TSTP Solution File: SEU659^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU659^2 : 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 : n015.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 : Tue Jul 19 13:55:36 EDT 2022
% Result : Theorem 2.26s 2.47s
% Output : Proof 2.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU659^2 : TPTP v8.1.0. Released v3.7.0.
% 0.11/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n015.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 : Sun Jun 19 14:43:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.26/2.47 % SZS status Theorem
% 2.26/2.47 % Mode: mode506
% 2.26/2.47 % Inferences: 38739
% 2.26/2.47 % SZS output start Proof
% 2.26/2.47 thf(def_cartprodmempair1,definition,(cartprodmempair1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))))).
% 2.26/2.47 thf(def_setukpairinjL,definition,(setukpairinjL = (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))))).
% 2.26/2.47 thf(cartprodpairmemEL,conjecture,((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1))))))))).
% 2.26/2.47 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))))))),inference(assume_negation,[status(cth)],[cartprodpairmemEL])).
% 2.26/2.47 thf(ax1006, axiom, (p1|~(p3)), file('<stdin>', ax1006)).
% 2.26/2.47 thf(ax1008, axiom, ~(p1), file('<stdin>', ax1008)).
% 2.26/2.47 thf(ax1004, axiom, (p3|~(p5)), file('<stdin>', ax1004)).
% 2.26/2.47 thf(ax1003, axiom, (p5|~(p6)), file('<stdin>', ax1003)).
% 2.26/2.47 thf(ax1002, axiom, (p6|~(p7)), file('<stdin>', ax1002)).
% 2.26/2.47 thf(ax1001, axiom, (p7|~(p8)), file('<stdin>', ax1001)).
% 2.26/2.47 thf(ax1000, axiom, (p8|~(p9)), file('<stdin>', ax1000)).
% 2.26/2.47 thf(ax792, axiom, (~(p2)|p209), file('<stdin>', ax792)).
% 2.26/2.47 thf(ax1007, axiom, (p1|p2), file('<stdin>', ax1007)).
% 2.26/2.47 thf(ax793, axiom, (~(p209)|p208), file('<stdin>', ax793)).
% 2.26/2.47 thf(ax980, axiom, (~(p4)|p28), file('<stdin>', ax980)).
% 2.26/2.47 thf(ax1005, axiom, (p3|p4), file('<stdin>', ax1005)).
% 2.26/2.47 thf(ax795, axiom, (~(p207)|~(p10)|~(p206)), file('<stdin>', ax795)).
% 2.26/2.47 thf(ax999, axiom, (p9|p10), file('<stdin>', ax999)).
% 2.26/2.47 thf(ax794, axiom, (~(p208)|p207), file('<stdin>', ax794)).
% 2.26/2.47 thf(ax806, axiom, (~(p28)|p195), file('<stdin>', ax806)).
% 2.26/2.47 thf(ax752, axiom, (~(p195)|p248), file('<stdin>', ax752)).
% 2.26/2.47 thf(ax765, axiom, (p206|~(p236)), file('<stdin>', ax765)).
% 2.26/2.47 thf(ax753, axiom, (~(p248)|p247), file('<stdin>', ax753)).
% 2.26/2.47 thf(ax763, axiom, (p236|~(p238)), file('<stdin>', ax763)).
% 2.26/2.47 thf(ax762, axiom, (p238|~(p239)), file('<stdin>', ax762)).
% 2.26/2.47 thf(ax754, axiom, (~(p247)|~(p241)|p246), file('<stdin>', ax754)).
% 2.26/2.47 thf(ax760, axiom, (p239|p241), file('<stdin>', ax760)).
% 2.26/2.47 thf(pax246, axiom, (p246=>(f__2)=(f__4)), file('<stdin>', pax246)).
% 2.26/2.47 thf(nax8, axiom, (p8<=![X1:$i]:(fin @ (fkpair @ f__2 @ X1) @ (fcartprod @ f__0 @ f__1)=>fin @ f__2 @ f__0)), file('<stdin>', nax8)).
% 2.26/2.47 thf(nax236, axiom, (p236<=(fin @ f__4 @ f__0=>![X1:$i]:(fin @ X1 @ f__1=>~((fkpair @ f__2 @ f__3)=(fkpair @ f__4 @ X1))))), file('<stdin>', nax236)).
% 2.26/2.47 thf(c_0_26, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1006])).
% 2.26/2.47 thf(c_0_27, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1008])).
% 2.26/2.47 thf(c_0_28, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1004])).
% 2.26/2.47 thf(c_0_29, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_26])).
% 2.26/2.47 thf(c_0_30, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_27])).
% 2.26/2.47 thf(c_0_31, plain, (p5|~p6), inference(fof_simplification,[status(thm)],[ax1003])).
% 2.26/2.47 thf(c_0_32, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_28])).
% 2.26/2.47 thf(c_0_33, plain, ~p3, inference(sr,[status(thm)],[c_0_29, c_0_30])).
% 2.26/2.47 thf(c_0_34, plain, (p6|~p7), inference(fof_simplification,[status(thm)],[ax1002])).
% 2.26/2.47 thf(c_0_35, plain, (p5|~p6), inference(split_conjunct,[status(thm)],[c_0_31])).
% 2.26/2.47 thf(c_0_36, plain, ~p5, inference(sr,[status(thm)],[c_0_32, c_0_33])).
% 2.26/2.47 thf(c_0_37, plain, (p7|~p8), inference(fof_simplification,[status(thm)],[ax1001])).
% 2.26/2.47 thf(c_0_38, plain, (p6|~p7), inference(split_conjunct,[status(thm)],[c_0_34])).
% 2.26/2.47 thf(c_0_39, plain, ~p6, inference(sr,[status(thm)],[c_0_35, c_0_36])).
% 2.26/2.47 thf(c_0_40, plain, (p8|~p9), inference(fof_simplification,[status(thm)],[ax1000])).
% 2.26/2.47 thf(c_0_41, plain, (p7|~p8), inference(split_conjunct,[status(thm)],[c_0_37])).
% 2.26/2.47 thf(c_0_42, plain, ~p7, inference(sr,[status(thm)],[c_0_38, c_0_39])).
% 2.26/2.47 thf(c_0_43, plain, (~p2|p209), inference(fof_simplification,[status(thm)],[ax792])).
% 2.26/2.47 thf(c_0_44, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax1007])).
% 2.26/2.47 thf(c_0_45, plain, (p8|~p9), inference(split_conjunct,[status(thm)],[c_0_40])).
% 2.26/2.47 thf(c_0_46, plain, ~p8, inference(sr,[status(thm)],[c_0_41, c_0_42])).
% 2.26/2.47 thf(c_0_47, plain, (~p209|p208), inference(fof_simplification,[status(thm)],[ax793])).
% 2.26/2.47 thf(c_0_48, plain, (p209|~p2), inference(split_conjunct,[status(thm)],[c_0_43])).
% 2.26/2.47 thf(c_0_49, plain, p2, inference(sr,[status(thm)],[c_0_44, c_0_30])).
% 2.26/2.47 thf(c_0_50, plain, (~p4|p28), inference(fof_simplification,[status(thm)],[ax980])).
% 2.26/2.47 thf(c_0_51, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax1005])).
% 2.26/2.47 thf(c_0_52, plain, (~p207|~p10|~p206), inference(fof_simplification,[status(thm)],[ax795])).
% 2.26/2.47 thf(c_0_53, plain, (p9|p10), inference(split_conjunct,[status(thm)],[ax999])).
% 2.26/2.47 thf(c_0_54, plain, ~p9, inference(sr,[status(thm)],[c_0_45, c_0_46])).
% 2.26/2.47 thf(c_0_55, plain, (~p208|p207), inference(fof_simplification,[status(thm)],[ax794])).
% 2.26/2.47 thf(c_0_56, plain, (p208|~p209), inference(split_conjunct,[status(thm)],[c_0_47])).
% 2.26/2.47 thf(c_0_57, plain, p209, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_49])])).
% 2.26/2.47 thf(c_0_58, plain, (~p28|p195), inference(fof_simplification,[status(thm)],[ax806])).
% 2.26/2.47 thf(c_0_59, plain, (p28|~p4), inference(split_conjunct,[status(thm)],[c_0_50])).
% 2.26/2.47 thf(c_0_60, plain, p4, inference(sr,[status(thm)],[c_0_51, c_0_33])).
% 2.26/2.47 thf(c_0_61, plain, (~p207|~p10|~p206), inference(split_conjunct,[status(thm)],[c_0_52])).
% 2.26/2.47 thf(c_0_62, plain, p10, inference(sr,[status(thm)],[c_0_53, c_0_54])).
% 2.26/2.47 thf(c_0_63, plain, (p207|~p208), inference(split_conjunct,[status(thm)],[c_0_55])).
% 2.26/2.47 thf(c_0_64, plain, p208, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_56, c_0_57])])).
% 2.26/2.47 thf(c_0_65, plain, (~p195|p248), inference(fof_simplification,[status(thm)],[ax752])).
% 2.26/2.47 thf(c_0_66, plain, (p195|~p28), inference(split_conjunct,[status(thm)],[c_0_58])).
% 2.26/2.47 thf(c_0_67, plain, p28, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_60])])).
% 2.26/2.47 thf(c_0_68, plain, (p206|~p236), inference(fof_simplification,[status(thm)],[ax765])).
% 2.26/2.47 thf(c_0_69, plain, (~p206|~p207), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_62])])).
% 2.26/2.47 thf(c_0_70, plain, p207, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_64])])).
% 2.26/2.47 thf(c_0_71, plain, (~p248|p247), inference(fof_simplification,[status(thm)],[ax753])).
% 2.26/2.47 thf(c_0_72, plain, (p248|~p195), inference(split_conjunct,[status(thm)],[c_0_65])).
% 2.26/2.47 thf(c_0_73, plain, p195, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66, c_0_67])])).
% 2.26/2.47 thf(c_0_74, plain, (p236|~p238), inference(fof_simplification,[status(thm)],[ax763])).
% 2.26/2.47 thf(c_0_75, plain, (p238|~p239), inference(fof_simplification,[status(thm)],[ax762])).
% 2.26/2.47 thf(c_0_76, plain, (p206|~p236), inference(split_conjunct,[status(thm)],[c_0_68])).
% 2.26/2.47 thf(c_0_77, plain, ~p206, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_69, c_0_70])])).
% 2.26/2.47 thf(c_0_78, plain, (~p247|~p241|p246), inference(fof_simplification,[status(thm)],[ax754])).
% 2.26/2.47 thf(c_0_79, plain, (p247|~p248), inference(split_conjunct,[status(thm)],[c_0_71])).
% 2.26/2.47 thf(c_0_80, plain, p248, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_72, c_0_73])])).
% 2.26/2.47 thf(c_0_81, plain, (p236|~p238), inference(split_conjunct,[status(thm)],[c_0_74])).
% 2.26/2.47 thf(c_0_82, plain, (p238|~p239), inference(split_conjunct,[status(thm)],[c_0_75])).
% 2.26/2.47 thf(c_0_83, plain, ~p236, inference(sr,[status(thm)],[c_0_76, c_0_77])).
% 2.26/2.47 thf(c_0_84, plain, (p246|~p247|~p241), inference(split_conjunct,[status(thm)],[c_0_78])).
% 2.26/2.47 thf(c_0_85, plain, p247, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_79, c_0_80])])).
% 2.26/2.47 thf(c_0_86, plain, (p239|p241), inference(split_conjunct,[status(thm)],[ax760])).
% 2.26/2.47 thf(c_0_87, plain, ~p239, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81, c_0_82]), c_0_83])).
% 2.26/2.47 thf(c_0_88, plain, (~p246|(f__2)=(f__4)), inference(fof_nnf,[status(thm)],[pax246])).
% 2.26/2.47 thf(c_0_89, plain, (p246|~p241), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_84, c_0_85])])).
% 2.26/2.47 thf(c_0_90, plain, p241, inference(sr,[status(thm)],[c_0_86, c_0_87])).
% 2.26/2.47 thf(c_0_91, plain, ((fin @ (fkpair @ f__2 @ esk918_0) @ (fcartprod @ f__0 @ f__1)|p8)&(~fin @ f__2 @ f__0|p8)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax8])])])])])).
% 2.26/2.47 thf(c_0_92, plain, ((fin @ f__4 @ f__0|p236)&((fin @ esk661_0 @ f__1|p236)&((fkpair @ f__2 @ f__3)=(fkpair @ f__4 @ esk661_0)|p236))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax236])])])])])).
% 2.26/2.47 thf(c_0_93, plain, ((f__2)=(f__4)|~p246), inference(split_conjunct,[status(thm)],[c_0_88])).
% 2.26/2.47 thf(c_0_94, plain, p246, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_89, c_0_90])])).
% 2.26/2.47 thf(c_0_95, plain, (p8|~fin @ f__2 @ f__0), inference(split_conjunct,[status(thm)],[c_0_91])).
% 2.26/2.47 thf(c_0_96, plain, (fin @ f__4 @ f__0|p236), inference(split_conjunct,[status(thm)],[c_0_92])).
% 2.26/2.47 thf(c_0_97, plain, (f__4)=(f__2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_93, c_0_94])])).
% 2.26/2.47 thf(c_0_98, plain, ~fin @ f__2 @ f__0, inference(sr,[status(thm)],[c_0_95, c_0_46])).
% 2.26/2.47 thf(c_0_99, plain, ($false), inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_96, c_0_97]), c_0_98]), c_0_83]), ['proof']).
% 2.26/2.47 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 2.26/2.47 thf(0,theorem,((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((kpair @ X1) @ X2) = ((kpair @ X3) @ X4)) => (X1 = X3)))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((in @ ((kpair @ X3) @ X4)) @ ((cartprod @ X1) @ X2)) => ((in @ X3) @ X1)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 2.26/2.47 % SZS output end Proof
%------------------------------------------------------------------------------