%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL495+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n014.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 8.16s 8.36s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL495+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 22:35:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.24/0.47 start to proof:theBenchmark.p
% 8.16/8.36 % Version : CSI_E---1.1
% 8.16/8.36 % Problem : theBenchmark.p
% 8.16/8.36 % Proof found!
% 8.16/8.36 % SZS status Theorem for theBenchmark.p
% 8.16/8.36 % SZS output start Proof
% 8.16/8.36 fof(op_implies_and, axiom, (op_implies_and=>![X1, X2]:implies(X1,X2)=not(and(X1,not(X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_implies_and)).
% 8.16/8.36 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/sandbox2/benchmark/Axioms/LCL006+0.ax', modus_ponens)).
% 8.16/8.36 fof(r3, axiom, (r3<=>![X4, X5]:is_a_theorem(implies(or(X4,X5),or(X5,X4)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r3)).
% 8.16/8.36 fof(op_or, axiom, (op_or=>![X1, X2]:or(X1,X2)=not(and(not(X1),not(X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_or)).
% 8.16/8.36 fof(hilbert_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', hilbert_op_implies_and)).
% 8.16/8.36 fof(principia_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_modus_ponens)).
% 8.16/8.36 fof(principia_r3, axiom, r3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r3)).
% 8.16/8.36 fof(op_implies_or, axiom, (op_implies_or=>![X1, X2]:implies(X1,X2)=or(not(X1),X2)), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_implies_or)).
% 8.16/8.36 fof(r1, axiom, (r1<=>![X4]:is_a_theorem(implies(or(X4,X4),X4))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r1)).
% 8.16/8.36 fof(hilbert_op_or, axiom, op_or, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', hilbert_op_or)).
% 8.16/8.36 fof(principia_op_implies_or, axiom, op_implies_or, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_op_implies_or)).
% 8.16/8.36 fof(principia_r1, axiom, r1, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r1)).
% 8.16/8.36 fof(r2, axiom, (r2<=>![X4, X5]:is_a_theorem(implies(X5,or(X4,X5)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r2)).
% 8.16/8.36 fof(principia_r2, axiom, r2, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r2)).
% 8.16/8.36 fof(r5, axiom, (r5<=>![X4, X5, X6]:is_a_theorem(implies(implies(X5,X6),implies(or(X4,X5),or(X4,X6))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r5)).
% 8.16/8.36 fof(principia_r5, axiom, r5, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r5)).
% 8.16/8.36 fof(op_and, axiom, (op_and=>![X1, X2]:and(X1,X2)=not(or(not(X1),not(X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_and)).
% 8.16/8.36 fof(principia_op_and, axiom, op_and, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_op_and)).
% 8.16/8.36 fof(op_equiv, axiom, (op_equiv=>![X1, X2]:equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+1.ax', op_equiv)).
% 8.16/8.36 fof(principia_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_op_equiv)).
% 8.16/8.36 fof(r4, axiom, (r4<=>![X4, X5, X6]:is_a_theorem(implies(or(X4,or(X5,X6)),or(X5,or(X4,X6))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', r4)).
% 8.16/8.36 fof(principia_r4, axiom, r4, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', principia_r4)).
% 8.16/8.36 fof(substitution_of_equivalents, axiom, (substitution_of_equivalents<=>![X1, X2]:(is_a_theorem(equiv(X1,X2))=>X1=X2)), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)).
% 8.16/8.36 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+4.ax', use_substitution_of_equivalents)).
% 8.16/8.36 fof(equivalence_3, axiom, (equivalence_3<=>![X1, X2]:is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', equivalence_3)).
% 8.16/8.36 fof(hilbert_equivalence_3, conjecture, equivalence_3, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', hilbert_equivalence_3)).
% 8.16/8.36 fof(c_0_26, 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])])])).
% 8.16/8.36 fof(c_0_27, 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])])])])])).
% 8.16/8.36 fof(c_0_28, 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])])])])).
% 8.16/8.36 fof(c_0_29, 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])])])).
% 8.16/8.36 cnf(c_0_30, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_26])).
% 8.16/8.36 cnf(c_0_31, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[hilbert_op_implies_and])).
% 8.16/8.36 cnf(c_0_32, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_27])).
% 8.16/8.36 cnf(c_0_33, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[principia_modus_ponens])).
% 8.16/8.36 cnf(c_0_34, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))|~r3), inference(split_conjunct,[status(thm)],[c_0_28])).
% 8.16/8.36 cnf(c_0_35, plain, (r3), inference(split_conjunct,[status(thm)],[principia_r3])).
% 8.16/8.36 fof(c_0_36, 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])])])).
% 8.16/8.36 fof(c_0_37, plain, ![X160]:((~r1|is_a_theorem(implies(or(X160,X160),X160)))&(~is_a_theorem(implies(or(esk45_0,esk45_0),esk45_0))|r1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r1])])])])).
% 8.16/8.36 cnf(c_0_38, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_29])).
% 8.16/8.36 cnf(c_0_39, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_31])])).
% 8.16/8.36 cnf(c_0_40, plain, (op_or), inference(split_conjunct,[status(thm)],[hilbert_op_or])).
% 8.16/8.36 cnf(c_0_41, 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_32, c_0_33])])).
% 8.16/8.36 cnf(c_0_42, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34, c_0_35])])).
% 8.16/8.36 cnf(c_0_43, plain, (implies(X1,X2)=or(not(X1),X2)|~op_implies_or), inference(split_conjunct,[status(thm)],[c_0_36])).
% 8.16/8.36 cnf(c_0_44, plain, (op_implies_or), inference(split_conjunct,[status(thm)],[principia_op_implies_or])).
% 8.16/8.36 cnf(c_0_45, plain, (is_a_theorem(implies(or(X1,X1),X1))|~r1), inference(split_conjunct,[status(thm)],[c_0_37])).
% 8.16/8.36 cnf(c_0_46, plain, (r1), inference(split_conjunct,[status(thm)],[principia_r1])).
% 8.16/8.36 fof(c_0_47, 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])])])])).
% 8.16/8.36 cnf(c_0_48, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39]), c_0_40])])).
% 8.16/8.36 cnf(c_0_49, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 8.16/8.36 cnf(c_0_50, plain, (or(not(X1),X2)=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])).
% 8.16/8.36 cnf(c_0_51, plain, (is_a_theorem(implies(or(X1,X1),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45, c_0_46])])).
% 8.16/8.36 cnf(c_0_52, plain, (is_a_theorem(implies(X1,or(X2,X1)))|~r2), inference(split_conjunct,[status(thm)],[c_0_47])).
% 8.16/8.36 cnf(c_0_53, plain, (r2), inference(split_conjunct,[status(thm)],[principia_r2])).
% 8.16/8.36 cnf(c_0_54, plain, (is_a_theorem(X1)|~is_a_theorem(or(X2,X1))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_41, c_0_48])).
% 8.16/8.36 cnf(c_0_55, plain, (is_a_theorem(or(X1,not(X2)))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_49, c_0_50])).
% 8.16/8.36 cnf(c_0_56, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,X1))), inference(spm,[status(thm)],[c_0_41, c_0_51])).
% 8.16/8.36 cnf(c_0_57, plain, (is_a_theorem(implies(X1,or(X2,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_52, c_0_53])])).
% 8.16/8.36 cnf(c_0_58, plain, (is_a_theorem(not(X1))|~is_a_theorem(implies(X1,X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_54, c_0_55])).
% 8.16/8.36 cnf(c_0_59, plain, (is_a_theorem(not(X1))|~is_a_theorem(implies(X1,not(X1)))), inference(spm,[status(thm)],[c_0_56, c_0_50])).
% 8.16/8.36 cnf(c_0_60, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_41, c_0_57])).
% 8.16/8.36 fof(c_0_61, plain, ![X176, X177, X178]:((~r5|is_a_theorem(implies(implies(X177,X178),implies(or(X176,X177),or(X176,X178)))))&(~is_a_theorem(implies(implies(esk54_0,esk55_0),implies(or(esk53_0,esk54_0),or(esk53_0,esk55_0))))|r5)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r5])])])])).
% 8.16/8.36 cnf(c_0_62, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(or(X1,X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_58, c_0_48])).
% 8.16/8.36 cnf(c_0_63, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(or(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_59, c_0_48])).
% 8.16/8.36 cnf(c_0_64, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_49, c_0_60])).
% 8.16/8.36 cnf(c_0_65, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))|~r5), inference(split_conjunct,[status(thm)],[c_0_61])).
% 8.16/8.36 cnf(c_0_66, plain, (r5), inference(split_conjunct,[status(thm)],[principia_r5])).
% 8.16/8.36 cnf(c_0_67, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(not(not(X2)))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_62, c_0_55])).
% 8.16/8.36 cnf(c_0_68, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_63, c_0_64])).
% 8.16/8.36 fof(c_0_69, 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])])])).
% 8.16/8.36 cnf(c_0_70, plain, (is_a_theorem(implies(implies(X1,X2),implies(or(X3,X1),or(X3,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65, c_0_66])])).
% 8.16/8.36 cnf(c_0_71, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_67, c_0_68])).
% 8.16/8.36 cnf(c_0_72, plain, (is_a_theorem(implies(X1,implies(X2,X1)))), inference(spm,[status(thm)],[c_0_57, c_0_50])).
% 8.16/8.36 cnf(c_0_73, plain, (and(X1,X2)=not(or(not(X1),not(X2)))|~op_and), inference(split_conjunct,[status(thm)],[c_0_69])).
% 8.16/8.36 cnf(c_0_74, plain, (op_and), inference(split_conjunct,[status(thm)],[principia_op_and])).
% 8.16/8.36 cnf(c_0_75, plain, (is_a_theorem(implies(or(X1,X2),or(X1,X3)))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_41, c_0_70])).
% 8.16/8.36 cnf(c_0_76, plain, (is_a_theorem(X1)|~is_a_theorem(not(not(X2)))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_54, c_0_50])).
% 8.16/8.36 cnf(c_0_77, plain, (is_a_theorem(not(not(or(X1,X2))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_71, c_0_57])).
% 8.16/8.36 cnf(c_0_78, plain, (is_a_theorem(or(X1,implies(X2,not(X1))))), inference(spm,[status(thm)],[c_0_72, c_0_48])).
% 8.16/8.36 cnf(c_0_79, plain, (not(implies(X1,not(X2)))=and(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73, c_0_50]), c_0_74])])).
% 8.16/8.36 cnf(c_0_80, plain, (is_a_theorem(not(or(X1,X1)))|~is_a_theorem(not(X1))), inference(spm,[status(thm)],[c_0_58, c_0_51])).
% 8.16/8.36 fof(c_0_81, 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])])])).
% 8.16/8.36 cnf(c_0_82, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X1,X3))|~is_a_theorem(implies(X3,X2))), inference(spm,[status(thm)],[c_0_41, c_0_75])).
% 8.16/8.36 cnf(c_0_83, plain, (is_a_theorem(X1)|~is_a_theorem(implies(or(X2,X3),X1))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_76, c_0_77])).
% 8.16/8.36 cnf(c_0_84, plain, (is_a_theorem(or(implies(X1,not(X2)),X2))), inference(spm,[status(thm)],[c_0_49, c_0_78])).
% 8.16/8.36 cnf(c_0_85, plain, (or(implies(X1,not(X2)),X3)=implies(and(X1,X2),X3)), inference(spm,[status(thm)],[c_0_48, c_0_79])).
% 8.16/8.36 cnf(c_0_86, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(not(not(X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80, c_0_50]), c_0_79])).
% 8.16/8.36 cnf(c_0_87, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_81])).
% 8.16/8.36 cnf(c_0_88, plain, (op_equiv), inference(split_conjunct,[status(thm)],[principia_op_equiv])).
% 8.16/8.36 cnf(c_0_89, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,X3))|~is_a_theorem(implies(X3,X2))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82, c_0_50]), c_0_50])).
% 8.16/8.36 cnf(c_0_90, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(implies(X3,X2))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_83, c_0_75])).
% 8.16/8.36 cnf(c_0_91, plain, (is_a_theorem(implies(and(X1,X2),X2))), inference(rw,[status(thm)],[c_0_84, c_0_85])).
% 8.16/8.36 cnf(c_0_92, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_86, c_0_68])).
% 8.16/8.36 cnf(c_0_93, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_87, c_0_88])])).
% 8.16/8.36 cnf(c_0_94, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(or(X3,X1),X2))), inference(spm,[status(thm)],[c_0_89, c_0_57])).
% 8.16/8.36 cnf(c_0_95, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(and(X3,X2))), inference(spm,[status(thm)],[c_0_90, c_0_91])).
% 8.16/8.36 cnf(c_0_96, plain, (is_a_theorem(equiv(X1,X1))|~is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_92, c_0_93])).
% 8.16/8.36 cnf(c_0_97, plain, (is_a_theorem(implies(X1,X1))), inference(spm,[status(thm)],[c_0_94, c_0_51])).
% 8.16/8.36 cnf(c_0_98, plain, (is_a_theorem(or(X1,implies(X2,X3)))|~is_a_theorem(equiv(X3,X2))), inference(spm,[status(thm)],[c_0_95, c_0_93])).
% 8.16/8.36 cnf(c_0_99, plain, (is_a_theorem(equiv(X1,X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96, c_0_97])])).
% 8.16/8.36 fof(c_0_100, plain, ![X170, X171, X172]:((~r4|is_a_theorem(implies(or(X170,or(X171,X172)),or(X171,or(X170,X172)))))&(~is_a_theorem(implies(or(esk50_0,or(esk51_0,esk52_0)),or(esk51_0,or(esk50_0,esk52_0))))|r4)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[r4])])])])).
% 8.16/8.36 cnf(c_0_101, plain, (implies(and(X1,not(X2)),X3)=or(implies(X1,X2),X3)), inference(spm,[status(thm)],[c_0_50, c_0_39])).
% 8.16/8.36 cnf(c_0_102, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(or(X1,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63, c_0_55]), c_0_48])).
% 8.16/8.36 cnf(c_0_103, plain, (is_a_theorem(or(X1,implies(X2,X2)))), inference(spm,[status(thm)],[c_0_98, c_0_99])).
% 8.16/8.36 cnf(c_0_104, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))|~r4), inference(split_conjunct,[status(thm)],[c_0_100])).
% 8.16/8.36 cnf(c_0_105, plain, (r4), inference(split_conjunct,[status(thm)],[principia_r4])).
% 8.16/8.36 cnf(c_0_106, plain, (is_a_theorem(X1)|~is_a_theorem(or(implies(X2,X3),X1))|~is_a_theorem(and(X2,not(X3)))), inference(spm,[status(thm)],[c_0_41, c_0_101])).
% 8.16/8.36 cnf(c_0_107, plain, (is_a_theorem(not(not(implies(X1,X1))))), inference(spm,[status(thm)],[c_0_102, c_0_103])).
% 8.16/8.36 cnf(c_0_108, plain, (is_a_theorem(implies(or(X1,or(X2,X3)),or(X2,or(X1,X3))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_104, c_0_105])])).
% 8.16/8.36 cnf(c_0_109, plain, (is_a_theorem(X1)|~is_a_theorem(and(X2,not(not(X1))))), inference(spm,[status(thm)],[c_0_106, c_0_84])).
% 8.16/8.36 cnf(c_0_110, plain, (is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,X2),X1))), inference(spm,[status(thm)],[c_0_76, c_0_107])).
% 8.16/8.36 cnf(c_0_111, plain, (is_a_theorem(implies(implies(X1,or(X2,X3)),or(X2,implies(X1,X3))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_50]), c_0_50])).
% 8.16/8.36 cnf(c_0_112, plain, (is_a_theorem(X1)|~is_a_theorem(not(not(X1)))), inference(spm,[status(thm)],[c_0_109, c_0_92])).
% 8.16/8.36 cnf(c_0_113, plain, (not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))), inference(spm,[status(thm)],[c_0_39, c_0_39])).
% 8.16/8.36 cnf(c_0_114, plain, (and(X1,implies(X2,not(X3)))=not(implies(X1,and(X2,X3)))), inference(spm,[status(thm)],[c_0_79, c_0_79])).
% 8.16/8.36 cnf(c_0_115, plain, (is_a_theorem(or(X1,implies(or(X1,X2),X2)))), inference(spm,[status(thm)],[c_0_110, c_0_111])).
% 8.16/8.36 fof(c_0_116, plain, ![X76, X77]:((~substitution_of_equivalents|(~is_a_theorem(equiv(X76,X77))|X76=X77))&((is_a_theorem(equiv(esk3_0,esk4_0))|substitution_of_equivalents)&(esk3_0!=esk4_0|substitution_of_equivalents))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[substitution_of_equivalents])])])])])).
% 8.16/8.36 cnf(c_0_117, plain, (is_a_theorem(and(X1,implies(X2,X3)))|~is_a_theorem(not(implies(X1,and(X2,not(X3)))))), inference(spm,[status(thm)],[c_0_112, c_0_113])).
% 8.16/8.36 cnf(c_0_118, plain, (not(implies(or(X1,X2),and(X2,X1)))=equiv(not(X1),X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93, c_0_48]), c_0_114])).
% 8.16/8.36 cnf(c_0_119, plain, (is_a_theorem(implies(X1,implies(implies(X1,X2),X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115, c_0_50]), c_0_50])).
% 8.16/8.36 cnf(c_0_120, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_116])).
% 8.16/8.36 cnf(c_0_121, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 8.16/8.36 cnf(c_0_122, plain, (is_a_theorem(equiv(X1,X2))|~is_a_theorem(equiv(not(not(X1)),X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_117, c_0_118]), c_0_50]), c_0_93])).
% 8.16/8.36 cnf(c_0_123, plain, (is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(implies(X2,not(X1)))), inference(spm,[status(thm)],[c_0_55, c_0_50])).
% 8.16/8.36 cnf(c_0_124, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_41, c_0_119])).
% 8.16/8.36 cnf(c_0_125, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_120, c_0_121])])).
% 8.16/8.36 cnf(c_0_126, plain, (is_a_theorem(equiv(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_122, c_0_99])).
% 8.16/8.36 cnf(c_0_127, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123, c_0_124]), c_0_79])).
% 8.16/8.36 cnf(c_0_128, plain, (not(not(X1))=X1), inference(spm,[status(thm)],[c_0_125, c_0_126])).
% 8.16/8.36 cnf(c_0_129, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X2)|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_41, c_0_127])).
% 8.16/8.36 cnf(c_0_130, plain, (implies(implies(X1,X2),and(X2,not(X1)))=not(equiv(X1,X2))), inference(spm,[status(thm)],[c_0_113, c_0_93])).
% 8.16/8.36 cnf(c_0_131, plain, (and(X1,not(X2))=not(implies(X1,X2))), inference(spm,[status(thm)],[c_0_79, c_0_128])).
% 8.16/8.36 cnf(c_0_132, plain, (is_a_theorem(equiv(X1,X2))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_129, c_0_93])).
% 8.16/8.36 fof(c_0_133, plain, ![X132, X133]:((~equivalence_3|is_a_theorem(implies(implies(X132,X133),implies(implies(X133,X132),equiv(X132,X133)))))&(~is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),equiv(esk31_0,esk32_0))))|equivalence_3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[equivalence_3])])])])).
% 8.16/8.36 fof(c_0_134, negated_conjecture, ~equivalence_3, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_equivalence_3])])).
% 8.16/8.36 cnf(c_0_135, plain, (implies(implies(X1,X2),not(implies(X2,X1)))=not(equiv(X1,X2))), inference(rw,[status(thm)],[c_0_130, c_0_131])).
% 8.16/8.36 cnf(c_0_136, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_125, c_0_132])).
% 8.16/8.36 cnf(c_0_137, plain, (equivalence_3|~is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),equiv(esk31_0,esk32_0))))), inference(split_conjunct,[status(thm)],[c_0_133])).
% 8.16/8.36 cnf(c_0_138, negated_conjecture, (~equivalence_3), inference(split_conjunct,[status(thm)],[c_0_134])).
% 8.16/8.36 cnf(c_0_139, plain, (is_a_theorem(implies(implies(X1,X2),or(equiv(X1,X2),not(implies(X2,X1)))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_119, c_0_135]), c_0_48])).
% 8.16/8.36 cnf(c_0_140, plain, (or(X1,X2)=or(X2,X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_136, c_0_42]), c_0_42])])).
% 8.16/8.36 cnf(c_0_141, plain, (~is_a_theorem(implies(implies(esk31_0,esk32_0),implies(implies(esk32_0,esk31_0),equiv(esk31_0,esk32_0))))), inference(sr,[status(thm)],[c_0_137, c_0_138])).
% 8.16/8.36 cnf(c_0_142, plain, (is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X1),equiv(X1,X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_139, c_0_140]), c_0_50])).
% 8.16/8.36 cnf(c_0_143, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_141, c_0_142])]), ['proof']).
% 8.16/8.36 % SZS output end Proof
% 8.16/8.36 % User time : 7.536 s
% 8.16/8.36 % System time : 0.338 s
% 8.16/8.36 % Total time : 7.874 s
% 8.16/8.36
%------------------------------------------------------------------------------