TSTP Solution File: SEU646^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU646^2 : 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 : n032.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 13:55:05 EDT 2022
% Result : Theorem 2.41s 2.61s
% Output : Proof 2.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU646^2 : TPTP v8.1.0. Released v3.7.0.
% 0.00/0.10 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 600
% 0.10/0.28 % DateTime : Sun Jun 19 20:53:48 EDT 2022
% 0.10/0.28 % CPUTime :
% 2.41/2.61 % SZS status Theorem
% 2.41/2.61 % Mode: mode506
% 2.41/2.61 % Inferences: 39306
% 2.41/2.61 % SZS output start Proof
% 2.41/2.61 thf(def_kpair,definition,(kpair = (^[X1:$i]:(^[X2:$i]:((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))).
% 2.41/2.61 thf(def_cartprodmempair1,definition,(cartprodmempair1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))))).
% 2.41/2.61 thf(def_kfstpairEq,definition,(kfstpairEq = (![X1:$i]:(![X2:$i]:((kfst @ ((kpair @ X1) @ X2)) = X1))))).
% 2.41/2.61 thf(cartprodfstin,conjecture,((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((setadjoin @ ((setadjoin @ X4) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X4) @ ((setadjoin @ X5) @ emptyset))) @ emptyset))))))))))))))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) = X1))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1)))))))).
% 2.41/2.61 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((setadjoin @ ((setadjoin @ X4) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X4) @ ((setadjoin @ X5) @ emptyset))) @ emptyset))))))))))))))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) = X1))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))))))),inference(assume_negation,[status(cth)],[cartprodfstin])).
% 2.41/2.61 thf(ax1491, axiom, (p1|~(p3)), file('<stdin>', ax1491)).
% 2.41/2.61 thf(ax1493, axiom, ~(p1), file('<stdin>', ax1493)).
% 2.41/2.61 thf(ax1489, axiom, (p3|~(p5)), file('<stdin>', ax1489)).
% 2.41/2.61 thf(ax1488, axiom, (p5|~(p6)), file('<stdin>', ax1488)).
% 2.41/2.61 thf(ax1487, axiom, (p6|~(p7)), file('<stdin>', ax1487)).
% 2.41/2.61 thf(ax1486, axiom, (p7|~(p8)), file('<stdin>', ax1486)).
% 2.41/2.61 thf(ax861, axiom, (~(p2)|p457), file('<stdin>', ax861)).
% 2.41/2.61 thf(ax1492, axiom, (p1|p2), file('<stdin>', ax1492)).
% 2.41/2.61 thf(ax862, axiom, (~(p457)|p456), file('<stdin>', ax862)).
% 2.41/2.61 thf(ax864, axiom, (~(p455)|~(p9)|~(p454)), file('<stdin>', ax864)).
% 2.41/2.61 thf(ax1485, axiom, (p8|p9), file('<stdin>', ax1485)).
% 2.41/2.61 thf(ax863, axiom, (~(p456)|p455), file('<stdin>', ax863)).
% 2.41/2.61 thf(pax4, axiom, (p4=>![X1:$i, X2:$i]:(fkfst @ (fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset)))=(X1)), file('<stdin>', pax4)).
% 2.41/2.61 thf(ax1490, axiom, (p3|p4), file('<stdin>', ax1490)).
% 2.41/2.61 thf(nax454, axiom, (p454<=![X1:$i]:(fin @ X1 @ f__0=>![X2:$i]:(fin @ X2 @ f__1=>~((f__2)=(fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset)))))), file('<stdin>', nax454)).
% 2.41/2.61 thf(nax8, axiom, (p8<=(fin @ f__2 @ (fcartprod @ f__0 @ f__1)=>fin @ (fkfst @ f__2) @ f__0)), file('<stdin>', nax8)).
% 2.41/2.61 thf(c_0_16, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1491])).
% 2.41/2.61 thf(c_0_17, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1493])).
% 2.41/2.61 thf(c_0_18, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1489])).
% 2.41/2.61 thf(c_0_19, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_16])).
% 2.41/2.61 thf(c_0_20, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_17])).
% 2.41/2.61 thf(c_0_21, plain, (p5|~p6), inference(fof_simplification,[status(thm)],[ax1488])).
% 2.41/2.61 thf(c_0_22, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_18])).
% 2.41/2.61 thf(c_0_23, plain, ~p3, inference(sr,[status(thm)],[c_0_19, c_0_20])).
% 2.41/2.61 thf(c_0_24, plain, (p6|~p7), inference(fof_simplification,[status(thm)],[ax1487])).
% 2.41/2.61 thf(c_0_25, plain, (p5|~p6), inference(split_conjunct,[status(thm)],[c_0_21])).
% 2.41/2.61 thf(c_0_26, plain, ~p5, inference(sr,[status(thm)],[c_0_22, c_0_23])).
% 2.41/2.61 thf(c_0_27, plain, (p7|~p8), inference(fof_simplification,[status(thm)],[ax1486])).
% 2.41/2.61 thf(c_0_28, plain, (p6|~p7), inference(split_conjunct,[status(thm)],[c_0_24])).
% 2.41/2.61 thf(c_0_29, plain, ~p6, inference(sr,[status(thm)],[c_0_25, c_0_26])).
% 2.41/2.61 thf(c_0_30, plain, (~p2|p457), inference(fof_simplification,[status(thm)],[ax861])).
% 2.41/2.61 thf(c_0_31, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax1492])).
% 2.41/2.61 thf(c_0_32, plain, (p7|~p8), inference(split_conjunct,[status(thm)],[c_0_27])).
% 2.41/2.61 thf(c_0_33, plain, ~p7, inference(sr,[status(thm)],[c_0_28, c_0_29])).
% 2.41/2.61 thf(c_0_34, plain, (~p457|p456), inference(fof_simplification,[status(thm)],[ax862])).
% 2.41/2.61 thf(c_0_35, plain, (p457|~p2), inference(split_conjunct,[status(thm)],[c_0_30])).
% 2.41/2.61 thf(c_0_36, plain, p2, inference(sr,[status(thm)],[c_0_31, c_0_20])).
% 2.41/2.61 thf(c_0_37, plain, (~p455|~p9|~p454), inference(fof_simplification,[status(thm)],[ax864])).
% 2.41/2.61 thf(c_0_38, plain, (p8|p9), inference(split_conjunct,[status(thm)],[ax1485])).
% 2.41/2.61 thf(c_0_39, plain, ~p8, inference(sr,[status(thm)],[c_0_32, c_0_33])).
% 2.41/2.61 thf(c_0_40, plain, (~p456|p455), inference(fof_simplification,[status(thm)],[ax863])).
% 2.41/2.61 thf(c_0_41, plain, (p456|~p457), inference(split_conjunct,[status(thm)],[c_0_34])).
% 2.41/2.61 thf(c_0_42, plain, p457, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_35, c_0_36])])).
% 2.41/2.61 thf(c_0_43, plain, (~p455|~p9|~p454), inference(split_conjunct,[status(thm)],[c_0_37])).
% 2.41/2.61 thf(c_0_44, plain, p9, inference(sr,[status(thm)],[c_0_38, c_0_39])).
% 2.41/2.61 thf(c_0_45, plain, (p455|~p456), inference(split_conjunct,[status(thm)],[c_0_40])).
% 2.41/2.61 thf(c_0_46, plain, p456, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_41, c_0_42])])).
% 2.41/2.61 thf(c_0_47, plain, ![X1524:$i, X1525:$i]:(~p4|(fkfst @ (fsetadjoin @ (fsetadjoin @ X1524 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1524 @ (fsetadjoin @ X1525 @ femptyset)) @ femptyset)))=(X1524)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 2.41/2.61 thf(c_0_48, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax1490])).
% 2.41/2.61 thf(c_0_49, plain, ((fin @ esk552_0 @ f__0|p454)&((fin @ esk553_0 @ f__1|p454)&((f__2)=(fsetadjoin @ (fsetadjoin @ esk552_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk552_0 @ (fsetadjoin @ esk553_0 @ femptyset)) @ femptyset))|p454))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax454])])])])])).
% 2.41/2.61 thf(c_0_50, plain, (~p454|~p455), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])).
% 2.41/2.61 thf(c_0_51, plain, p455, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 2.41/2.61 thf(c_0_52, plain, ((fin @ f__2 @ (fcartprod @ f__0 @ f__1)|p8)&(~fin @ (fkfst @ f__2) @ f__0|p8)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax8])])])).
% 2.41/2.61 thf(c_0_53, plain, ![X2:$i, X1:$i]:((fkfst @ (fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset)))=(X1)|~p4), inference(split_conjunct,[status(thm)],[c_0_47])).
% 2.41/2.61 thf(c_0_54, plain, p4, inference(sr,[status(thm)],[c_0_48, c_0_23])).
% 2.41/2.61 thf(c_0_55, plain, ((f__2)=(fsetadjoin @ (fsetadjoin @ esk552_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk552_0 @ (fsetadjoin @ esk553_0 @ femptyset)) @ femptyset))|p454), inference(split_conjunct,[status(thm)],[c_0_49])).
% 2.41/2.61 thf(c_0_56, plain, ~p454, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_50, c_0_51])])).
% 2.41/2.61 thf(c_0_57, plain, (p8|~fin @ (fkfst @ f__2) @ f__0), inference(split_conjunct,[status(thm)],[c_0_52])).
% 2.41/2.61 thf(c_0_58, plain, ![X2:$i, X1:$i]:(fkfst @ (fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset)))=(X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54])])).
% 2.41/2.61 thf(c_0_59, plain, (fsetadjoin @ (fsetadjoin @ esk552_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk552_0 @ (fsetadjoin @ esk553_0 @ femptyset)) @ femptyset))=(f__2), inference(sr,[status(thm)],[c_0_55, c_0_56])).
% 2.41/2.61 thf(c_0_60, plain, (fin @ esk552_0 @ f__0|p454), inference(split_conjunct,[status(thm)],[c_0_49])).
% 2.41/2.61 thf(c_0_61, plain, ~fin @ (fkfst @ f__2) @ f__0, inference(sr,[status(thm)],[c_0_57, c_0_39])).
% 2.41/2.61 thf(c_0_62, plain, (fkfst @ f__2)=(esk552_0), inference(spm,[status(thm)],[c_0_58, c_0_59])).
% 2.41/2.61 thf(c_0_63, plain, fin @ esk552_0 @ f__0, inference(sr,[status(thm)],[c_0_60, c_0_56])).
% 2.41/2.61 thf(c_0_64, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_62]), c_0_63])]), ['proof']).
% 2.41/2.61 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 2.41/2.61 thf(0,theorem,((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((setadjoin @ ((setadjoin @ X4) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X4) @ ((setadjoin @ X5) @ emptyset))) @ emptyset))))))))))))))) => ((![X1:$i]:(![X2:$i]:((kfst @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) = X1))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => ((in @ (kfst @ X3)) @ X1))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 2.41/2.61 % SZS output end Proof
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