(fless @ X1 @ X2=>(fless @ X3 @ X4=>fless @ (fts @ X1 @ X3) @ (fts @ X2 @ X4)))), file('<stdin>', pax5)).
% 48.70/48.76 thf(pax3, axiom, (p3=>fless @ (fts @ (fnum @ fy) @ (fden @ fz)) @ (fts @ (fnum @ fz) @ (fden @ fy))), file('<stdin>', pax3)).
% 48.70/48.76 thf(ax11, axiom, p5, file('<stdin>', ax11)).
% 48.70/48.76 thf(ax13, axiom, p3, file('<stdin>', ax13)).
% 48.70/48.76 thf(pax2, axiom, (p2=>fless @ (fts @ (fnum @ fx) @ (fden @ fy)) @ (fts @ (fnum @ fy) @ (fden @ fx))), file('<stdin>', pax2)).
% 48.70/48.76 thf(ax14, axiom, p2, file('<stdin>', ax14)).
% 48.70/48.76 thf(nax1, axiom, (p1<=fless @ (fts @ (fnum @ fx) @ (fden @ fz)) @ (fts @ (fnum @ fz) @ (fden @ fx))), file('<stdin>', nax1)).
% 48.70/48.76 thf(ax15, axiom, ~(p1), file('<stdin>', ax15)).
% 48.70/48.76 thf(c_0_14, plain, ![X53:nat, X54:nat, X55:nat]:(~p4|(~fless @ (fts @ X53 @ X55) @ (fts @ X54 @ X55)|fless @ X53 @ X54)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 48.70/48.76 thf(c_0_15, plain, ![X41:nat, X42:nat]:(~p6|(fts @ X41 @ X42)=(fts @ X42 @ X41)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax6])])])).
% 48.70/48.76 thf(c_0_16, plain, ![X1:nat, X3:nat, X2:nat]:(fless @ X1 @ X3|~p4|~fless @ (fts @ X1 @ X2) @ (fts @ X3 @ X2)), inference(split_conjunct,[status(thm)],[c_0_14])).
% 48.70/48.76 thf(c_0_17, plain, p4, inference(split_conjunct,[status(thm)],[ax12])).
% 48.70/48.76 thf(c_0_18, plain, ![X2:nat, X1:nat]:((fts @ X1 @ X2)=(fts @ X2 @ X1)|~p6), inference(split_conjunct,[status(thm)],[c_0_15])).
% 48.70/48.76 thf(c_0_19, plain, p6, inference(split_conjunct,[status(thm)],[ax10])).
% 48.70/48.76 thf(c_0_20, plain, ![X35:nat, X36:nat, X37:nat]:(~p7|(fts @ (fts @ X35 @ X36) @ X37)=(fts @ X35 @ (fts @ X36 @ X37))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax7])])])).
% 48.70/48.76 thf(c_0_21, plain, ![X1:nat, X2:nat, X3:nat]:(fless @ X1 @ X2|~fless @ (fts @ X1 @ X3) @ (fts @ X2 @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16, c_0_17])])).
% 48.70/48.76 thf(c_0_22, plain, ![X2:nat, X1:nat]:(fts @ X1 @ X2)=(fts @ X2 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])])).
% 48.70/48.76 thf(c_0_23, plain, ![X1:nat, X2:nat, X3:nat]:((fts @ (fts @ X1 @ X2) @ X3)=(fts @ X1 @ (fts @ X2 @ X3))|~p7), inference(split_conjunct,[status(thm)],[c_0_20])).
% 48.70/48.76 thf(c_0_24, plain, p7, inference(split_conjunct,[status(thm)],[ax9])).
% 48.70/48.76 thf(c_0_25, plain, ![X45:nat, X46:nat, X47:nat, X48:nat]:(~p5|(~fless @ X45 @ X46|(~fless @ X47 @ X48|fless @ (fts @ X45 @ X47) @ (fts @ X46 @ X48)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax5])])])).
% 48.70/48.76 thf(c_0_26, plain, (~p3|fless @ (fts @ (fnum @ fy) @ (fden @ fz)) @ (fts @ (fnum @ fz) @ (fden @ fy))), inference(fof_nnf,[status(thm)],[pax3])).
% 48.70/48.76 thf(c_0_27, plain, ![X1:nat, X2:nat, X3:nat]:(fless @ X1 @ X2|~fless @ (fts @ X3 @ X1) @ (fts @ X2 @ X3)), inference(spm,[status(thm)],[c_0_21, c_0_22])).
% 48.70/48.76 thf(c_0_28, plain, ![X1:nat, X2:nat, X3:nat]:(fts @ (fts @ X1 @ X2) @ X3)=(fts @ X1 @ (fts @ X2 @ X3)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 48.70/48.76 thf(c_0_29, plain, ![X1:nat, X2:nat, X3:nat, X4:nat]:(fless @ (fts @ X1 @ X3) @ (fts @ X2 @ X4)|~p5|~fless @ X1 @ X2|~fless @ X3 @ X4), inference(split_conjunct,[status(thm)],[c_0_25])).
% 48.70/48.76 thf(c_0_30, plain, p5, inference(split_conjunct,[status(thm)],[ax11])).
% 48.70/48.76 thf(c_0_31, plain, (fless @ (fts @ (fnum @ fy) @ (fden @ fz)) @ (fts @ (fnum @ fz) @ (fden @ fy))|~p3), inference(split_conjunct,[status(thm)],[c_0_26])).
% 48.70/48.76 thf(c_0_32, plain, p3, inference(split_conjunct,[status(thm)],[ax13])).
% 48.70/48.76 thf(c_0_33, plain, (~p2|fless @ (fts @ (fnum @ fx) @ (fden @ fy)) @ (fts @ (fnum @ fy) @ (fden @ fx))), inference(fof_nnf,[status(thm)],[pax2])).
% 48.70/48.76 thf(c_0_34, plain, ![X1:nat, X3:nat, X2:nat]:(fless @ X1 @ X2|~fless @ (fts @ X3 @ X1) @ (fts @ X3 @ X2)), inference(spm,[status(thm)],[c_0_27, c_0_22])).
% 48.70/48.76 thf(c_0_35, plain, ![X3:nat, X2:nat, X1:nat]:(fts @ X1 @ (fts @ X2 @ X3))=(fts @ X2 @ (fts @ X3 @ X1)), inference(spm,[status(thm)],[c_0_28, c_0_22])).
% 48.70/48.76 thf(c_0_36, plain, ![X2:nat, X1:nat, X4:nat, X3:nat]:(fless @ (fts @ X1 @ X2) @ (fts @ X3 @ X4)|~fless @ X2 @ X4|~fless @ X1 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 48.70/48.76 thf(c_0_37, plain, fless @ (fts @ (fnum @ fy) @ (fden @ fz)) @ (fts @ (fnum @ fz) @ (fden @ fy)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 48.70/48.76 thf(c_0_38, plain, (fless @ (fts @ (fnum @ fx) @ (fden @ fy)) @ (fts @ (fnum @ fy) @ (fden @ fx))|~p2), inference(split_conjunct,[status(thm)],[c_0_33])).
% 48.70/48.76 thf(c_0_39, plain, p2, inference(split_conjunct,[status(thm)],[ax14])).
% 48.70/48.76 thf(c_0_40, plain, ![X1:nat, X4:nat, X3:nat, X2:nat]:(fless @ X1 @ (fts @ X2 @ X3)|~fless @ (fts @ X4 @ X1) @ (fts @ X3 @ (fts @ X4 @ X2))), inference(spm,[status(thm)],[c_0_34, c_0_35])).
% 48.70/48.76 thf(c_0_41, plain, ![X1:nat, X2:nat, X3:nat]:(fts @ X1 @ (fts @ X2 @ X3))=(fts @ X2 @ (fts @ X1 @ X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_22]), c_0_28])).
% 48.70/48.76 thf(c_0_42, plain, ![X1:nat, X2:nat]:(fless @ (fts @ X1 @ (fts @ (fnum @ fy) @ (fden @ fz))) @ (fts @ X2 @ (fts @ (fnum @ fz) @ (fden @ fy)))|~fless @ X1 @ X2), inference(spm,[status(thm)],[c_0_36, c_0_37])).
% 48.70/48.76 thf(c_0_43, plain, fless @ (fts @ (fnum @ fx) @ (fden @ fy)) @ (fts @ (fnum @ fy) @ (fden @ fx)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])).
% 48.70/48.76 thf(c_0_44, plain, (~fless @ (fts @ (fnum @ fx) @ (fden @ fz)) @ (fts @ (fnum @ fz) @ (fden @ fx))|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 48.70/48.76 thf(c_0_45, plain, ~p1, inference(fof_simplification,[status(thm)],[ax15])).
% 48.70/48.76 thf(c_0_46, plain, ![X1:nat, X2:nat, X3:nat, X4:nat]:(fless @ X1 @ (fts @ X2 @ X3)|~fless @ (fts @ X1 @ X4) @ (fts @ X2 @ (fts @ X3 @ X4))), inference(spm,[status(thm)],[c_0_21, c_0_28])).
% 48.70/48.76 thf(c_0_47, plain, ![X1:nat, X2:nat, X5:nat, X4:nat, X3:nat]:(fless @ (fts @ X1 @ X2) @ (fts @ X3 @ X4)|~fless @ (fts @ X1 @ (fts @ X5 @ X2)) @ (fts @ X4 @ (fts @ X5 @ X3))), inference(spm,[status(thm)],[c_0_40, c_0_41])).
% 48.70/48.76 thf(c_0_48, plain, fless @ (fts @ (fnum @ fx) @ (fts @ (fnum @ fy) @ (fts @ (fden @ fz) @ (fden @ fy)))) @ (fts @ (fnum @ fz) @ (fts @ (fnum @ fy) @ (fts @ (fden @ fx) @ (fden @ fy)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42, c_0_43]), c_0_28]), c_0_28]), c_0_35]), c_0_35]), c_0_22]), c_0_35]), c_0_28]), c_0_22]), c_0_35]), c_0_22])).
% 48.70/48.76 thf(c_0_49, plain, (p1|~fless @ (fts @ (fnum @ fx) @ (fden @ fz)) @ (fts @ (fnum @ fz) @ (fden @ fx))), inference(split_conjunct,[status(thm)],[c_0_44])).
% 48.70/48.76 thf(c_0_50, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_45])).
% 48.70/48.76 thf(c_0_51, plain, ![X1:nat, X2:nat, X3:nat, X4:nat, X5:nat]:(fless @ (fts @ X1 @ X2) @ (fts @ X3 @ X4)|~fless @ (fts @ X1 @ (fts @ X2 @ X5)) @ (fts @ X3 @ (fts @ X4 @ X5))), inference(spm,[status(thm)],[c_0_46, c_0_28])).
% 48.70/48.76 thf(c_0_52, plain, fless @ (fts @ (fnum @ fx) @ (fts @ (fden @ fz) @ (fden @ fy))) @ (fts @ (fnum @ fz) @ (fts @ (fden @ fx) @ (fden @ fy))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_28]), c_0_22]), c_0_35]), c_0_22])).
% 48.70/48.76 thf(c_0_53, plain, ~fless @ (fts @ (fnum @ fx) @ (fden @ fz)) @ (fts @ (fnum @ fz) @ (fden @ fx)), inference(sr,[status(thm)],[c_0_49, c_0_50])).
% 48.70/48.76 thf(c_0_54, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_51, c_0_52]), c_0_53]), ['proof']).
% 48.70/48.76 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 48.70/48.76 thf(0,theorem,((less @ ((ts @ (num @ x)) @ (den @ z))) @ ((ts @ (num @ z)) @ (den @ x))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 48.70/48.76 % SZS output end Proof
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