TSTP Solution File: LCL714^1 by Satallax---3.5
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%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : LCL714^1 : 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 : n005.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 2.66s 2.84s
% Output : Proof 2.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : LCL714^1 : TPTP v8.1.0. Bugfixed v5.0.0.
% 0.09/0.12 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 03:02:07 EDT 2022
% 0.12/0.33 % CPUTime :
% 2.66/2.84 % SZS status Theorem
% 2.66/2.84 % Mode: mode506
% 2.66/2.84 % Inferences: 38726
% 2.66/2.84 % SZS output start Proof
% 2.66/2.84 thf(def_meq_ind,definition,(meq_ind = (^[X1:mu]:(^[X2:mu]:(^[X3:$i]:(X1 = X2)))))).
% 2.66/2.84 thf(def_meq_prop,definition,(meq_prop = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((X1 @ X3) = (X2 @ X3))))))).
% 2.66/2.84 thf(def_mnot,definition,(mnot = (^[X1:$i>$o]:(^[X2:$i]:(~((X1 @ X2))))))).
% 2.66/2.84 thf(def_mor,definition,(mor = (^[X1:$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:((~((X1 @ X3))) => (X2 @ X3))))))).
% 2.66/2.84 thf(def_mand,definition,(mand = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mor @ (mnot @ X1)) @ (mnot @ X2))))))).
% 2.66/2.84 thf(def_mimplies,definition,(mimplies = (^[X1:$i>$o]:(mor @ (mnot @ X1))))).
% 2.66/2.84 thf(def_mimplied,definition,(mimplied = (^[X1:$i>$o]:(^[X2:$i>$o]:((mor @ (mnot @ X2)) @ X1))))).
% 2.66/2.84 thf(def_mequiv,definition,(mequiv = (^[X1:$i>$o]:(^[X2:$i>$o]:((mand @ ((mimplies @ X1) @ X2)) @ ((mimplies @ X2) @ X1)))))).
% 2.66/2.84 thf(def_mxor,definition,(mxor = (^[X1:$i>$o]:(^[X2:$i>$o]:(mnot @ ((mequiv @ X1) @ X2)))))).
% 2.66/2.84 thf(def_mforall_ind,definition,(mforall_ind = (^[X1:mu>$i>$o]:(^[X2:$i]:(![X3:mu]:((X1 @ X3) @ X2)))))).
% 2.66/2.84 thf(def_mforall_prop,definition,(mforall_prop = (^[X1:($i>$o)>$i>$o]:(^[X2:$i]:(![X3:$i>$o]:((X1 @ X3) @ X2)))))).
% 2.66/2.84 thf(def_mexists_ind,definition,(mexists_ind = (^[X1:mu>$i>$o]:(mnot @ (mforall_ind @ (^[X2:mu]:(mnot @ (X1 @ X2)))))))).
% 2.66/2.84 thf(def_mexists_prop,definition,(mexists_prop = (^[X1:($i>$o)>$i>$o]:(mnot @ (mforall_prop @ (^[X2:$i>$o]:(mnot @ (X1 @ X2)))))))).
% 2.66/2.84 thf(def_mtrue,definition,(mtrue = (^[X1:$i]:(~($false))))).
% 2.66/2.84 thf(def_mfalse,definition,(mfalse = (mnot @ mtrue))).
% 2.66/2.84 thf(def_mbox,definition,(mbox = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(^[X3:$i]:(![X4:$i]:(((X1 @ X3) @ X4) => (X2 @ X4)))))))).
% 2.66/2.84 thf(def_mdia,definition,(mdia = (^[X1:$i>$i>$o]:(^[X2:$i>$o]:(mnot @ ((mbox @ X1) @ (mnot @ X2))))))).
% 2.66/2.84 thf(def_mreflexive,definition,(mreflexive = (^[X1:$i>$i>$o]:(![X2:$i]:((X1 @ X2) @ X2))))).
% 2.66/2.84 thf(def_msymmetric,definition,(msymmetric = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(((X1 @ X2) @ X3) => ((X1 @ X3) @ X2))))))).
% 2.66/2.84 thf(def_mserial,definition,(mserial = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(~(((X1 @ X2) @ X3)))))))))).
% 2.66/2.84 thf(def_mtransitive,definition,(mtransitive = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X3) @ X4)))))) => ((X1 @ X2) @ X4)))))))).
% 2.66/2.84 thf(def_meuclidean,definition,(meuclidean = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((X1 @ X3) @ X4)))))))).
% 2.66/2.84 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)))))))).
% 2.66/2.84 thf(def_mfunctional,definition,(mfunctional = (^[X1:$i>$i>$o]:(![X2:$i]:(~((![X3:$i]:(((X1 @ X2) @ X3) => (~((![X4:$i]:(((X1 @ X2) @ X4) => (X3 = X4))))))))))))).
% 2.66/2.84 thf(def_mweakly_dense,definition,(mweakly_dense = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:(((X1 @ X2) @ X3) => (~((![X5:$i]:(((X1 @ X2) @ X5) => (~(((X1 @ X5) @ X3)))))))))))))).
% 2.66/2.84 thf(def_mweakly_connected,definition,(mweakly_connected = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => ((~(((~(((X1 @ X3) @ X4))) => (X3 = X4)))) => ((X1 @ X4) @ X3))))))))).
% 2.66/2.84 thf(def_mweakly_directed,definition,(mweakly_directed = (^[X1:$i>$i>$o]:(![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (~((![X5:$i]:(((X1 @ X3) @ X5) => (~(((X1 @ X4) @ X5)))))))))))))).
% 2.66/2.84 thf(def_mvalid,definition,(mvalid = (!!))).
% 2.66/2.84 thf(def_minvalid,definition,(minvalid = (^[X1:$i>$o]:(![X2:$i]:(~((X1 @ X2))))))).
% 2.66/2.84 thf(def_msatisfiable,definition,(msatisfiable = (^[X1:$i>$o]:(~((![X2:$i]:(~((X1 @ X2))))))))).
% 2.66/2.84 thf(def_mcountersatisfiable,definition,(mcountersatisfiable = (^[X1:$i>$o]:(~(((!!) @ X1)))))).
% 2.66/2.84 thf(conj,conjecture,(![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((~((~((![X4:$i]:(((X1 @ X2) @ X4) => (~((X3 @ X4))))))))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (X3 @ X4)))))) => (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4)))))))).
% 2.66/2.84 thf(h0,negated_conjecture,(~((![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((![X4:$i]:(((X1 @ X2) @ X4) => (~((X3 @ X4))))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (X3 @ X4)))))) => (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4))))))))),inference(assume_negation,[status(cth)],[conj])).
% 2.66/2.84 thf(ax1141, axiom, (p1|~(p2)), file('<stdin>', ax1141)).
% 2.66/2.84 thf(ax1142, axiom, ~(p1), file('<stdin>', ax1142)).
% 2.66/2.84 thf(ax1139, axiom, (p2|~(p4)), file('<stdin>', ax1139)).
% 2.66/2.84 thf(ax1138, axiom, (p4|~(p5)), file('<stdin>', ax1138)).
% 2.66/2.84 thf(ax1124, axiom, (~(p3)|p18), file('<stdin>', ax1124)).
% 2.66/2.84 thf(ax1140, axiom, (p2|p3), file('<stdin>', ax1140)).
% 2.66/2.84 thf(ax1137, axiom, (p5|~(p6)), file('<stdin>', ax1137)).
% 2.66/2.84 thf(ax1065, axiom, (~(p18)|p89), file('<stdin>', ax1065)).
% 2.66/2.84 thf(nax6, axiom, (p6<=![X1:$i]:(~((f__0 @ f__1 @ f__2=>~(f__0 @ f__1 @ X1)))=>(f__2)=(X1))), file('<stdin>', nax6)).
% 2.66/2.84 thf(ax1057, axiom, (~(p89)|p101|p102), file('<stdin>', ax1057)).
% 2.66/2.84 thf(pax101, axiom, (p101=>![X1:$i]:(f__0 @ f__1 @ X1=>~((X1)=(f__2)))), file('<stdin>', pax101)).
% 2.66/2.84 thf(ax1136, axiom, (p6|~(p7)), file('<stdin>', ax1136)).
% 2.66/2.84 thf(pax102, axiom, (p102=>![X1:$i]:(f__0 @ f__1 @ X1=>(X1)=(f__2))), file('<stdin>', pax102)).
% 2.66/2.84 thf(nax7, axiom, (p7<=(~((f__0 @ f__1 @ f__2=>~(f__0 @ f__1 @ f__3)))=>(f__2)=(f__3))), file('<stdin>', nax7)).
% 2.66/2.84 thf(c_0_14, plain, (p1|~p2), inference(fof_simplification,[status(thm)],[ax1141])).
% 2.66/2.84 thf(c_0_15, plain, ~p1, inference(fof_simplification,[status(thm)],[ax1142])).
% 2.66/2.84 thf(c_0_16, plain, (p2|~p4), inference(fof_simplification,[status(thm)],[ax1139])).
% 2.66/2.84 thf(c_0_17, plain, (p1|~p2), inference(split_conjunct,[status(thm)],[c_0_14])).
% 2.66/2.84 thf(c_0_18, plain, ~p1, inference(split_conjunct,[status(thm)],[c_0_15])).
% 2.66/2.84 thf(c_0_19, plain, (p4|~p5), inference(fof_simplification,[status(thm)],[ax1138])).
% 2.66/2.84 thf(c_0_20, plain, (p2|~p4), inference(split_conjunct,[status(thm)],[c_0_16])).
% 2.66/2.84 thf(c_0_21, plain, ~p2, inference(sr,[status(thm)],[c_0_17, c_0_18])).
% 2.66/2.84 thf(c_0_22, plain, (~p3|p18), inference(fof_simplification,[status(thm)],[ax1124])).
% 2.66/2.84 thf(c_0_23, plain, (p2|p3), inference(split_conjunct,[status(thm)],[ax1140])).
% 2.66/2.84 thf(c_0_24, plain, (p5|~p6), inference(fof_simplification,[status(thm)],[ax1137])).
% 2.66/2.84 thf(c_0_25, plain, (p4|~p5), inference(split_conjunct,[status(thm)],[c_0_19])).
% 2.66/2.84 thf(c_0_26, plain, ~p4, inference(sr,[status(thm)],[c_0_20, c_0_21])).
% 2.66/2.84 thf(c_0_27, plain, (~p18|p89), inference(fof_simplification,[status(thm)],[ax1065])).
% 2.66/2.84 thf(c_0_28, plain, (p18|~p3), inference(split_conjunct,[status(thm)],[c_0_22])).
% 2.66/2.84 thf(c_0_29, plain, p3, inference(sr,[status(thm)],[c_0_23, c_0_21])).
% 2.66/2.84 thf(c_0_30, plain, (((f__0 @ f__1 @ f__2|p6)&(f__0 @ f__1 @ esk2370_0|p6))&((f__2)!=(esk2370_0)|p6)), inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax6])])])])])).
% 2.66/2.84 thf(c_0_31, plain, (p5|~p6), inference(split_conjunct,[status(thm)],[c_0_24])).
% 2.66/2.84 thf(c_0_32, plain, ~p5, inference(sr,[status(thm)],[c_0_25, c_0_26])).
% 2.66/2.84 thf(c_0_33, plain, (~p89|p101|p102), inference(fof_simplification,[status(thm)],[ax1057])).
% 2.66/2.84 thf(c_0_34, plain, (p89|~p18), inference(split_conjunct,[status(thm)],[c_0_27])).
% 2.66/2.84 thf(c_0_35, plain, p18, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])).
% 2.66/2.84 thf(c_0_36, plain, ![X4516:$i]:(~p101|(~f__0 @ f__1 @ X4516|(X4516)!=(f__2))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[pax101])])])])).
% 2.66/2.84 thf(c_0_37, plain, (f__0 @ f__1 @ f__2|p6), inference(split_conjunct,[status(thm)],[c_0_30])).
% 2.66/2.84 thf(c_0_38, plain, ~p6, inference(sr,[status(thm)],[c_0_31, c_0_32])).
% 2.66/2.84 thf(c_0_39, plain, (p101|p102|~p89), inference(split_conjunct,[status(thm)],[c_0_33])).
% 2.66/2.84 thf(c_0_40, plain, p89, inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35])])).
% 2.66/2.84 thf(c_0_41, plain, ![X1:$i]:(~p101|~f__0 @ f__1 @ X1|(X1)!=(f__2)), inference(split_conjunct,[status(thm)],[c_0_36])).
% 2.66/2.84 thf(c_0_42, plain, f__0 @ f__1 @ f__2, inference(sr,[status(thm)],[c_0_37, c_0_38])).
% 2.66/2.84 thf(c_0_43, plain, (p6|~p7), inference(fof_simplification,[status(thm)],[ax1136])).
% 2.66/2.84 thf(c_0_44, plain, ![X4514:$i]:(~p102|(~f__0 @ f__1 @ X4514|(X4514)=(f__2))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax102])])])).
% 2.66/2.84 thf(c_0_45, plain, (p102|p101), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])])).
% 2.66/2.84 thf(c_0_46, plain, ~p101, inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_41]), c_0_42])])).
% 2.66/2.84 thf(c_0_47, plain, (((f__0 @ f__1 @ f__2|p7)&(f__0 @ f__1 @ f__3|p7))&((f__2)!=(f__3)|p7)), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax7])])])).
% 2.66/2.84 thf(c_0_48, plain, (p6|~p7), inference(split_conjunct,[status(thm)],[c_0_43])).
% 2.66/2.84 thf(c_0_49, plain, ![X1:$i]:((X1)=(f__2)|~p102|~f__0 @ f__1 @ X1), inference(split_conjunct,[status(thm)],[c_0_44])).
% 2.66/2.84 thf(c_0_50, plain, p102, inference(sr,[status(thm)],[c_0_45, c_0_46])).
% 2.66/2.84 thf(c_0_51, plain, (p7|(f__2)!=(f__3)), inference(split_conjunct,[status(thm)],[c_0_47])).
% 2.66/2.84 thf(c_0_52, plain, ~p7, inference(sr,[status(thm)],[c_0_48, c_0_38])).
% 2.66/2.84 thf(c_0_53, plain, (f__0 @ f__1 @ f__3|p7), inference(split_conjunct,[status(thm)],[c_0_47])).
% 2.66/2.84 thf(c_0_54, plain, ![X1:$i]:((X1)=(f__2)|~f__0 @ f__1 @ X1), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_49, c_0_50])])).
% 2.66/2.84 thf(c_0_55, plain, (f__3)!=(f__2), inference(sr,[status(thm)],[c_0_51, c_0_52])).
% 2.66/2.84 thf(c_0_56, plain, f__0 @ f__1 @ f__3, inference(sr,[status(thm)],[c_0_53, c_0_52])).
% 2.66/2.84 thf(c_0_57, plain, ($false), inference(cdclpropres,[status(thm)],[c_0_54, c_0_55, c_0_56]), ['proof']).
% 2.66/2.84 thf(1,plain,$false,inference(eprover,[status(thm),assumptions([h0])],[])).
% 2.66/2.84 thf(0,theorem,(![X1:$i>$i>$o]:((![X2:$i]:(![X3:$i>$o]:((~((~((~((![X4:$i]:(((X1 @ X2) @ X4) => (~((X3 @ X4))))))))))) => (![X4:$i]:(((X1 @ X2) @ X4) => (X3 @ X4)))))) => (![X2:$i]:(![X3:$i]:(![X4:$i]:((~((((X1 @ X2) @ X3) => (~(((X1 @ X2) @ X4)))))) => (X3 = X4))))))),inference(contra,[status(thm),contra(discharge,[h0])],[1,h0])).
% 2.66/2.84 % SZS output end Proof
%------------------------------------------------------------------------------