TSTP Solution File: SEU706^2 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU706^2 : 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 : n020.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 13:57:57 EDT 2022
% Result : Theorem 2.57s 2.72s
% Output : Proof 2.57s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SEU706^2 : TPTP v8.1.0. Released v3.7.0.
% 0.10/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.33 % Computer : n020.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Mon Jun 20 03:23:03 EDT 2022
% 0.14/0.33 % CPUTime :
% 2.57/2.72 % SZS status Theorem
% 2.57/2.72 % Mode: mode506
% 2.57/2.72 % Inferences: 35
% 2.57/2.72 % SZS output start Proof
% 2.57/2.72 thf(def_uniqinunit,definition,(uniqinunit = (![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))))).
% 2.57/2.72 thf(def_in__Cong,definition,(in__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))))).
% 2.57/2.72 thf(def_setadjoin__Cong,definition,(setadjoin__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))))).
% 2.57/2.72 thf(def_setunion__Cong,definition,(setunion__Cong = (![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))))).
% 2.57/2.72 thf(def_setunionsingleton,definition,(setunionsingleton = (![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)))).
% 2.57/2.72 thf(def_singleton,definition,(singleton = (^[X1:$i]:(~((![X2:$i]:(((in @ X2) @ X1) => (~((X1 = ((setadjoin @ X2) @ emptyset))))))))))).
% 2.57/2.72 thf(theeq,conjecture,((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => (![X1:$i]:((~((![X2:$i]:(((in @ X2) @ X1) => (~((X1 = ((setadjoin @ X2) @ emptyset)))))))) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2))))))))))).
% 2.57/2.72 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => (![X1:$i]:((~((![X2:$i]:(((in @ X2) @ X1) => (~((X1 = ((setadjoin @ X2) @ emptyset)))))))) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2)))))))))))),inference(assume_negation,[status(cth)],[theeq])).
% 2.57/2.72 thf(ax1085, axiom, (p1|~(p3)), file('<stdin>', ax1085)).
% 2.57/2.72 thf(ax1087, axiom, ~(p1), file('<stdin>', ax1087)).
% 2.57/2.72 thf(ax1083, axiom, (p3|~(p5)), file('<stdin>', ax1083)).
% 2.57/2.72 thf(nax5, axiom, (p5<=(![X1:$i, X2:$i]:((X1)=(X2)=>![X3:$i, X4:$i]:((X3)=(X4)=>(fsetadjoin @ X1 @ X3)=(fsetadjoin @ X2 @ X4)))=>(![X1:$i, X2:$i]:((X1)=(X2)=>(fsetunion @ X1)=(fsetunion @ X2))=>(![X1:$i]:(fsetunion @ (fsetadjoin @ X1 @ femptyset))=(X1)=>![X1:$i]:(~(![X2:$i]:(fin @ X2 @ X1=>~((X1)=(fsetadjoin @ X2 @ femptyset))))=>![X2:$i]:(fin @ X2 @ X1=>(fsetunion @ X1)=(X2))))))), file('<stdin>', nax5)).
% 2.57/2.72 thf(pax2, axiom, (p2=>![X1:$i, X2:$i]:(fin @ X1 @ (fsetadjoin @ X2 @ femptyset)=>(X1)=(X2))), file('<stdin>', pax2)).
% 2.57/2.72 thf(ax1086, axiom, (p1|p2), file('<stdin>', ax1086)).
% 2.57/2.72 thf(c_0_6, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1085])).
% 2.57/2.72 thf(c_0_7, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1087])).
% 2.57/2.72 thf(c_0_8, plain, (p3|~p5), inference(fof_simplification,[status(thm)],[ax1083])).
% 2.57/2.72 thf(c_0_9, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_6])).
% 2.57/2.72 thf(c_0_10, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_7])).
% 2.57/2.72 thf(c_0_11, plain, ![X1656:$i, X1657:$i, X1658:$i, X1659:$i, X1660:$i, X1661:$i, X1662:$i]:(((X1656)!=(X1657)|((X1658)!=(X1659)|(fsetadjoin @ X1656 @ X1658)=(fsetadjoin @ X1657 @ X1659))|p5)&(((X1660)!=(X1661)|(fsetunion @ X1660)=(fsetunion @ X1661)|p5)&(((fsetunion @ (fsetadjoin @ X1662 @ femptyset))=(X1662)|p5)&(((fin @ esk829_0 @ esk828_0|p5)&((esk828_0)=(fsetadjoin @ esk829_0 @ femptyset)|p5))&((fin @ esk830_0 @ esk828_0|p5)&((fsetunion @ esk828_0)!=(esk830_0)|p5)))))), 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)],[nax5])])])])])])).
% 2.57/2.72 thf(c_0_12, plain, (p3|~p5), inference(split_conjunct,[status(thm)],[c_0_8])).
% 2.57/2.72 thf(c_0_13, plain, ~p3, inference(sr,[status(thm)],[c_0_9, c_0_10])).
% 2.57/2.72 thf(c_0_14, plain, ![X1666:$i, X1667:$i]:(~p2|(~fin @ X1666 @ (fsetadjoin @ X1667 @ femptyset)|(X1666)=(X1667))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 2.57/2.72 thf(c_0_15, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax1086])).
% 2.57/2.72 thf(c_0_16, plain, ![X1:$i]:((fsetunion @ (fsetadjoin @ X1 @ femptyset))=(X1)|p5), inference(split_conjunct,[status(thm)],[c_0_11])).
% 2.57/2.72 thf(c_0_17, plain, ~p5, inference(sr,[status(thm)],[c_0_12, c_0_13])).
% 2.57/2.72 thf(c_0_18, plain, ((esk828_0)=(fsetadjoin @ esk829_0 @ femptyset)|p5), inference(split_conjunct,[status(thm)],[c_0_11])).
% 2.57/2.72 thf(c_0_19, plain, ![X1:$i, X2:$i]:((X1)=(X2)|~p2|~fin @ X1 @ (fsetadjoin @ X2 @ femptyset)), inference(split_conjunct,[status(thm)],[c_0_14])).
% 2.57/2.72 thf(c_0_20, plain, p2, inference(sr,[status(thm)],[c_0_15, c_0_10])).
% 2.57/2.72 thf(c_0_21, plain, (p5|(fsetunion @ esk828_0)!=(esk830_0)), inference(split_conjunct,[status(thm)],[c_0_11])).
% 2.57/2.72 thf(c_0_22, plain, ![X1:$i]:(fsetunion @ (fsetadjoin @ X1 @ femptyset))=(X1), inference(sr,[status(thm)],[c_0_16, c_0_17])).
% 2.57/2.72 thf(c_0_23, plain, (fsetadjoin @ esk829_0 @ femptyset)=(esk828_0), inference(sr,[status(thm)],[c_0_18, c_0_17])).
% 2.57/2.72 thf(c_0_24, plain, ![X1:$i, X2:$i]:((X1)=(X2)|~fin @ X1 @ (fsetadjoin @ X2 @ femptyset)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_19, c_0_20])])).
% 2.57/2.72 thf(c_0_25, plain, (fin @ esk830_0 @ esk828_0|p5), inference(split_conjunct,[status(thm)],[c_0_11])).
% 2.57/2.72 thf(c_0_26, plain, (fsetunion @ esk828_0)!=(esk830_0), inference(sr,[status(thm)],[c_0_21, c_0_17])).
% 2.57/2.72 thf(c_0_27, plain, (fsetunion @ esk828_0)=(esk829_0), inference(spm,[status(thm)],[c_0_22, c_0_23])).
% 2.57/2.72 thf(c_0_28, plain, ![X1:$i]:((X1)=(esk829_0)|~fin @ X1 @ esk828_0), inference(spm,[status(thm)],[c_0_24, c_0_23])).
% 2.57/2.72 thf(c_0_29, plain, fin @ esk830_0 @ esk828_0, inference(sr,[status(thm)],[c_0_25, c_0_17])).
% 2.57/2.72 thf(c_0_30, plain, (esk830_0)!=(esk829_0), inference(rw,[status(thm)],[c_0_26, c_0_27])).
% 2.57/2.72 thf(c_0_31, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30]), ['proof']).
% 2.57/2.72 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 2.57/2.72 thf(0,theorem,((![X1:$i]:(![X2:$i]:(((in @ X1) @ ((setadjoin @ X2) @ emptyset)) => (X1 = X2)))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((in @ X3) @ X1) = ((in @ X4) @ X2)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => (![X3:$i]:(![X4:$i]:((X3 = X4) => (((setadjoin @ X1) @ X3) = ((setadjoin @ X2) @ X4)))))))) => ((![X1:$i]:(![X2:$i]:((X1 = X2) => ((setunion @ X1) = (setunion @ X2))))) => ((![X1:$i]:((setunion @ ((setadjoin @ X1) @ emptyset)) = X1)) => (![X1:$i]:((~((![X2:$i]:(((in @ X2) @ X1) => (~((X1 = ((setadjoin @ X2) @ emptyset)))))))) => (![X2:$i]:(((in @ X2) @ X1) => ((setunion @ X1) = X2)))))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 2.57/2.72 % SZS output end Proof
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