%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL508+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n017.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 11:21:06 AM UTC 2026
% Result : Theorem 4.76s 4.94s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL508+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.08/0.34 % Computer : n017.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Sat Sep 5 00:40:21 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.12/0.46 start to proof:theBenchmark.p
% 4.76/4.94 % Version : CSI_E---1.1
% 4.76/4.94 % Problem : theBenchmark.p
% 4.76/4.94 % Proof found!
% 4.76/4.94 % SZS status Theorem for theBenchmark.p
% 4.76/4.94 % SZS output start Proof
% 4.76/4.94 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)).
% 4.76/4.94 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)).
% 4.76/4.94 fof(rosser_op_implies_and, axiom, op_implies_and, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_op_implies_and)).
% 4.76/4.94 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)).
% 4.76/4.94 fof(kn3, axiom, (kn3<=>![X4, X5, X6]:is_a_theorem(implies(implies(X4,X5),implies(not(and(X5,X6)),not(and(X6,X4)))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn3)).
% 4.76/4.94 fof(rosser_op_or, axiom, op_or, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_op_or)).
% 4.76/4.94 fof(rosser_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_modus_ponens)).
% 4.76/4.94 fof(rosser_kn3, axiom, kn3, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_kn3)).
% 4.76/4.94 fof(kn2, axiom, (kn2<=>![X4, X5]:is_a_theorem(implies(and(X4,X5),X4))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn2)).
% 4.76/4.94 fof(rosser_kn2, axiom, kn2, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_kn2)).
% 4.76/4.94 fof(kn1, axiom, (kn1<=>![X4]:is_a_theorem(implies(X4,and(X4,X4)))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', kn1)).
% 4.76/4.94 fof(rosser_kn1, axiom, kn1, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_kn1)).
% 4.76/4.94 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)).
% 4.76/4.94 fof(rosser_op_equiv, axiom, op_equiv, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', rosser_op_equiv)).
% 4.76/4.94 fof(substitution_of_equivalents, axiom, (substitution_of_equivalents<=>![X1, X2]:(is_a_theorem(equiv(X1,X2))=>X1=X2)), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', substitution_of_equivalents)).
% 4.76/4.94 fof(use_substitution_of_equivalents, axiom, substitution_of_equivalents, file('/export/starexec/sandbox/benchmark/Axioms/LCL006+5.ax', use_substitution_of_equivalents)).
% 4.76/4.94 fof(and_3, axiom, (and_3<=>![X1, X2]:is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax', and_3)).
% 4.76/4.94 fof(hilbert_and_3, conjecture, and_3, file('/export/starexec/sandbox/benchmark/theBenchmark.p', hilbert_and_3)).
% 4.76/4.94 fof(c_0_18, 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])])])).
% 4.76/4.94 fof(c_0_19, 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])])])).
% 4.76/4.94 cnf(c_0_20, plain, (implies(X1,X2)=not(and(X1,not(X2)))|~op_implies_and), inference(split_conjunct,[status(thm)],[c_0_18])).
% 4.76/4.94 cnf(c_0_21, plain, (op_implies_and), inference(split_conjunct,[status(thm)],[rosser_op_implies_and])).
% 4.76/4.94 fof(c_0_22, 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])])])])])).
% 4.76/4.94 fof(c_0_23, plain, ![X142, X143, X144]:((~kn3|is_a_theorem(implies(implies(X142,X143),implies(not(and(X143,X144)),not(and(X144,X142))))))&(~is_a_theorem(implies(implies(esk36_0,esk37_0),implies(not(and(esk37_0,esk38_0)),not(and(esk38_0,esk36_0)))))|kn3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn3])])])])).
% 4.76/4.94 cnf(c_0_24, plain, (or(X1,X2)=not(and(not(X1),not(X2)))|~op_or), inference(split_conjunct,[status(thm)],[c_0_19])).
% 4.76/4.94 cnf(c_0_25, plain, (not(and(X1,not(X2)))=implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 4.76/4.94 cnf(c_0_26, plain, (op_or), inference(split_conjunct,[status(thm)],[rosser_op_or])).
% 4.76/4.94 cnf(c_0_27, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_22])).
% 4.76/4.94 cnf(c_0_28, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[rosser_modus_ponens])).
% 4.76/4.94 cnf(c_0_29, plain, (is_a_theorem(implies(implies(X1,X2),implies(not(and(X2,X3)),not(and(X3,X1)))))|~kn3), inference(split_conjunct,[status(thm)],[c_0_23])).
% 4.76/4.94 cnf(c_0_30, plain, (implies(not(X1),X2)=or(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25]), c_0_26])])).
% 4.76/4.94 cnf(c_0_31, plain, (kn3), inference(split_conjunct,[status(thm)],[rosser_kn3])).
% 4.76/4.94 cnf(c_0_32, 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_27, c_0_28])])).
% 4.76/4.94 cnf(c_0_33, plain, (is_a_theorem(implies(implies(X1,X2),or(and(X2,X3),not(and(X3,X1)))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29, c_0_30]), c_0_31])])).
% 4.76/4.94 cnf(c_0_34, plain, (is_a_theorem(X1)|~is_a_theorem(or(X2,X1))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_32, c_0_30])).
% 4.76/4.94 cnf(c_0_35, plain, (is_a_theorem(or(and(X1,X2),not(and(X2,X3))))|~is_a_theorem(implies(X3,X1))), inference(spm,[status(thm)],[c_0_32, c_0_33])).
% 4.76/4.94 fof(c_0_36, plain, ![X138, X139]:((~kn2|is_a_theorem(implies(and(X138,X139),X138)))&(~is_a_theorem(implies(and(esk34_0,esk35_0),esk34_0))|kn2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn2])])])])).
% 4.76/4.94 cnf(c_0_37, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(not(and(X3,X1)))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_34, c_0_35])).
% 4.76/4.94 cnf(c_0_38, plain, (is_a_theorem(implies(and(X1,X2),X1))|~kn2), inference(split_conjunct,[status(thm)],[c_0_36])).
% 4.76/4.94 cnf(c_0_39, plain, (kn2), inference(split_conjunct,[status(thm)],[rosser_kn2])).
% 4.76/4.94 fof(c_0_40, plain, ![X136]:((~kn1|is_a_theorem(implies(X136,and(X136,X136))))&(~is_a_theorem(implies(esk33_0,and(esk33_0,esk33_0)))|kn1)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[kn1])])])])).
% 4.76/4.94 cnf(c_0_41, plain, (is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(implies(X3,X1))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_37, c_0_25])).
% 4.76/4.94 cnf(c_0_42, plain, (is_a_theorem(implies(and(X1,X2),X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_38, c_0_39])])).
% 4.76/4.94 cnf(c_0_43, plain, (is_a_theorem(implies(X1,and(X1,X1)))|~kn1), inference(split_conjunct,[status(thm)],[c_0_40])).
% 4.76/4.94 cnf(c_0_44, plain, (kn1), inference(split_conjunct,[status(thm)],[rosser_kn1])).
% 4.76/4.94 cnf(c_0_45, plain, (is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(implies(X2,and(X1,X3)))), inference(spm,[status(thm)],[c_0_41, c_0_42])).
% 4.76/4.94 cnf(c_0_46, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43, c_0_44])])).
% 4.76/4.94 cnf(c_0_47, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X2,and(X1,X3)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45, c_0_30]), c_0_25]), c_0_30])).
% 4.76/4.94 cnf(c_0_48, plain, (is_a_theorem(or(X1,and(not(X1),not(X1))))), inference(spm,[status(thm)],[c_0_46, c_0_30])).
% 4.76/4.94 cnf(c_0_49, plain, (is_a_theorem(or(not(X1),X1))), inference(spm,[status(thm)],[c_0_47, c_0_48])).
% 4.76/4.94 cnf(c_0_50, plain, (is_a_theorem(or(X1,not(and(X1,X2))))), inference(spm,[status(thm)],[c_0_47, c_0_49])).
% 4.76/4.94 cnf(c_0_51, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(not(X1))), inference(spm,[status(thm)],[c_0_34, c_0_50])).
% 4.76/4.94 cnf(c_0_52, plain, (is_a_theorem(not(and(not(X1),X1)))), inference(spm,[status(thm)],[c_0_45, c_0_46])).
% 4.76/4.94 cnf(c_0_53, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,X3))|~is_a_theorem(not(X3))), inference(spm,[status(thm)],[c_0_37, c_0_51])).
% 4.76/4.94 cnf(c_0_54, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,not(X1)))), inference(spm,[status(thm)],[c_0_37, c_0_52])).
% 4.76/4.94 cnf(c_0_55, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(not(and(X2,X2)))), inference(spm,[status(thm)],[c_0_53, c_0_46])).
% 4.76/4.94 cnf(c_0_56, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54, c_0_25]), c_0_30])).
% 4.76/4.94 cnf(c_0_57, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_55, c_0_51])).
% 4.76/4.94 cnf(c_0_58, plain, (is_a_theorem(implies(X1,not(not(X1))))), inference(spm,[status(thm)],[c_0_56, c_0_49])).
% 4.76/4.94 cnf(c_0_59, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(not(not(X2)))), inference(spm,[status(thm)],[c_0_57, c_0_25])).
% 4.76/4.94 cnf(c_0_60, plain, (is_a_theorem(not(not(X1)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_32, c_0_58])).
% 4.76/4.94 cnf(c_0_61, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_59, c_0_60])).
% 4.76/4.94 cnf(c_0_62, plain, (is_a_theorem(or(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_50, c_0_25])).
% 4.76/4.94 cnf(c_0_63, plain, (is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(and(X1,X3))), inference(spm,[status(thm)],[c_0_45, c_0_61])).
% 4.76/4.94 cnf(c_0_64, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_32, c_0_46])).
% 4.76/4.94 cnf(c_0_65, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(not(X1))), inference(spm,[status(thm)],[c_0_34, c_0_62])).
% 4.76/4.94 cnf(c_0_66, plain, (is_a_theorem(not(and(not(X1),X2)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_63, c_0_64])).
% 4.76/4.94 cnf(c_0_67, plain, (is_a_theorem(or(and(X1,X2),implies(X2,X3)))|~is_a_theorem(or(X3,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35, c_0_25]), c_0_30])).
% 4.76/4.94 cnf(c_0_68, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,not(X2)))), inference(spm,[status(thm)],[c_0_55, c_0_54])).
% 4.76/4.94 cnf(c_0_69, plain, (is_a_theorem(implies(and(not(X1),X1),X2))), inference(spm,[status(thm)],[c_0_65, c_0_52])).
% 4.76/4.94 cnf(c_0_70, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,not(X3)))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_37, c_0_66])).
% 4.76/4.94 cnf(c_0_71, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(not(and(X3,X1)))|~is_a_theorem(or(X2,X3))), inference(spm,[status(thm)],[c_0_34, c_0_67])).
% 4.76/4.94 cnf(c_0_72, plain, (is_a_theorem(not(and(X1,and(not(X2),X2))))), inference(spm,[status(thm)],[c_0_68, c_0_69])).
% 4.76/4.94 cnf(c_0_73, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,not(X3)))|~is_a_theorem(X3)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70, c_0_30]), c_0_25])).
% 4.76/4.94 cnf(c_0_74, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(implies(X3,X1))|~is_a_theorem(or(X2,X3))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71, c_0_25]), c_0_30])).
% 4.76/4.94 cnf(c_0_75, plain, (is_a_theorem(not(and(and(not(X1),X1),X2)))|~is_a_theorem(implies(X2,X3))), inference(spm,[status(thm)],[c_0_37, c_0_72])).
% 4.76/4.94 cnf(c_0_76, plain, (is_a_theorem(implies(X1,not(not(X2))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_73, c_0_49])).
% 4.76/4.94 cnf(c_0_77, plain, (not(and(X1,implies(X2,X3)))=implies(X1,and(X2,not(X3)))), inference(spm,[status(thm)],[c_0_25, c_0_25])).
% 4.76/4.94 cnf(c_0_78, plain, (is_a_theorem(or(and(X1,X1),X2))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_74, c_0_46])).
% 4.76/4.94 cnf(c_0_79, plain, (is_a_theorem(not(and(and(not(X1),X1),X2)))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_75, c_0_76])).
% 4.76/4.94 cnf(c_0_80, plain, (is_a_theorem(or(and(X1,implies(X2,X3)),and(implies(X1,and(X2,not(X3))),implies(X1,and(X2,not(X3))))))), inference(spm,[status(thm)],[c_0_48, c_0_77])).
% 4.76/4.94 cnf(c_0_81, plain, (is_a_theorem(X1)|~is_a_theorem(not(and(X2,X2)))|~is_a_theorem(or(X1,X2))), inference(spm,[status(thm)],[c_0_34, c_0_78])).
% 4.76/4.94 cnf(c_0_82, plain, (is_a_theorem(not(and(and(not(X1),X1),X2)))), inference(spm,[status(thm)],[c_0_79, c_0_80])).
% 4.76/4.94 cnf(c_0_83, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,X2))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_81, c_0_51])).
% 4.76/4.94 cnf(c_0_84, plain, (is_a_theorem(not(and(X1,X2)))|~is_a_theorem(implies(X2,and(not(X3),X3)))), inference(spm,[status(thm)],[c_0_37, c_0_82])).
% 4.76/4.94 cnf(c_0_85, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,X1))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_83, c_0_48]), c_0_25]), c_0_30])).
% 4.76/4.94 cnf(c_0_86, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(or(X2,and(not(X3),X3)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84, c_0_30]), c_0_25])).
% 4.76/4.94 cnf(c_0_87, plain, (is_a_theorem(or(implies(X1,X2),and(X1,not(X2))))), inference(spm,[status(thm)],[c_0_49, c_0_25])).
% 4.76/4.94 cnf(c_0_88, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,not(X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_81, c_0_66])).
% 4.76/4.94 cnf(c_0_89, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(or(and(X1,X1),X1))), inference(spm,[status(thm)],[c_0_85, c_0_78])).
% 4.76/4.94 cnf(c_0_90, plain, (is_a_theorem(implies(X1,or(not(X2),X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86, c_0_87]), c_0_30])).
% 4.76/4.94 cnf(c_0_91, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(and(X2,X3))|~is_a_theorem(implies(X3,X1))), inference(spm,[status(thm)],[c_0_88, c_0_35])).
% 4.76/4.94 cnf(c_0_92, plain, (is_a_theorem(and(X1,X1))|~is_a_theorem(or(X1,X1))), inference(spm,[status(thm)],[c_0_89, c_0_78])).
% 4.76/4.94 cnf(c_0_93, plain, (is_a_theorem(or(or(not(X1),X1),X2))|~is_a_theorem(or(X2,X3))), inference(spm,[status(thm)],[c_0_74, c_0_90])).
% 4.76/4.94 cnf(c_0_94, plain, (is_a_theorem(or(X1,not(not(X2))))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_76, c_0_30])).
% 4.76/4.94 cnf(c_0_95, plain, (implies(X1,and(not(X2),not(X3)))=not(and(X1,or(X2,X3)))), inference(spm,[status(thm)],[c_0_77, c_0_30])).
% 4.76/4.94 fof(c_0_96, 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])])])).
% 4.76/4.94 cnf(c_0_97, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(or(X2,X2))), inference(spm,[status(thm)],[c_0_91, c_0_92])).
% 4.76/4.94 cnf(c_0_98, plain, (is_a_theorem(or(or(not(X1),X1),X2))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_93, c_0_94])).
% 4.76/4.94 cnf(c_0_99, plain, (is_a_theorem(or(and(X1,or(X2,X3)),or(and(and(not(X2),not(X3)),X4),not(and(X4,X1)))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_95]), c_0_30])).
% 4.76/4.94 cnf(c_0_100, plain, (equiv(X1,X2)=and(implies(X1,X2),implies(X2,X1))|~op_equiv), inference(split_conjunct,[status(thm)],[c_0_96])).
% 4.76/4.94 cnf(c_0_101, plain, (op_equiv), inference(split_conjunct,[status(thm)],[rosser_op_equiv])).
% 4.76/4.94 fof(c_0_102, 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])])])])])).
% 4.76/4.94 cnf(c_0_103, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(or(X2,X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_97, c_0_61])).
% 4.76/4.94 cnf(c_0_104, plain, (is_a_theorem(or(or(not(X1),X1),X2))), inference(spm,[status(thm)],[c_0_98, c_0_99])).
% 4.76/4.94 cnf(c_0_105, plain, (and(implies(X1,X2),implies(X2,X1))=equiv(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_100, c_0_101])])).
% 4.76/4.94 cnf(c_0_106, plain, (X1=X2|~substitution_of_equivalents|~is_a_theorem(equiv(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_102])).
% 4.76/4.94 cnf(c_0_107, plain, (substitution_of_equivalents), inference(split_conjunct,[status(thm)],[use_substitution_of_equivalents])).
% 4.76/4.94 cnf(c_0_108, plain, (is_a_theorem(and(X1,or(not(X2),X2)))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_103, c_0_104])).
% 4.76/4.94 cnf(c_0_109, plain, (and(implies(X1,not(X2)),or(X2,X1))=equiv(X1,not(X2))), inference(spm,[status(thm)],[c_0_105, c_0_30])).
% 4.76/4.94 cnf(c_0_110, plain, (X1=X2|~is_a_theorem(equiv(X1,X2))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_106, c_0_107])])).
% 4.76/4.94 cnf(c_0_111, plain, (is_a_theorem(equiv(X1,not(not(X1))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108, c_0_109]), c_0_58])])).
% 4.76/4.94 cnf(c_0_112, plain, (not(not(X1))=X1), inference(spm,[status(thm)],[c_0_110, c_0_111])).
% 4.76/4.94 cnf(c_0_113, plain, (not(and(X1,X2))=implies(X1,not(X2))), inference(spm,[status(thm)],[c_0_25, c_0_112])).
% 4.76/4.94 cnf(c_0_114, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,and(not(X2),X2)))), inference(spm,[status(thm)],[c_0_81, c_0_72])).
% 4.76/4.94 cnf(c_0_115, plain, (not(implies(X1,not(X2)))=and(X1,X2)), inference(spm,[status(thm)],[c_0_112, c_0_113])).
% 4.76/4.94 cnf(c_0_116, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65, c_0_60]), c_0_30])).
% 4.76/4.94 cnf(c_0_117, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,and(X2,not(X2))))), inference(spm,[status(thm)],[c_0_114, c_0_112])).
% 4.76/4.94 cnf(c_0_118, plain, (and(X1,not(X2))=not(implies(X1,X2))), inference(spm,[status(thm)],[c_0_115, c_0_112])).
% 4.76/4.94 cnf(c_0_119, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X2,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_56, c_0_112]), c_0_30])).
% 4.76/4.94 cnf(c_0_120, plain, (or(not(X1),X2)=implies(X1,X2)), inference(spm,[status(thm)],[c_0_30, c_0_112])).
% 4.76/4.94 cnf(c_0_121, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_47, c_0_116])).
% 4.76/4.94 cnf(c_0_122, plain, (is_a_theorem(X1)|~is_a_theorem(or(X1,not(implies(X2,X2))))), inference(rw,[status(thm)],[c_0_117, c_0_118])).
% 4.76/4.94 cnf(c_0_123, plain, (is_a_theorem(or(X1,not(X2)))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_119, c_0_120])).
% 4.76/4.94 cnf(c_0_124, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(X1)|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_103, c_0_121])).
% 4.76/4.94 cnf(c_0_125, plain, (is_a_theorem(X1)|~is_a_theorem(implies(implies(X2,X2),X1))), inference(spm,[status(thm)],[c_0_122, c_0_123])).
% 4.76/4.94 cnf(c_0_126, plain, (is_a_theorem(implies(or(X1,X2),or(and(X2,X3),implies(X3,X1))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33, c_0_25]), c_0_30])).
% 4.76/4.94 cnf(c_0_127, plain, (or(and(X1,not(X2)),X3)=implies(implies(X1,X2),X3)), inference(spm,[status(thm)],[c_0_30, c_0_25])).
% 4.76/4.94 cnf(c_0_128, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(X2,not(X3)))|~is_a_theorem(or(X3,X1))), inference(spm,[status(thm)],[c_0_74, c_0_30])).
% 4.76/4.94 cnf(c_0_129, plain, (is_a_theorem(or(X1,not(or(X1,X1))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_48, c_0_118]), c_0_30])).
% 4.76/4.94 cnf(c_0_130, plain, (is_a_theorem(equiv(X1,X2))|~is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_124, c_0_105])).
% 4.76/4.94 cnf(c_0_131, plain, (is_a_theorem(X1)|~is_a_theorem(implies(or(X2,not(X2)),X1))), inference(spm,[status(thm)],[c_0_125, c_0_30])).
% 4.76/4.94 cnf(c_0_132, plain, (is_a_theorem(implies(or(X1,X2),implies(implies(X2,X3),or(X3,X1))))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126, c_0_30]), c_0_127])).
% 4.76/4.94 cnf(c_0_133, plain, (is_a_theorem(implies(and(X1,X2),X3))|~is_a_theorem(not(X2))), inference(spm,[status(thm)],[c_0_65, c_0_57])).
% 4.76/4.94 cnf(c_0_134, plain, (is_a_theorem(or(X1,X2))|~is_a_theorem(or(or(X2,X2),X1))), inference(spm,[status(thm)],[c_0_128, c_0_129])).
% 4.76/4.94 cnf(c_0_135, plain, (X1=X2|~is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_110, c_0_130])).
% 4.76/4.94 cnf(c_0_136, plain, (is_a_theorem(implies(or(X1,X2),or(X2,X1)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131, c_0_132]), c_0_30])).
% 4.76/4.94 cnf(c_0_137, plain, (is_a_theorem(not(and(X1,and(X2,X3))))|~is_a_theorem(not(X3))|~is_a_theorem(X4)), inference(spm,[status(thm)],[c_0_70, c_0_133])).
% 4.76/4.94 cnf(c_0_138, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,or(X2,X2)))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_134, c_0_123]), c_0_120])).
% 4.76/4.94 cnf(c_0_139, plain, (is_a_theorem(implies(implies(X1,X2),or(X2,X3)))|~is_a_theorem(or(X3,X1))), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67, c_0_30]), c_0_127])).
% 4.76/4.94 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_135, c_0_136]), c_0_136])])).
% 4.76/4.94 cnf(c_0_141, plain, (is_a_theorem(not(and(X1,and(X2,not(X3)))))|~is_a_theorem(X4)|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_137, c_0_60])).
% 4.76/4.94 cnf(c_0_142, plain, (and(or(X1,X2),implies(X2,not(X1)))=equiv(not(X1),X2)), inference(spm,[status(thm)],[c_0_105, c_0_30])).
% 4.76/4.94 cnf(c_0_143, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_138, c_0_139])).
% 4.76/4.94 cnf(c_0_144, plain, (not(or(X1,not(X2)))=and(not(X1),X2)), inference(spm,[status(thm)],[c_0_115, c_0_30])).
% 4.76/4.94 cnf(c_0_145, plain, (or(X1,not(X2))=implies(X2,X1)), inference(spm,[status(thm)],[c_0_120, c_0_140])).
% 4.76/4.94 cnf(c_0_146, plain, (is_a_theorem(and(X1,X2))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_91, c_0_64])).
% 4.76/4.94 cnf(c_0_147, plain, (is_a_theorem(implies(X1,implies(X2,X3)))|~is_a_theorem(X4)|~is_a_theorem(X3)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_141, c_0_113]), c_0_25])).
% 4.76/4.94 cnf(c_0_148, plain, (is_a_theorem(or(or(X1,X2),not(equiv(not(X1),X2))))), inference(spm,[status(thm)],[c_0_50, c_0_142])).
% 4.76/4.94 cnf(c_0_149, plain, (is_a_theorem(implies(X1,not(X2)))|~is_a_theorem(implies(X2,not(X1)))), inference(rw,[status(thm)],[c_0_54, c_0_113])).
% 4.76/4.94 cnf(c_0_150, plain, (is_a_theorem(implies(implies(X1,X2),X2))|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_143, c_0_121])).
% 4.76/4.94 cnf(c_0_151, plain, (and(not(X1),X2)=not(implies(X2,X1))), inference(rw,[status(thm)],[c_0_144, c_0_145])).
% 4.76/4.94 cnf(c_0_152, plain, (is_a_theorem(equiv(X1,X2))|~is_a_theorem(implies(implies(X2,X1),implies(X1,X2)))|~is_a_theorem(implies(X2,X1))), inference(spm,[status(thm)],[c_0_146, c_0_105])).
% 4.76/4.94 cnf(c_0_153, plain, (is_a_theorem(implies(X1,implies(X2,X3)))|~is_a_theorem(X3)), inference(spm,[status(thm)],[c_0_147, c_0_148])).
% 4.76/4.94 cnf(c_0_154, plain, (is_a_theorem(implies(X1,and(X2,X1)))|~is_a_theorem(X2)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149, c_0_150]), c_0_115])).
% 4.76/4.94 cnf(c_0_155, plain, (and(X1,X2)=and(X2,X1)), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_151, c_0_112]), c_0_115])).
% 4.76/4.94 cnf(c_0_156, plain, (is_a_theorem(equiv(X1,X2))|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_152, c_0_153])).
% 4.76/4.94 cnf(c_0_157, plain, (is_a_theorem(or(not(X1),or(X1,X2)))), inference(spm,[status(thm)],[c_0_62, c_0_30])).
% 4.76/4.94 cnf(c_0_158, plain, (is_a_theorem(implies(X1,and(X1,X2)))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_154, c_0_155])).
% 4.76/4.94 cnf(c_0_159, plain, (X1=X2|~is_a_theorem(implies(X2,X1))|~is_a_theorem(X2)), inference(spm,[status(thm)],[c_0_110, c_0_156])).
% 4.76/4.94 cnf(c_0_160, plain, (is_a_theorem(implies(X1,or(X1,X2)))), inference(rw,[status(thm)],[c_0_157, c_0_120])).
% 4.76/4.94 cnf(c_0_161, plain, (and(X1,X2)=X1|~is_a_theorem(X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135, c_0_158]), c_0_42])])).
% 4.76/4.94 cnf(c_0_162, plain, (is_a_theorem(implies(X1,X1))), inference(rw,[status(thm)],[c_0_58, c_0_112])).
% 4.76/4.94 cnf(c_0_163, plain, (or(X1,X2)=X1|~is_a_theorem(X1)), inference(spm,[status(thm)],[c_0_159, c_0_160])).
% 4.76/4.94 cnf(c_0_164, plain, (and(X1,implies(X2,X2))=X1), inference(spm,[status(thm)],[c_0_161, c_0_162])).
% 4.76/4.94 cnf(c_0_165, plain, (or(X1,X2)=or(X2,X1)|~is_a_theorem(or(X2,X1))), inference(spm,[status(thm)],[c_0_159, c_0_136])).
% 4.76/4.94 cnf(c_0_166, plain, (or(implies(X1,X1),X2)=implies(X1,X1)), inference(spm,[status(thm)],[c_0_163, c_0_162])).
% 4.76/4.94 cnf(c_0_167, plain, (is_a_theorem(implies(implies(implies(X1,not(X2)),X3),or(and(X3,or(X2,X1)),not(equiv(not(X2),X1)))))), inference(spm,[status(thm)],[c_0_33, c_0_142])).
% 4.76/4.94 cnf(c_0_168, plain, (and(or(X1,not(X2)),or(X2,not(X1)))=equiv(not(X1),not(X2))), inference(spm,[status(thm)],[c_0_109, c_0_30])).
% 4.76/4.94 cnf(c_0_169, plain, (not(implies(implies(X1,X1),X2))=not(X2)), inference(spm,[status(thm)],[c_0_151, c_0_164])).
% 4.76/4.94 cnf(c_0_170, plain, (or(X1,implies(X2,X2))=implies(X2,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_165, c_0_166]), c_0_162])])).
% 4.76/4.94 fof(c_0_171, plain, ![X106, X107]:((~and_3|is_a_theorem(implies(X106,implies(X107,and(X106,X107)))))&(~is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))|and_3)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[and_3])])])])).
% 4.76/4.94 fof(c_0_172, negated_conjecture, ~and_3, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[hilbert_and_3])])).
% 4.76/4.94 cnf(c_0_173, plain, (is_a_theorem(implies(implies(or(X1,not(X2)),X3),or(and(X3,or(X2,not(X1))),not(equiv(not(X2),not(X1))))))), inference(spm,[status(thm)],[c_0_167, c_0_30])).
% 4.76/4.94 cnf(c_0_174, plain, (equiv(not(X1),not(X2))=equiv(X2,X1)), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_168, c_0_145]), c_0_145]), c_0_105])).
% 4.76/4.94 cnf(c_0_175, plain, (implies(implies(X1,X1),X2)=X2), inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112, c_0_169]), c_0_112])).
% 4.76/4.94 cnf(c_0_176, plain, (implies(X1,implies(X2,X2))=implies(X2,X2)), inference(spm,[status(thm)],[c_0_120, c_0_170])).
% 4.76/4.94 cnf(c_0_177, plain, (and_3|~is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))), inference(split_conjunct,[status(thm)],[c_0_171])).
% 4.76/4.94 cnf(c_0_178, negated_conjecture, (~and_3), inference(split_conjunct,[status(thm)],[c_0_172])).
% 4.76/4.94 cnf(c_0_179, plain, (is_a_theorem(implies(implies(implies(X1,X2),X3),implies(equiv(X2,X1),and(X3,implies(X2,X1)))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_173, c_0_145]), c_0_145]), c_0_145]), c_0_174])).
% 4.76/4.94 cnf(c_0_180, plain, (equiv(implies(X1,X1),X2)=X2), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105, c_0_175]), c_0_176]), c_0_164])).
% 4.76/4.94 cnf(c_0_181, plain, (~is_a_theorem(implies(esk18_0,implies(esk19_0,and(esk18_0,esk19_0))))), inference(sr,[status(thm)],[c_0_177, c_0_178])).
% 4.76/4.94 cnf(c_0_182, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_179, c_0_180]), c_0_176]), c_0_175]), c_0_175])).
% 4.76/4.94 cnf(c_0_183, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_181, c_0_182])]), ['proof']).
% 4.76/4.94 % SZS output end Proof
% 4.76/4.94 % User time : 4.280 s
% 4.76/4.94 % System time : 0.187 s
% 4.76/4.94 % Total time : 4.467 s
% 4.76/4.94
%------------------------------------------------------------------------------