%------------------------------------------------------------------------------
% File : CSI_E---1.1
% Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar mcs_scs.jar %d %s
% Computer : n006.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 11:21:08 AM UTC 2026
% Result : Theorem 0.24s 0.53s
% Output : Assurance 0s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL531+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.03 % Command : java -jar mcs_scs.jar %d %s
% 0.08/0.33 % Computer : n006.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Fri Sep 4 18:28:01 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.12/0.45 start to proof:theBenchmark.p
% 0.24/0.53 % Version : CSI_E---1.1
% 0.24/0.53 % Problem : theBenchmark.p
% 0.24/0.53 % Proof found!
% 0.24/0.53 % SZS status Theorem for theBenchmark.p
% 0.24/0.53 % SZS output start Proof
% 0.24/0.53 fof(necessitation, axiom, (necessitation<=>![X1]:(is_a_theorem(X1)=>is_a_theorem(necessarily(X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', necessitation)).
% 0.24/0.53 fof(op_strict_implies, axiom, (op_strict_implies=>![X1, X2]:strict_implies(X1,X2)=necessarily(implies(X1,X2))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+1.ax', op_strict_implies)).
% 0.24/0.53 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)).
% 0.24/0.53 fof(implies_2, axiom, (implies_2<=>![X1, X2]:is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', implies_2)).
% 0.24/0.53 fof(axiom_m4, axiom, (axiom_m4<=>![X1]:is_a_theorem(strict_implies(X1,and(X1,X1)))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+0.ax', axiom_m4)).
% 0.24/0.53 fof(s1_0_axiom_m4, conjecture, axiom_m4, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', s1_0_axiom_m4)).
% 0.24/0.53 fof(km5_necessitation, axiom, necessitation, file('/export/starexec/sandbox2/benchmark/Axioms/LCL007+2.ax', km5_necessitation)).
% 0.24/0.53 fof(s1_0_op_strict_implies, axiom, op_strict_implies, file('/export/starexec/sandbox2/benchmark/theBenchmark.p', s1_0_op_strict_implies)).
% 0.24/0.53 fof(hilbert_modus_ponens, axiom, modus_ponens, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_modus_ponens)).
% 0.24/0.53 fof(hilbert_implies_2, axiom, implies_2, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_implies_2)).
% 0.24/0.53 fof(and_3, axiom, (and_3<=>![X1, X2]:is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+0.ax', and_3)).
% 0.24/0.53 fof(hilbert_and_3, axiom, and_3, file('/export/starexec/sandbox2/benchmark/Axioms/LCL006+2.ax', hilbert_and_3)).
% 0.24/0.53 fof(c_0_12, plain, ![X237]:((~necessitation|(~is_a_theorem(X237)|is_a_theorem(necessarily(X237))))&((is_a_theorem(esk56_0)|necessitation)&(~is_a_theorem(necessarily(esk56_0))|necessitation))), inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[necessitation])])])])])).
% 0.24/0.53 fof(c_0_13, plain, ![X317, X318]:(~op_strict_implies|strict_implies(X317,X318)=necessarily(implies(X317,X318))), inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[op_strict_implies])])])).
% 0.24/0.53 fof(c_0_14, plain, ![X117, X118]:((~modus_ponens|(~is_a_theorem(X117)|~is_a_theorem(implies(X117,X118))|is_a_theorem(X118)))&(((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])])])])])).
% 0.24/0.53 fof(c_0_15, plain, ![X133, X134]:((~implies_2|is_a_theorem(implies(implies(X133,implies(X133,X134)),implies(X133,X134))))&(~is_a_theorem(implies(implies(esk9_0,implies(esk9_0,esk10_0)),implies(esk9_0,esk10_0)))|implies_2)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[implies_2])])])])).
% 0.24/0.53 fof(c_0_16, plain, ![X293]:((~axiom_m4|is_a_theorem(strict_implies(X293,and(X293,X293))))&(~is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0)))|axiom_m4)), inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[axiom_m4])])])])).
% 0.24/0.53 fof(c_0_17, negated_conjecture, ~axiom_m4, inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[s1_0_axiom_m4])])).
% 0.24/0.53 cnf(c_0_18, plain, (is_a_theorem(necessarily(X1))|~necessitation|~is_a_theorem(X1)), inference(split_conjunct,[status(thm)],[c_0_12])).
% 0.24/0.53 cnf(c_0_19, plain, (necessitation), inference(split_conjunct,[status(thm)],[km5_necessitation])).
% 0.24/0.53 cnf(c_0_20, plain, (strict_implies(X1,X2)=necessarily(implies(X1,X2))|~op_strict_implies), inference(split_conjunct,[status(thm)],[c_0_13])).
% 0.24/0.53 cnf(c_0_21, plain, (op_strict_implies), inference(split_conjunct,[status(thm)],[s1_0_op_strict_implies])).
% 0.24/0.53 cnf(c_0_22, plain, (is_a_theorem(X2)|~modus_ponens|~is_a_theorem(X1)|~is_a_theorem(implies(X1,X2))), inference(split_conjunct,[status(thm)],[c_0_14])).
% 0.24/0.53 cnf(c_0_23, plain, (modus_ponens), inference(split_conjunct,[status(thm)],[hilbert_modus_ponens])).
% 0.24/0.53 cnf(c_0_24, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))|~implies_2), inference(split_conjunct,[status(thm)],[c_0_15])).
% 0.24/0.53 cnf(c_0_25, plain, (implies_2), inference(split_conjunct,[status(thm)],[hilbert_implies_2])).
% 0.24/0.53 fof(c_0_26, plain, ![X151, X152]:((~and_3|is_a_theorem(implies(X151,implies(X152,and(X151,X152)))))&(~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])])])])).
% 0.24/0.53 cnf(c_0_27, plain, (axiom_m4|~is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0)))), inference(split_conjunct,[status(thm)],[c_0_16])).
% 0.24/0.53 cnf(c_0_28, negated_conjecture, (~axiom_m4), inference(split_conjunct,[status(thm)],[c_0_17])).
% 0.24/0.53 cnf(c_0_29, plain, (is_a_theorem(necessarily(X1))|~is_a_theorem(X1)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_18, c_0_19])])).
% 0.24/0.53 cnf(c_0_30, plain, (necessarily(implies(X1,X2))=strict_implies(X1,X2)), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_21])])).
% 0.24/0.53 cnf(c_0_31, 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_22, c_0_23])])).
% 0.24/0.53 cnf(c_0_32, plain, (is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2)))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_24, c_0_25])])).
% 0.24/0.53 cnf(c_0_33, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))|~and_3), inference(split_conjunct,[status(thm)],[c_0_26])).
% 0.24/0.53 cnf(c_0_34, plain, (and_3), inference(split_conjunct,[status(thm)],[hilbert_and_3])).
% 0.24/0.53 cnf(c_0_35, plain, (~is_a_theorem(strict_implies(esk84_0,and(esk84_0,esk84_0)))), inference(sr,[status(thm)],[c_0_27, c_0_28])).
% 0.24/0.53 cnf(c_0_36, plain, (is_a_theorem(strict_implies(X1,X2))|~is_a_theorem(implies(X1,X2))), inference(spm,[status(thm)],[c_0_29, c_0_30])).
% 0.24/0.53 cnf(c_0_37, plain, (is_a_theorem(implies(X1,X2))|~is_a_theorem(implies(X1,implies(X1,X2)))), inference(spm,[status(thm)],[c_0_31, c_0_32])).
% 0.24/0.53 cnf(c_0_38, plain, (is_a_theorem(implies(X1,implies(X2,and(X1,X2))))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33, c_0_34])])).
% 0.24/0.53 cnf(c_0_39, plain, (~is_a_theorem(implies(esk84_0,and(esk84_0,esk84_0)))), inference(spm,[status(thm)],[c_0_35, c_0_36])).
% 0.24/0.53 cnf(c_0_40, plain, (is_a_theorem(implies(X1,and(X1,X1)))), inference(spm,[status(thm)],[c_0_37, c_0_38])).
% 0.24/0.53 cnf(c_0_41, plain, ($false), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_40])]), ['proof']).
% 0.24/0.53 % SZS output end Proof
% 0.24/0.53 % User time : 0.056 s
% 0.24/0.53 % System time : 0.006 s
% 0.24/0.53 % Total time : 0.062 s
% 0.24/0.53
%------------------------------------------------------------------------------