TSTP Solution File: LCL713^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL713^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n023.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 : Sun Jul 17 14:10:32 EDT 2022
% Result : Theorem 215.58s 215.76s
% Output : Proof 215.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL713^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 3 20:14:13 EDT 2022
% 0.12/0.34 % CPUTime :
% 215.58/215.76 % SZS status Theorem
% 215.58/215.76 % Mode: mode447
% 215.58/215.76 % Inferences: 28
% 215.58/215.76 % SZS output start Proof
% 215.58/215.76 thf(ty_eigen__2, type, eigen__2 : $i).
% 215.58/215.76 thf(ty_eigen__1, type, eigen__1 : $i).
% 215.58/215.76 thf(ty_eigen__0, type, eigen__0 : ($i>$i>$o)).
% 215.58/215.76 thf(ty_eigen__3, type, eigen__3 : $i).
% 215.58/215.76 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 215.58/215.76 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 215.58/215.76 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 215.58/215.76 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 215.58/215.76 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 215.58/215.76 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 215.58/215.76 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 215.58/215.76 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 215.58/215.76 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 215.58/215.76 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 215.58/215.76 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 215.58/215.76 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 215.58/215.76 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 215.58/215.76 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 215.58/215.76 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 215.58/215.76 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 215.58/215.76 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 215.58/215.76 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 215.58/215.76 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 215.58/215.76 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 215.58/215.76 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 215.58/215.76 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 215.58/215.76 thf(def_mpartially_functional,definition,(mpartially_functional = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 215.58/215.76 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 215.58/215.76 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 215.58/215.76 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 215.58/215.76 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 215.58/215.76 thf(def_mvalid,definition,(mvalid = (!!))).
% 215.58/215.76 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 215.58/215.76 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 215.58/215.76 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 215.58/215.76 thf(conj,conjecture,(![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((~((~((![X4:$i]:(((X1 @ X2) @ X4) => (~((X3 @ X4))))))))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (~((X3 @ X5)))))))))))) => (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 215.58/215.76 thf(h0,negated_conjecture,(~((![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((![X4:$i]:(((X1 @ X2) @ X4) => (~((X3 @ X4))))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (~((X3 @ X5)))))))))))) => (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4))))))))),inference(assume_negation,[status(cth)],[conj])).
% 215.58/215.76 thf(h1,assumption,(~(((![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((eigen__0 @ X1) @ X3) => (~((X2 @ X3))))))) => (![X3:$i]:(((eigen__0 @ X1) @ X3) => (~((![X4:$i]:(((eigen__0 @ X3) @ X4) => (~((X2 @ X4)))))))))))) => (![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3)))))))),introduced(assumption,[])).
% 215.58/215.76 thf(h2,assumption,(![X1:$i]:(![X2:$i>$o]:((~((![X3:$i]:(((eigen__0 @ X1) @ X3) => (~((X2 @ X3))))))) => (![X3:$i]:(((eigen__0 @ X1) @ X3) => (~((![X4:$i]:(((eigen__0 @ X3) @ X4) => (~((X2 @ X4)))))))))))),introduced(assumption,[])).
% 215.58/215.76 thf(h3,assumption,(~((![X1:$i]:(![X2:$i]:(![X3:$i]:((~((((eigen__0 @ X1) @ X2) => (~(((eigen__0 @ X1) @ X3)))))) => ((eigen__0 @ X2) @ X3))))))),introduced(assumption,[])).
% 215.58/215.76 thf(h4,assumption,(~((![X1:$i]:(![X2:$i]:((~((((eigen__0 @ eigen__1) @ X1) => (~(((eigen__0 @ eigen__1) @ X2)))))) => ((eigen__0 @ X1) @ X2)))))),introduced(assumption,[])).
% 215.58/215.76 thf(h5,assumption,(~((![X1:$i]:((~((((eigen__0 @ eigen__1) @ eigen__2) => (~(((eigen__0 @ eigen__1) @ X1)))))) => ((eigen__0 @ eigen__2) @ X1))))),introduced(assumption,[])).
% 215.58/215.76 thf(h6,assumption,(~(((~((((eigen__0 @ eigen__1) @ eigen__2) => (~(((eigen__0 @ eigen__1) @ eigen__3)))))) => ((eigen__0 @ eigen__2) @ eigen__3)))),introduced(assumption,[])).
% 215.58/215.76 thf(h7,assumption,(~((((eigen__0 @ eigen__1) @ eigen__2) => (~(((eigen__0 @ eigen__1) @ eigen__3)))))),introduced(assumption,[])).
% 215.58/215.76 thf(h8,assumption,(~(((eigen__0 @ eigen__2) @ eigen__3))),introduced(assumption,[])).
% 215.58/215.76 thf(h9,assumption,((eigen__0 @ eigen__1) @ eigen__2),introduced(assumption,[])).
% 215.58/215.76 thf(h10,assumption,((eigen__0 @ eigen__1) @ eigen__3),introduced(assumption,[])).
% 215.58/215.76 thf(ax99, axiom, (~(p4)|p5), file('<stdin>', ax99)).
% 215.58/215.76 thf(ax87, axiom, (~(p5)|p18), file('<stdin>', ax87)).
% 215.58/215.76 thf(ax100, axiom, p4, file('<stdin>', ax100)).
% 215.58/215.76 thf(pax18, axiom, (p18=>(~(![X1:$i]:(f__0 @ f__1 @ X1=>f__0 @ f__2 @ X1))=>![X1:$i]:(f__0 @ f__1 @ X1=>~(![X2:$i]:(f__0 @ X1 @ X2=>f__0 @ f__2 @ X2))))), file('<stdin>', pax18)).
% 215.58/215.76 thf(pax2, axiom, (p2=>f__0 @ f__1 @ f__3), file('<stdin>', pax2)).
% 215.58/215.76 thf(nax1, axiom, (p1<=f__0 @ f__2 @ f__3), file('<stdin>', nax1)).
% 215.58/215.76 thf(ax103, axiom, ~(p1), file('<stdin>', ax103)).
% 215.58/215.76 thf(ax102, axiom, p2, file('<stdin>', ax102)).
% 215.58/215.76 thf(pax3, axiom, (p3=>f__0 @ f__1 @ f__2), file('<stdin>', pax3)).
% 215.58/215.76 thf(ax101, axiom, p3, file('<stdin>', ax101)).
% 215.58/215.76 thf(c_0_10, plain, (~p4|p5), inference(fof_simplification,[status(thm)],[ax99])).
% 215.58/215.76 thf(c_0_11, plain, (~p5|p18), inference(fof_simplification,[status(thm)],[ax87])).
% 215.58/215.76 thf(c_0_12, plain, (p5|~p4), inference(split_conjunct,[status(thm)],[c_0_10])).
% 215.58/215.76 thf(c_0_13, plain, p4, inference(split_conjunct,[status(thm)],[ax100])).
% 215.58/215.76 thf(c_0_14, plain, ![X412:$i, X413:$i]:((f__0 @ X413 @ (esk205_1 @ X413)|~f__0 @ f__1 @ X413|(~f__0 @ f__1 @ X412|f__0 @ f__2 @ X412)|~p18)&(~f__0 @ f__2 @ (esk205_1 @ X413)|~f__0 @ f__1 @ X413|(~f__0 @ f__1 @ X412|f__0 @ f__2 @ X412)|~p18)), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax18])])])])])).
% 215.58/215.76 thf(c_0_15, plain, (p18|~p5), inference(split_conjunct,[status(thm)],[c_0_11])).
% 215.58/215.76 thf(c_0_16, plain, p5, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_12, c_0_13])])).
% 215.58/215.76 thf(c_0_17, plain, (~p2|f__0 @ f__1 @ f__3), inference(fof_nnf,[status(thm)],[pax2])).
% 215.58/215.76 thf(c_0_18, plain, (~f__0 @ f__2 @ f__3|p1), inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax1])])).
% 215.58/215.76 thf(c_0_19, plain, ~p1, inference(fof_simplification,[status(thm)],[ax103])).
% 215.58/215.76 thf(c_0_20, plain, ![X1:$i, X2:$i]:(f__0 @ X1 @ (esk205_1 @ X1)|f__0 @ f__2 @ X2|~f__0 @ f__1 @ X1|~f__0 @ f__1 @ X2|~p18), inference(split_conjunct,[status(thm)],[c_0_14])).
% 215.58/215.76 thf(c_0_21, plain, p18, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_15, c_0_16])])).
% 215.58/215.76 thf(c_0_22, plain, (f__0 @ f__1 @ f__3|~p2), inference(split_conjunct,[status(thm)],[c_0_17])).
% 215.58/215.76 thf(c_0_23, plain, p2, inference(split_conjunct,[status(thm)],[ax102])).
% 215.58/215.76 thf(c_0_24, plain, (p1|~f__0 @ f__2 @ f__3), inference(split_conjunct,[status(thm)],[c_0_18])).
% 215.58/215.76 thf(c_0_25, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_19])).
% 215.58/215.76 thf(c_0_26, plain, (~p3|f__0 @ f__1 @ f__2), inference(fof_nnf,[status(thm)],[pax3])).
% 215.58/215.76 thf(c_0_27, plain, ![X1:$i, X2:$i]:(f__0 @ f__2 @ X2|~f__0 @ f__2 @ (esk205_1 @ X1)|~f__0 @ f__1 @ X1|~f__0 @ f__1 @ X2|~p18), inference(split_conjunct,[status(thm)],[c_0_14])).
% 215.58/215.76 thf(c_0_28, plain, ![X2:$i, X1:$i]:(f__0 @ X1 @ (esk205_1 @ X1)|f__0 @ f__2 @ X2|~f__0 @ f__1 @ X2|~f__0 @ f__1 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 215.58/215.76 thf(c_0_29, plain, f__0 @ f__1 @ f__3, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23])])).
% 215.58/215.76 thf(c_0_30, plain, ~f__0 @ f__2 @ f__3, inference(sr,[status(thm)],[c_0_24, c_0_25])).
% 215.58/215.76 thf(c_0_31, plain, (f__0 @ f__1 @ f__2|~p3), inference(split_conjunct,[status(thm)],[c_0_26])).
% 215.58/215.76 thf(c_0_32, plain, p3, inference(split_conjunct,[status(thm)],[ax101])).
% 215.58/215.76 thf(c_0_33, plain, ![X1:$i, X2:$i]:(f__0 @ f__2 @ X1|~f__0 @ f__2 @ (esk205_1 @ X2)|~f__0 @ f__1 @ X1|~f__0 @ f__1 @ X2), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27, c_0_21])])).
% 215.58/215.76 thf(c_0_34, plain, ![X1:$i]:(f__0 @ X1 @ (esk205_1 @ X1)|~f__0 @ f__1 @ X1), inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28, c_0_29]), c_0_30])).
% 215.58/215.76 thf(c_0_35, plain, f__0 @ f__1 @ f__2, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_31, c_0_32])])).
% 215.58/215.76 thf(c_0_36, plain, ![X1:$i]:(f__0 @ f__2 @ X1|~f__0 @ f__1 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_34]), c_0_35])])).
% 215.58/215.76 thf(c_0_37, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30, c_0_36]), c_0_29])]), ['proof']).
% 215.58/215.76 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h9,h10,h7,h8,h6,h5,h4,h2,h3,h1,h0])],[])).
% 215.58/215.76 thf(2,plain,$false,inference(tab_negimp,[status(thm),assumptions([h7,h8,h6,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h9,h10])],[h7,1,h9,h10])).
% 215.58/215.76 thf(3,plain,$false,inference(tab_negimp,[status(thm),assumptions([h6,h5,h4,h2,h3,h1,h0]),tab_negimp(discharge,[h7,h8])],[h6,2,h7,h8])).
% 215.58/215.76 thf(4,plain,$false,inference(tab_negall,[status(thm),assumptions([h5,h4,h2,h3,h1,h0]),tab_negall(discharge,[h6]),tab_negall(eigenvar,eigen__3)],[h5,3,h6])).
% 215.58/215.76 thf(5,plain,$false,inference(tab_negall,[status(thm),assumptions([h4,h2,h3,h1,h0]),tab_negall(discharge,[h5]),tab_negall(eigenvar,eigen__2)],[h4,4,h5])).
% 215.58/215.76 thf(6,plain,$false,inference(tab_negall,[status(thm),assumptions([h2,h3,h1,h0]),tab_negall(discharge,[h4]),tab_negall(eigenvar,eigen__1)],[h3,5,h4])).
% 215.58/215.76 thf(7,plain,$false,inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[h1,6,h2,h3])).
% 215.58/215.76 thf(8,plain,$false,inference(tab_negall,[status(thm),assumptions([h0]),tab_negall(discharge,[h1]),tab_negall(eigenvar,eigen__0)],[h0,7,h1])).
% 215.58/215.76 thf(0,theorem,(![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((~((~((![X4:$i]:(((X1 @ X2) @ X4) => (~((X3 @ X4))))))))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (~((![X5:$i]:(((X1 @ X4) @ X5) => (~((X3 @ X5)))))))))))) => (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[8,h0])).
% 215.58/215.76 % SZS output end Proof
%------------------------------------------------------------------------------