TSTP Solution File: ITP050^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP050^1 : 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 : n018.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 00:28:54 EDT 2022
% Result : Theorem 218.16s 218.23s
% Output : Proof 218.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : ITP050^1 : TPTP v8.1.0. Released v7.5.0.
% 0.12/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n018.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 : Fri Jun 3 12:30:01 EDT 2022
% 0.12/0.34 % CPUTime :
% 218.16/218.23 % SZS status Theorem
% 218.16/218.23 % Mode: mode505:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=256:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 218.16/218.23 % Inferences: 0
% 218.16/218.23 % SZS output start Proof
% 218.16/218.23 thf(conj_0,conjecture,((ord_le841296385at_nat @ edges) @ (e_a @ c))).
% 218.16/218.23 thf(h0,negated_conjecture,(~(((ord_le841296385at_nat @ edges) @ (e_a @ c)))),inference(assume_negation,[status(cth)],[conj_0])).
% 218.16/218.23 thf(pax55, axiom, (p55=>![X42:set_Pr1986765409at_nat, X43:set_Pr1986765409at_nat, X44:product_prod_nat_nat]:(ford_le841296385at_nat @ X42 @ X43=>(fmember701585322at_nat @ X44 @ X42=>fmember701585322at_nat @ X44 @ X43))), file('<stdin>', pax55)).
% 218.16/218.23 thf(pax3, axiom, (p3=>ford_le841296385at_nat @ fedges @ (fset_Pr2131844118at_nat @ fp)), file('<stdin>', pax3)).
% 218.16/218.23 thf(pax64, axiom, (p64=>![X33:product_prod_nat_nat > a, X34:nat, X35:list_P559422087at_nat, X29:nat, X36:product_prod_nat_nat]:(fisPath_a @ X33 @ X34 @ X35 @ X29=>(fmember701585322at_nat @ X36 @ (fset_Pr2131844118at_nat @ X35)=>fmember701585322at_nat @ X36 @ (fe_a @ X33)))), file('<stdin>', pax64)).
% 218.16/218.23 thf(ax56, axiom, p55, file('<stdin>', ax56)).
% 218.16/218.23 thf(ax108, axiom, p3, file('<stdin>', ax108)).
% 218.16/218.23 thf(pax17, axiom, (p17=>![X133:nat, X134:list_P559422087at_nat, X132:nat]:(fisShortestPath_a @ fc @ X133 @ X134 @ X132=>fisPath_a @ fc @ X133 @ X134 @ X132)), file('<stdin>', pax17)).
% 218.16/218.23 thf(pax2, axiom, (p2=>fisShortestPath_a @ fc @ fs @ fp @ ft), file('<stdin>', pax2)).
% 218.16/218.23 thf(ax47, axiom, p64, file('<stdin>', ax47)).
% 218.16/218.23 thf(ax94, axiom, p17, file('<stdin>', ax94)).
% 218.16/218.23 thf(ax109, axiom, p2, file('<stdin>', ax109)).
% 218.16/218.23 thf(pax11, axiom, (p11=>![X136:set_Pr1986765409at_nat, X137:set_Pr1986765409at_nat]:(![X138:product_prod_nat_nat]:(fmember701585322at_nat @ X138 @ X136=>fmember701585322at_nat @ X138 @ X137)=>ford_le841296385at_nat @ X136 @ X137)), file('<stdin>', pax11)).
% 218.16/218.23 thf(ax100, axiom, p11, file('<stdin>', ax100)).
% 218.16/218.23 thf(nax1, axiom, (p1<=ford_le841296385at_nat @ fedges @ (fe_a @ fc)), file('<stdin>', nax1)).
% 218.16/218.23 thf(ax110, axiom, ~(p1), file('<stdin>', ax110)).
% 218.16/218.23 thf(c_0_14, plain, ![X365:set_Pr1986765409at_nat, X366:set_Pr1986765409at_nat, X367:product_prod_nat_nat]:(~p55|(~ford_le841296385at_nat @ X365 @ X366|(~fmember701585322at_nat @ X367 @ X365|fmember701585322at_nat @ X367 @ X366))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax55])])])).
% 218.16/218.23 thf(c_0_15, plain, (~p3|ford_le841296385at_nat @ fedges @ (fset_Pr2131844118at_nat @ fp)), inference(fof_nnf,[status(thm)],[pax3])).
% 218.16/218.23 thf(c_0_16, plain, ![X329:product_prod_nat_nat > a, X330:nat, X331:list_P559422087at_nat, X332:nat, X333:product_prod_nat_nat]:(~p64|(~fisPath_a @ X329 @ X330 @ X331 @ X332|(~fmember701585322at_nat @ X333 @ (fset_Pr2131844118at_nat @ X331)|fmember701585322at_nat @ X333 @ (fe_a @ X329)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax64])])])).
% 218.16/218.23 thf(c_0_17, plain, ![X36:product_prod_nat_nat, X2:set_Pr1986765409at_nat, X1:set_Pr1986765409at_nat]:(fmember701585322at_nat @ X36 @ X2|~p55|~ford_le841296385at_nat @ X1 @ X2|~fmember701585322at_nat @ X36 @ X1), inference(split_conjunct,[status(thm)],[c_0_14])).
% 218.16/218.23 thf(c_0_18, plain, p55, inference(split_conjunct,[status(thm)],[ax56])).
% 218.16/218.23 thf(c_0_19, plain, (ford_le841296385at_nat @ fedges @ (fset_Pr2131844118at_nat @ fp)|~p3), inference(split_conjunct,[status(thm)],[c_0_15])).
% 218.16/218.23 thf(c_0_20, plain, p3, inference(split_conjunct,[status(thm)],[ax108])).
% 218.16/218.23 thf(c_0_21, plain, ![X661:nat, X662:list_P559422087at_nat, X663:nat]:(~p17|(~fisShortestPath_a @ fc @ X661 @ X662 @ X663|fisPath_a @ fc @ X661 @ X662 @ X663)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax17])])])).
% 218.16/218.23 thf(c_0_22, plain, (~p2|fisShortestPath_a @ fc @ fs @ fp @ ft), inference(fof_nnf,[status(thm)],[pax2])).
% 218.16/218.23 thf(c_0_23, plain, ![X3:nat, X12:product_prod_nat_nat > a, X14:nat, X36:product_prod_nat_nat, X16:list_P559422087at_nat]:(fmember701585322at_nat @ X36 @ (fe_a @ X12)|~p64|~fisPath_a @ X12 @ X3 @ X16 @ X14|~fmember701585322at_nat @ X36 @ (fset_Pr2131844118at_nat @ X16)), inference(split_conjunct,[status(thm)],[c_0_16])).
% 218.16/218.23 thf(c_0_24, plain, p64, inference(split_conjunct,[status(thm)],[ax47])).
% 218.16/218.23 thf(c_0_25, plain, ![X1:set_Pr1986765409at_nat, X36:product_prod_nat_nat, X2:set_Pr1986765409at_nat]:(fmember701585322at_nat @ X36 @ X1|~ford_le841296385at_nat @ X2 @ X1|~fmember701585322at_nat @ X36 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18])])).
% 218.16/218.23 thf(c_0_26, plain, ford_le841296385at_nat @ fedges @ (fset_Pr2131844118at_nat @ fp), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 218.16/218.23 thf(c_0_27, plain, ![X3:nat, X16:list_P559422087at_nat, X14:nat]:(fisPath_a @ fc @ X3 @ X16 @ X14|~p17|~fisShortestPath_a @ fc @ X3 @ X16 @ X14), inference(split_conjunct,[status(thm)],[c_0_21])).
% 218.16/218.23 thf(c_0_28, plain, p17, inference(split_conjunct,[status(thm)],[ax94])).
% 218.16/218.23 thf(c_0_29, plain, (fisShortestPath_a @ fc @ fs @ fp @ ft|~p2), inference(split_conjunct,[status(thm)],[c_0_22])).
% 218.16/218.23 thf(c_0_30, plain, p2, inference(split_conjunct,[status(thm)],[ax109])).
% 218.16/218.23 thf(c_0_31, plain, ![X681:set_Pr1986765409at_nat, X682:set_Pr1986765409at_nat]:((fmember701585322at_nat @ (esk271_2 @ X681 @ X682) @ X681|ford_le841296385at_nat @ X681 @ X682|~p11)&(~fmember701585322at_nat @ (esk271_2 @ X681 @ X682) @ X682|ford_le841296385at_nat @ X681 @ X682|~p11)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax11])])])])])).
% 218.16/218.23 thf(c_0_32, plain, ![X3:nat, X12:product_prod_nat_nat > a, X36:product_prod_nat_nat, X16:list_P559422087at_nat, X14:nat]:(fmember701585322at_nat @ X36 @ (fe_a @ X12)|~fmember701585322at_nat @ X36 @ (fset_Pr2131844118at_nat @ X16)|~fisPath_a @ X12 @ X3 @ X16 @ X14), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 218.16/218.23 thf(c_0_33, plain, ![X36:product_prod_nat_nat]:(fmember701585322at_nat @ X36 @ (fset_Pr2131844118at_nat @ fp)|~fmember701585322at_nat @ X36 @ fedges), inference(spm,[status(thm)],[c_0_25, c_0_26])).
% 218.16/218.23 thf(c_0_34, plain, ![X3:nat, X16:list_P559422087at_nat, X14:nat]:(fisPath_a @ fc @ X3 @ X16 @ X14|~fisShortestPath_a @ fc @ X3 @ X16 @ X14), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_28])])).
% 218.16/218.23 thf(c_0_35, plain, fisShortestPath_a @ fc @ fs @ fp @ ft, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30])])).
% 218.16/218.23 thf(c_0_36, plain, ![X1:set_Pr1986765409at_nat, X2:set_Pr1986765409at_nat]:(ford_le841296385at_nat @ X1 @ X2|~fmember701585322at_nat @ (esk271_2 @ X1 @ X2) @ X2|~p11), inference(split_conjunct,[status(thm)],[c_0_31])).
% 218.16/218.23 thf(c_0_37, plain, p11, inference(split_conjunct,[status(thm)],[ax100])).
% 218.16/218.23 thf(c_0_38, plain, ![X3:nat, X12:product_prod_nat_nat > a, X14:nat, X36:product_prod_nat_nat]:(fmember701585322at_nat @ X36 @ (fe_a @ X12)|~fisPath_a @ X12 @ X3 @ fp @ X14|~fmember701585322at_nat @ X36 @ fedges), inference(spm,[status(thm)],[c_0_32, c_0_33])).
% 218.16/218.23 thf(c_0_39, plain, fisPath_a @ fc @ fs @ fp @ ft, inference(spm,[status(thm)],[c_0_34, c_0_35])).
% 218.16/218.23 thf(c_0_40, plain, (~ford_le841296385at_nat @ fedges @ (fe_a @ fc)|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 218.16/218.23 thf(c_0_41, plain, ~p1, inference(fof_simplification,[status(thm)],[ax110])).
% 218.16/218.23 thf(c_0_42, plain, ![X1:set_Pr1986765409at_nat, X2:set_Pr1986765409at_nat]:(ford_le841296385at_nat @ X1 @ X2|~fmember701585322at_nat @ (esk271_2 @ X1 @ X2) @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37])])).
% 218.16/218.23 thf(c_0_43, plain, ![X36:product_prod_nat_nat]:(fmember701585322at_nat @ X36 @ (fe_a @ fc)|~fmember701585322at_nat @ X36 @ fedges), inference(spm,[status(thm)],[c_0_38, c_0_39])).
% 218.16/218.23 thf(c_0_44, plain, ![X1:set_Pr1986765409at_nat, X2:set_Pr1986765409at_nat]:(fmember701585322at_nat @ (esk271_2 @ X1 @ X2) @ X1|ford_le841296385at_nat @ X1 @ X2|~p11), inference(split_conjunct,[status(thm)],[c_0_31])).
% 218.16/218.23 thf(c_0_45, plain, (p1|~ford_le841296385at_nat @ fedges @ (fe_a @ fc)), inference(split_conjunct,[status(thm)],[c_0_40])).
% 218.16/218.23 thf(c_0_46, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_41])).
% 218.16/218.23 thf(c_0_47, plain, ![X1:set_Pr1986765409at_nat]:(ford_le841296385at_nat @ X1 @ (fe_a @ fc)|~fmember701585322at_nat @ (esk271_2 @ X1 @ (fe_a @ fc)) @ fedges), inference(spm,[status(thm)],[c_0_42, c_0_43])).
% 218.16/218.23 thf(c_0_48, plain, ![X1:set_Pr1986765409at_nat, X2:set_Pr1986765409at_nat]:(fmember701585322at_nat @ (esk271_2 @ X1 @ X2) @ X1|ford_le841296385at_nat @ X1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_37])])).
% 218.16/218.23 thf(c_0_49, plain, ~ford_le841296385at_nat @ fedges @ (fe_a @ fc), inference(sr,[status(thm)],[c_0_45, c_0_46])).
% 218.16/218.23 thf(c_0_50, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47, c_0_48]), c_0_49]), ['proof']).
% 218.16/218.23 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 218.16/218.23 thf(0,theorem,((ord_le841296385at_nat @ edges) @ (e_a @ c)),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 218.16/218.23 % SZS output end Proof
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