TSTP Solution File: SEU647^2 by Satallax---3.5

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% File     : Satallax---3.5
% Problem  : SEU647^2 : 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 : n010.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 13:55:06 EDT 2022

% Result   : Theorem 2.73s 2.91s
% Output   : Proof 2.73s
% Verified : 
% SZS Type : -

% Comments : 
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SEU647^2 : TPTP v8.1.0. Released v3.7.0.
% 0.04/0.13  % Command  : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.34  % Computer : n010.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jun 20 13:50:52 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 2.73/2.91  % SZS status Theorem
% 2.73/2.91  % Mode: mode506
% 2.73/2.91  % Inferences: 105
% 2.73/2.91  % SZS output start Proof
% 2.73/2.91  thf(def_setadjoinIL,definition,(setadjoinIL = (![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))))).
% 2.73/2.91  thf(def_setukpairinjL1,definition,(setukpairinjL1 = (![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))))).
% 2.73/2.91  thf(setukpairinjL2,conjecture,((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3))))))))).
% 2.73/2.91  thf(h0,negated_conjecture,(~(((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))))))),inference(assume_negation,[status(cth)],[setukpairinjL2])).
% 2.73/2.91  thf(ax1073, axiom, (p1|~(p3)), file('<stdin>', ax1073)).
% 2.73/2.91  thf(ax1075, axiom, ~(p1), file('<stdin>', ax1075)).
% 2.73/2.91  thf(pax4, axiom, (p4=>![X1:$i, X2:$i, X3:$i]:(fin @ (fsetadjoin @ X3 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset))=>(X1)=(X3))), file('<stdin>', pax4)).
% 2.73/2.91  thf(ax1072, axiom, (p3|p4), file('<stdin>', ax1072)).
% 2.73/2.91  thf(nax1, axiom, (p1<=(![X1:$i, X2:$i]:fin @ X1 @ (fsetadjoin @ X1 @ X2)=>(![X1:$i, X2:$i, X3:$i]:(fin @ (fsetadjoin @ X3 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset))=>(X1)=(X3))=>![X1:$i, X2:$i, X3:$i, X4:$i]:((fsetadjoin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X1 @ (fsetadjoin @ X2 @ femptyset)) @ femptyset))=(fsetadjoin @ (fsetadjoin @ X3 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X3 @ (fsetadjoin @ X4 @ femptyset)) @ femptyset))=>(X1)=(X3))))), file('<stdin>', nax1)).
% 2.73/2.91  thf(c_0_5, plain, (p1|~p3), inference(fof_simplification,[status(thm)],[ax1073])).
% 2.73/2.91  thf(c_0_6, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1075])).
% 2.73/2.91  thf(c_0_7, plain, (p1|~p3), inference(split_conjunct,[status(thm)],[c_0_5])).
% 2.73/2.91  thf(c_0_8, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_6])).
% 2.73/2.91  thf(c_0_9, plain, ![X4034:$i, X4035:$i, X4036:$i]:(~p4|(~fin @ (fsetadjoin @ X4036 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X4034 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X4034 @ (fsetadjoin @ X4035 @ femptyset)) @ femptyset))|(X4034)=(X4036))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax4])])])).
% 2.73/2.91  thf(c_0_10, plain, (p3|p4), inference(split_conjunct,[status(thm)],[ax1072])).
% 2.73/2.91  thf(c_0_11, plain, ~p3, inference(sr,[status(thm)],[c_0_7, c_0_8])).
% 2.73/2.91  thf(c_0_12, plain, ![X4067:$i, X4068:$i, X4069:$i, X4070:$i, X4071:$i]:((fin @ X4067 @ (fsetadjoin @ X4067 @ X4068)|p1)&((~fin @ (fsetadjoin @ X4071 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X4069 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X4069 @ (fsetadjoin @ X4070 @ femptyset)) @ femptyset))|(X4069)=(X4071)|p1)&(((fsetadjoin @ (fsetadjoin @ esk2032_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk2032_0 @ (fsetadjoin @ esk2033_0 @ femptyset)) @ femptyset))=(fsetadjoin @ (fsetadjoin @ esk2034_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk2034_0 @ (fsetadjoin @ esk2035_0 @ femptyset)) @ femptyset))|p1)&((esk2032_0)!=(esk2034_0)|p1)))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])])])])])).
% 2.73/2.91  thf(c_0_13, plain, ![X1:$i, X2:$i, X3:$i]:((X2)=(X1)|~p4|~fin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset)) @ femptyset))), inference(split_conjunct,[status(thm)],[c_0_9])).
% 2.73/2.91  thf(c_0_14, plain, p4, inference(sr,[status(thm)],[c_0_10, c_0_11])).
% 2.73/2.91  thf(c_0_15, plain, ((fsetadjoin @ (fsetadjoin @ esk2032_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk2032_0 @ (fsetadjoin @ esk2033_0 @ femptyset)) @ femptyset))=(fsetadjoin @ (fsetadjoin @ esk2034_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk2034_0 @ (fsetadjoin @ esk2035_0 @ femptyset)) @ femptyset))|p1), inference(split_conjunct,[status(thm)],[c_0_12])).
% 2.73/2.91  thf(c_0_16, plain, ![X1:$i, X2:$i, X3:$i]:((X1)=(X2)|~fin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ X2 @ (fsetadjoin @ X3 @ femptyset)) @ femptyset))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_14])])).
% 2.73/2.91  thf(c_0_17, plain, (fsetadjoin @ (fsetadjoin @ esk2032_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk2032_0 @ (fsetadjoin @ esk2033_0 @ femptyset)) @ femptyset))=(fsetadjoin @ (fsetadjoin @ esk2034_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk2034_0 @ (fsetadjoin @ esk2035_0 @ femptyset)) @ femptyset)), inference(sr,[status(thm)],[c_0_15, c_0_8])).
% 2.73/2.91  thf(c_0_18, plain, ![X1:$i, X2:$i]:(fin @ X1 @ (fsetadjoin @ X1 @ X2)|p1), inference(split_conjunct,[status(thm)],[c_0_12])).
% 2.73/2.91  thf(c_0_19, plain, (p1|(esk2032_0)!=(esk2034_0)), inference(split_conjunct,[status(thm)],[c_0_12])).
% 2.73/2.91  thf(c_0_20, plain, ![X1:$i]:((X1)=(esk2032_0)|~fin @ (fsetadjoin @ X1 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk2034_0 @ femptyset) @ (fsetadjoin @ (fsetadjoin @ esk2034_0 @ (fsetadjoin @ esk2035_0 @ femptyset)) @ femptyset))), inference(spm,[status(thm)],[c_0_16, c_0_17])).
% 2.73/2.91  thf(c_0_21, plain, ![X1:$i, X2:$i]:fin @ X1 @ (fsetadjoin @ X1 @ X2), inference(sr,[status(thm)],[c_0_18, c_0_8])).
% 2.73/2.91  thf(c_0_22, plain, (esk2032_0)!=(esk2034_0), inference(sr,[status(thm)],[c_0_19, c_0_8])).
% 2.73/2.91  thf(c_0_23, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20, c_0_21]), c_0_22]), ['proof']).
% 2.73/2.91  thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 2.73/2.91  thf(0,theorem,((![X1:$i]:(![X2:$i]:((in @ X1) @ ((setadjoin @ X1) @ X2)))) => ((![X1:$i]:(![X2:$i]:(![X3:$i]:(((in @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset))) => (X1 = X3))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((((setadjoin @ ((setadjoin @ X1) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X1) @ ((setadjoin @ X2) @ emptyset))) @ emptyset)) = ((setadjoin @ ((setadjoin @ X3) @ emptyset)) @ ((setadjoin @ ((setadjoin @ X3) @ ((setadjoin @ X4) @ emptyset))) @ emptyset))) => (X1 = X3)))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 2.73/2.91  % SZS output end Proof
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