%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : SEU618^2 : TPTP v9.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n014.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 : 300s
% DateTime : Thu Oct 9 02:44:10 PM UTC 2025
% Result : Theorem 18.65s 19.00s
% Output : Proof 18.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU618^2 : TPTP v9.2.0. Released v3.7.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 20:46:23 EDT 2025
% 0.14/0.35 % CPUTime :
% 18.65/19.00 % SZS status Theorem
% 18.65/19.00 % Mode: mode485
% 18.65/19.00 % Inferences: 49
% 18.65/19.00 % SZS output start Proof
% 18.65/19.00 thf(def_setunionI,definition,(setunionI = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))))).
% 18.65/19.00 thf(def_secondinupair,definition,(secondinupair = (![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))))).
% 18.65/19.00 thf(setukpairIR,conjecture,((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => (![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))))))))).
% 18.65/19.00 thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => (![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))))))),inference(assume_negation,[status(cth)],[setukpairIR])).
% 18.65/19.00 thf(ax976, axiom, ~(p1), file('<stdin>', ax976)).
% 18.65/19.00 thf(pax2, axiom, (p2=>![X1:$i, X2:$i, X3:$i]:(fin @ X2 @ X3=>(fin @ X3 @ X1=>fin @ X2 @ (fsetunion @ X1)))), file('<stdin>', pax2)).
% 18.65/19.00 thf(ax975, axiom, (p1|p2), file('<stdin>', ax975)).
% 18.65/19.00 thf(nax1, axiom, (p1<=(![X1:$i, X2:$i, X3:$i]:(fin @ X2 @ X3=>(fin @ X3 @ X1=>fin @ X2 @ (fsetunion @ X1)))=>(![X1:$i, X2:$i]:fin @ X2 @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset))=>![X1:$i, X2:$i]:fin @ X2 @ (fsetunion @ (fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset)))))), file('<stdin>', nax1)).
% 18.65/19.00 thf(c_0_4, plain, ~p1, inference(fof_simplification,[status(thm)],[ax976])).
% 18.65/19.00 thf(c_0_5, plain, ![X622:$i, X623:$i, X624:$i]:(~p2|(~fin @ X623 @ X624|(~fin @ X624 @ X622|fin @ X623 @ (fsetunion @ X622)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax2])])])).
% 18.65/19.00 thf(c_0_6, plain, (p1|p2), inference(split_conjunct,[status(thm)],[ax975])).
% 18.65/19.00 thf(c_0_7, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_4])).
% 18.65/19.00 thf(c_0_8, plain, ![X635:$i, X636:$i, X637:$i, X638:$i, X639:$i]:((~fin @ X636 @ X637|(~fin @ X637 @ X635|fin @ X636 @ (fsetunion @ X635))|p1)&((fin @ X639 @ (fsetadjoin @ X638 @ (fsetadjoin @ X639 @ femptyset))|p1)&(~fin @ esk319_0 @ (fsetunion @ (fsetadjoin @ (fsetadjoin @ esk318_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk318_0 @ (fsetadjoin @ esk319_0 @ femptyset)) @ femptyset)))|p1))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])])).
% 18.65/19.00 thf(c_0_9, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ (fsetunion @ X3)|~p2|~fin @ X1 @ X2|~fin @ X2 @ X3), inference(split_conjunct,[status(thm)],[c_0_5])).
% 18.65/19.00 thf(c_0_10, plain, p2, inference(sr,[status(thm)],[c_0_6, c_0_7])).
% 18.65/19.00 thf(c_0_11, plain, ![X2:$i, X1:$i]:(fin @ X1 @ (fsetadjoin @ X2 @ (fsetadjoin @ X1 @ femptyset))|p1), inference(split_conjunct,[status(thm)],[c_0_8])).
% 18.65/19.00 thf(c_0_12, plain, (p1|~fin @ esk319_0 @ (fsetunion @ (fsetadjoin @ (fsetadjoin @ esk318_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk318_0 @ (fsetadjoin @ esk319_0 @ femptyset)) @ femptyset)))), inference(split_conjunct,[status(thm)],[c_0_8])).
% 18.65/19.00 thf(c_0_13, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ (fsetunion @ X2)|~fin @ X3 @ X2|~fin @ X1 @ X3), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_9, c_0_10])])).
% 18.65/19.00 thf(c_0_14, plain, ![X2:$i, X1:$i]:fin @ X1 @ (fsetadjoin @ X2 @ (fsetadjoin @ X1 @ femptyset)), inference(sr,[status(thm)],[c_0_11, c_0_7])).
% 18.65/19.00 thf(c_0_15, plain, ~fin @ esk319_0 @ (fsetunion @ (fsetadjoin @ (fsetadjoin @ esk318_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk318_0 @ (fsetadjoin @ esk319_0 @ femptyset)) @ femptyset))), inference(sr,[status(thm)],[c_0_12, c_0_7])).
% 18.65/19.00 thf(c_0_16, plain, ![X1:$i, X2:$i, X3:$i]:(fin @ X1 @ (fsetunion @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset)))|~fin @ X1 @ X3), inference(spm,[status(thm)],[c_0_13, c_0_14])).
% 18.65/19.00 thf(c_0_17, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15, c_0_16]), c_0_14])]), ['proof']).
% 18.65/19.00 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 18.65/19.00 thf(0,theorem,((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ X2) @ X3) => (((in @ X3) @ X1) => ((in @ X2) @ (setunion @ X1))))))) => ((![X1:$i]:(![X2:$i]:((in @ X2) @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))))) => (![X1:$i]:(![X2:$i]:((in @ X2) @ (setunion @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 18.65/19.00 % SZS output end Proof
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