%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n018.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 11:21:05 AM UTC 2026
% Result : Theorem 0.41s 0.60s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL494+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.02 % Command : java -jar mcs_scs.jar %d %s
% 0.06/0.33 % Computer : n018.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Fri Sep 4 19:03:32 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.12/0.45 start to proof:theBenchmark.p
% 0.41/0.60 % Version : CSI_E---1.1
% 0.41/0.60 % Problem : theBenchmark.p
% 0.41/0.60 % Proof found!
% 0.41/0.60 % SZS status Theorem for theBenchmark.p
% 0.41/0.60 % SZS output start Proof
% 0.41/0.60 fof(r2, axiom, (r2<=>![X4, X5]:is_a_theorem(implies(X5,or(X4,X5)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r2)).
% 0.41/0.60 fof(op_implies_or, axiom, (op_implies_or=>![X1, X2]:implies(X1,X2)=or(not(X1),X2)), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_implies_or)).
% 0.41/0.60 fof(op_implies_and, axiom, (op_implies_and=>![X1, X2]:implies(X1,X2)=not(and(X1,not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_implies_and)).
% 0.41/0.60 fof(modus_ponens, axiom, (modus_ponens<=>![X1, X2]:((is_a_theorem(X1)&is_a_theorem(implies(X1,X2)))=>is_a_theorem(X2))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', modus_ponens)).
% 0.41/0.60 fof(r3, axiom, (r3<=>![X4, X5]:is_a_theorem(implies(or(X4,X5),or(X5,X4)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', r3)).
% 0.41/0.60 fof(principia_r2, axiom, r2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax', principia_r2)).
% 0.41/0.60 fof(principia_op_implies_or, axiom, op_implies_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax', principia_op_implies_or)).
% 0.41/0.60 fof(op_or, axiom, (op_or=>![X1, X2]:or(X1,X2)=not(and(not(X1),not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_or)).
% 0.41/0.60 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_op_implies_and)).
% 0.41/0.60 fof(principia_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax', principia_modus_ponens)).
% 0.41/0.60 fof(principia_r3, axiom, r3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax', principia_r3)).
% 0.41/0.60 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_op_or)).
% 0.41/0.60 fof(op_and, axiom, (op_and=>![X1, X2]:and(X1,X2)=not(or(not(X1),not(X2)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_and)).
% 0.41/0.60 fof(principia_op_and, axiom, op_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax', principia_op_and)).
% 0.41/0.60 fof(op_equiv, axiom, (op_equiv=>![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+1.ax', op_equiv)).
% 0.41/0.60 fof(equivalence_2, axiom, (equivalence_2<=>![X1, X2]:is_a_theorem(implies(equiv(X1,X2),implies(X2,X1)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', equivalence_2)).
% 0.41/0.60 fof(hilbert_equivalence_2, conjecture, equivalence_2, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_equivalence_2)).
% 0.41/0.60 fof(principia_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+4.ax', principia_op_equiv)).
% 0.41/0.60 fof(c_0_18, plain, ![X162, X163]:((~r2|is_a_theorem(implies(X163,or(X162,X163))))&(~is_a_theorem(implies(esk47_0,or(esk46_0,esk47_0)))|r2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r2])])])])).
% 0.41/0.60 fof(c_0_19, plain, ![X188, X189]:(~op_implies_or|implies(X188,X189)=or(not(X188),X189)), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_or])])])).
% 0.41/0.60 fof(c_0_20, plain, ![X186, X187]:(~op_implies_and|implies(X186,X187)=not(and(X186,not(X187)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_implies_and])])])).
% 0.41/0.60 fof(c_0_21, plain, ![X72, X73]:((~modus_ponens|(~is_a_theorem(X72)|~is_a_theorem(implies(X72,X73))|is_a_theorem(X73)))&(((is_a_theorem(esk1_0)|modus_ponens)&(is_a_theorem(implies(esk1_0,esk2_0))|modus_ponens))&(~is_a_theorem(esk2_0)|modus_ponens))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[modus_ponens])])])])])).
% 0.41/0.60 fof(c_0_22, plain, ![X166, X167]:((~r3|is_a_theorem(implies(or(X166,X167),or(X167,X166))))&(~is_a_theorem(implies(or(esk48_0,esk49_0),or(esk49_0,esk48_0)))|r3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r3])])])])).
% 0.41/0.60 cnf(c_0_23, plain, (is_a_theorem(implies(X1,or(X2,X1)))|~r2), inference(split_conjunct,[status(thm)],[c_0_18])).
% 0.41/0.60 cnf(c_0_24, plain, (r2), inference(split_conjunct,[status(thm)],[principia_r2])).
% 0.41/0.60 cnf(c_0_25, plain, (implies(X1,X2)=or(not(X1),X2)|~op_implies_or), inference(split_conjunct,[status(thm)],[c_0_19])).
% 0.41/0.60 cnf(c_0_26, plain, (op_implies_or), inference(split_conjunct,[status(thm)],[principia_op_implies_or])).
% 0.41/0.60 fof(c_0_27, plain, ![X182, X183]:(~op_or|or(X182,X183)=not(and(not(X182),not(X183)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_or])])])).
% 0.41/0.60 cnf(c_0_28, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_20])).
% 0.41/0.60 cnf(c_0_29, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 0.41/0.60 cnf(c_0_30, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_21])).
% 0.41/0.60 cnf(c_0_31, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[principia_modus_ponens])).
% 0.41/0.60 cnf(c_0_32, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3), inference(split_conjunct,[status(thm)],[c_0_22])).
% 0.41/0.60 cnf(c_0_33, plain, (r3), inference(split_conjunct,[status(thm)],[principia_r3])).
% 0.41/0.60 cnf(c_0_34, plain, (is_a_theorem(implies(X1,or(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23, c_0_24])])).
% 0.41/0.60 cnf(c_0_35, plain, (or(not(X1),X2)=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25, c_0_26])])).
% 0.41/0.60 cnf(c_0_36, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_27])).
% 0.41/0.60 cnf(c_0_37, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_28, c_0_29])])).
% 0.41/0.60 cnf(c_0_38, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])).
% 0.41/0.60 fof(c_0_39, plain, ![X184, X185]:(~op_and|and(X184,X185)=not(or(not(X184),not(X185)))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_and])])])).
% 0.41/0.60 cnf(c_0_40, plain, (is_a_theorem(X1)|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31])])).
% 0.41/0.60 cnf(c_0_41, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])).
% 0.41/0.60 cnf(c_0_42, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(spm,[status(thm)],[c_0_34, c_0_35])).
% 0.41/0.60 cnf(c_0_43, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_37]), c_0_38])])).
% 0.41/0.60 cnf(c_0_44, plain, (and(X1,X2)=not(or(not(X1),not(X2)))|~op_and), inference(split_conjunct,[status(thm)],[c_0_39])).
% 0.41/0.60 cnf(c_0_45, plain, (op_and), inference(split_conjunct,[status(thm)],[principia_op_and])).
% 0.41/0.60 cnf(c_0_46, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_40, c_0_41])).
% 0.41/0.60 cnf(c_0_47, plain, (is_a_theorem(or(X1,implies(X2,not(X1))))), inference(spm,[status(thm)],[c_0_42, c_0_43])).
% 0.41/0.60 cnf(c_0_48, plain, (not(implies(X1,not(X2)))=and(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_44, c_0_35]), c_0_45])])).
% 0.41/0.60 fof(c_0_49, plain, ![X190, X191]:(~op_equiv|equiv(X190,X191)=and(implies(X190,X191),implies(X191,X190))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_equiv])])])).
% 0.41/0.60 fof(c_0_50, plain, ![X128, X129]:((~equivalence_2|is_a_theorem(implies(equiv(X128,X129),implies(X129,X128))))&(~is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))|equivalence_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_2])])])])).
% 0.41/0.60 fof(c_0_51, negated_conjecture, ~equivalence_2, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_equivalence_2])])).
% 0.41/0.60 cnf(c_0_52, plain, (is_a_theorem(or(implies(X1,not(X2)),X2))), inference(spm,[status(thm)],[c_0_46, c_0_47])).
% 0.41/0.60 cnf(c_0_53, plain, (or(implies(X1,not(X2)),X3)=implies(and(X1,X2),X3)), inference(spm,[status(thm)],[c_0_43, c_0_48])).
% 0.41/0.60 cnf(c_0_54, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_49])).
% 0.41/0.60 cnf(c_0_55, plain, (op_equiv), inference(split_conjunct,[status(thm)],[principia_op_equiv])).
% 0.41/0.60 cnf(c_0_56, plain, (equivalence_2|~is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))), inference(split_conjunct,[status(thm)],[c_0_50])).
% 0.41/0.60 cnf(c_0_57, negated_conjecture, (~equivalence_2), inference(split_conjunct,[status(thm)],[c_0_51])).
% 0.41/0.60 cnf(c_0_58, plain, (is_a_theorem(implies(and(X1,X2),X2))), inference(rw,[status(thm)],[c_0_52, c_0_53])).
% 0.41/0.60 cnf(c_0_59, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_54, c_0_55])])).
% 0.41/0.60 cnf(c_0_60, plain, (~is_a_theorem(implies(equiv(esk29_0,esk30_0),implies(esk30_0,esk29_0)))), inference(sr,[status(thm)],[c_0_56, c_0_57])).
% 0.41/0.60 cnf(c_0_61, plain, (is_a_theorem(implies(equiv(X1,X2),implies(X2,X1)))), inference(spm,[status(thm)],[c_0_58, c_0_59])).
% 0.41/0.60 cnf(c_0_62, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_60, c_0_61])]), ['proof']).
% 0.41/0.60 % SZS output end Proof
% 0.41/0.60 % User time : 0.108 s
% 0.41/0.60 % System time : 0.014 s
% 0.41/0.60 % Total time : 0.123 s
% 0.41/0.60
%------------------------------------------------------------------------------