%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL954^19 : TPTP v9.3.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 01:02:57 PM UTC 2026
% Result : Theorem 0.14s 0.47s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL954^19 : TPTP v9.3.1. Released v8.1.0.
% 0.00/0.04 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 4 14:28:49 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.47 % SZS status Theorem
% 0.14/0.47 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 0.14/0.47 % Inferences: 0
% 0.14/0.47 % SZS output start Proof
% 0.14/0.47 thf(ty_mworld, type, mworld : $tType).
% 0.14/0.47 thf(ty_eigen__1, type, eigen__1 : mworld).
% 0.14/0.47 thf(ty_eigen__0, type, eigen__0 : mworld).
% 0.14/0.47 thf(ty_mrel, type, mrel : (mworld>mworld>$o)).
% 0.14/0.47 thf(ty_mactual, type, mactual : mworld).
% 0.14/0.47 thf(ty_true, type, true : (mworld>$o)).
% 0.14/0.47 thf(def_mlocal,definition,(mlocal = (^[X1:mworld>$o]:(X1 @ mactual)))).
% 0.14/0.47 thf(def_mimplies,definition,(mimplies = (^[X1:mworld>$o]:(^[X2:mworld>$o]:(^[X3:mworld]:((X1 @ X3) => (X2 @ X3))))))).
% 0.14/0.47 thf(def_mbox,definition,(mbox = (^[X1:mworld>$o]:(^[X2:mworld]:(![X3:mworld]:(((mrel @ X2) @ X3) => (X1 @ X3))))))).
% 0.14/0.47 thf(cl5_nebula_array_0001,conjecture,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2))))))).
% 0.14/0.47 thf(h0,negated_conjecture,(~((![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2)))))))),inference(assume_negation,[status(cth)],[cl5_nebula_array_0001])).
% 0.14/0.47 thf(h1,assumption,(~((((mrel @ mactual) @ eigen__0) => ((![X1:mworld]:(((mrel @ eigen__0) @ X1) => (true @ X1))) => (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (true @ X1))))))),introduced(assumption,[])).
% 0.14/0.47 thf(h2,assumption,((mrel @ mactual) @ eigen__0),introduced(assumption,[])).
% 0.14/0.47 thf(h3,assumption,(~(((![X1:mworld]:(((mrel @ eigen__0) @ X1) => (true @ X1))) => (![X1:mworld]:(((mrel @ eigen__0) @ X1) => (true @ X1)))))),introduced(assumption,[])).
% 0.14/0.47 thf(h4,assumption,(![X1:mworld]:(((mrel @ eigen__0) @ X1) => (true @ X1))),introduced(assumption,[])).
% 0.14/0.47 thf(h5,assumption,(~((![X1:mworld]:(((mrel @ eigen__0) @ X1) => (true @ X1))))),introduced(assumption,[])).
% 0.14/0.47 thf(h6,assumption,(~((((mrel @ eigen__0) @ eigen__1) => (true @ eigen__1)))),introduced(assumption,[])).
% 0.14/0.47 thf(h7,assumption,((mrel @ eigen__0) @ eigen__1),introduced(assumption,[])).
% 0.14/0.47 thf(h8,assumption,(~((true @ eigen__1))),introduced(assumption,[])).
% 0.14/0.47 thf(pax104, axiom, (p104=>![X1:mworld]:(fmrel @ f__0 @ X1=>ftrue @ X1)), file('<stdin>', pax104)).
% 0.14/0.47 thf(pax103, axiom, (p103=>fmrel @ f__0 @ f__1), file('<stdin>', pax103)).
% 0.14/0.47 thf(nax102, axiom, (p102<=ftrue @ f__1), file('<stdin>', nax102)).
% 0.14/0.47 thf(ax6, axiom, ~(p102), file('<stdin>', ax6)).
% 0.14/0.47 thf(ax4, axiom, p104, file('<stdin>', ax4)).
% 0.14/0.47 thf(ax5, axiom, p103, file('<stdin>', ax5)).
% 0.14/0.47 thf(c_0_6, plain, ![X10:mworld]:(~p104|(~fmrel @ f__0 @ X10|ftrue @ X10)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax104])])])).
% 0.14/0.47 thf(c_0_7, plain, (~p103|fmrel @ f__0 @ f__1), inference(fof_nnf,[status(thm)],[pax103])).
% 0.14/0.47 thf(c_0_8, plain, (~ftrue @ f__1|p102), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax102])])).
% 0.14/0.47 thf(c_0_9, plain, ~p102, inference(fof_simplification,[status(thm)],[ax6])).
% 0.14/0.47 thf(c_0_10, plain, ![X1:mworld]:(ftrue @ X1|~p104|~fmrel @ f__0 @ X1), inference(split_conjunct,[status(thm)],[c_0_6])).
% 0.14/0.47 thf(c_0_11, plain, p104, inference(split_conjunct,[status(thm)],[ax4])).
% 0.14/0.47 thf(c_0_12, plain, (fmrel @ f__0 @ f__1|~p103), inference(split_conjunct,[status(thm)],[c_0_7])).
% 0.14/0.47 thf(c_0_13, plain, p103, inference(split_conjunct,[status(thm)],[ax5])).
% 0.14/0.47 thf(c_0_14, plain, (p102|~ftrue @ f__1), inference(split_conjunct,[status(thm)],[c_0_8])).
% 0.14/0.47 thf(c_0_15, plain, ~p102, inference(split_conjunct,[status(thm)],[c_0_9])).
% 0.14/0.47 thf(c_0_16, plain, ![X1:mworld]:(ftrue @ X1|~fmrel @ f__0 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_10, c_0_11])])).
% 0.14/0.47 thf(c_0_17, plain, fmrel @ f__0 @ f__1, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 0.14/0.47 thf(c_0_18, plain, ~ftrue @ f__1, inference(sr,[status(thm)],[c_0_14, c_0_15])).
% 0.14/0.47 thf(c_0_19, plain, ($false), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16, c_0_17]), c_0_18]), ['proof']).
% 0.14/0.47 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h7,h8,h6,h4,h5,h2,h3,h1,h0])],[])).
% 0.14/0.47 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h4,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,1,h7,h8])).
% 0.14/0.47 thf(3,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h5,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__1)],[h5,2,h6])).
% 0.14/0.47 thf(4,plain,$false,inference(tab_negimp,[status(thm),assumptions([h2,h3,h1,h0]),tab_negimp(discharge,[h4,h5])],[h3,3,h4,h5])).
% 0.14/0.47 thf(5,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,4,h2,h3])).
% 0.14/0.47 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,5,h1])).
% 0.14/0.47 thf(0,theorem,(![X1:mworld]:(((mrel @ mactual) @ X1) => ((![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2))) => (![X2:mworld]:(((mrel @ X1) @ X2) => (true @ X2)))))),inference(contra,[status(thm),contra(discharge,[h0])],[6,h0])).
% 0.14/0.47 % SZS output end Proof
%------------------------------------------------------------------------------