TSTP Solution File: SEU664^2 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU664^2 : 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 : n007.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 13:55:52 EDT 2022
% Result : Theorem 44.01s 44.11s
% Output : Proof 44.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SEU664^2 : TPTP v8.1.0. Released v3.7.0.
% 0.09/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.36 % Computer : n007.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sun Jun 19 04:33:13 EDT 2022
% 0.14/0.36 % CPUTime :
% 44.01/44.11 % SZS status Theorem
% 44.01/44.11 % Mode: mode459
% 44.01/44.11 % Inferences: 52
% 44.01/44.11 % SZS output start Proof
% 44.01/44.11 thf(def_cartprodmempair1,definition,(cartprodmempair1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (~((![X4:$i]:(((in @ X4) @ X1) => (![X5:$i]:(((in @ X5) @ X2) => (~((X3 = ((kpair @ X4) @ X5)))))))))))))))).
% 44.01/44.11 thf(def_cartprodfstpairEq,definition,(cartprodfstpairEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))))).
% 44.01/44.11 thf(def_cartprodsndpairEq,definition,(cartprodsndpairEq = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))))).
% 44.01/44.11 thf(cartprodpairsurjEq,conjecture,((![X1:$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:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3))))))))).
% 44.01/44.11 thf(h0,negated_conjecture,(~(((![X1:$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:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3)))))))))),inference(assume_negation,[status(cth)],[cartprodpairsurjEq])).
% 44.01/44.11 thf(ax116, axiom, (p1|~(p3)), file('<stdin>', ax116)).
% 44.01/44.11 thf(ax118, axiom, ~(p1), file('<stdin>', ax118)).
% 44.01/44.11 thf(ax114, axiom, (p3|~(p5)), file('<stdin>', ax114)).
% 44.01/44.11 thf(ax110, axiom, (p5|~(p9)), file('<stdin>', ax110)).
% 44.01/44.11 thf(ax108, axiom, (p9|~(p11)), file('<stdin>', ax108)).
% 44.01/44.11 thf(ax107, axiom, (p11|~(p12)), file('<stdin>', ax107)).
% 44.01/44.11 thf(ax106, axiom, (p12|~(p13)), file('<stdin>', ax106)).
% 44.01/44.11 thf(ax100, axiom, (~(p2)|p19), file('<stdin>', ax100)).
% 44.01/44.11 thf(ax117, axiom, (p1|p2), file('<stdin>', ax117)).
% 44.01/44.11 thf(ax101, axiom, (~(p19)|p18), file('<stdin>', ax101)).
% 44.01/44.11 thf(ax103, axiom, (~(p17)|~(p14)|~(p16)), file('<stdin>', ax103)).
% 44.01/44.11 thf(ax105, axiom, (p13|p14), file('<stdin>', ax105)).
% 44.01/44.11 thf(ax102, axiom, (~(p18)|p17), file('<stdin>', ax102)).
% 44.01/44.11 thf(nax24, axiom, (p24<=![X1:$i]:((f__3)=(X1)=>(X1)=(f__3))), file('<stdin>', nax24)).
% 44.01/44.11 thf(ax86, axiom, (p16|~(p32)), file('<stdin>', ax86)).
% 44.01/44.11 thf(ax94, axiom, (~(p24)|p25), file('<stdin>', ax94)).
% 44.01/44.11 thf(ax104, axiom, (p13|~(p15)), file('<stdin>', ax104)).
% 44.01/44.11 thf(nax1, axiom, (p1<=(![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ (fcartprod @ X1 @ X2)=>~(![X4:$i]:(fin @ X4 @ X1=>![X5:$i]:(fin @ X5 @ X2=>~((X3)=(fkpair @ X4 @ X5))))))=>(![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ X1=>![X4:$i]:(fin @ X4 @ X2=>(fkfst @ (fkpair @ X3 @ X4))=(X3)))=>(![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ X1=>![X4:$i]:(fin @ X4 @ X2=>(fksnd @ (fkpair @ X3 @ X4))=(X4)))=>![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ (fcartprod @ X1 @ X2)=>(fkpair @ (fkfst @ X3) @ (fksnd @ X3))=(X3)))))), file('<stdin>', nax1)).
% 44.01/44.11 thf(nax16, axiom, (p16<=![X1:$i]:(fin @ X1 @ f__1=>![X2:$i]:(fin @ X2 @ f__2=>~((f__3)=(fkpair @ X1 @ X2))))), file('<stdin>', nax16)).
% 44.01/44.11 thf(ax84, axiom, (p32|~(p34)), file('<stdin>', ax84)).
% 44.01/44.11 thf(ax83, axiom, (p34|~(p35)), file('<stdin>', ax83)).
% 44.01/44.11 thf(ax93, axiom, (~(p25)|~(p20)|p15), file('<stdin>', ax93)).
% 44.01/44.11 thf(nax32, axiom, (p32<=(fin @ f__4 @ f__1=>![X1:$i]:(fin @ X1 @ f__2=>~((f__3)=(fkpair @ f__4 @ X1))))), file('<stdin>', nax32)).
% 44.01/44.11 thf(nax35, axiom, (p35<=(fin @ f__5 @ f__2=>~((f__3)=(fkpair @ f__4 @ f__5)))), file('<stdin>', nax35)).
% 44.01/44.11 thf(nax20, axiom, (p20<=(f__3)=(fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))), file('<stdin>', nax20)).
% 44.01/44.11 thf(pax33, axiom, (p33=>fin @ f__4 @ f__1), file('<stdin>', pax33)).
% 44.01/44.11 thf(ax85, axiom, (p32|p33), file('<stdin>', ax85)).
% 44.01/44.11 thf(pax44, axiom, (p44=>(fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))=(fkpair @ f__4 @ f__5)), file('<stdin>', pax44)).
% 44.01/44.11 thf(pax8, axiom, (p8=>![X1:$i, X2:$i, X3:$i]:(fin @ X3 @ X1=>![X4:$i]:(fin @ X4 @ X2=>(fksnd @ (fkpair @ X3 @ X4))=(X4)))), file('<stdin>', pax8)).
% 44.01/44.11 thf(ax111, axiom, (p5|p8), file('<stdin>', ax111)).
% 44.01/44.11 thf(nax44, axiom, (p44<=(fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))=(fkpair @ f__4 @ f__5)), file('<stdin>', nax44)).
% 44.01/44.11 thf(c_0_31, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax116])).
% 44.01/44.11 thf(c_0_32, plain, ~p1, inference(fof_simplification,[status(thm)],[ax118])).
% 44.01/44.11 thf(c_0_33, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax114])).
% 44.01/44.11 thf(c_0_34, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_31])).
% 44.01/44.11 thf(c_0_35, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_32])).
% 44.01/44.11 thf(c_0_36, plain, (p5|~p9), inference(fof_simplification,[status(thm)],[ax110])).
% 44.01/44.11 thf(c_0_37, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_33])).
% 44.01/44.11 thf(c_0_38, plain, ~p3, inference(sr,[status(thm)],[c_0_34, c_0_35])).
% 44.01/44.11 thf(c_0_39, plain, (p9|~p11), inference(fof_simplification,[status(thm)],[ax108])).
% 44.01/44.11 thf(c_0_40, plain, (p5|~p9), inference(split_conjunct,[status(thm)],[c_0_36])).
% 44.01/44.11 thf(c_0_41, plain, ~p5, inference(sr,[status(thm)],[c_0_37, c_0_38])).
% 44.01/44.11 thf(c_0_42, plain, (p11|~p12), inference(fof_simplification,[status(thm)],[ax107])).
% 44.01/44.11 thf(c_0_43, plain, (p9|~p11), inference(split_conjunct,[status(thm)],[c_0_39])).
% 44.01/44.11 thf(c_0_44, plain, ~p9, inference(sr,[status(thm)],[c_0_40, c_0_41])).
% 44.01/44.11 thf(c_0_45, plain, (p12|~p13), inference(fof_simplification,[status(thm)],[ax106])).
% 44.01/44.11 thf(c_0_46, plain, (p11|~p12), inference(split_conjunct,[status(thm)],[c_0_42])).
% 44.01/44.11 thf(c_0_47, plain, ~p11, inference(sr,[status(thm)],[c_0_43, c_0_44])).
% 44.01/44.11 thf(c_0_48, plain, (~p2|p19), inference(fof_simplification,[status(thm)],[ax100])).
% 44.01/44.11 thf(c_0_49, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax117])).
% 44.01/44.11 thf(c_0_50, plain, (p12|~p13), inference(split_conjunct,[status(thm)],[c_0_45])).
% 44.01/44.11 thf(c_0_51, plain, ~p12, inference(sr,[status(thm)],[c_0_46, c_0_47])).
% 44.01/44.11 thf(c_0_52, plain, (~p19|p18), inference(fof_simplification,[status(thm)],[ax101])).
% 44.01/44.11 thf(c_0_53, plain, (p19|~p2), inference(split_conjunct,[status(thm)],[c_0_48])).
% 44.01/44.11 thf(c_0_54, plain, p2, inference(sr,[status(thm)],[c_0_49, c_0_35])).
% 44.01/44.11 thf(c_0_55, plain, (~p17|~p14|~p16), inference(fof_simplification,[status(thm)],[ax103])).
% 44.01/44.11 thf(c_0_56, plain, (p13|p14), inference(split_conjunct,[status(thm)],[ax105])).
% 44.01/44.11 thf(c_0_57, plain, ~p13, inference(sr,[status(thm)],[c_0_50, c_0_51])).
% 44.01/44.11 thf(c_0_58, plain, (~p18|p17), inference(fof_simplification,[status(thm)],[ax102])).
% 44.01/44.11 thf(c_0_59, plain, (p18|~p19), inference(split_conjunct,[status(thm)],[c_0_52])).
% 44.01/44.11 thf(c_0_60, plain, p19, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_53, c_0_54])])).
% 44.01/44.11 thf(c_0_61, plain, (~p17|~p14|~p16), inference(split_conjunct,[status(thm)],[c_0_55])).
% 44.01/44.11 thf(c_0_62, plain, p14, inference(sr,[status(thm)],[c_0_56, c_0_57])).
% 44.01/44.11 thf(c_0_63, plain, (p17|~p18), inference(split_conjunct,[status(thm)],[c_0_58])).
% 44.01/44.11 thf(c_0_64, plain, p18, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_59, c_0_60])])).
% 44.01/44.11 thf(c_0_65, plain, (((f__3)=(esk134_0)|p24)&((esk134_0)!=(f__3)|p24)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax24])])])])])).
% 44.01/44.11 thf(c_0_66, plain, (p16|~p32), inference(fof_simplification,[status(thm)],[ax86])).
% 44.01/44.11 thf(c_0_67, plain, (~p16|~p17), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_61, c_0_62])])).
% 44.01/44.11 thf(c_0_68, plain, p17, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_63, c_0_64])])).
% 44.01/44.11 thf(c_0_69, plain, (~p24|p25), inference(fof_simplification,[status(thm)],[ax94])).
% 44.01/44.11 thf(c_0_70, plain, ((f__3)=(esk134_0)|p24), inference(split_conjunct,[status(thm)],[c_0_65])).
% 44.01/44.11 thf(c_0_71, plain, (p24|(esk134_0)!=(f__3)), inference(split_conjunct,[status(thm)],[c_0_65])).
% 44.01/44.11 thf(c_0_72, plain, (p13|~p15), inference(fof_simplification,[status(thm)],[ax104])).
% 44.01/44.11 thf(c_0_73, plain, ![X412:$i, X413:$i, X414:$i, X417:$i, X418:$i, X419:$i, X420:$i, X421:$i, X422:$i, X423:$i, X424:$i]:(((fin @ (esk207_3 @ X412 @ X413 @ X414) @ X412|~fin @ X414 @ (fcartprod @ X412 @ X413)|p1)&((fin @ (esk208_3 @ X412 @ X413 @ X414) @ X413|~fin @ X414 @ (fcartprod @ X412 @ X413)|p1)&((X414)=(fkpair @ (esk207_3 @ X412 @ X413 @ X414) @ (esk208_3 @ X412 @ X413 @ X414))|~fin @ X414 @ (fcartprod @ X412 @ X413)|p1)))&((~fin @ X419 @ X417|(~fin @ X420 @ X418|(fkfst @ (fkpair @ X419 @ X420))=(X419))|p1)&((~fin @ X423 @ X421|(~fin @ X424 @ X422|(fksnd @ (fkpair @ X423 @ X424))=(X424))|p1)&((fin @ esk211_0 @ (fcartprod @ esk209_0 @ esk210_0)|p1)&((fkpair @ (fkfst @ esk211_0) @ (fksnd @ esk211_0))!=(esk211_0)|p1))))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])])).
% 44.01/44.11 thf(c_0_74, plain, ((fin @ esk147_0 @ f__1|p16)&((fin @ esk148_0 @ f__2|p16)&((f__3)=(fkpair @ esk147_0 @ esk148_0)|p16))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax16])])])])])).
% 44.01/44.11 thf(c_0_75, plain, (p32|~p34), inference(fof_simplification,[status(thm)],[ax84])).
% 44.01/44.11 thf(c_0_76, plain, (p34|~p35), inference(fof_simplification,[status(thm)],[ax83])).
% 44.01/44.11 thf(c_0_77, plain, (p16|~p32), inference(split_conjunct,[status(thm)],[c_0_66])).
% 44.01/44.11 thf(c_0_78, plain, ~p16, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_67, c_0_68])])).
% 44.01/44.11 thf(c_0_79, plain, (~p25|~p20|p15), inference(fof_simplification,[status(thm)],[ax93])).
% 44.01/44.11 thf(c_0_80, plain, (p25|~p24), inference(split_conjunct,[status(thm)],[c_0_69])).
% 44.01/44.11 thf(c_0_81, plain, p24, inference(csr,[status(thm)],[c_0_70, c_0_71])).
% 44.01/44.11 thf(c_0_82, plain, (p13|~p15), inference(split_conjunct,[status(thm)],[c_0_72])).
% 44.01/44.11 thf(c_0_83, plain, ((fin @ f__4 @ f__1|p32)&((fin @ esk113_0 @ f__2|p32)&((f__3)=(fkpair @ f__4 @ esk113_0)|p32))), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax32])])])])])).
% 44.01/44.11 thf(c_0_84, plain, ![X1:$i, X2:$i, X3:$i, X4:$i]:((fkfst @ (fkpair @ X1 @ X3))=(X1)|p1|~fin @ X1 @ X2|~fin @ X3 @ X4), inference(split_conjunct,[status(thm)],[c_0_73])).
% 44.01/44.11 thf(c_0_85, plain, (fin @ esk148_0 @ f__2|p16), inference(split_conjunct,[status(thm)],[c_0_74])).
% 44.01/44.11 thf(c_0_86, plain, ((fin @ f__5 @ f__2|p35)&((f__3)=(fkpair @ f__4 @ f__5)|p35)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax35])])])).
% 44.01/44.11 thf(c_0_87, plain, (p32|~p34), inference(split_conjunct,[status(thm)],[c_0_75])).
% 44.01/44.11 thf(c_0_88, plain, (p34|~p35), inference(split_conjunct,[status(thm)],[c_0_76])).
% 44.01/44.11 thf(c_0_89, plain, ~p32, inference(sr,[status(thm)],[c_0_77, c_0_78])).
% 44.01/44.11 thf(c_0_90, plain, ((f__3)!=(fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))|p20), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax20])])).
% 44.01/44.11 thf(c_0_91, plain, (p15|~p25|~p20), inference(split_conjunct,[status(thm)],[c_0_79])).
% 44.01/44.11 thf(c_0_92, plain, p25, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_80, c_0_81])])).
% 44.01/44.11 thf(c_0_93, plain, ~p15, inference(sr,[status(thm)],[c_0_82, c_0_57])).
% 44.01/44.11 thf(c_0_94, plain, (fin @ esk113_0 @ f__2|p32), inference(split_conjunct,[status(thm)],[c_0_83])).
% 44.01/44.11 thf(c_0_95, plain, (~p33|fin @ f__4 @ f__1), inference(fof_nnf,[status(thm)],[pax33])).
% 44.01/44.11 thf(c_0_96, plain, (p32|p33), inference(split_conjunct,[status(thm)],[ax85])).
% 44.01/44.11 thf(c_0_97, plain, ![X1:$i, X2:$i, X3:$i, X4:$i]:((fkfst @ (fkpair @ X1 @ X2))=(X1)|~fin @ X2 @ X3|~fin @ X1 @ X4), inference(sr,[status(thm)],[c_0_84, c_0_35])).
% 44.01/44.11 thf(c_0_98, plain, fin @ esk148_0 @ f__2, inference(sr,[status(thm)],[c_0_85, c_0_78])).
% 44.01/44.11 thf(c_0_99, plain, (fin @ esk147_0 @ f__1|p16), inference(split_conjunct,[status(thm)],[c_0_74])).
% 44.01/44.11 thf(c_0_100, plain, ((f__3)=(fkpair @ esk147_0 @ esk148_0)|p16), inference(split_conjunct,[status(thm)],[c_0_74])).
% 44.01/44.11 thf(c_0_101, plain, (~p44|(fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))=(fkpair @ f__4 @ f__5)), inference(fof_nnf,[status(thm)],[pax44])).
% 44.01/44.11 thf(c_0_102, plain, ((f__3)=(fkpair @ f__4 @ f__5)|p35), inference(split_conjunct,[status(thm)],[c_0_86])).
% 44.01/44.11 thf(c_0_103, plain, ~p35, inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_87, c_0_88]), c_0_89])).
% 44.01/44.11 thf(c_0_104, plain, (p20|(f__3)!=(fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))), inference(split_conjunct,[status(thm)],[c_0_90])).
% 44.01/44.11 thf(c_0_105, plain, ~p20, inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_91, c_0_92])]), c_0_93])).
% 44.01/44.11 thf(c_0_106, plain, ![X320:$i, X321:$i, X322:$i, X323:$i]:(~p8|(~fin @ X322 @ X320|(~fin @ X323 @ X321|(fksnd @ (fkpair @ X322 @ X323))=(X323)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax8])])])).
% 44.01/44.11 thf(c_0_107, plain, (p5|p8), inference(split_conjunct,[status(thm)],[ax111])).
% 44.01/44.11 thf(c_0_108, plain, fin @ esk113_0 @ f__2, inference(sr,[status(thm)],[c_0_94, c_0_89])).
% 44.01/44.11 thf(c_0_109, plain, (fin @ f__4 @ f__1|~p33), inference(split_conjunct,[status(thm)],[c_0_95])).
% 44.01/44.11 thf(c_0_110, plain, p33, inference(sr,[status(thm)],[c_0_96, c_0_89])).
% 44.01/44.11 thf(c_0_111, plain, ((f__3)=(fkpair @ f__4 @ esk113_0)|p32), inference(split_conjunct,[status(thm)],[c_0_83])).
% 44.01/44.11 thf(c_0_112, plain, ![X1:$i, X2:$i]:((fkfst @ (fkpair @ X1 @ esk148_0))=(X1)|~fin @ X1 @ X2), inference(spm,[status(thm)],[c_0_97, c_0_98])).
% 44.01/44.11 thf(c_0_113, plain, fin @ esk147_0 @ f__1, inference(sr,[status(thm)],[c_0_99, c_0_78])).
% 44.01/44.11 thf(c_0_114, plain, (fkpair @ esk147_0 @ esk148_0)=(f__3), inference(sr,[status(thm)],[c_0_100, c_0_78])).
% 44.01/44.11 thf(c_0_115, plain, ((fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))!=(fkpair @ f__4 @ f__5)|p44), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax44])])).
% 44.01/44.11 thf(c_0_116, plain, ((fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))=(fkpair @ f__4 @ f__5)|~p44), inference(split_conjunct,[status(thm)],[c_0_101])).
% 44.01/44.11 thf(c_0_117, plain, (fkpair @ f__4 @ f__5)=(f__3), inference(sr,[status(thm)],[c_0_102, c_0_103])).
% 44.01/44.11 thf(c_0_118, plain, (fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))!=(f__3), inference(sr,[status(thm)],[c_0_104, c_0_105])).
% 44.01/44.11 thf(c_0_119, plain, ![X1:$i, X2:$i, X3:$i, X4:$i]:((fksnd @ (fkpair @ X1 @ X3))=(X3)|~p8|~fin @ X1 @ X2|~fin @ X3 @ X4), inference(split_conjunct,[status(thm)],[c_0_106])).
% 44.01/44.11 thf(c_0_120, plain, p8, inference(sr,[status(thm)],[c_0_107, c_0_41])).
% 44.01/44.11 thf(c_0_121, plain, ![X1:$i, X2:$i]:((fkfst @ (fkpair @ X1 @ esk113_0))=(X1)|~fin @ X1 @ X2), inference(spm,[status(thm)],[c_0_97, c_0_108])).
% 44.01/44.11 thf(c_0_122, plain, fin @ f__4 @ f__1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_109, c_0_110])])).
% 44.01/44.11 thf(c_0_123, plain, (fkpair @ f__4 @ esk113_0)=(f__3), inference(sr,[status(thm)],[c_0_111, c_0_89])).
% 44.01/44.11 thf(c_0_124, plain, (fkfst @ f__3)=(esk147_0), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_113]), c_0_114])).
% 44.01/44.11 thf(c_0_125, plain, (p44|(fkpair @ (fkfst @ f__3) @ (fksnd @ f__3))!=(fkpair @ f__4 @ f__5)), inference(split_conjunct,[status(thm)],[c_0_115])).
% 44.01/44.11 thf(c_0_126, plain, ~p44, inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_116, c_0_117]), c_0_118])).
% 44.01/44.11 thf(c_0_127, plain, ![X1:$i, X2:$i, X3:$i, X4:$i]:((fksnd @ (fkpair @ X1 @ X2))=(X2)|~fin @ X2 @ X3|~fin @ X1 @ X4), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_119, c_0_120])])).
% 44.01/44.11 thf(c_0_128, plain, (esk147_0)=(f__4), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121, c_0_122]), c_0_123]), c_0_124])).
% 44.01/44.11 thf(c_0_129, plain, (fkpair @ esk147_0 @ (fksnd @ f__3))!=(f__3), inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_125, c_0_117]), c_0_124]), c_0_126])).
% 44.01/44.11 thf(c_0_130, plain, ![X1:$i, X2:$i]:((fksnd @ (fkpair @ X1 @ esk148_0))=(esk148_0)|~fin @ X1 @ X2), inference(spm,[status(thm)],[c_0_127, c_0_98])).
% 44.01/44.11 thf(c_0_131, plain, (fkpair @ f__4 @ esk148_0)=(f__3), inference(rw,[status(thm)],[c_0_114, c_0_128])).
% 44.01/44.11 thf(c_0_132, plain, (fkpair @ f__4 @ (fksnd @ f__3))!=(f__3), inference(rw,[status(thm)],[c_0_129, c_0_128])).
% 44.01/44.11 thf(c_0_133, plain, (fksnd @ f__3)=(esk148_0), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130, c_0_122]), c_0_131])).
% 44.01/44.11 thf(c_0_134, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_132, c_0_133]), c_0_131])]), ['proof']).
% 44.01/44.11 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 44.01/44.11 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]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((kfst @ ((kpair @ X3) @ X4)) = X3))))))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ X1) => (![X4:$i]:(((in @ X4) @ X2) => ((ksnd @ ((kpair @ X3) @ X4)) = X4))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X3) @ ((cartprod @ X1) @ X2)) => (((kpair @ (kfst @ X3)) @ (ksnd @ X3)) = X3)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 44.01/44.11 % SZS output end Proof
%------------------------------------------------------------------------------