%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL122-1 : TPTP v9.2.1. Bugfixed v2.3.0.
% 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 : n022.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 04:39:28 PM UTC 2026
% Result : Unsatisfiable 1.67s 1.84s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 3
% Syntax : Number of clauses : 56 ( 14 unt; 0 nHn; 45 RR)
% Number of literals : 134 ( 0 equ; 112 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 142 ( 25 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(lg_2,axiom,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lg_2) ).
cnf(prove_lg_3,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,e)),equivalent(b,equivalent(equivalent(c,f),equivalent(e,f))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_3) ).
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(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))),
lg_2 ).
cnf(c_0_5,plain,
( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).
cnf(c_0_6,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3))))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_3,c_0_5]) ).
cnf(c_0_7,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
| ~ is_a_theorem(equivalent(X1,X3))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_3,c_0_6]) ).
cnf(c_0_8,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,e)),equivalent(b,equivalent(equivalent(c,f),equivalent(e,f))))))),
prove_lg_3 ).
cnf(c_0_9,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X3,X2))
| ~ is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(equivalent(b,equivalent(c,e)),equivalent(b,equivalent(equivalent(c,f),equivalent(e,f)))))))
| ~ is_a_theorem(equivalent(X1,a))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_11,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(a,equivalent(equivalent(b,equivalent(c,e)),equivalent(b,equivalent(equivalent(c,f),equivalent(e,f)))))))
| ~ is_a_theorem(equivalent(X1,a)) ),
inference(spm,[status(thm)],[c_0_10,c_0_4]) ).
cnf(c_0_12,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(b,equivalent(c,e)),equivalent(b,equivalent(equivalent(c,f),equivalent(e,f))))),a))
| ~ is_a_theorem(equivalent(X1,a))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_13,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(b,equivalent(c,e)),equivalent(b,equivalent(equivalent(c,f),equivalent(e,f))))),a))
| ~ is_a_theorem(equivalent(X1,a)) ),
inference(spm,[status(thm)],[c_0_12,c_0_4]) ).
cnf(c_0_14,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(b,equivalent(c,e)),equivalent(b,equivalent(equivalent(c,f),equivalent(e,f)))))))
| ~ is_a_theorem(equivalent(X2,a))
| ~ is_a_theorem(equivalent(X1,a))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_9]) ).
cnf(c_0_15,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(b,equivalent(c,e)),equivalent(b,equivalent(equivalent(c,f),equivalent(e,f)))))))
| ~ is_a_theorem(equivalent(X2,a))
| ~ is_a_theorem(equivalent(X1,a)) ),
inference(spm,[status(thm)],[c_0_14,c_0_4]) ).
cnf(c_0_16,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(equivalent(c,f),equivalent(e,f)))),a))
| ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(c,e))),a))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_15,c_0_6]) ).
cnf(c_0_17,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(equivalent(c,f),equivalent(e,f)))),a))
| ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(c,e))),a)) ),
inference(spm,[status(thm)],[c_0_16,c_0_4]) ).
cnf(c_0_18,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(b,equivalent(equivalent(c,f),equivalent(e,f))))))
| ~ is_a_theorem(equivalent(equivalent(X2,equivalent(b,equivalent(c,e))),a))
| ~ is_a_theorem(equivalent(X1,a))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(b,equivalent(equivalent(c,f),equivalent(e,f))))))
| ~ is_a_theorem(equivalent(equivalent(X2,equivalent(b,equivalent(c,e))),a))
| ~ is_a_theorem(equivalent(X1,a)) ),
inference(spm,[status(thm)],[c_0_18,c_0_4]) ).
cnf(c_0_20,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
| ~ is_a_theorem(equivalent(X1,X3)) ),
inference(spm,[status(thm)],[c_0_7,c_0_4]) ).
cnf(c_0_21,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X3,X2))
| ~ is_a_theorem(equivalent(X3,X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_4]) ).
cnf(c_0_22,plain,
is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X1,X3),equivalent(X2,X3)))),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_23,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(equivalent(c,f),equivalent(e,f)))),a))
| ~ is_a_theorem(equivalent(equivalent(X2,equivalent(b,equivalent(c,e))),a))
| ~ is_a_theorem(equivalent(X1,X2)) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),X4))
| ~ is_a_theorem(equivalent(equivalent(X1,X3),X4)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(b,equivalent(equivalent(c,f),equivalent(e,f)))),a))
| ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(c,e))))
| ~ is_a_theorem(equivalent(equivalent(X2,b),a)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(c,f),equivalent(e,f))),equivalent(X2,equivalent(c,e))))
| ~ is_a_theorem(equivalent(equivalent(X2,b),a))
| ~ is_a_theorem(equivalent(equivalent(X1,b),a)) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_27,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(c,f)),equivalent(X2,equivalent(c,e))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(e,f)),b),a))
| ~ is_a_theorem(equivalent(equivalent(X2,b),a)) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_28,plain,
( is_a_theorem(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3))))
| ~ is_a_theorem(equivalent(equivalent(X2,X4),X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(e,f)),b),a))
| ~ is_a_theorem(equivalent(equivalent(X2,c),equivalent(X1,equivalent(c,f))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,e),b),a)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,f),equivalent(e,f)),b),a))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X1,e),b),a)) ),
inference(spm,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_31,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(equivalent(X2,X3))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_3,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X2,f),equivalent(e,f)),b)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,e),b),a))
| ~ is_a_theorem(equivalent(X1,a)) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_33,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(equivalent(X3,X4))
| ~ is_a_theorem(equivalent(X3,X2))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_34,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,f),equivalent(e,f))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,e),b),a))
| ~ is_a_theorem(equivalent(equivalent(X1,b),a)) ),
inference(spm,[status(thm)],[c_0_32,c_0_20]) ).
cnf(c_0_35,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(X2,X1))
| ~ is_a_theorem(equivalent(X3,X2))
| ~ is_a_theorem(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_5]),c_0_22])]) ).
cnf(c_0_36,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(X1,e),b),a)),
inference(spm,[status(thm)],[c_0_34,c_0_22]) ).
cnf(c_0_37,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X3,X2),X4))
| ~ is_a_theorem(equivalent(X3,X1))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_31,c_0_20]) ).
cnf(c_0_38,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,X3),equivalent(X4,X3)),X1))
| ~ is_a_theorem(equivalent(X2,X4)) ),
inference(spm,[status(thm)],[c_0_35,c_0_22]) ).
cnf(c_0_39,negated_conjecture,
( ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X2,e),b)))
| ~ is_a_theorem(equivalent(equivalent(X1,a),X3))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_40,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X4,X2),X3)))
| ~ is_a_theorem(equivalent(X1,X4)) ),
inference(spm,[status(thm)],[c_0_38,c_0_22]) ).
cnf(c_0_41,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,e),b),a),X2))
| ~ is_a_theorem(equivalent(X1,X3))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_42,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,e),b),a),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_41,c_0_4]) ).
cnf(c_0_43,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,e),b),X2),equivalent(a,X2))),
inference(spm,[status(thm)],[c_0_42,c_0_22]) ).
cnf(c_0_44,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(X1,e),X2),equivalent(a,equivalent(X2,b)))),
inference(spm,[status(thm)],[c_0_43,c_0_24]) ).
cnf(c_0_45,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(a,equivalent(equivalent(X2,e),b)))),
inference(spm,[status(thm)],[c_0_44,c_0_24]) ).
cnf(c_0_46,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(equivalent(X4,X3),X1))
| ~ is_a_theorem(equivalent(X4,X2)) ),
inference(spm,[status(thm)],[c_0_21,c_0_20]) ).
cnf(c_0_47,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,e),b)),equivalent(X3,X2)))
| ~ is_a_theorem(equivalent(X1,a)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_48,negated_conjecture,
~ is_a_theorem(equivalent(X1,a)),
inference(spm,[status(thm)],[c_0_47,c_0_4]) ).
cnf(c_0_49,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,a),X2))
| ~ is_a_theorem(equivalent(X1,X3))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_37]) ).
cnf(c_0_50,negated_conjecture,
( ~ is_a_theorem(equivalent(equivalent(X1,a),X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_49,c_0_4]) ).
cnf(c_0_51,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(a,X2))),
inference(spm,[status(thm)],[c_0_50,c_0_22]) ).
cnf(c_0_52,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(X1,X2),equivalent(a,equivalent(X2,X3)))),
inference(spm,[status(thm)],[c_0_51,c_0_24]) ).
cnf(c_0_53,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,equivalent(equivalent(X3,X4),equivalent(equivalent(X3,X5),equivalent(X4,X5))))))
| ~ is_a_theorem(equivalent(X2,X1)) ),
inference(spm,[status(thm)],[c_0_21,c_0_4]) ).
cnf(c_0_54,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(X1,equivalent(X2,X3)))),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(spm,[status(thm)],[c_0_54,c_0_4]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL122-1 : TPTP v9.2.1. Bugfixed v2.3.0.
% 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
% 0.14/0.32 % Computer : n022.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 22:01:51 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.67/1.84 % Version : CSE_E---1.7
% 1.67/1.84 % Problem : theBenchmark.p
% 1.67/1.84 % SZS status Unsatisfiable for theBenchmark.p
% 1.67/1.84 % SZS output start CNFRefutation
% See solution above
% 1.67/1.84 % Total time : 1.370s
%------------------------------------------------------------------------------