%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL395+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 : Thu Sep 24 01:12:38 PM UTC 2026
% Result : Theorem 94.03s 14.36s
% Output : CNFRefutation 94.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 5
% Syntax : Number of formulae : 128 ( 50 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 216 ( 112 ~; 102 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 315 ( 78 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X1,X2] :
( ( is_a_theorem(X1)
& is_a_theorem(implies(X1,X2)) )
=> is_a_theorem(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(cn_1,axiom,
! [X1,X2,X3] : is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_1) ).
fof(cn_2,axiom,
! [X1] : is_a_theorem(implies(implies(not(X1),X1),X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_2) ).
fof(cn_3,axiom,
! [X1,X2] : is_a_theorem(implies(X1,implies(not(X1),X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_3) ).
fof(prove_cn_61,conjecture,
is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(not(x),z),y)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_61) ).
fof(c_0_5,plain,
! [X4,X5] :
( is_a_theorem(X5)
| ~ is_a_theorem(X4)
| ~ is_a_theorem(implies(X4,X5)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[condensed_detachment])])]) ).
fof(c_0_6,plain,
! [X6,X7,X8] : is_a_theorem(implies(implies(X6,X7),implies(implies(X7,X8),implies(X6,X8)))),
inference(variable_rename,[status(thm)],[cn_1]) ).
cnf(c_0_7,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
fof(c_0_10,plain,
! [X9] : is_a_theorem(implies(implies(not(X9),X9),X9)),
inference(variable_rename,[status(thm)],[cn_2]) ).
cnf(c_0_11,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_7,c_0_9]) ).
fof(c_0_12,plain,
! [X10,X11] : is_a_theorem(implies(X10,implies(not(X10),X11))),
inference(variable_rename,[status(thm)],[cn_3]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(implies(not(X1),X1),X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,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_11,c_0_9]) ).
cnf(c_0_15,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_16,plain,
( ~ is_a_theorem(implies(X1,implies(not(X2),X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_17,plain,
( ~ is_a_theorem(implies(X2,not(X1)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( ~ is_a_theorem(implies(not(X2),not(X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_15]) ).
cnf(c_0_20,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_21,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_14,c_0_20]) ).
cnf(c_0_22,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X1,implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_23,plain,
( ~ is_a_theorem(implies(not(X2),X1))
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_9]) ).
cnf(c_0_24,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_13]) ).
cnf(c_0_25,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_11,c_0_8]) ).
cnf(c_0_26,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_21,c_0_20]) ).
cnf(c_0_27,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_11,c_0_22]) ).
cnf(c_0_28,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_11,c_0_23]) ).
cnf(c_0_29,plain,
( ~ is_a_theorem(implies(implies(not(X2),X4),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_30,plain,
is_a_theorem(implies(implies(not(implies(not(X1),X1)),implies(not(X1),X1)),X1)),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_31,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_24,c_0_25]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(implies(not(X3),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_33,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_27,c_0_13]) ).
cnf(c_0_34,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_28,c_0_8]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_29,c_0_13]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_39,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(implies(not(X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_40,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_27,c_0_15]) ).
cnf(c_0_41,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_21,c_0_8]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_43,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_27,c_0_8]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_45,plain,
( ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(implies(not(X1),X2))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_7,c_0_23]) ).
cnf(c_0_46,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_26,c_0_38]) ).
cnf(c_0_47,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_11,c_0_39]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(X1,implies(not(implies(not(X1),X2)),X3))),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X3),implies(implies(X3,X2),X2)))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(implies(X1,X2),implies(not(implies(X3,implies(X1,X2))),X4))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(X2,X3),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,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_14,c_0_8]) ).
cnf(c_0_53,plain,
( ~ is_a_theorem(implies(implies(not(X1),X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_24,c_0_49]) ).
cnf(c_0_55,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_22]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X1,X2)))),
inference(spm,[status(thm)],[c_0_16,c_0_50]) ).
cnf(c_0_57,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_51,c_0_52]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(X1,implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_53,c_0_54]) ).
cnf(c_0_59,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_55,c_0_13]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(not(X2),X4))))),
inference(spm,[status(thm)],[c_0_29,c_0_56]) ).
cnf(c_0_61,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_55,c_0_9]) ).
cnf(c_0_62,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_51,c_0_8]) ).
cnf(c_0_63,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(not(implies(X1,implies(X2,implies(not(X1),X3)))),X4)),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,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_61,c_0_62]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_67,plain,
( ~ is_a_theorem(implies(not(X2),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_59]) ).
cnf(c_0_68,plain,
( ~ is_a_theorem(X4)
| is_a_theorem(implies(not(implies(X1,implies(X2,X1))),X3)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,plain,
( ~ is_a_theorem(implies(not(implies(X3,X1)),implies(X3,X1)))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_31,c_0_67]) ).
cnf(c_0_70,plain,
is_a_theorem(implies(not(implies(X1,implies(X2,X1))),X3)),
inference(spm,[status(thm)],[c_0_68,c_0_64]) ).
cnf(c_0_71,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(implies(X1,not(not(implies(X1,X2)))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_34,c_0_15]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_7,c_0_71]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(implies(not(X1),not(not(implies(not(X1),X1)))),X1)),
inference(spm,[status(thm)],[c_0_16,c_0_72]) ).
cnf(c_0_75,plain,
is_a_theorem(implies(not(not(implies(not(X1),X1))),X1)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_76,plain,
( ~ is_a_theorem(implies(not(X3),X3))
| ~ is_a_theorem(implies(X1,not(X3)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_11,c_0_59]) ).
cnf(c_0_77,plain,
( ~ is_a_theorem(implies(not(X2),not(implies(not(X1),X3))))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_48]) ).
cnf(c_0_78,plain,
is_a_theorem(implies(X1,not(implies(not(not(X1)),not(X1))))),
inference(spm,[status(thm)],[c_0_18,c_0_75]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_80,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_45,c_0_22]) ).
cnf(c_0_81,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(implies(not(not(X1)),not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_13]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(not(not(X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_79]) ).
cnf(c_0_84,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_80,c_0_81]) ).
cnf(c_0_85,plain,
( ~ is_a_theorem(implies(not(X3),not(X2)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_29,c_0_23]) ).
cnf(c_0_86,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_18,c_0_82]) ).
cnf(c_0_87,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_28,c_0_20]) ).
cnf(c_0_88,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_31,c_0_83]) ).
cnf(c_0_89,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_84,c_0_82]) ).
cnf(c_0_90,plain,
is_a_theorem(implies(X1,implies(not(not(X2)),X2))),
inference(spm,[status(thm)],[c_0_85,c_0_86]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_20]) ).
fof(c_0_92,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(not(x),z),y)))),
inference(assume_negation,[status(cth)],[prove_cn_61]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_62]) ).
cnf(c_0_94,plain,
( ~ is_a_theorem(not(not(implies(not(X2),X1))))
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_88]) ).
cnf(c_0_95,plain,
is_a_theorem(not(not(implies(not(not(X1)),X1)))),
inference(spm,[status(thm)],[c_0_89,c_0_90]) ).
cnf(c_0_96,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_29,c_0_38]) ).
cnf(c_0_97,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_91,c_0_8]) ).
fof(c_0_98,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(not(x),z),y)))),
inference(fof_simplification,[status(thm)],[c_0_92]) ).
cnf(c_0_99,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_11,c_0_93]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_101,plain,
( ~ is_a_theorem(implies(implies(X2,implies(not(X2),X3)),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_45,c_0_96]) ).
cnf(c_0_102,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_14,c_0_97]) ).
cnf(c_0_103,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_73,c_0_54]) ).
fof(c_0_104,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(not(x),z),y)))),
inference(fof_nnf,[status(thm)],[c_0_98]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_99,c_0_8]) ).
cnf(c_0_106,plain,
( ~ is_a_theorem(implies(X1,implies(X2,not(X2))))
| is_a_theorem(implies(X1,not(X2))) ),
inference(spm,[status(thm)],[c_0_11,c_0_100]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(not(not(implies(X1,X2))))
| is_a_theorem(implies(X1,implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_101,c_0_88]) ).
cnf(c_0_108,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_102,c_0_103]) ).
cnf(c_0_109,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(implies(z,y),implies(implies(not(x),z),y)))),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_110,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_28,c_0_105]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(not(not(implies(X1,X2))))
| is_a_theorem(implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_112,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_89,c_0_108]) ).
cnf(c_0_113,negated_conjecture,
( ~ is_a_theorem(implies(y,implies(implies(z,y),implies(implies(not(x),z),y))))
| ~ is_a_theorem(implies(not(implies(implies(z,y),implies(implies(not(x),z),y))),x)) ),
inference(spm,[status(thm)],[c_0_109,c_0_110]) ).
cnf(c_0_114,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_73,c_0_66]) ).
cnf(c_0_115,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_111,c_0_112]) ).
cnf(c_0_116,negated_conjecture,
~ is_a_theorem(implies(not(implies(implies(z,y),implies(implies(not(x),z),y))),x)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_113,c_0_114])]) ).
cnf(c_0_117,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_18,c_0_115]) ).
cnf(c_0_118,negated_conjecture,
~ is_a_theorem(implies(implies(z,y),implies(not(x),implies(implies(not(x),z),y)))),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_119,negated_conjecture,
~ is_a_theorem(implies(not(implies(not(x),implies(implies(not(x),z),y))),z)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_110]),c_0_114])]) ).
cnf(c_0_120,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_14,c_0_25]) ).
cnf(c_0_121,negated_conjecture,
~ is_a_theorem(implies(not(x),implies(not(z),implies(implies(not(x),z),y)))),
inference(spm,[status(thm)],[c_0_119,c_0_117]) ).
cnf(c_0_122,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_120,c_0_15]) ).
cnf(c_0_123,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_28,c_0_25]) ).
cnf(c_0_124,plain,
is_a_theorem(implies(X1,implies(X2,not(not(X2))))),
inference(spm,[status(thm)],[c_0_85,c_0_82]) ).
cnf(c_0_125,negated_conjecture,
~ is_a_theorem(implies(not(x),implies(implies(not(x),z),not(not(z))))),
inference(spm,[status(thm)],[c_0_121,c_0_122]) ).
cnf(c_0_126,plain,
( ~ is_a_theorem(implies(X1,implies(X2,X3)))
| is_a_theorem(implies(X1,implies(X2,not(not(X3))))) ),
inference(spm,[status(thm)],[c_0_123,c_0_124]) ).
cnf(c_0_127,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_126]),c_0_103])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL395+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.35 % Computer : n006.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 00:27:42 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.42 Running first-order theorem proving
% 0.18/0.42 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
% 94.03/14.36 % Version: 3.5.1
% 94.03/14.36 % Preprocessing class: FSSSSMSSSSSNFFN.
% 94.03/14.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.03/14.36 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 94.03/14.36 % Starting new_bool_3 with 300s (1) cores
% 94.03/14.36 % Starting new_bool_1 with 300s (1) cores
% 94.03/14.36 % Starting sh5l with 300s (1) cores
% 94.03/14.36 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1628705 completed with status 0
% 94.03/14.36 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 94.03/14.36 % Preprocessing class: FSSSSMSSSSSNFFN.
% 94.03/14.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.03/14.36 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 94.03/14.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 94.03/14.36 % No SInE strategy applied
% 94.03/14.36 % Search class: FHUNS-FFSF21-MFFFFFNN
% 94.03/14.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 94.03/14.36 % Starting SubtermCWHack with 136s (1) cores
% 94.03/14.36 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 94.03/14.36 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 94.03/14.36 % Starting H----_011_C07_F1_PI_SE_SP_S0V with 136s (1) cores
% 94.03/14.36 % Starting new_bool_3 with 136s (1) cores
% 94.03/14.36 % H----_011_C07_F1_PI_SE_SP_S0V with pid 1628712 completed with status 0
% 94.03/14.36 % Result found by H----_011_C07_F1_PI_SE_SP_S0V
% 94.03/14.36 % Preprocessing class: FSSSSMSSSSSNFFN.
% 94.03/14.36 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 94.03/14.36 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 94.03/14.36 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 94.03/14.36 % No SInE strategy applied
% 94.03/14.36 % Search class: FHUNS-FFSF21-MFFFFFNN
% 94.03/14.36 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 94.03/14.36 % Starting SubtermCWHack with 136s (1) cores
% 94.03/14.36 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 94.03/14.36 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 94.03/14.36 % Starting H----_011_C07_F1_PI_SE_SP_S0V with 136s (1) cores
% 94.03/14.36 % Preprocessing time : 0.002 s
% 94.03/14.36
% 94.03/14.36 % Proof found!
% 94.03/14.36 % SZS status Theorem
% 94.03/14.36 % SZS output start CNFRefutation
% See solution above
% 94.03/14.36 % Parsed axioms : 5
% 94.03/14.36 % Removed by relevancy pruning/SinE : 0
% 94.03/14.36 % Initial clauses : 5
% 94.03/14.36 % Removed in clause preprocessing : 0
% 94.03/14.36 % Initial clauses in saturation : 5
% 94.03/14.36 % Processed clauses : 78030
% 94.03/14.36 % ...of these trivial : 1036
% 94.03/14.36 % ...subsumed : 72589
% 94.03/14.36 % ...remaining for further processing : 4405
% 94.03/14.36 % Other redundant clauses eliminated : 0
% 94.03/14.36 % Clauses deleted for lack of memory : 0
% 94.03/14.36 % Backward-subsumed : 959
% 94.03/14.36 % Backward-rewritten : 50
% 94.03/14.36 % Generated clauses : 521407
% 94.03/14.36 % ...of the previous two non-redundant : 495189
% 94.03/14.36 % ...aggressively subsumed : 0
% 94.03/14.36 % Contextual simplify-reflections : 0
% 94.03/14.36 % Paramodulations : 521407
% 94.03/14.36 % Factorizations : 0
% 94.03/14.36 % NegExts : 0
% 94.03/14.36 % Equation resolutions : 0
% 94.03/14.36 % Disequality decompositions : 0
% 94.03/14.36 % Total rewrite steps : 29609
% 94.03/14.36 % ...of those cached : 26434
% 94.03/14.36 % Propositional unsat checks : 0
% 94.03/14.36 % Propositional check models : 0
% 94.03/14.36 % Propositional check unsatisfiable : 0
% 94.03/14.36 % Propositional clauses : 0
% 94.03/14.36 % Propositional clauses after purity: 0
% 94.03/14.36 % Propositional unsat core size : 0
% 94.03/14.36 % Propositional preprocessing time : 0.000
% 94.03/14.36 % Propositional encoding time : 0.000
% 94.03/14.36 % Propositional solver time : 0.000
% 94.03/14.36 % Success case prop preproc time : 0.000
% 94.03/14.36 % Success case prop encoding time : 0.000
% 94.03/14.36 % Success case prop solver time : 0.000
% 94.03/14.36 % Current number of processed clauses : 3396
% 94.03/14.36 % Positive orientable unit clauses : 537
% 94.03/14.36 % Positive unorientable unit clauses: 0
% 94.03/14.36 % Negative unit clauses : 663
% 94.03/14.36 % Non-unit-clauses : 2196
% 94.03/14.36 % Current number of unprocessed clauses: 416022
% 94.03/14.36 % ...number of literals in the above : 1316291
% 94.03/14.36 % Current number of archived formulas : 0
% 94.03/14.36 % Current number of archived clauses : 1009
% 94.03/14.36 % Clause-clause subsumption calls (NU) : 1204764
% 94.03/14.36 % Rec. Clause-clause subsumption calls : 1034768
% 94.03/14.36 % Non-unit clause-clause subsumptions : 47299
% 94.03/14.36 % Unit Clause-clause subsumption calls : 102446
% 94.03/14.36 % Rewrite failures with RHS unbound : 0
% 94.03/14.36 % BW rewrite match attempts : 145461
% 94.03/14.36 % BW rewrite match successes : 35
% 94.03/14.36 % Condensation attempts : 0
% 94.03/14.36 % Condensation successes : 0
% 94.03/14.36 % Termbank termtop insertions : 7919790
% 94.03/14.36 % Search garbage collected termcells : 19
% 94.03/14.36
% 94.03/14.36 % -------------------------------------------------
% 94.03/14.36 % User time : 12.848 s
% 94.03/14.36 % System time : 0.416 s
% 94.03/14.36 % Total time : 13.264 s
% 94.03/14.36 % Maximum resident set size: 3636 pages
% 94.03/14.36
% 94.03/14.36 % -------------------------------------------------
% 94.03/14.36 % User time : 65.178 s
% 94.03/14.36 % System time : 2.202 s
% 94.03/14.36 % Total time : 67.380 s
% 94.03/14.36 % Maximum resident set size: 4608 pages
% 94.03/14.36 % E exiting
%------------------------------------------------------------------------------