%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL037-1 : 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 : n008.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 01:11:35 PM UTC 2026
% Result : Unsatisfiable 239.17s 48.58s
% Output : CNFRefutation 239.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 3
% Syntax : Number of clauses : 143 ( 80 unt; 0 nHn; 33 RR)
% Number of literals : 214 ( 0 equ; 74 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; 4 con; 0-2 aty)
% Number of variables : 474 ( 211 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(c0_CAMeredith,axiom,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),implies(X3,falsehood)),X4),X5),implies(implies(X5,X1),implies(X3,X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c0_CAMeredith) ).
cnf(prove_c0_6,negated_conjecture,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c0_6) ).
cnf(c_0_3,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_4,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
c_0_3 ).
cnf(c_0_5,axiom,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),implies(X3,falsehood)),X4),X5),implies(implies(X5,X1),implies(X3,X1)))),
c0_CAMeredith ).
cnf(c_0_6,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X2,X4),implies(X3,falsehood)),X5),X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_4,c_0_5]) ).
cnf(c_0_7,plain,
is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),implies(X2,X4)),implies(X5,implies(X2,X4)))),
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_8,plain,
is_a_theorem(implies(implies(implies(X1,implies(falsehood,X2)),X3),implies(X4,X3))),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
( ~ is_a_theorem(implies(implies(X3,implies(falsehood,X4)),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_8]) ).
cnf(c_0_10,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(falsehood,X3))),
inference(spm,[status(thm)],[c_0_6,c_0_8]) ).
cnf(c_0_11,plain,
is_a_theorem(implies(X1,implies(X2,implies(falsehood,X3)))),
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_12,plain,
( ~ is_a_theorem(implies(implies(X2,X3),X1))
| is_a_theorem(implies(falsehood,X1)) ),
inference(spm,[status(thm)],[c_0_4,c_0_10]) ).
cnf(c_0_13,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(falsehood,X2))) ),
inference(spm,[status(thm)],[c_0_4,c_0_11]) ).
cnf(c_0_14,plain,
is_a_theorem(implies(falsehood,implies(X1,X2))),
inference(spm,[status(thm)],[c_0_12,c_0_8]) ).
cnf(c_0_15,plain,
( ~ is_a_theorem(implies(implies(implies(X4,X2),implies(X5,X2)),implies(X2,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_4,c_0_7]) ).
cnf(c_0_16,plain,
is_a_theorem(implies(implies(implies(falsehood,X1),X2),implies(X3,X2))),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_17,plain,
is_a_theorem(implies(X1,implies(falsehood,X2))),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(falsehood,X1)) ),
inference(spm,[status(thm)],[c_0_4,c_0_17]) ).
cnf(c_0_20,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_4,c_0_18]) ).
cnf(c_0_21,plain,
is_a_theorem(implies(falsehood,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_22,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),implies(X4,X3))),
inference(spm,[status(thm)],[c_0_6,c_0_18]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(implies(X2,X3),implies(X4,falsehood)),X5)),X2),implies(X4,X2))),
inference(spm,[status(thm)],[c_0_6,c_0_22]) ).
cnf(c_0_25,plain,
( ~ is_a_theorem(implies(implies(X3,implies(X4,X3)),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_23]) ).
cnf(c_0_26,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(implies(X2,X4),implies(X1,falsehood)),X3))),
inference(spm,[status(thm)],[c_0_6,c_0_24]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),implies(X4,falsehood)),implies(X5,implies(X4,X2))))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,plain,
( ~ is_a_theorem(X5)
| is_a_theorem(implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X4,implies(X3,X1)))) ),
inference(spm,[status(thm)],[c_0_4,c_0_27]) ).
cnf(c_0_29,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X4,implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_28,c_0_21]) ).
cnf(c_0_30,plain,
( ~ is_a_theorem(implies(implies(X3,X4),implies(X2,falsehood)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_4,c_0_29]) ).
cnf(c_0_31,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),implies(X4,falsehood)),implies(X4,X2)))),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(X4)
| is_a_theorem(implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X3,X1))) ),
inference(spm,[status(thm)],[c_0_4,c_0_31]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,falsehood)),implies(X3,X1))),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_34,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X2),implies(X4,X2))),
inference(spm,[status(thm)],[c_0_6,c_0_33]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_6,c_0_34]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_35]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(implies(X1,falsehood),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_36,c_0_33]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_30,c_0_37]) ).
cnf(c_0_39,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))),
inference(spm,[status(thm)],[c_0_6,c_0_38]) ).
cnf(c_0_40,plain,
( ~ is_a_theorem(implies(implies(X3,X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_39]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(implies(implies(implies(X1,falsehood),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_6,c_0_35]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X2,falsehood),X3)))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_43,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(implies(X1,falsehood),X2))) ),
inference(spm,[status(thm)],[c_0_4,c_0_42]) ).
cnf(c_0_44,plain,
( ~ is_a_theorem(implies(implies(implies(X1,falsehood),X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_41]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(X1,implies(implies(X1,falsehood),X2))),
inference(spm,[status(thm)],[c_0_43,c_0_21]) ).
cnf(c_0_46,plain,
( ~ is_a_theorem(implies(implies(X2,X3),implies(X1,falsehood)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_33]) ).
cnf(c_0_47,plain,
is_a_theorem(implies(X1,implies(implies(implies(implies(X1,falsehood),X2),falsehood),X3))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),falsehood),X3),falsehood),X1)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X3,implies(X1,X2)))),
inference(spm,[status(thm)],[c_0_6,c_0_48]) ).
cnf(c_0_50,plain,
( ~ is_a_theorem(implies(X2,implies(X2,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_4,c_0_49]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X2),X3),X3))),
inference(spm,[status(thm)],[c_0_50,c_0_39]) ).
cnf(c_0_52,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(implies(implies(X1,X1),X2),X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_51]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),
inference(spm,[status(thm)],[c_0_52,c_0_21]) ).
cnf(c_0_54,plain,
( ~ is_a_theorem(implies(implies(X2,X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_53]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(X1,implies(implies(implies(falsehood,X2),X3),X3))),
inference(spm,[status(thm)],[c_0_50,c_0_16]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X3,X2),implies(X4,X2))))),
inference(spm,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(implies(implies(falsehood,X1),X2),X2)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_58,plain,
( ~ is_a_theorem(X4)
| is_a_theorem(implies(X1,implies(implies(X2,X1),implies(X3,X1)))) ),
inference(spm,[status(thm)],[c_0_4,c_0_56]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(implies(implies(falsehood,X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_57]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,X2)),X4),X4))),
inference(spm,[status(thm)],[c_0_50,c_0_23]) ).
cnf(c_0_61,plain,
is_a_theorem(implies(X1,implies(implies(X2,X1),implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_58,c_0_21]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X1)),X3),X3)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,plain,
( ~ is_a_theorem(implies(implies(falsehood,X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_16]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_4,c_0_61]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X1),falsehood),X3))),
inference(spm,[status(thm)],[c_0_36,c_0_45]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(X3,X1))),
inference(spm,[status(thm)],[c_0_6,c_0_41]) ).
cnf(c_0_67,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_22]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(implies(implies(X2,implies(X3,X2)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_62]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,implies(X3,X4)),X3),X3))),
inference(spm,[status(thm)],[c_0_50,c_0_34]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_71,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,implies(implies(X1,falsehood),X3)),falsehood),X4))),
inference(spm,[status(thm)],[c_0_44,c_0_65]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),X2))),
inference(spm,[status(thm)],[c_0_50,c_0_66]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_6,c_0_67]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X2),X2)),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X4,X3))) ),
inference(spm,[status(thm)],[c_0_6,c_0_70]) ).
cnf(c_0_76,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(implies(X2,X3),falsehood),X4)),falsehood),X2)),
inference(spm,[status(thm)],[c_0_46,c_0_71]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X1),X1),X3),implies(X4,X3))),
inference(spm,[status(thm)],[c_0_6,c_0_72]) ).
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_4,c_0_73]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(implies(implies(X2,implies(X1,X3)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_74]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(X1,implies(implies(X2,implies(X2,X3)),implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_50,c_0_49]) ).
cnf(c_0_81,plain,
( ~ is_a_theorem(X4)
| ~ is_a_theorem(implies(implies(X3,X4),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_75]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X1,X3),falsehood),X2))),
inference(spm,[status(thm)],[c_0_6,c_0_76]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X3,X4),X3),X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_77]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(implies(implies(X4,X2),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_78,c_0_35]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_36,c_0_5]) ).
cnf(c_0_86,plain,
is_a_theorem(implies(implies(X1,implies(X1,X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_81,c_0_5]) ).
cnf(c_0_88,plain,
( ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(implies(implies(X1,X2),falsehood),X3)) ),
inference(spm,[status(thm)],[c_0_4,c_0_82]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(X1,implies(implies(implies(X2,X3),X2),implies(X4,X2)))),
inference(spm,[status(thm)],[c_0_83,c_0_5]) ).
cnf(c_0_90,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(implies(X3,X2),X4),implies(X5,X4))))),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(implies(X1,implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_86]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),implies(X5,X4))) ),
inference(spm,[status(thm)],[c_0_6,c_0_87]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(implies(implies(X2,X4),X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_6,c_0_88]) ).
cnf(c_0_94,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X1),implies(X3,X1)),X4),implies(X5,X4))),
inference(spm,[status(thm)],[c_0_6,c_0_89]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(implies(X2,X1),X3),implies(X4,X3))),X5),implies(X6,X5))),
inference(spm,[status(thm)],[c_0_6,c_0_90]) ).
cnf(c_0_96,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X2,X3),implies(X4,X3))))),
inference(spm,[status(thm)],[c_0_84,c_0_5]) ).
cnf(c_0_97,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(implies(implies(X1,X2),implies(X3,X2)),X4),X4)) ),
inference(spm,[status(thm)],[c_0_91,c_0_92]) ).
cnf(c_0_98,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X3),implies(X4,X3)),X1),implies(X5,X1))),
inference(spm,[status(thm)],[c_0_93,c_0_85]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X1),implies(X3,X1)),X4),X4)),
inference(spm,[status(thm)],[c_0_91,c_0_94]) ).
cnf(c_0_100,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X4,implies(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_93,c_0_88]) ).
cnf(c_0_101,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(implies(X2,X1),X3),implies(X4,X3))),X5),X5)),
inference(spm,[status(thm)],[c_0_91,c_0_95]) ).
cnf(c_0_102,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X1)),implies(X4,implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_93,c_0_35]) ).
cnf(c_0_103,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(X1,X2),implies(X3,X2))),X4),implies(X5,X4))),
inference(spm,[status(thm)],[c_0_6,c_0_96]) ).
cnf(c_0_104,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(implies(implies(X2,X3),implies(X4,X3)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_97]) ).
cnf(c_0_105,plain,
is_a_theorem(implies(implies(implies(implies(implies(X1,X2),X3),implies(X4,X3)),X1),X1)),
inference(spm,[status(thm)],[c_0_91,c_0_98]) ).
cnf(c_0_106,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X2,X3),X2),implies(X4,X2)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_99]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_91,c_0_100]) ).
cnf(c_0_108,plain,
( ~ is_a_theorem(implies(implies(X2,implies(implies(implies(X3,X2),X4),implies(X5,X4))),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_101]) ).
cnf(c_0_109,plain,
is_a_theorem(implies(implies(implies(X1,X2),implies(X3,X1)),implies(X3,X1))),
inference(spm,[status(thm)],[c_0_91,c_0_102]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(X1,X2),implies(X3,X2))),X4),X4)),
inference(spm,[status(thm)],[c_0_91,c_0_103]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(implies(implies(implies(X1,implies(X2,X3)),X4),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_112,plain,
( ~ is_a_theorem(implies(X1,implies(implies(X2,X3),X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(X2,X3),X4)),X3),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,plain,
( ~ is_a_theorem(implies(implies(X2,implies(implies(X2,X3),implies(X4,X3))),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_4,c_0_110]) ).
cnf(c_0_115,plain,
( ~ is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X3,implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_107]) ).
cnf(c_0_116,plain,
( ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_111,c_0_88]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(implies(implies(X1,implies(implies(implies(X2,X3),X2),X4)),X2),X2)),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_118,plain,
is_a_theorem(implies(implies(implies(X1,X2),falsehood),implies(implies(X1,X3),implies(X4,X3)))),
inference(spm,[status(thm)],[c_0_114,c_0_82]) ).
cnf(c_0_119,plain,
( ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_115,c_0_116]) ).
cnf(c_0_120,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(implies(X1,X3),X1),X2))),
inference(spm,[status(thm)],[c_0_6,c_0_117]) ).
cnf(c_0_121,plain,
( ~ is_a_theorem(implies(X1,implies(X2,implies(X2,X3))))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_115,c_0_49]) ).
cnf(c_0_122,plain,
( ~ is_a_theorem(implies(implies(X2,X3),implies(X1,X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_4,c_0_109]) ).
cnf(c_0_123,plain,
is_a_theorem(implies(X1,implies(X2,implies(implies(X1,X3),implies(X4,X3))))),
inference(spm,[status(thm)],[c_0_111,c_0_118]) ).
cnf(c_0_124,plain,
( ~ is_a_theorem(implies(implies(implies(implies(X1,X4),X1),X2),X3))
| is_a_theorem(implies(implies(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_119,c_0_120]) ).
cnf(c_0_125,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_121,c_0_85]) ).
cnf(c_0_126,plain,
( ~ is_a_theorem(implies(X2,implies(X1,implies(X2,X3))))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_122,c_0_88]) ).
cnf(c_0_127,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_115,c_0_123]) ).
cnf(c_0_128,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X3,X1),implies(X4,X1)))),
inference(spm,[status(thm)],[c_0_124,c_0_5]) ).
cnf(c_0_129,plain,
( ~ is_a_theorem(implies(implies(implies(X1,X3),X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_119,c_0_125]) ).
cnf(c_0_130,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_131,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(implies(X3,X1),X1))),
inference(spm,[status(thm)],[c_0_121,c_0_128]) ).
cnf(c_0_132,plain,
( ~ is_a_theorem(implies(X2,implies(X1,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_129,c_0_130]) ).
cnf(c_0_133,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,implies(X1,X3)),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_124,c_0_131]) ).
cnf(c_0_134,plain,
( ~ is_a_theorem(implies(implies(implies(X1,X3),implies(X4,X3)),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_119,c_0_85]) ).
cnf(c_0_135,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X2,X1),implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_132,c_0_133]) ).
cnf(c_0_136,plain,
is_a_theorem(implies(X1,implies(implies(X2,implies(X1,X3)),implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_134,c_0_135]) ).
cnf(c_0_137,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X2,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_132,c_0_136]) ).
cnf(c_0_138,negated_conjecture,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))),
inference(fof_simplification,[status(thm)],[prove_c0_6]) ).
cnf(c_0_139,plain,
( ~ is_a_theorem(implies(implies(X2,implies(X1,X3)),X4))
| is_a_theorem(implies(implies(X1,implies(X2,X3)),X4)) ),
inference(spm,[status(thm)],[c_0_119,c_0_137]) ).
cnf(c_0_140,negated_conjecture,
~ is_a_theorem(implies(implies(a,implies(b,c)),implies(implies(a,b),implies(a,c)))),
c_0_138 ).
cnf(c_0_141,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_139,c_0_135]) ).
cnf(c_0_142,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_140,c_0_141])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL037-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.43 % Computer : n008.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 00:01:58 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.17/0.54 Running first-order theorem proving
% 0.17/0.54 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
% 239.17/48.58 % Version: 3.5.1
% 239.17/48.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 239.17/48.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 239.17/48.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 239.17/48.58 % Starting new_bool_3 with 300s (1) cores
% 239.17/48.58 % Starting new_bool_1 with 300s (1) cores
% 239.17/48.58 % Starting sh5l with 300s (1) cores
% 239.17/48.58 % new_bool_1 with pid 3921895 completed with status 9
% 239.17/48.58 % new_bool_3 with pid 3921894 completed with status 9
% 239.17/48.58 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 3921890 completed with status 0
% 239.17/48.58 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 239.17/48.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 239.17/48.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 239.17/48.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 239.17/48.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 239.17/48.58 % No SInE strategy applied
% 239.17/48.58 % Search class: FHUNF-FFSF22-MFFFFFNN
% 239.17/48.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 239.17/48.58 % Starting SubtermCWHack with 136s (1) cores
% 239.17/48.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 239.17/48.58 % Starting G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with 136s (1) cores
% 239.17/48.58 % Starting new_bool_3 with 136s (1) cores
% 239.17/48.58 % Starting U----_206c_00_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 239.17/48.58 % G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with pid 3921893 completed with status 0
% 239.17/48.58 % Result found by G-E--_060_C18_F1_PI_AE_CS_SP_S0Y
% 239.17/48.58 % Preprocessing class: FSSSSMSSSSSNFFN.
% 239.17/48.58 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 239.17/48.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 239.17/48.58 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 239.17/48.58 % No SInE strategy applied
% 239.17/48.58 % Search class: FHUNF-FFSF22-MFFFFFNN
% 239.17/48.58 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 239.17/48.58 % Starting SubtermCWHack with 136s (1) cores
% 239.17/48.58 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 239.17/48.58 % Starting G-E--_060_C18_F1_PI_AE_CS_SP_S0Y with 136s (1) cores
% 239.17/48.58 % Preprocessing time : 0.002 s
% 239.17/48.58
% 239.17/48.58 % Proof found!
% 239.17/48.58 % SZS status Unsatisfiable
% 239.17/48.58 % SZS output start CNFRefutation
% See solution above
% 239.17/48.59 % Parsed axioms : 3
% 239.17/48.59 % Removed by relevancy pruning/SinE : 0
% 239.17/48.59 % Initial clauses : 3
% 239.17/48.59 % Removed in clause preprocessing : 0
% 239.17/48.59 % Initial clauses in saturation : 3
% 239.17/48.59 % Processed clauses : 365189
% 239.17/48.59 % ...of these trivial : 26044
% 239.17/48.59 % ...subsumed : 333608
% 239.17/48.59 % ...remaining for further processing : 5537
% 239.17/48.59 % Other redundant clauses eliminated : 0
% 239.17/48.59 % Clauses deleted for lack of memory : 0
% 239.17/48.59 % Backward-subsumed : 113
% 239.17/48.59 % Backward-rewritten : 872
% 239.17/48.59 % Generated clauses : 5028765
% 239.17/48.59 % ...of the previous two non-redundant : 4222290
% 239.17/48.59 % ...aggressively subsumed : 0
% 239.17/48.59 % Contextual simplify-reflections : 0
% 239.17/48.59 % Paramodulations : 5028765
% 239.17/48.59 % Factorizations : 0
% 239.17/48.59 % NegExts : 0
% 239.17/48.59 % Equation resolutions : 0
% 239.17/48.59 % Disequality decompositions : 0
% 239.17/48.59 % Total rewrite steps : 832122
% 239.17/48.59 % ...of those cached : 755974
% 239.17/48.59 % Propositional unsat checks : 0
% 239.17/48.59 % Propositional check models : 0
% 239.17/48.59 % Propositional check unsatisfiable : 0
% 239.17/48.59 % Propositional clauses : 0
% 239.17/48.59 % Propositional clauses after purity: 0
% 239.17/48.59 % Propositional unsat core size : 0
% 239.17/48.59 % Propositional preprocessing time : 0.000
% 239.17/48.59 % Propositional encoding time : 0.000
% 239.17/48.59 % Propositional solver time : 0.000
% 239.17/48.59 % Success case prop preproc time : 0.000
% 239.17/48.59 % Success case prop encoding time : 0.000
% 239.17/48.59 % Success case prop solver time : 0.000
% 239.17/48.59 % Current number of processed clauses : 4552
% 239.17/48.59 % Positive orientable unit clauses : 2320
% 239.17/48.59 % Positive unorientable unit clauses: 0
% 239.17/48.59 % Negative unit clauses : 183
% 239.17/48.59 % Non-unit-clauses : 2049
% 239.17/48.59 % Current number of unprocessed clauses: 2847325
% 239.17/48.59 % ...number of literals in the above : 3337267
% 239.17/48.59 % Current number of archived formulas : 0
% 239.17/48.59 % Current number of archived clauses : 985
% 239.17/48.59 % Clause-clause subsumption calls (NU) : 33362266
% 239.17/48.59 % Rec. Clause-clause subsumption calls : 33211150
% 239.17/48.59 % Non-unit clause-clause subsumptions : 295795
% 239.17/48.59 % Unit Clause-clause subsumption calls : 644120
% 239.17/48.59 % Rewrite failures with RHS unbound : 0
% 239.17/48.59 % BW rewrite match attempts : 2407295
% 239.17/48.59 % BW rewrite match successes : 872
% 239.17/48.59 % Condensation attempts : 0
% 239.17/48.59 % Condensation successes : 0
% 239.17/48.59 % Termbank termtop insertions : 60433339
% 239.17/48.59 % Search garbage collected termcells : 8
% 239.17/48.59
% 239.17/48.59 % -------------------------------------------------
% 239.17/48.59 % User time : 46.613 s
% 239.17/48.59 % System time : 1.007 s
% 239.17/48.59 % Total time : 47.621 s
% 239.17/48.59 % Maximum resident set size: 3636 pages
% 239.17/48.59
% 239.17/48.59 % -------------------------------------------------
% 239.17/48.59 % User time : 233.280 s
% 239.17/48.59 % System time : 5.767 s
% 239.17/48.59 % Total time : 239.047 s
% 239.17/48.59 % Maximum resident set size: 4608 pages
% 239.17/48.59 % E exiting
%------------------------------------------------------------------------------