%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL377-1 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n001.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 01:12:34 PM UTC 2026
% Result : Unsatisfiable 83.35s 12.98s
% Output : CNFRefutation 83.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 5
% Syntax : Number of clauses : 114 ( 39 unt; 0 nHn; 45 RR)
% Number of literals : 211 ( 0 equ; 105 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 278 ( 59 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cn_1) ).
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
cnf(prove_cn_34,negated_conjecture,
~ is_a_theorem(implies(implies(x,implies(y,implies(z,u))),implies(implies(z,x),implies(y,implies(z,u))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_34) ).
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,X2))
| is_a_theorem(implies(implies(not(X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_25]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(implies(implies(implies(X2,X5),implies(X1,X5)),X3))
| is_a_theorem(implies(implies(X1,X2),implies(not(X3),X4))) ),
inference(spm,[status(thm)],[c_0_21,c_0_7]) ).
cnf(c_0_33,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_34,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_35,plain,
( ~ is_a_theorem(implies(not(X3),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_30,c_0_10]) ).
cnf(c_0_36,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_31]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(implies(X2,X1),X1)),X3))),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_23,c_0_10]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(implies(implies(implies(X2,X1),X1),X3))
| is_a_theorem(implies(implies(not(X1),X2),X3)) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_23,c_0_40]) ).
cnf(c_0_44,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_45,plain,
is_a_theorem(implies(implies(not(X1),X1),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_34,c_0_43]) ).
cnf(c_0_47,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_48,plain,
is_a_theorem(implies(X1,implies(not(implies(X2,X1)),X3))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(implies(implies(not(not(X1)),X2),X1),X1)),
inference(spm,[status(thm)],[c_0_13,c_0_46]) ).
cnf(c_0_50,plain,
( ~ is_a_theorem(not(not(X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_35,c_0_47]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_36,c_0_48]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(implies(not(X1),not(not(X1))),X1)),
inference(spm,[status(thm)],[c_0_41,c_0_49]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_34,c_0_50]) ).
cnf(c_0_54,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_55,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_30,c_0_40]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_53]) ).
cnf(c_0_58,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_54,c_0_10]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_34,c_0_55]) ).
cnf(c_0_60,plain,
( ~ is_a_theorem(implies(not(implies(not(X2),X2)),X1))
| is_a_theorem(implies(implies(X1,implies(not(X2),X2)),X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_19]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_15,c_0_56]) ).
cnf(c_0_62,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_63,plain,
( ~ is_a_theorem(not(not(X3)))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_57]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(implies(not(X2),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_15,c_0_58]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_13,c_0_59]) ).
cnf(c_0_66,plain,
( ~ is_a_theorem(implies(not(implies(not(X2),X2)),X3))
| ~ is_a_theorem(implies(X1,implies(X3,implies(not(X2),X2))))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_60]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(X1,not(not(implies(X2,X1))))),
inference(spm,[status(thm)],[c_0_51,c_0_61]) ).
cnf(c_0_69,plain,
( ~ is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(implies(not(X2),X3),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_62,c_0_18]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(implies(not(implies(X1,X2)),implies(X1,X2)),X2)) ),
inference(spm,[status(thm)],[c_0_63,c_0_10]) ).
cnf(c_0_71,plain,
( ~ is_a_theorem(implies(not(implies(implies(X2,X3),implies(X4,X3))),implies(X4,X2)))
| is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_64,c_0_29]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(implies(not(X1),X1),implies(not(X1),X2))),
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(not(implies(implies(X1,X2),implies(X3,X2))),X4)) ),
inference(spm,[status(thm)],[c_0_54,c_0_7]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_9,c_0_65]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(implies(not(implies(not(X2),X2)),X1))
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_76,plain,
is_a_theorem(implies(not(implies(X1,not(X2))),X2)),
inference(spm,[status(thm)],[c_0_15,c_0_68]) ).
cnf(c_0_77,plain,
( ~ is_a_theorem(not(not(X2)))
| ~ is_a_theorem(implies(not(X1),implies(X2,X1)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_78,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(implies(not(X2),X2),X3)))),
inference(spm,[status(thm)],[c_0_71,c_0_27]) ).
cnf(c_0_79,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_72]) ).
cnf(c_0_80,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_15,c_0_73]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_13,c_0_37]) ).
cnf(c_0_82,negated_conjecture,
~ is_a_theorem(implies(implies(x,implies(y,implies(z,u))),implies(implies(z,x),implies(y,implies(z,u))))),
inference(fof_simplification,[status(thm)],[prove_cn_34]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_74,c_0_7]) ).
cnf(c_0_84,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(not(not(implies(X1,X2))))
| is_a_theorem(implies(implies(not(X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
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_79]) ).
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_80]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_51,c_0_81]) ).
cnf(c_0_89,negated_conjecture,
~ is_a_theorem(implies(implies(x,implies(y,implies(z,u))),implies(implies(z,x),implies(y,implies(z,u))))),
c_0_82 ).
cnf(c_0_90,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_83]) ).
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_44,c_0_85]) ).
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_56]) ).
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(not(implies(implies(z,x),implies(y,implies(z,u)))),x))
| ~ is_a_theorem(implies(implies(y,implies(z,u)),implies(implies(z,x),implies(y,implies(z,u))))) ),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,plain,
( ~ is_a_theorem(implies(X3,implies(X2,X4)))
| is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X1,X4)))) ),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
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(implies(z,x),implies(implies(z,u),implies(z,u))))
| ~ is_a_theorem(implies(not(implies(implies(z,x),implies(y,implies(z,u)))),x)) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]) ).
cnf(c_0_100,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_101,negated_conjecture,
~ is_a_theorem(implies(not(implies(implies(z,x),implies(y,implies(z,u)))),x)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_39])]) ).
cnf(c_0_102,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_100]) ).
cnf(c_0_103,plain,
( ~ is_a_theorem(implies(X1,implies(X2,X4)))
| ~ is_a_theorem(implies(not(implies(X2,X3)),implies(X4,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_22,c_0_29]) ).
cnf(c_0_104,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_23,c_0_45]) ).
cnf(c_0_105,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_106,negated_conjecture,
~ is_a_theorem(implies(implies(z,x),implies(not(x),implies(y,implies(z,u))))),
inference(spm,[status(thm)],[c_0_101,c_0_102]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(implies(X1,implies(X2,X4)))
| is_a_theorem(implies(X1,implies(X2,implies(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_108,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_109,plain,
is_a_theorem(implies(X1,implies(X2,not(not(X2))))),
inference(spm,[status(thm)],[c_0_105,c_0_56]) ).
cnf(c_0_110,negated_conjecture,
~ is_a_theorem(implies(implies(z,x),implies(not(x),implies(z,u)))),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_111,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_108,c_0_12]) ).
cnf(c_0_112,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,not(not(X2))))),
inference(spm,[status(thm)],[c_0_26,c_0_109]) ).
cnf(c_0_113,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_112])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL377-1 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.19/0.45 % Computer : n001.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Mon Sep 21 00:30:58 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.27/0.55 Running first-order theorem proving
% 0.27/0.56 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 83.35/12.98 % Version: 3.5.1
% 83.35/12.98 % Preprocessing class: FSSSSMSSSSSNFFN.
% 83.35/12.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.35/12.98 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 83.35/12.98 % Starting new_bool_3 with 300s (1) cores
% 83.35/12.98 % Starting new_bool_1 with 300s (1) cores
% 83.35/12.98 % Starting sh5l with 300s (1) cores
% 83.35/12.98 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1812906 completed with status 0
% 83.35/12.98 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 83.35/12.98 % Preprocessing class: FSSSSMSSSSSNFFN.
% 83.35/12.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.35/12.98 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 83.35/12.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 83.35/12.98 % No SInE strategy applied
% 83.35/12.98 % Search class: FHUNS-FFSF21-MFFFFFNN
% 83.35/12.98 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 83.35/12.98 % Starting SubtermCWHack with 136s (1) cores
% 83.35/12.98 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 83.35/12.98 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 83.35/12.98 % Starting H----_011_C07_F1_PI_SE_SP_S0V with 136s (1) cores
% 83.35/12.98 % Starting new_bool_3 with 136s (1) cores
% 83.35/12.98 % H----_011_C07_F1_PI_SE_SP_S0V with pid 1812914 completed with status 0
% 83.35/12.98 % Result found by H----_011_C07_F1_PI_SE_SP_S0V
% 83.35/12.98 % Preprocessing class: FSSSSMSSSSSNFFN.
% 83.35/12.98 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 83.35/12.98 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 83.35/12.98 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 83.35/12.98 % No SInE strategy applied
% 83.35/12.98 % Search class: FHUNS-FFSF21-MFFFFFNN
% 83.35/12.98 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 83.35/12.98 % Starting SubtermCWHack with 136s (1) cores
% 83.35/12.98 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 83.35/12.98 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 83.35/12.98 % Starting H----_011_C07_F1_PI_SE_SP_S0V with 136s (1) cores
% 83.35/12.98 % Preprocessing time : 0.002 s
% 83.35/12.98
% 83.35/12.98 % Proof found!
% 83.35/12.98 % SZS status Unsatisfiable
% 83.35/12.98 % SZS output start CNFRefutation
% See solution above
% 83.35/12.98 % Parsed axioms : 5
% 83.35/12.98 % Removed by relevancy pruning/SinE : 0
% 83.35/12.98 % Initial clauses : 5
% 83.35/12.98 % Removed in clause preprocessing : 0
% 83.35/12.98 % Initial clauses in saturation : 5
% 83.35/12.98 % Processed clauses : 81126
% 83.35/12.98 % ...of these trivial : 815
% 83.35/12.98 % ...subsumed : 75941
% 83.35/12.98 % ...remaining for further processing : 4370
% 83.35/12.98 % Other redundant clauses eliminated : 0
% 83.35/12.98 % Clauses deleted for lack of memory : 0
% 83.35/12.98 % Backward-subsumed : 819
% 83.35/12.98 % Backward-rewritten : 68
% 83.35/12.98 % Generated clauses : 445082
% 83.35/12.98 % ...of the previous two non-redundant : 423270
% 83.35/12.98 % ...aggressively subsumed : 0
% 83.35/12.98 % Contextual simplify-reflections : 0
% 83.35/12.98 % Paramodulations : 445082
% 83.35/12.98 % Factorizations : 0
% 83.35/12.98 % NegExts : 0
% 83.35/12.98 % Equation resolutions : 0
% 83.35/12.98 % Disequality decompositions : 0
% 83.35/12.98 % Total rewrite steps : 24175
% 83.35/12.98 % ...of those cached : 21597
% 83.35/12.98 % Propositional unsat checks : 0
% 83.35/12.98 % Propositional check models : 0
% 83.35/12.98 % Propositional check unsatisfiable : 0
% 83.35/12.98 % Propositional clauses : 0
% 83.35/12.98 % Propositional clauses after purity: 0
% 83.35/12.98 % Propositional unsat core size : 0
% 83.35/12.98 % Propositional preprocessing time : 0.000
% 83.35/12.98 % Propositional encoding time : 0.000
% 83.35/12.98 % Propositional solver time : 0.000
% 83.35/12.98 % Success case prop preproc time : 0.000
% 83.35/12.98 % Success case prop encoding time : 0.000
% 83.35/12.98 % Success case prop solver time : 0.000
% 83.35/12.98 % Current number of processed clauses : 3483
% 83.35/12.98 % Positive orientable unit clauses : 475
% 83.35/12.98 % Positive unorientable unit clauses: 0
% 83.35/12.98 % Negative unit clauses : 860
% 83.35/12.98 % Non-unit-clauses : 2148
% 83.35/12.98 % Current number of unprocessed clauses: 341150
% 83.35/12.98 % ...number of literals in the above : 1137124
% 83.35/12.98 % Current number of archived formulas : 0
% 83.35/12.98 % Current number of archived clauses : 887
% 83.35/12.98 % Clause-clause subsumption calls (NU) : 3085458
% 83.35/12.98 % Rec. Clause-clause subsumption calls : 1528166
% 83.35/12.98 % Non-unit clause-clause subsumptions : 43264
% 83.35/12.98 % Unit Clause-clause subsumption calls : 280304
% 83.35/12.98 % Rewrite failures with RHS unbound : 0
% 83.35/12.98 % BW rewrite match attempts : 124194
% 83.35/12.98 % BW rewrite match successes : 28
% 83.35/12.98 % Condensation attempts : 0
% 83.35/12.98 % Condensation successes : 0
% 83.35/12.98 % Termbank termtop insertions : 6737320
% 83.35/12.98 % Search garbage collected termcells : 8
% 83.35/12.98
% 83.35/12.98 % -------------------------------------------------
% 83.35/12.98 % User time : 11.652 s
% 83.35/12.98 % System time : 0.331 s
% 83.35/12.98 % Total time : 11.984 s
% 83.35/12.98 % Maximum resident set size: 3380 pages
% 83.35/12.98
% 83.35/12.98 % -------------------------------------------------
% 83.35/12.98 % User time : 57.837 s
% 83.35/12.98 % System time : 1.922 s
% 83.35/12.98 % Total time : 59.759 s
% 83.35/12.98 % Maximum resident set size: 4608 pages
% 83.35/12.98 % E exiting
%------------------------------------------------------------------------------