%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL051-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 : Thu Sep 24 01:18:20 PM UTC 2026
% Result : Unsatisfiable 29.94s 5.58s
% Output : CNFRefutation 29.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 5
% Syntax : Number of clauses : 110 ( 41 unt; 0 nHn; 41 RR)
% Number of literals : 200 ( 0 equ; 96 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 268 ( 65 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
cnf(prove_cn_22,negated_conjecture,
~ is_a_theorem(implies(implies(b,c),implies(implies(a,b),implies(a,c)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_22) ).
cnf(c_0_5,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
inference(fof_simplification,[status(thm)],[condensed_detachment]) ).
cnf(c_0_6,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
c_0_5 ).
cnf(c_0_7,axiom,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
cn_1 ).
cnf(c_0_8,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
( ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_10,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)),
cn_2 ).
cnf(c_0_11,plain,
( ~ is_a_theorem(implies(X2,X4))
| ~ is_a_theorem(implies(X1,implies(X4,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_9,c_0_8]) ).
cnf(c_0_12,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))),
cn_3 ).
cnf(c_0_13,plain,
( ~ is_a_theorem(implies(X1,implies(not(X2),X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
( ~ is_a_theorem(implies(X2,not(X1)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,plain,
( ~ is_a_theorem(implies(not(X2),not(X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_12]) ).
cnf(c_0_17,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X1,implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_9,c_0_12]) ).
cnf(c_0_19,plain,
( ~ is_a_theorem(implies(not(X2),X1))
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_8]) ).
cnf(c_0_20,plain,
( ~ is_a_theorem(implies(X4,X3))
| ~ is_a_theorem(implies(X2,X4))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_17]) ).
cnf(c_0_21,plain,
( ~ is_a_theorem(implies(X4,X2))
| ~ is_a_theorem(implies(X1,X4))
| is_a_theorem(implies(X1,implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_9,c_0_18]) ).
cnf(c_0_22,plain,
( ~ is_a_theorem(implies(not(X2),X3))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_23,plain,
( ~ is_a_theorem(implies(implies(not(X2),X4),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(implies(not(implies(not(X1),X1)),implies(not(X1),X1)),X1)),
inference(spm,[status(thm)],[c_0_13,c_0_10]) ).
cnf(c_0_25,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(implies(not(X1),X1),implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_21,c_0_10]) ).
cnf(c_0_26,plain,
( ~ is_a_theorem(implies(not(implies(X1,X3)),implies(X2,X3)))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_22,c_0_7]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_29,plain,
( ~ is_a_theorem(implies(X1,implies(X4,X2)))
| is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_30,plain,
( ~ is_a_theorem(X4)
| ~ is_a_theorem(implies(X4,X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_20,c_0_17]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(implies(not(X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_25]) ).
cnf(c_0_33,plain,
( ~ is_a_theorem(implies(implies(not(X1),X4),X2))
| is_a_theorem(implies(X1,implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_21,c_0_12]) ).
cnf(c_0_34,plain,
( ~ is_a_theorem(implies(implies(implies(X3,X5),implies(X2,X5)),X4))
| is_a_theorem(implies(X1,implies(implies(X2,X3),X4))) ),
inference(spm,[status(thm)],[c_0_20,c_0_7]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(implies(not(implies(implies(X1,X2),implies(X3,X2))),implies(X3,X1)))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_37,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,implies(not(X3),X3)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_32]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(X1,implies(not(implies(not(X1),X2)),X3))),
inference(spm,[status(thm)],[c_0_33,c_0_31]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X3),implies(implies(X3,X2),X2)))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
( ~ is_a_theorem(implies(implies(not(X1),X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_28,c_0_40]) ).
cnf(c_0_44,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_18]) ).
cnf(c_0_45,plain,
( ~ is_a_theorem(X4)
| ~ is_a_theorem(implies(X1,implies(X4,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_9,c_0_41]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_44,c_0_10]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_49,plain,
( ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(not(X1),X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_19]) ).
cnf(c_0_50,plain,
( ~ is_a_theorem(implies(X1,X4))
| ~ is_a_theorem(implies(X4,X2))
| is_a_theorem(implies(not(implies(X1,X2)),X3)) ),
inference(spm,[status(thm)],[c_0_44,c_0_8]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(not(implies(X1,X1)),X2)),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(implies(implies(not(not(X1)),X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_12]) ).
cnf(c_0_54,plain,
( ~ is_a_theorem(X5)
| ~ is_a_theorem(implies(X1,implies(X5,X3)))
| is_a_theorem(implies(not(implies(X1,implies(X2,X3))),X4)) ),
inference(spm,[status(thm)],[c_0_50,c_0_41]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( ~ is_a_theorem(implies(implies(not(not(implies(implies(X1,X2),implies(X3,X2)))),X4),implies(X3,X1)))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_53,c_0_29]) ).
cnf(c_0_57,plain,
( ~ is_a_theorem(X4)
| is_a_theorem(implies(not(implies(X1,implies(X2,X1))),X3)) ),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,plain,
( ~ is_a_theorem(implies(not(implies(X3,X1)),not(not(implies(implies(X1,X2),implies(X3,X2))))))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_56,c_0_19]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(not(implies(X1,implies(X2,X1))),X3)),
inference(spm,[status(thm)],[c_0_57,c_0_52]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_58,c_0_59]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(implies(X1,not(not(implies(X1,X2)))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_12]) ).
cnf(c_0_62,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_60]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(implies(not(X1),not(not(implies(not(X1),X1)))),X1)),
inference(spm,[status(thm)],[c_0_13,c_0_61]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(not(not(implies(not(X1),X1))),X1)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(implies(not(X2),not(implies(not(X1),X3))))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_39]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(X1,not(implies(not(not(X1)),not(X1))))),
inference(spm,[status(thm)],[c_0_15,c_0_64]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_17]) ).
cnf(c_0_69,plain,
( ~ is_a_theorem(implies(not(X3),not(X2)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_15,c_0_67]) ).
cnf(c_0_71,plain,
( ~ is_a_theorem(not(not(X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_68]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(X1,implies(not(not(X2)),X2))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(not(X2),X3))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(not(not(implies(X3,X1))))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_36,c_0_71]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(implies(X1,not(X1)))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_67]) ).
cnf(c_0_76,plain,
is_a_theorem(implies(not(implies(not(not(X1)),X1)),X2)),
inference(spm,[status(thm)],[c_0_47,c_0_72]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(implies(not(X1),X1),implies(not(X1),X2))),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_78,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_73,c_0_17]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(not(not(implies(not(X2),X1))))
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_74]) ).
cnf(c_0_80,plain,
is_a_theorem(not(not(implies(not(not(X1)),X1)))),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_23,c_0_31]) ).
cnf(c_0_82,plain,
( ~ is_a_theorem(implies(not(X2),not(X1)))
| is_a_theorem(implies(implies(not(X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_77]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(implies(X4,X2))
| is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_78,c_0_7]) ).
cnf(c_0_84,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(implies(implies(X2,implies(not(X2),X3)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_81]) ).
cnf(c_0_86,plain,
( ~ is_a_theorem(implies(not(X2),X2))
| ~ is_a_theorem(implies(not(X1),not(X2)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_82]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(implies(X3,X5))
| ~ is_a_theorem(implies(X2,implies(X5,X4)))
| is_a_theorem(implies(X1,implies(X2,implies(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_11,c_0_83]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_62,c_0_43]) ).
cnf(c_0_89,negated_conjecture,
~ is_a_theorem(implies(implies(b,c),implies(implies(a,b),implies(a,c)))),
inference(fof_simplification,[status(thm)],[prove_cn_22]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_26,c_0_17]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(implies(X1,implies(X2,not(X2))))
| is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_9,c_0_84]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(not(not(implies(X1,X2))))
| is_a_theorem(implies(X1,implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_85,c_0_74]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_86,c_0_67]) ).
cnf(c_0_94,plain,
( ~ is_a_theorem(implies(X3,implies(X2,X4)))
| is_a_theorem(implies(X1,implies(X2,implies(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,negated_conjecture,
~ is_a_theorem(implies(implies(b,c),implies(implies(a,b),implies(a,c)))),
c_0_89 ).
cnf(c_0_96,plain,
( ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(not(X3),X1))
| is_a_theorem(implies(implies(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_22,c_0_90]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(not(not(implies(X1,X2))))
| is_a_theorem(implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,plain,
( ~ is_a_theorem(implies(X2,implies(X1,X3)))
| is_a_theorem(not(not(implies(X1,implies(X2,X3))))) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,negated_conjecture,
( ~ is_a_theorem(implies(c,implies(implies(a,b),implies(a,c))))
| ~ is_a_theorem(implies(not(implies(implies(a,b),implies(a,c))),b)) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_62,c_0_55]) ).
cnf(c_0_101,plain,
( ~ is_a_theorem(implies(X2,implies(X1,X3)))
| is_a_theorem(implies(X1,not(not(implies(X2,X3))))) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_102,negated_conjecture,
~ is_a_theorem(implies(not(implies(implies(a,b),implies(a,c))),b)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100])]) ).
cnf(c_0_103,plain,
( ~ is_a_theorem(implies(X1,implies(not(X3),X2)))
| is_a_theorem(implies(not(implies(X1,X2)),X3)) ),
inference(spm,[status(thm)],[c_0_15,c_0_101]) ).
cnf(c_0_104,plain,
( ~ is_a_theorem(implies(X1,implies(X3,X5)))
| ~ is_a_theorem(implies(X2,implies(X5,X4)))
| is_a_theorem(implies(X1,implies(X2,implies(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_11,c_0_29]) ).
cnf(c_0_105,plain,
is_a_theorem(implies(X1,implies(X2,not(not(X2))))),
inference(spm,[status(thm)],[c_0_69,c_0_67]) ).
cnf(c_0_106,negated_conjecture,
~ is_a_theorem(implies(implies(a,b),implies(not(b),implies(a,c)))),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(implies(X1,implies(X3,not(X2))))
| is_a_theorem(implies(X1,implies(X2,implies(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_104,c_0_12]) ).
cnf(c_0_108,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,not(not(X2))))),
inference(spm,[status(thm)],[c_0_26,c_0_105]) ).
cnf(c_0_109,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_107]),c_0_108])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL051-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/1.13 % Computer : n012.cluster.edu
% 0.04/1.13 % Model : x86_64 x86_64
% 0.04/1.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/1.13 % Memory : 8046.5625MB
% 0.04/1.13 % OS : Linux 6.8.0-71-generic
% 0.04/1.13 % CPULimit : 300
% 0.04/1.13 % WCLimit : 300
% 0.04/1.13 % DateTime : Mon Sep 21 00:01:41 UTC 2026
% 0.04/1.14 % CPUTime :
% 0.04/1.14 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/1.16 Running first-order theorem proving
% 0.04/1.16 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 29.94/5.58 % Version: 3.5.1
% 29.94/5.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 29.94/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.94/5.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 29.94/5.58 % Starting new_bool_3 with 300s (1) cores
% 29.94/5.58 % Starting new_bool_1 with 300s (1) cores
% 29.94/5.58 % Starting sh5l with 300s (1) cores
% 29.94/5.58 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1187824 completed with status 0
% 29.94/5.58 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 29.94/5.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 29.94/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.94/5.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 29.94/5.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 29.94/5.58 % No SInE strategy applied
% 29.94/5.58 % Search class: FHUNS-FFSF21-MFFFFFNN
% 29.94/5.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 29.94/5.58 % Starting SubtermCWHack with 136s (1) cores
% 29.94/5.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 29.94/5.58 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 29.94/5.58 % Starting H----_011_C07_F1_PI_SE_SP_S0V with 136s (1) cores
% 29.94/5.58 % Starting new_bool_3 with 136s (1) cores
% 29.94/5.58 % H----_011_C07_F1_PI_SE_SP_S0V with pid 1187834 completed with status 0
% 29.94/5.58 % Result found by H----_011_C07_F1_PI_SE_SP_S0V
% 29.94/5.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 29.94/5.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 29.94/5.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 29.94/5.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 29.94/5.58 % No SInE strategy applied
% 29.94/5.58 % Search class: FHUNS-FFSF21-MFFFFFNN
% 29.94/5.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 29.94/5.58 % Starting SubtermCWHack with 136s (1) cores
% 29.94/5.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 29.94/5.58 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 29.94/5.58 % Starting H----_011_C07_F1_PI_SE_SP_S0V with 136s (1) cores
% 29.94/5.58 % Preprocessing time : 0.001 s
% 29.94/5.58
% 29.94/5.58 % Proof found!
% 29.94/5.58 % SZS status Unsatisfiable
% 29.94/5.58 % SZS output start CNFRefutation
% See solution above
% 29.94/5.58 % Parsed axioms : 5
% 29.94/5.58 % Removed by relevancy pruning/SinE : 0
% 29.94/5.58 % Initial clauses : 5
% 29.94/5.58 % Removed in clause preprocessing : 0
% 29.94/5.58 % Initial clauses in saturation : 5
% 29.94/5.58 % Processed clauses : 55908
% 29.94/5.58 % ...of these trivial : 1271
% 29.94/5.58 % ...subsumed : 51036
% 29.94/5.58 % ...remaining for further processing : 3601
% 29.94/5.58 % Other redundant clauses eliminated : 0
% 29.94/5.58 % Clauses deleted for lack of memory : 0
% 29.94/5.58 % Backward-subsumed : 448
% 29.94/5.58 % Backward-rewritten : 47
% 29.94/5.58 % Generated clauses : 485580
% 29.94/5.58 % ...of the previous two non-redundant : 455688
% 29.94/5.58 % ...aggressively subsumed : 0
% 29.94/5.58 % Contextual simplify-reflections : 0
% 29.94/5.58 % Paramodulations : 485580
% 29.94/5.58 % Factorizations : 0
% 29.94/5.58 % NegExts : 0
% 29.94/5.58 % Equation resolutions : 0
% 29.94/5.58 % Disequality decompositions : 0
% 29.94/5.58 % Total rewrite steps : 33719
% 29.94/5.58 % ...of those cached : 29650
% 29.94/5.58 % Propositional unsat checks : 0
% 29.94/5.58 % Propositional check models : 0
% 29.94/5.58 % Propositional check unsatisfiable : 0
% 29.94/5.58 % Propositional clauses : 0
% 29.94/5.58 % Propositional clauses after purity: 0
% 29.94/5.58 % Propositional unsat core size : 0
% 29.94/5.58 % Propositional preprocessing time : 0.000
% 29.94/5.58 % Propositional encoding time : 0.000
% 29.94/5.58 % Propositional solver time : 0.000
% 29.94/5.58 % Success case prop preproc time : 0.000
% 29.94/5.58 % Success case prop encoding time : 0.000
% 29.94/5.58 % Success case prop solver time : 0.000
% 29.94/5.58 % Current number of processed clauses : 3106
% 29.94/5.58 % Positive orientable unit clauses : 607
% 29.94/5.58 % Positive unorientable unit clauses: 0
% 29.94/5.58 % Negative unit clauses : 226
% 29.94/5.58 % Non-unit-clauses : 2273
% 29.94/5.58 % Current number of unprocessed clauses: 398855
% 29.94/5.58 % ...number of literals in the above : 1187730
% 29.94/5.58 % Current number of archived formulas : 0
% 29.94/5.58 % Current number of archived clauses : 495
% 29.94/5.58 % Clause-clause subsumption calls (NU) : 2793078
% 29.94/5.58 % Rec. Clause-clause subsumption calls : 1549355
% 29.94/5.58 % Non-unit clause-clause subsumptions : 38026
% 29.94/5.58 % Unit Clause-clause subsumption calls : 60997
% 29.94/5.58 % Rewrite failures with RHS unbound : 0
% 29.94/5.58 % BW rewrite match attempts : 156289
% 29.94/5.58 % BW rewrite match successes : 31
% 29.94/5.58 % Condensation attempts : 0
% 29.94/5.58 % Condensation successes : 0
% 29.94/5.58 % Termbank termtop insertions : 7603588
% 29.94/5.58 % Search garbage collected termcells : 8
% 29.94/5.58
% 29.94/5.58 % -------------------------------------------------
% 29.94/5.58 % User time : 4.076 s
% 29.94/5.58 % System time : 0.159 s
% 29.94/5.58 % Total time : 4.235 s
% 29.94/5.58 % Maximum resident set size: 3632 pages
% 29.94/5.58
% 29.94/5.58 % -------------------------------------------------
% 29.94/5.58 % User time : 20.574 s
% 29.94/5.58 % System time : 0.819 s
% 29.94/5.58 % Total time : 21.393 s
% 29.94/5.58 % Maximum resident set size: 4864 pages
% 29.94/5.58 % E exiting
%------------------------------------------------------------------------------