%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL077-2 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 04:39:20 PM UTC 2026
% Result : Unsatisfiable 0.99s 1.62s
% Output : CNFRefutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of clauses : 113 ( 66 unt; 0 nHn; 44 RR)
% Number of literals : 195 ( 0 equ; 89 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 277 ( 62 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cn_35,axiom,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_35) ).
cnf(cn_49,axiom,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_49) ).
cnf(transitivity,axiom,
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
cnf(cn_18,axiom,
is_a_theorem(implies(X1,implies(X2,X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cn_18) ).
cnf(prove_cn_39,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_39) ).
cnf(condensed_detachment,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(i_0_6,axiom,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
cn_35,
[final] ).
cnf(i_0_7,axiom,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
cn_49,
[final] ).
cnf(i_0_8,axiom,
( is_a_theorem(implies(X1,X3))
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X2,X3)) ),
transitivity,
[final] ).
cnf(i_0_9,axiom,
is_a_theorem(implies(X1,implies(X2,X1))),
cn_18,
[final] ).
cnf(i_0_10,negated_conjecture,
~ is_a_theorem(implies(not(not(a)),a)),
prove_cn_39,
[final] ).
cnf(i_0_11,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
condensed_detachment,
[final] ).
cnf(i_0_12,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(scs_inference,[],[i_0_7,i_0_9,i_0_8]) ).
cnf(i_0_13,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_14,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_15,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),not(X3)),implies(X3,X2)))),
inference(scs_inference,[],[i_0_7,i_0_9,i_0_13,i_0_8,i_0_11]) ).
cnf(i_0_16,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_17,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_18,plain,
is_a_theorem(implies(not(X1),implies(implies(X1,X2),implies(X1,X3)))),
inference(scs_inference,[],[i_0_12,i_0_6,i_0_8]) ).
cnf(i_0_19,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_20,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_21,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_22,plain,
~ is_a_theorem(not(not(not(a)))),
inference(scs_inference,[],[i_0_10,i_0_12,i_0_20,i_0_6,i_0_8,i_0_11]) ).
cnf(i_0_23,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_24,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_25,plain,
is_a_theorem(implies(implies(not(X1),implies(X1,X2)),implies(not(X1),implies(X1,X3)))),
inference(scs_inference,[],[i_0_18,i_0_6,i_0_11]) ).
cnf(i_0_26,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_27,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_28,plain,
is_a_theorem(implies(not(not(X1)),implies(X2,X1))),
inference(scs_inference,[],[i_0_18,i_0_12,i_0_6,i_0_7,i_0_11,i_0_8]) ).
cnf(i_0_29,plain,
is_a_theorem(implies(not(X1),implies(X1,X2))),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_30,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_31,plain,
~ is_a_theorem(not(not(a))),
inference(scs_inference,[],[i_0_10,i_0_28,i_0_11]) ).
cnf(i_0_32,plain,
is_a_theorem(implies(not(not(X1)),implies(X2,X1))),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_33,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_34,plain,
is_a_theorem(implies(not(not(X1)),implies(X2,implies(X3,X1)))),
inference(scs_inference,[],[i_0_10,i_0_28,i_0_32,i_0_9,i_0_11,i_0_8]) ).
cnf(i_0_35,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_36,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_37,plain,
is_a_theorem(implies(not(not(not(X1))),implies(X1,X2))),
inference(scs_inference,[],[i_0_28,i_0_7,i_0_8]) ).
cnf(i_0_38,plain,
is_a_theorem(implies(not(not(X1)),implies(X2,X1))),
inference(rename_variables,[],[i_0_28]) ).
cnf(i_0_39,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_40,plain,
( ~ is_a_theorem(not(not(X1)))
| is_a_theorem(implies(X2,implies(X3,X1))) ),
inference(scs_inference,[],[i_0_34,i_0_28,i_0_7,i_0_8,i_0_11]) ).
cnf(i_0_41,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_42,plain,
( ~ is_a_theorem(not(X1))
| is_a_theorem(implies(implies(X1,X2),implies(X1,X3))) ),
inference(scs_inference,[],[i_0_18,i_0_11]) ).
cnf(i_0_43,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_44,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X2,X4))))
| ~ is_a_theorem(implies(X1,not(X2))) ),
inference(scs_inference,[],[i_0_18,i_0_11,i_0_8]) ).
cnf(i_0_45,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_46,plain,
( is_a_theorem(implies(X1,implies(X2,implies(X3,X4))))
| ~ is_a_theorem(implies(X1,not(not(X4)))) ),
inference(scs_inference,[],[i_0_34,i_0_8]) ).
cnf(i_0_47,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_48,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,not(X2))) ),
inference(scs_inference,[],[i_0_12,i_0_8]) ).
cnf(i_0_49,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_50,plain,
~ is_a_theorem(implies(implies(not(not(X1)),implies(X2,implies(X3,X1))),not(not(not(a))))),
inference(scs_inference,[],[i_0_10,i_0_34,i_0_12,i_0_8,i_0_11]) ).
cnf(i_0_51,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,not(not(X3)))) ),
inference(scs_inference,[],[i_0_28,i_0_8]) ).
cnf(i_0_52,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_53,plain,
~ is_a_theorem(implies(implies(not(X1),implies(implies(X1,X2),implies(X1,X3))),not(not(a)))),
inference(scs_inference,[],[i_0_10,i_0_18,i_0_28,i_0_8,i_0_11]) ).
cnf(i_0_54,plain,
is_a_theorem(implies(implies(not(implies(X1,X2)),not(X3)),implies(implies(X3,X1),implies(X3,X2)))),
inference(scs_inference,[],[i_0_7,i_0_6,i_0_8]) ).
cnf(i_0_55,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_56,plain,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X2,X1))),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_57,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_58,plain,
( ~ is_a_theorem(implies(not(implies(X1,X2)),not(X3)))
| is_a_theorem(implies(implies(X3,X1),implies(X3,X2))) ),
inference(scs_inference,[],[i_0_7,i_0_6,i_0_8,i_0_11]) ).
cnf(i_0_59,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_60,plain,
is_a_theorem(implies(implies(not(X1),not(X2)),implies(X3,implies(X2,X1)))),
inference(scs_inference,[],[i_0_7,i_0_9,i_0_8]) ).
cnf(i_0_61,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_62,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_63,plain,
( ~ is_a_theorem(implies(not(X1),not(X2)))
| is_a_theorem(implies(X3,implies(X2,X1))) ),
inference(scs_inference,[],[i_0_7,i_0_9,i_0_8,i_0_11]) ).
cnf(i_0_64,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_65,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,X1))),
inference(scs_inference,[],[i_0_9,i_0_6,i_0_11]) ).
cnf(i_0_66,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_67,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_68,plain,
is_a_theorem(implies(not(X1),implies(X2,implies(X1,X3)))),
inference(scs_inference,[],[i_0_9,i_0_60,i_0_6,i_0_11,i_0_8]) ).
cnf(i_0_69,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_70,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_71,plain,
is_a_theorem(implies(X1,X1)),
inference(scs_inference,[],[i_0_9,i_0_65,i_0_11]) ).
cnf(i_0_72,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,X1))),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_73,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_74,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
inference(scs_inference,[],[i_0_9,i_0_6,i_0_65,i_0_11,i_0_8]) ).
cnf(i_0_75,plain,
is_a_theorem(implies(implies(X1,implies(X2,X3)),implies(implies(X1,X2),implies(X1,X3)))),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_76,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_77,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_78,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(scs_inference,[],[i_0_71,i_0_63]) ).
cnf(i_0_79,plain,
is_a_theorem(implies(X1,X1)),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_80,plain,
( ~ is_a_theorem(implies(not(X1),not(X2)))
| is_a_theorem(implies(X3,implies(X2,X1))) ),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_81,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2))),
inference(scs_inference,[],[i_0_54,i_0_71,i_0_79,i_0_63,i_0_11]) ).
cnf(i_0_82,plain,
is_a_theorem(implies(implies(not(implies(X1,X2)),not(X3)),implies(implies(X3,X1),implies(X3,X2)))),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_83,plain,
is_a_theorem(implies(X1,X1)),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_84,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_85,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X2,X1)))),
inference(scs_inference,[],[i_0_9,i_0_54,i_0_74,i_0_71,i_0_79,i_0_63,i_0_11,i_0_8]) ).
cnf(i_0_86,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_87,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_88,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X2)))),
inference(scs_inference,[],[i_0_9,i_0_74,i_0_11]) ).
cnf(i_0_89,plain,
is_a_theorem(implies(implies(X1,X2),implies(implies(X3,X1),implies(X3,X2)))),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_90,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_91,plain,
is_a_theorem(implies(X1,implies(X2,implies(X2,X1)))),
inference(scs_inference,[],[i_0_9,i_0_74,i_0_11,i_0_8]) ).
cnf(i_0_92,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_93,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),
inference(scs_inference,[],[i_0_78,i_0_81,i_0_11]) ).
cnf(i_0_94,plain,
is_a_theorem(implies(implies(implies(X1,X2),X1),implies(implies(X1,X2),X2))),
inference(rename_variables,[],[i_0_81]) ).
cnf(i_0_95,plain,
is_a_theorem(implies(X1,implies(X2,X2))),
inference(rename_variables,[],[i_0_78]) ).
cnf(i_0_96,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_97,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X1)))),
inference(scs_inference,[],[i_0_9,i_0_78,i_0_81,i_0_88,i_0_11,i_0_8]) ).
cnf(i_0_98,plain,
is_a_theorem(implies(implies(X1,X2),implies(X1,implies(X3,X2)))),
inference(rename_variables,[],[i_0_88]) ).
cnf(i_0_99,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_100,plain,
is_a_theorem(implies(implies(implies(X1,X1),not(X2)),implies(implies(X2,X3),implies(X2,X4)))),
inference(scs_inference,[],[i_0_9,i_0_78,i_0_81,i_0_88,i_0_11,i_0_8,i_0_44]) ).
cnf(i_0_101,plain,
( ~ is_a_theorem(implies(X1,not(X2)))
| is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X2,X4)))) ),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_102,plain,
is_a_theorem(implies(implies(implies(X1,X1),not(X2)),implies(X2,X3))),
inference(scs_inference,[],[i_0_9,i_0_78,i_0_81,i_0_88,i_0_11,i_0_8,i_0_44,i_0_48]) ).
cnf(i_0_103,plain,
( ~ is_a_theorem(implies(X1,not(X2)))
| is_a_theorem(implies(X1,implies(X2,X3))) ),
inference(rename_variables,[],[i_0_48]) ).
cnf(i_0_104,plain,
is_a_theorem(implies(implies(implies(X1,X1),not(not(X2))),implies(X3,X2))),
inference(scs_inference,[],[i_0_9,i_0_78,i_0_81,i_0_88,i_0_11,i_0_8,i_0_44,i_0_48,i_0_51]) ).
cnf(i_0_105,plain,
( ~ is_a_theorem(implies(X1,not(not(X2))))
| is_a_theorem(implies(X1,implies(X3,X2))) ),
inference(rename_variables,[],[i_0_51]) ).
cnf(i_0_106,plain,
~ is_a_theorem(implies(implies(X1,X1),not(not(a)))),
inference(scs_inference,[],[i_0_104,i_0_10,i_0_11]) ).
cnf(i_0_107,plain,
is_a_theorem(implies(implies(implies(X1,X1),not(not(X2))),implies(X3,X2))),
inference(rename_variables,[],[i_0_104]) ).
cnf(i_0_108,plain,
( ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1)
| is_a_theorem(X2) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_109,plain,
is_a_theorem(implies(implies(implies(X1,X1),not(X2)),implies(X3,implies(X2,X4)))),
inference(scs_inference,[],[i_0_104,i_0_68,i_0_10,i_0_93,i_0_11,i_0_8]) ).
cnf(i_0_110,plain,
is_a_theorem(implies(implies(implies(X1,X1),X2),X2)),
inference(rename_variables,[],[i_0_93]) ).
cnf(i_0_111,plain,
( ~ is_a_theorem(implies(X1,X2))
| is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_112,plain,
$false,
inference(scs_inference,[],[i_0_28,i_0_10,i_0_93,i_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL077-2 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n023.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 21:58:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.99/1.62 % Version : CSE_E---1.7
% 0.99/1.62 % Problem : theBenchmark.p
% 0.99/1.62 % SZS status Unsatisfiable for theBenchmark.p
% 0.99/1.62 % SZS output start CNFRefutation
% See solution above
% 1.09/1.76 % Total time : 1.271s
%------------------------------------------------------------------------------