%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL394+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 : n002.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 67.33s 10.29s
% Output : CNFRefutation 67.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 5
% Syntax : Number of formulae : 112 ( 50 unt; 0 def)
% Number of atoms : 194 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 171 ( 89 ~; 80 |; 1 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 8 ( 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 : 248 ( 56 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_58,conjecture,
is_a_theorem(implies(implies(implies(implies(x,y),implies(implies(y,z),z)),u),implies(implies(not(x),z),u))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_58) ).
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(X1,X2))
| is_a_theorem(implies(X1,implies(not(X2),X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_22,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_23,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_24,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_21]) ).
cnf(c_0_25,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_22]) ).
cnf(c_0_26,plain,
( ~ is_a_theorem(implies(implies(not(X2),X4),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_23,c_0_15]) ).
cnf(c_0_27,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_28,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_24,c_0_13]) ).
cnf(c_0_29,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_25,c_0_8]) ).
cnf(c_0_30,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,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_32,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_33,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_23,c_0_20]) ).
cnf(c_0_34,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_28]) ).
cnf(c_0_35,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_24,c_0_8]) ).
cnf(c_0_36,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,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_31,c_0_32]) ).
cnf(c_0_38,plain,
( ~ is_a_theorem(implies(not(X3),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_33,c_0_13]) ).
cnf(c_0_39,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_34]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(implies(X2,X1),X1)),X3))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_13]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_44,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_39,c_0_40]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),implies(X3,X2))),
inference(spm,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_26,c_0_43]) ).
cnf(c_0_47,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_24,c_0_15]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(implies(not(X1),X1),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_37,c_0_46]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(X1,implies(not(implies(X2,X1)),X3))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
is_a_theorem(implies(implies(implies(not(not(X1)),X2),X1),X1)),
inference(spm,[status(thm)],[c_0_16,c_0_49]) ).
cnf(c_0_52,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_50]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(not(X1),not(not(X1))),X1)),
inference(spm,[status(thm)],[c_0_44,c_0_51]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_55,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_18,c_0_54]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(X1,not(not(implies(X2,X1))))),
inference(spm,[status(thm)],[c_0_52,c_0_55]) ).
cnf(c_0_57,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_21]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(not(implies(X1,not(X2))),X2)),
inference(spm,[status(thm)],[c_0_18,c_0_56]) ).
cnf(c_0_59,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_22]) ).
cnf(c_0_60,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_33,c_0_43]) ).
cnf(c_0_61,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_57,c_0_13]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(X1,implies(X2,not(not(X1))))),
inference(spm,[status(thm)],[c_0_18,c_0_58]) ).
fof(c_0_63,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(implies(y,z),z)),u),implies(implies(not(x),z),u))),
inference(assume_negation,[status(cth)],[prove_cn_58]) ).
cnf(c_0_64,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(X2,X3),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_65,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_66,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_61]) ).
cnf(c_0_67,plain,
( ~ is_a_theorem(implies(not(not(X1)),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_62]) ).
fof(c_0_68,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(implies(y,z),z)),u),implies(implies(not(x),z),u))),
inference(fof_simplification,[status(thm)],[c_0_63]) ).
cnf(c_0_69,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_64,c_0_8]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(not(not(X2)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_65]) ).
cnf(c_0_71,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_59,c_0_21]) ).
cnf(c_0_72,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_66,c_0_13]) ).
cnf(c_0_73,plain,
( ~ is_a_theorem(implies(X1,implies(not(X2),X2)))
| is_a_theorem(implies(implies(not(X1),X1),X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_34]) ).
cnf(c_0_74,plain,
is_a_theorem(implies(X1,implies(X2,not(not(not(not(X1))))))),
inference(spm,[status(thm)],[c_0_67,c_0_62]) ).
fof(c_0_75,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(implies(y,z),z)),u),implies(implies(not(x),z),u))),
inference(fof_nnf,[status(thm)],[c_0_68]) ).
cnf(c_0_76,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_57,c_0_9]) ).
cnf(c_0_77,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_69]) ).
cnf(c_0_78,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_37,c_0_70]) ).
cnf(c_0_79,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_71,c_0_72]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(implies(not(X1),X1),not(not(not(not(X1)))))),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_44,c_0_49]) ).
cnf(c_0_82,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(implies(y,z),z)),u),implies(implies(not(x),z),u))),
inference(split_conjunct,[status(thm)],[c_0_75]) ).
cnf(c_0_83,plain,
( ~ is_a_theorem(implies(X1,not(X1)))
| is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_59,c_0_54]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(implies(X1,not(not(X2))))
| is_a_theorem(implies(not(implies(X1,X2)),X3)) ),
inference(spm,[status(thm)],[c_0_76,c_0_54]) ).
cnf(c_0_85,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_77]) ).
cnf(c_0_86,plain,
( ~ is_a_theorem(not(not(implies(X2,not(X1)))))
| is_a_theorem(implies(X1,implies(not(implies(X2,X3)),X4))) ),
inference(spm,[status(thm)],[c_0_47,c_0_78]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_79,c_0_54]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(X1,implies(X2,not(not(not(not(X2))))))),
inference(spm,[status(thm)],[c_0_26,c_0_80]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_52,c_0_81]) ).
cnf(c_0_90,negated_conjecture,
~ is_a_theorem(not(not(implies(implies(not(x),z),implies(implies(x,y),implies(implies(y,z),z)))))),
inference(spm,[status(thm)],[c_0_82,c_0_78]) ).
cnf(c_0_91,plain,
( ~ is_a_theorem(implies(X1,not(not(X2))))
| is_a_theorem(not(not(implies(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_83,c_0_84]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_85,c_0_8]) ).
cnf(c_0_93,plain,
( ~ is_a_theorem(not(not(implies(X2,not(X1)))))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_16,c_0_86]) ).
cnf(c_0_94,plain,
is_a_theorem(not(not(implies(X1,not(not(not(not(X1)))))))),
inference(spm,[status(thm)],[c_0_87,c_0_88]) ).
cnf(c_0_95,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_39,c_0_89]) ).
cnf(c_0_96,negated_conjecture,
~ is_a_theorem(implies(implies(not(x),z),not(not(implies(implies(x,y),implies(implies(y,z),z)))))),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_97,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_25,c_0_92]) ).
cnf(c_0_98,plain,
is_a_theorem(implies(X1,not(not(implies(X2,implies(X3,X1)))))),
inference(spm,[status(thm)],[c_0_52,c_0_56]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(not(not(not(X1))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_100,plain,
( ~ is_a_theorem(implies(X1,implies(not(X2),X2)))
| is_a_theorem(implies(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_95]) ).
cnf(c_0_101,plain,
is_a_theorem(implies(X1,implies(not(implies(implies(X1,X2),X2)),X3))),
inference(spm,[status(thm)],[c_0_52,c_0_40]) ).
cnf(c_0_102,negated_conjecture,
~ is_a_theorem(implies(not(not(not(implies(implies(x,y),implies(implies(y,z),z))))),not(x))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_98])]) ).
cnf(c_0_103,plain,
( ~ is_a_theorem(implies(not(X2),X1))
| is_a_theorem(implies(not(not(not(X1))),X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_99]) ).
cnf(c_0_104,plain,
is_a_theorem(implies(not(not(X1)),implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_100,c_0_101]) ).
cnf(c_0_105,negated_conjecture,
~ is_a_theorem(implies(not(not(x)),implies(implies(x,y),implies(implies(y,z),z)))),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_106,plain,
( ~ is_a_theorem(implies(X2,implies(X1,X3)))
| is_a_theorem(implies(not(not(X1)),implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_104]) ).
cnf(c_0_107,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_16,c_0_40]) ).
cnf(c_0_108,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(x,implies(implies(y,z),z)))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_109,plain,
( ~ is_a_theorem(implies(X2,X4))
| ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X4))) ),
inference(spm,[status(thm)],[c_0_14,c_0_92]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_52,c_0_107]) ).
cnf(c_0_111,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_109]),c_0_43]),c_0_110])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL394+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n002.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 00:30:31 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 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
% 67.33/10.29 % Version: 3.5.1
% 67.33/10.29 % Preprocessing class: FSSSSMSSSSSNFFN.
% 67.33/10.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.33/10.29 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 67.33/10.29 % Starting new_bool_3 with 300s (1) cores
% 67.33/10.29 % Starting new_bool_1 with 300s (1) cores
% 67.33/10.29 % Starting sh5l with 300s (1) cores
% 67.33/10.29 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 2065479 completed with status 0
% 67.33/10.29 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 67.33/10.29 % Preprocessing class: FSSSSMSSSSSNFFN.
% 67.33/10.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.33/10.29 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 67.33/10.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 67.33/10.29 % No SInE strategy applied
% 67.33/10.29 % Search class: FHUNS-FFSF21-MFFFFFNN
% 67.33/10.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 67.33/10.29 % Starting SubtermCWHack with 136s (1) cores
% 67.33/10.29 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 67.33/10.29 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 67.33/10.29 % Starting H----_011_C07_F1_PI_SE_SP_S0V with 136s (1) cores
% 67.33/10.29 % Starting new_bool_3 with 136s (1) cores
% 67.33/10.29 % H----_011_C07_F1_PI_SE_SP_S0V with pid 2065498 completed with status 0
% 67.33/10.29 % Result found by H----_011_C07_F1_PI_SE_SP_S0V
% 67.33/10.29 % Preprocessing class: FSSSSMSSSSSNFFN.
% 67.33/10.29 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 67.33/10.29 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 67.33/10.29 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 67.33/10.29 % No SInE strategy applied
% 67.33/10.29 % Search class: FHUNS-FFSF21-MFFFFFNN
% 67.33/10.29 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 67.33/10.29 % Starting SubtermCWHack with 136s (1) cores
% 67.33/10.29 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 67.33/10.29 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 67.33/10.29 % Starting H----_011_C07_F1_PI_SE_SP_S0V with 136s (1) cores
% 67.33/10.29 % Preprocessing time : 0.002 s
% 67.33/10.29
% 67.33/10.29 % Proof found!
% 67.33/10.29 % SZS status Theorem
% 67.33/10.29 % SZS output start CNFRefutation
% See solution above
% 67.33/10.29 % Parsed axioms : 5
% 67.33/10.29 % Removed by relevancy pruning/SinE : 0
% 67.33/10.29 % Initial clauses : 5
% 67.33/10.29 % Removed in clause preprocessing : 0
% 67.33/10.29 % Initial clauses in saturation : 5
% 67.33/10.29 % Processed clauses : 70830
% 67.33/10.29 % ...of these trivial : 543
% 67.33/10.29 % ...subsumed : 65754
% 67.33/10.29 % ...remaining for further processing : 4533
% 67.33/10.29 % Other redundant clauses eliminated : 0
% 67.33/10.29 % Clauses deleted for lack of memory : 0
% 67.33/10.29 % Backward-subsumed : 1372
% 67.33/10.29 % Backward-rewritten : 226
% 67.33/10.29 % Generated clauses : 343638
% 67.33/10.29 % ...of the previous two non-redundant : 328822
% 67.33/10.29 % ...aggressively subsumed : 0
% 67.33/10.29 % Contextual simplify-reflections : 0
% 67.33/10.29 % Paramodulations : 343638
% 67.33/10.29 % Factorizations : 0
% 67.33/10.29 % NegExts : 0
% 67.33/10.29 % Equation resolutions : 0
% 67.33/10.29 % Disequality decompositions : 0
% 67.33/10.29 % Total rewrite steps : 17548
% 67.33/10.29 % ...of those cached : 15527
% 67.33/10.29 % Propositional unsat checks : 0
% 67.33/10.29 % Propositional check models : 0
% 67.33/10.29 % Propositional check unsatisfiable : 0
% 67.33/10.29 % Propositional clauses : 0
% 67.33/10.29 % Propositional clauses after purity: 0
% 67.33/10.29 % Propositional unsat core size : 0
% 67.33/10.29 % Propositional preprocessing time : 0.000
% 67.33/10.29 % Propositional encoding time : 0.000
% 67.33/10.29 % Propositional solver time : 0.000
% 67.33/10.29 % Success case prop preproc time : 0.000
% 67.33/10.29 % Success case prop encoding time : 0.000
% 67.33/10.29 % Success case prop solver time : 0.000
% 67.33/10.29 % Current number of processed clauses : 2935
% 67.33/10.29 % Positive orientable unit clauses : 437
% 67.33/10.29 % Positive unorientable unit clauses: 0
% 67.33/10.29 % Negative unit clauses : 811
% 67.33/10.29 % Non-unit-clauses : 1687
% 67.33/10.29 % Current number of unprocessed clauses: 257676
% 67.33/10.29 % ...number of literals in the above : 895449
% 67.33/10.29 % Current number of archived formulas : 0
% 67.33/10.29 % Current number of archived clauses : 1598
% 67.33/10.29 % Clause-clause subsumption calls (NU) : 1230539
% 67.33/10.29 % Rec. Clause-clause subsumption calls : 738133
% 67.33/10.29 % Non-unit clause-clause subsumptions : 40674
% 67.33/10.29 % Unit Clause-clause subsumption calls : 124161
% 67.33/10.29 % Rewrite failures with RHS unbound : 0
% 67.33/10.29 % BW rewrite match attempts : 105178
% 67.33/10.29 % BW rewrite match successes : 24
% 67.33/10.29 % Condensation attempts : 0
% 67.33/10.29 % Condensation successes : 0
% 67.33/10.29 % Termbank termtop insertions : 4950611
% 67.33/10.29 % Search garbage collected termcells : 19
% 67.33/10.29
% 67.33/10.29 % -------------------------------------------------
% 67.33/10.29 % User time : 9.365 s
% 67.33/10.29 % System time : 0.254 s
% 67.33/10.29 % Total time : 9.618 s
% 67.33/10.29 % Maximum resident set size: 3328 pages
% 67.33/10.29
% 67.33/10.29 % -------------------------------------------------
% 67.33/10.29 % User time : 46.086 s
% 67.33/10.29 % System time : 1.533 s
% 67.33/10.29 % Total time : 47.619 s
% 67.33/10.29 % Maximum resident set size: 4864 pages
% 67.33/10.29 % E exiting
%------------------------------------------------------------------------------