%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL020-1 : TPTP v9.2.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n031.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 04:39:12 PM UTC 2026
% Result : Unsatisfiable 6.22s 4.57s
% Output : CNFRefutation 6.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 3
% Syntax : Number of clauses : 99 ( 29 unt; 0 nHn; 51 RR)
% Number of literals : 202 ( 0 equ; 105 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 279 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(xhk,axiom,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X1,X3),X2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xhk) ).
cnf(prove_xgk,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(c,b)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xgk) ).
cnf(c_0_3,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X1) ),
condensed_detachment ).
cnf(c_0_4,axiom,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X1,X3),X2)))),
xhk ).
cnf(c_0_5,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X1)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X3))
| ~ is_a_theorem(equivalent(X3,X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,X3))
| ~ is_a_theorem(equivalent(X1,X3))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_3,c_0_6]) ).
cnf(c_0_8,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),X4)))
| ~ is_a_theorem(equivalent(X4,X3))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_7,c_0_5]) ).
cnf(c_0_9,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_4]) ).
cnf(c_0_10,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,X3))
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_9,c_0_6]) ).
cnf(c_0_11,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X3),equivalent(equivalent(X4,X3),X2)))
| ~ is_a_theorem(equivalent(X1,X4)) ),
inference(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_12,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X4,X3),X2))))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_13,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_5]) ).
cnf(c_0_14,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),X2))
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_5]) ).
cnf(c_0_15,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X3))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1)
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_16,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_17,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X3),equivalent(equivalent(X1,X3),X2))) ),
inference(spm,[status(thm)],[c_0_13,c_0_4]) ).
cnf(c_0_18,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(X2)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_4]) ).
cnf(c_0_19,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X3,X2),X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_5]) ).
cnf(c_0_20,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X1,X2),X3))
| ~ is_a_theorem(equivalent(X3,X2)) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X4),X2),X1)),X4))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_4]) ).
cnf(c_0_22,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X3,equivalent(equivalent(equivalent(X4,X3),X2),X1)))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X1)),X2))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_22,c_0_4]) ).
cnf(c_0_24,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X1),equivalent(X3,X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_23]) ).
cnf(c_0_25,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_23]) ).
cnf(c_0_26,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,equivalent(X2,X1)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_27,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,X3),equivalent(equivalent(equivalent(X1,X4),X3),X2)),X4)) ),
inference(spm,[status(thm)],[c_0_20,c_0_4]) ).
cnf(c_0_28,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X2),X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_26,c_0_4]) ).
cnf(c_0_29,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X2),X3))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_27,c_0_14]) ).
cnf(c_0_30,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,equivalent(X3,X1)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_23]) ).
cnf(c_0_31,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X2),X1)),
inference(spm,[status(thm)],[c_0_28,c_0_4]) ).
cnf(c_0_32,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X3),equivalent(equivalent(equivalent(equivalent(X1,X4),X4),X3),X2))) ),
inference(spm,[status(thm)],[c_0_29,c_0_4]) ).
cnf(c_0_33,plain,
( is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X1),X3),X3)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,equivalent(X2,X2))) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),X2)),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_36,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X2),X1)) ),
inference(spm,[status(thm)],[c_0_3,c_0_35]) ).
cnf(c_0_37,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X3,X3),X2),X1))),
inference(spm,[status(thm)],[c_0_36,c_0_4]) ).
cnf(c_0_38,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X3,X3),X2),X1)) ),
inference(spm,[status(thm)],[c_0_13,c_0_37]) ).
cnf(c_0_39,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),X1))
| ~ is_a_theorem(equivalent(X3,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_4]) ).
cnf(c_0_40,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,X1)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_41,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X1),X2),X3),equivalent(X3,X2))),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_42,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,X3),X1),X3))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_5]) ).
cnf(c_0_43,plain,
( is_a_theorem(equivalent(equivalent(X1,X1),X2))
| ~ is_a_theorem(equivalent(equivalent(X3,X2),X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_41]) ).
cnf(c_0_44,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X1)),X3)),
inference(spm,[status(thm)],[c_0_40,c_0_4]) ).
cnf(c_0_45,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X2),X3))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_46,plain,
is_a_theorem(equivalent(equivalent(X1,X1),equivalent(equivalent(equivalent(X2,X3),X3),X2))),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X2))
| ~ is_a_theorem(X3)
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_45]) ).
cnf(c_0_48,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X3,equivalent(equivalent(X3,X2),X1))) ),
inference(spm,[status(thm)],[c_0_20,c_0_44]) ).
cnf(c_0_49,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X2),X1),equivalent(X3,X3))),
inference(spm,[status(thm)],[c_0_40,c_0_46]) ).
cnf(c_0_50,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_4]) ).
cnf(c_0_51,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X2),X1),X3),X3)),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
( is_a_theorem(equivalent(X1,X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_19,c_0_50]) ).
cnf(c_0_53,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(equivalent(X2,X3),X3),X2),X1))),
inference(spm,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_54,plain,
is_a_theorem(equivalent(X1,X1)),
inference(spm,[status(thm)],[c_0_52,c_0_4]) ).
cnf(c_0_55,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X2,X3),X3)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_53]) ).
cnf(c_0_56,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),X3),X2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_46]),c_0_54])]) ).
cnf(c_0_57,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X2),equivalent(X3,X1)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_55]) ).
cnf(c_0_58,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X1),X2),equivalent(equivalent(X2,X3),X3))),
inference(spm,[status(thm)],[c_0_56,c_0_41]) ).
cnf(c_0_59,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X1,X3),X3),X2)) ),
inference(spm,[status(thm)],[c_0_48,c_0_57]) ).
cnf(c_0_60,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_40,c_0_31]) ).
cnf(c_0_61,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X2),equivalent(equivalent(X3,X3),X1))),
inference(spm,[status(thm)],[c_0_40,c_0_58]) ).
cnf(c_0_62,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(equivalent(X1,X2),X2),X3),X3))),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(X1,X3),X3))))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_61]) ).
cnf(c_0_64,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X1),X3),X3),X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_62]) ).
cnf(c_0_65,plain,
( is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_63]) ).
cnf(c_0_66,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X1),equivalent(equivalent(X2,X3),X3))) ),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_67,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X3),X2),X1)),
inference(spm,[status(thm)],[c_0_66,c_0_44]) ).
cnf(c_0_68,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X3),X2))),
inference(spm,[status(thm)],[c_0_40,c_0_67]) ).
cnf(c_0_69,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,X3),X2),X3))) ),
inference(spm,[status(thm)],[c_0_11,c_0_68]) ).
cnf(c_0_70,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X3,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_5]) ).
cnf(c_0_71,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),X3),X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_60]) ).
cnf(c_0_72,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X2),X3)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_73,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X3)),X2)) ),
inference(spm,[status(thm)],[c_0_71,c_0_55]) ).
cnf(c_0_74,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X2),X3))
| ~ is_a_theorem(equivalent(X1,X3)) ),
inference(spm,[status(thm)],[c_0_48,c_0_63]) ).
cnf(c_0_75,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X3),X2),X1),X3)) ),
inference(spm,[status(thm)],[c_0_64,c_0_72]) ).
cnf(c_0_76,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X1),X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_60]) ).
cnf(c_0_77,plain,
( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),X3)))
| ~ is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X1,X3))
| ~ is_a_theorem(equivalent(X3,X2)) ),
inference(spm,[status(thm)],[c_0_20,c_0_39]) ).
cnf(c_0_79,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X2,X1))),
inference(spm,[status(thm)],[c_0_75,c_0_44]) ).
cnf(c_0_80,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X2,X3),X3),X1),X2)) ),
inference(spm,[status(thm)],[c_0_76,c_0_77]) ).
cnf(c_0_81,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X2,X3),equivalent(X1,X3)))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_5]) ).
cnf(c_0_82,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X3))
| ~ is_a_theorem(equivalent(equivalent(X2,X1),X3)) ),
inference(spm,[status(thm)],[c_0_78,c_0_79]) ).
cnf(c_0_83,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X2,X3)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_21]) ).
cnf(c_0_84,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(X1,X2),X3))
| ~ is_a_theorem(equivalent(X2,X3)) ),
inference(spm,[status(thm)],[c_0_81,c_0_39]) ).
cnf(c_0_85,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(X3,X2)),X1)),
inference(spm,[status(thm)],[c_0_82,c_0_44]) ).
cnf(c_0_86,plain,
( is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X2)),X3))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_83]) ).
cnf(c_0_87,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),X3))
| ~ is_a_theorem(equivalent(equivalent(X3,X2),X1)) ),
inference(spm,[status(thm)],[c_0_84,c_0_85]) ).
cnf(c_0_88,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X3,X2),X3))) ),
inference(spm,[status(thm)],[c_0_59,c_0_86]) ).
cnf(c_0_89,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,X2),X3)),equivalent(X3,X2))),
inference(spm,[status(thm)],[c_0_87,c_0_44]) ).
cnf(c_0_90,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X1,X2),equivalent(X2,X3))),X3)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_91,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(equivalent(X2,X1),X3),X3))),
inference(spm,[status(thm)],[c_0_82,c_0_60]) ).
cnf(c_0_92,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X3,X2),X1),X3)) ),
inference(spm,[status(thm)],[c_0_84,c_0_44]) ).
cnf(c_0_93,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X3,X1))),X2)),
inference(spm,[status(thm)],[c_0_87,c_0_90]) ).
cnf(c_0_94,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(equivalent(X3,X2),X1)) ),
inference(spm,[status(thm)],[c_0_30,c_0_91]) ).
cnf(c_0_95,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X2,equivalent(X1,X3))),X3)),
inference(spm,[status(thm)],[c_0_92,c_0_93]) ).
cnf(c_0_96,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(equivalent(b,equivalent(c,a)),equivalent(c,b)))),
prove_xgk ).
cnf(c_0_97,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X1)),equivalent(X3,X2)))),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_98,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_96,c_0_97])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL020-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.33 % Computer : n031.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 21:54:08 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 6.22/4.57 % Version : CSE_E---1.7
% 6.22/4.57 % Problem : theBenchmark.p
% 6.22/4.57 % SZS status Unsatisfiable for theBenchmark.p
% 6.22/4.57 % SZS output start CNFRefutation
% See solution above
% 6.22/4.59 % Total time : 3.371s
%------------------------------------------------------------------------------