%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : LCL981+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 : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:24:37 PM UTC 2026
% Result : Theorem 167.18s 34.10s
% Output : CNFRefutation 167.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 66
% Number of leaves : 3
% Syntax : Number of formulae : 137 ( 71 unt; 0 def)
% Number of atoms : 215 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 159 ( 81 ~; 78 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 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 : 408 ( 153 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(condensed_detachment,axiom,
! [X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
fof(a4,axiom,
! [X3,X4,X5,X6,X7] : is_a_theorem(implies(X3,implies(implies(not(X4),implies(implies(not(X5),X6),implies(X7,X4))),implies(implies(X5,X7),implies(X5,X4))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4) ).
fof(prove_cn_1,conjecture,
! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_1) ).
fof(c_0_3,plain,
! [X1,X2] :
( is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2)) ),
inference(fof_simplification,[status(thm)],[condensed_detachment]) ).
fof(c_0_4,plain,
! [X8,X9] :
( is_a_theorem(X9)
| ~ is_a_theorem(X8)
| ~ is_a_theorem(implies(X8,X9)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_3])]) ).
fof(c_0_5,plain,
! [X10,X11,X12,X13,X14] : is_a_theorem(implies(X10,implies(implies(not(X11),implies(implies(not(X12),X13),implies(X14,X11))),implies(implies(X12,X14),implies(X12,X11))))),
inference(variable_rename,[status(thm)],[a4]) ).
cnf(c_0_6,plain,
( ~ is_a_theorem(X1)
| ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(X2) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),implies(implies(not(X3),X4),implies(X5,X2))),implies(implies(X3,X5),implies(X3,X2))))),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_8,plain,
( ~ is_a_theorem(X5)
| is_a_theorem(implies(implies(not(X1),implies(implies(not(X2),X3),implies(X4,X1))),implies(implies(X2,X4),implies(X2,X1)))) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,plain,
is_a_theorem(implies(implies(not(X1),implies(implies(not(X2),X3),implies(X4,X1))),implies(implies(X2,X4),implies(X2,X1)))),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
( ~ is_a_theorem(implies(not(X3),implies(implies(not(X1),X4),implies(X2,X3))))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_6,c_0_9]) ).
cnf(c_0_11,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(X1,implies(X2,X1)))),
inference(spm,[status(thm)],[c_0_10,c_0_7]) ).
cnf(c_0_12,plain,
( ~ is_a_theorem(implies(X1,implies(X2,X3)))
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_6,c_0_11]) ).
cnf(c_0_13,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),implies(implies(not(X3),X4),implies(X5,X2))),X1))),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_14,plain,
( ~ is_a_theorem(X5)
| is_a_theorem(implies(implies(not(X1),implies(implies(not(X2),X3),implies(X4,X1))),X5)) ),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_15,plain,
( ~ is_a_theorem(implies(X5,X6))
| is_a_theorem(implies(implies(not(X1),implies(implies(not(X2),X3),implies(X4,X1))),implies(X5,implies(not(X1),implies(implies(not(X2),X3),implies(X4,X1)))))) ),
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_16,plain,
is_a_theorem(implies(implies(not(X1),implies(implies(not(X2),X3),implies(X4,X1))),implies(X5,implies(not(X1),implies(implies(not(X2),X3),implies(X4,X1)))))),
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_17,plain,
( ~ is_a_theorem(implies(not(X2),implies(implies(not(X3),X4),implies(X5,X2))))
| is_a_theorem(implies(X1,implies(not(X2),implies(implies(not(X3),X4),implies(X5,X2))))) ),
inference(spm,[status(thm)],[c_0_6,c_0_16]) ).
cnf(c_0_18,plain,
( ~ is_a_theorem(implies(not(X2),implies(implies(not(X3),X4),implies(X5,X2))))
| is_a_theorem(implies(X1,implies(not(X2),X1))) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_19,plain,
is_a_theorem(implies(X1,implies(not(implies(X2,X3)),X1))),
inference(spm,[status(thm)],[c_0_18,c_0_7]) ).
cnf(c_0_20,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(not(implies(X1,X2)),X3)) ),
inference(spm,[status(thm)],[c_0_6,c_0_19]) ).
cnf(c_0_21,plain,
( ~ is_a_theorem(implies(implies(not(X1),X5),implies(X2,implies(X3,X4))))
| is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_10,c_0_20]) ).
cnf(c_0_22,plain,
( ~ is_a_theorem(implies(X2,implies(X3,X4)))
| is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_23,plain,
( ~ is_a_theorem(implies(X1,X4))
| ~ is_a_theorem(implies(X4,implies(X2,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_6,c_0_22]) ).
cnf(c_0_24,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),implies(implies(not(X3),X4),implies(X5,X2)))),implies(X1,implies(not(X1),X6)))),
inference(spm,[status(thm)],[c_0_21,c_0_13]) ).
cnf(c_0_25,plain,
( ~ is_a_theorem(implies(X1,implies(X2,implies(not(X4),implies(implies(not(X5),X6),implies(X7,X4))))))
| is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(not(X1),implies(implies(not(X3),X4),implies(X5,X1)))))),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_27,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(not(X1),X3)))),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_28,plain,
( ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,implies(not(X1),X2))) ),
inference(spm,[status(thm)],[c_0_6,c_0_27]) ).
cnf(c_0_29,plain,
( ~ is_a_theorem(implies(X2,X3))
| ~ is_a_theorem(implies(X1,implies(not(X4),implies(implies(not(X5),X6),implies(X7,X4)))))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_23,c_0_14]) ).
cnf(c_0_30,plain,
is_a_theorem(implies(X1,implies(not(X1),X2))),
inference(spm,[status(thm)],[c_0_28,c_0_7]) ).
cnf(c_0_31,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_32,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(X1,implies(X2,X1))) ),
inference(spm,[status(thm)],[c_0_12,c_0_31]) ).
cnf(c_0_33,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_32,c_0_7]) ).
cnf(c_0_34,plain,
( ~ is_a_theorem(implies(X1,X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_23,c_0_33]) ).
cnf(c_0_35,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(X3,X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_34]) ).
cnf(c_0_36,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_35,c_0_33]) ).
cnf(c_0_37,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_35,c_0_34]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(implies(X1,not(implies(X2,X3))),implies(X1,implies(not(X1),X4)))),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_39,plain,
( ~ is_a_theorem(implies(X2,X3))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_10,c_0_36]) ).
cnf(c_0_40,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,implies(not(X3),X4)))) ),
inference(spm,[status(thm)],[c_0_37,c_0_30]) ).
cnf(c_0_41,plain,
( ~ is_a_theorem(implies(X1,implies(X2,not(implies(X4,X5)))))
| is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))) ),
inference(spm,[status(thm)],[c_0_23,c_0_38]) ).
cnf(c_0_42,plain,
( ~ is_a_theorem(implies(X1,implies(X2,implies(X3,X4))))
| is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))) ),
inference(spm,[status(thm)],[c_0_23,c_0_11]) ).
cnf(c_0_43,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_6,c_0_39]) ).
cnf(c_0_44,plain,
( ~ is_a_theorem(X4)
| is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))) ),
inference(spm,[status(thm)],[c_0_25,c_0_40]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(not(implies(X1,X2)),implies(X3,implies(not(X3),X4)))),
inference(spm,[status(thm)],[c_0_41,c_0_33]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(implies(X1,X2),implies(X3,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_42,c_0_33]) ).
cnf(c_0_47,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_33]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_44,c_0_45]) ).
cnf(c_0_49,plain,
( ~ is_a_theorem(implies(X3,X4))
| is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))) ),
inference(spm,[status(thm)],[c_0_35,c_0_46]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),implies(implies(not(X3),X4),implies(X5,X2)))),implies(X1,implies(implies(X3,X5),implies(X3,X2))))),
inference(spm,[status(thm)],[c_0_21,c_0_7]) ).
cnf(c_0_51,plain,
( ~ is_a_theorem(implies(implies(not(X1),X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_30]) ).
cnf(c_0_52,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_47,c_0_33]) ).
cnf(c_0_53,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_21,c_0_48]) ).
cnf(c_0_54,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_49,c_0_7]) ).
cnf(c_0_55,plain,
( ~ is_a_theorem(implies(X1,implies(not(X4),implies(implies(not(X2),X5),implies(X3,X4)))))
| is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X2,X4)))) ),
inference(spm,[status(thm)],[c_0_6,c_0_50]) ).
cnf(c_0_56,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,implies(not(X1),X4))))),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_57,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X1),X3)))),
inference(spm,[status(thm)],[c_0_47,c_0_53]) ).
cnf(c_0_58,plain,
( ~ is_a_theorem(implies(implies(X3,implies(X4,X3)),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_54]) ).
cnf(c_0_59,plain,
is_a_theorem(implies(X1,implies(implies(X2,not(X1)),implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_60,plain,
is_a_theorem(implies(implies(X1,not(not(X2))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_10,c_0_57]) ).
cnf(c_0_61,plain,
( ~ is_a_theorem(implies(implies(X4,X2),X3))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_58,c_0_39]) ).
cnf(c_0_62,plain,
is_a_theorem(implies(implies(X1,not(X1)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_10,c_0_59]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(not(not(X1)),implies(X2,X1))),
inference(spm,[status(thm)],[c_0_47,c_0_60]) ).
cnf(c_0_64,plain,
is_a_theorem(implies(X1,implies(not(X2),implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_65,plain,
( ~ is_a_theorem(implies(implies(X3,X1),X2))
| is_a_theorem(implies(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_63]) ).
cnf(c_0_66,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(X1,implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_21,c_0_64]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_47,c_0_62]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(implies(X1,not(X1)),implies(X1,implies(X2,not(X1))))),
inference(spm,[status(thm)],[c_0_21,c_0_11]) ).
cnf(c_0_69,plain,
is_a_theorem(implies(not(not(not(X1))),implies(X2,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_70,plain,
( ~ is_a_theorem(implies(implies(X1,X3),X2))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_67]) ).
cnf(c_0_71,plain,
is_a_theorem(implies(implies(X1,not(X1)),implies(X1,implies(X2,not(not(X1)))))),
inference(spm,[status(thm)],[c_0_21,c_0_68]) ).
cnf(c_0_72,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,not(not(X2))))),
inference(spm,[status(thm)],[c_0_10,c_0_69]) ).
cnf(c_0_73,plain,
is_a_theorem(implies(not(X1),implies(X2,implies(not(implies(X1,X3)),X4)))),
inference(spm,[status(thm)],[c_0_70,c_0_57]) ).
cnf(c_0_74,plain,
( ~ is_a_theorem(implies(X1,implies(X2,not(X2))))
| is_a_theorem(implies(X1,implies(X2,implies(X3,not(not(X2)))))) ),
inference(spm,[status(thm)],[c_0_23,c_0_71]) ).
cnf(c_0_75,plain,
( ~ is_a_theorem(implies(X1,not(X1)))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_62]) ).
cnf(c_0_76,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X1,not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_6,c_0_72]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(implies(X1,not(implies(X2,X3))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_10,c_0_73]) ).
cnf(c_0_78,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,not(not(implies(not(X1),X3)))))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_74]),c_0_63])]) ).
cnf(c_0_79,plain,
( ~ is_a_theorem(implies(not(X1),X1))
| is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(not(implies(X1,X2)),implies(X3,X1))),
inference(spm,[status(thm)],[c_0_47,c_0_77]) ).
cnf(c_0_81,plain,
is_a_theorem(implies(X1,implies(X2,not(not(implies(not(X2),X3)))))),
inference(spm,[status(thm)],[c_0_47,c_0_78]) ).
cnf(c_0_82,plain,
is_a_theorem(implies(implies(X1,not(implies(not(X1),X2))),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_10,c_0_48]) ).
cnf(c_0_83,plain,
is_a_theorem(implies(not(implies(X1,X1)),X2)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,not(not(implies(not(X1),X2))))) ),
inference(spm,[status(thm)],[c_0_6,c_0_81]) ).
cnf(c_0_85,plain,
is_a_theorem(implies(not(implies(not(X1),X2)),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_47,c_0_82]) ).
cnf(c_0_86,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X3)))),
inference(spm,[status(thm)],[c_0_10,c_0_83]) ).
cnf(c_0_87,plain,
( ~ is_a_theorem(X2)
| ~ is_a_theorem(implies(X2,X1))
| is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_6,c_0_76]) ).
cnf(c_0_88,plain,
is_a_theorem(implies(X1,not(not(implies(not(X1),X2))))),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_89,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X3)))),
inference(spm,[status(thm)],[c_0_47,c_0_86]) ).
cnf(c_0_90,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(not(not(implies(X1,implies(X2,X1))))) ),
inference(spm,[status(thm)],[c_0_87,c_0_54]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(not(X1),not(not(implies(not(implies(X1,X2)),X3))))),
inference(spm,[status(thm)],[c_0_70,c_0_88]) ).
cnf(c_0_92,plain,
( ~ is_a_theorem(X3)
| is_a_theorem(implies(X1,implies(X2,X2))) ),
inference(spm,[status(thm)],[c_0_6,c_0_89]) ).
cnf(c_0_93,plain,
is_a_theorem(not(not(implies(X1,implies(X2,X1))))),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_94,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_95,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X1)) ),
inference(spm,[status(thm)],[c_0_6,c_0_94]) ).
cnf(c_0_96,plain,
( ~ is_a_theorem(implies(X1,not(not(X2))))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_60]) ).
cnf(c_0_97,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_95,c_0_93]) ).
cnf(c_0_98,plain,
( ~ is_a_theorem(implies(X2,not(not(X3))))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_35,c_0_60]) ).
cnf(c_0_99,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_96,c_0_97]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(X1,implies(not(not(X2)),X2))),
inference(spm,[status(thm)],[c_0_98,c_0_97]) ).
cnf(c_0_101,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(not(not(X1)),X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_99]) ).
cnf(c_0_102,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(not(not(implies(not(not(X1)),X1)))) ),
inference(spm,[status(thm)],[c_0_87,c_0_100]) ).
cnf(c_0_103,plain,
( ~ is_a_theorem(implies(X2,X1))
| ~ is_a_theorem(not(not(X2)))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_6,c_0_101]) ).
cnf(c_0_104,plain,
is_a_theorem(not(not(implies(not(not(X1)),X1)))),
inference(spm,[status(thm)],[c_0_102,c_0_93]) ).
cnf(c_0_105,plain,
( ~ is_a_theorem(implies(not(X3),implies(X2,X3)))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_10,c_0_34]) ).
cnf(c_0_106,plain,
is_a_theorem(implies(X1,implies(implies(X2,not(X2)),implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_55,c_0_89]) ).
cnf(c_0_107,plain,
( ~ is_a_theorem(implies(implies(not(not(X2)),X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_104]) ).
cnf(c_0_108,plain,
is_a_theorem(implies(implies(X1,implies(X2,not(X2))),implies(X1,implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_105,c_0_106]) ).
cnf(c_0_109,plain,
is_a_theorem(implies(not(not(implies(X1,not(X1)))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_107,c_0_108]) ).
cnf(c_0_110,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,not(implies(X2,not(X2)))))),
inference(spm,[status(thm)],[c_0_105,c_0_109]) ).
cnf(c_0_111,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(not(not(implies(X1,X1)))) ),
inference(spm,[status(thm)],[c_0_87,c_0_94]) ).
cnf(c_0_112,plain,
( ~ is_a_theorem(implies(X1,not(X2)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_6,c_0_66]) ).
cnf(c_0_113,plain,
is_a_theorem(implies(not(not(X1)),not(implies(X1,not(X1))))),
inference(spm,[status(thm)],[c_0_107,c_0_110]) ).
cnf(c_0_114,plain,
is_a_theorem(not(not(implies(X1,X1)))),
inference(spm,[status(thm)],[c_0_111,c_0_93]) ).
cnf(c_0_115,plain,
is_a_theorem(implies(not(not(X1)),implies(implies(X1,not(X1)),X2))),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,plain,
( ~ is_a_theorem(implies(implies(X2,X2),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_114]) ).
cnf(c_0_117,plain,
is_a_theorem(implies(implies(X1,implies(X2,not(X2))),implies(X1,not(X2)))),
inference(spm,[status(thm)],[c_0_105,c_0_115]) ).
cnf(c_0_118,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_33]) ).
cnf(c_0_119,plain,
is_a_theorem(implies(implies(X1,not(X1)),not(X1))),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_120,plain,
( ~ is_a_theorem(implies(implies(not(X1),X4),implies(X2,X3)))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_10,c_0_118]) ).
cnf(c_0_121,plain,
is_a_theorem(implies(implies(not(X1),not(not(X1))),X1)),
inference(spm,[status(thm)],[c_0_96,c_0_119]) ).
cnf(c_0_122,plain,
( ~ is_a_theorem(X2)
| is_a_theorem(not(not(implies(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_87,c_0_33]) ).
cnf(c_0_123,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_120,c_0_121]) ).
cnf(c_0_124,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_55,c_0_52]) ).
cnf(c_0_125,plain,
( ~ is_a_theorem(X3)
| ~ is_a_theorem(implies(implies(X2,X3),X1))
| is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_103,c_0_122]) ).
cnf(c_0_126,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_47,c_0_123]) ).
cnf(c_0_127,plain,
( ~ is_a_theorem(implies(implies(implies(X4,X1),implies(X4,X2)),X3))
| is_a_theorem(implies(implies(X1,X2),X3)) ),
inference(spm,[status(thm)],[c_0_43,c_0_124]) ).
cnf(c_0_128,plain,
( ~ is_a_theorem(X1)
| is_a_theorem(implies(implies(X1,X2),X2)) ),
inference(spm,[status(thm)],[c_0_125,c_0_123]) ).
fof(c_0_129,negated_conjecture,
~ ! [X3,X4,X5] : is_a_theorem(implies(implies(X3,X4),implies(implies(X4,X5),implies(X3,X5)))),
inference(assume_negation,[status(cth)],[prove_cn_1]) ).
cnf(c_0_130,plain,
( ~ is_a_theorem(implies(implies(implies(X1,X3),X3),X2))
| is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_43,c_0_126]) ).
cnf(c_0_131,plain,
( ~ is_a_theorem(implies(X3,X1))
| is_a_theorem(implies(implies(X1,X2),implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_127,c_0_128]) ).
fof(c_0_132,negated_conjecture,
~ is_a_theorem(implies(implies(esk1_0,esk2_0),implies(implies(esk2_0,esk3_0),implies(esk1_0,esk3_0)))),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_129])])])]) ).
cnf(c_0_133,plain,
( ~ is_a_theorem(implies(X2,implies(X1,X3)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(spm,[status(thm)],[c_0_130,c_0_131]) ).
cnf(c_0_134,negated_conjecture,
~ is_a_theorem(implies(implies(esk1_0,esk2_0),implies(implies(esk2_0,esk3_0),implies(esk1_0,esk3_0)))),
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_135,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_133,c_0_124]) ).
cnf(c_0_136,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_134,c_0_135])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL981+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 01:15:21 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 167.18/34.10 % Version: 3.5.1
% 167.18/34.10 % Preprocessing class: FSSSSMSSSSSNFFN.
% 167.18/34.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 167.18/34.10 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 167.18/34.10 % Starting new_bool_3 with 300s (1) cores
% 167.18/34.10 % Starting new_bool_1 with 300s (1) cores
% 167.18/34.10 % Starting sh5l with 300s (1) cores
% 167.18/34.10 % new_bool_3 with pid 1286527 completed with status 9
% 167.18/34.10 % new_bool_1 with pid 1286528 completed with status 9
% 167.18/34.10 % G-E--_302_C18_F1_URBAN_RG_S04BN with pid 1286526 completed with status 0
% 167.18/34.10 % Result found by G-E--_302_C18_F1_URBAN_RG_S04BN
% 167.18/34.10 % Preprocessing class: FSSSSMSSSSSNFFN.
% 167.18/34.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 167.18/34.10 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 167.18/34.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 167.18/34.10 % No SInE strategy applied
% 167.18/34.10 % Search class: FHUNF-FFSF21-DFFFFFNN
% 167.18/34.10 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 167.18/34.10 % Starting SubtermCWHack with 136s (1) cores
% 167.18/34.10 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 151s (1) cores
% 167.18/34.10 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04BN with 136s (1) cores
% 167.18/34.10 % Starting new_bool_3 with 136s (1) cores
% 167.18/34.10 % Starting new_bool_1 with 136s (1) cores
% 167.18/34.10 % SubtermCWHack with pid 1286531 completed with status 0
% 167.18/34.10 % Result found by SubtermCWHack
% 167.18/34.10 % Preprocessing class: FSSSSMSSSSSNFFN.
% 167.18/34.10 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 167.18/34.10 % Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 167.18/34.10 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 167.18/34.10 % No SInE strategy applied
% 167.18/34.10 % Search class: FHUNF-FFSF21-DFFFFFNN
% 167.18/34.10 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 167.18/34.10 % Starting SubtermCWHack with 136s (1) cores
% 167.18/34.10 % Preprocessing time : 0.001 s
% 167.18/34.10
% 167.18/34.10 % Proof found!
% 167.18/34.10 % SZS status Theorem
% 167.18/34.10 % SZS output start CNFRefutation
% See solution above
% 167.18/34.10 % Parsed axioms : 3
% 167.18/34.10 % Removed by relevancy pruning/SinE : 0
% 167.18/34.10 % Initial clauses : 3
% 167.18/34.10 % Removed in clause preprocessing : 0
% 167.18/34.10 % Initial clauses in saturation : 3
% 167.18/34.10 % Processed clauses : 111063
% 167.18/34.10 % ...of these trivial : 5537
% 167.18/34.10 % ...subsumed : 97897
% 167.18/34.10 % ...remaining for further processing : 7629
% 167.18/34.10 % Other redundant clauses eliminated : 0
% 167.18/34.10 % Clauses deleted for lack of memory : 0
% 167.18/34.10 % Backward-subsumed : 421
% 167.18/34.10 % Backward-rewritten : 303
% 167.18/34.10 % Generated clauses : 3065207
% 167.18/34.10 % ...of the previous two non-redundant : 2576609
% 167.18/34.10 % ...aggressively subsumed : 0
% 167.18/34.10 % Contextual simplify-reflections : 4
% 167.18/34.10 % Paramodulations : 3065207
% 167.18/34.10 % Factorizations : 0
% 167.18/34.10 % NegExts : 0
% 167.18/34.10 % Equation resolutions : 0
% 167.18/34.10 % Disequality decompositions : 0
% 167.18/34.10 % Total rewrite steps : 503643
% 167.18/34.10 % ...of those cached : 444380
% 167.18/34.10 % Propositional unsat checks : 0
% 167.18/34.10 % Propositional check models : 0
% 167.18/34.10 % Propositional check unsatisfiable : 0
% 167.18/34.10 % Propositional clauses : 0
% 167.18/34.10 % Propositional clauses after purity: 0
% 167.18/34.10 % Propositional unsat core size : 0
% 167.18/34.10 % Propositional preprocessing time : 0.000
% 167.18/34.10 % Propositional encoding time : 0.000
% 167.18/34.10 % Propositional solver time : 0.000
% 167.18/34.10 % Success case prop preproc time : 0.000
% 167.18/34.10 % Success case prop encoding time : 0.000
% 167.18/34.10 % Success case prop solver time : 0.000
% 167.18/34.10 % Current number of processed clauses : 6905
% 167.18/34.10 % Positive orientable unit clauses : 2559
% 167.18/34.10 % Positive unorientable unit clauses: 0
% 167.18/34.10 % Negative unit clauses : 17
% 167.18/34.10 % Non-unit-clauses : 4329
% 167.18/34.10 % Current number of unprocessed clauses: 2452382
% 167.18/34.10 % ...number of literals in the above : 4695191
% 167.18/34.10 % Current number of archived formulas : 0
% 167.18/34.10 % Current number of archived clauses : 724
% 167.18/34.10 % Clause-clause subsumption calls (NU) : 13449648
% 167.18/34.10 % Rec. Clause-clause subsumption calls : 10458781
% 167.18/34.10 % Non-unit clause-clause subsumptions : 98241
% 167.18/34.10 % Unit Clause-clause subsumption calls : 603423
% 167.18/34.10 % Rewrite failures with RHS unbound : 0
% 167.18/34.10 % BW rewrite match attempts : 1796400
% 167.18/34.10 % BW rewrite match successes : 291
% 167.18/34.10 % Condensation attempts : 0
% 167.18/34.10 % Condensation successes : 0
% 167.18/34.10 % Termbank termtop insertions : 52747686
% 167.18/34.10 % Search garbage collected termcells : 30
% 167.18/34.10
% 167.18/34.10 % -------------------------------------------------
% 167.18/34.10 % User time : 32.032 s
% 167.18/34.10 % System time : 1.098 s
% 167.18/34.10 % Total time : 33.130 s
% 167.18/34.10 % Maximum resident set size: 3380 pages
% 167.18/34.10
% 167.18/34.10 % -------------------------------------------------
% 167.18/34.10 % User time : 161.872 s
% 167.18/34.10 % System time : 5.395 s
% 167.18/34.10 % Total time : 167.267 s
% 167.18/34.10 % Maximum resident set size: 4608 pages
% 167.18/34.10 % E exiting
%------------------------------------------------------------------------------