%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL121-1 : 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 : n026.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 4.09s 3.30s
% Output : CNFRefutation 4.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 3
% Syntax : Number of clauses : 40 ( 17 unt; 0 nHn; 17 RR)
% Number of literals : 70 ( 0 equ; 32 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 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 : 127 ( 1 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_1,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lg_1) ).
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(equivalent(X1,X3),equivalent(X2,X3)))),
inference(spm,[status(thm)],[c_0_6,c_0_4]) ).
cnf(c_0_8,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
| ~ is_a_theorem(equivalent(X1,X3)) ),
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_9,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_3,c_0_8]) ).
cnf(c_0_10,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_9,c_0_7]) ).
cnf(c_0_11,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
| ~ is_a_theorem(equivalent(equivalent(X1,X3),X4))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_3,c_0_10]) ).
cnf(c_0_12,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_9,c_0_8]) ).
cnf(c_0_13,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
| ~ is_a_theorem(equivalent(equivalent(X1,X4),equivalent(X3,X4))) ),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_14,plain,
( is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X4,X3)))
| ~ is_a_theorem(equivalent(X1,X4)) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_15,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X4),X2)))
| ~ is_a_theorem(equivalent(X1,equivalent(equivalent(X3,X5),equivalent(X4,X5)))) ),
inference(spm,[status(thm)],[c_0_13,c_0_5]) ).
cnf(c_0_16,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X3,X4),equivalent(X2,X4)))
| ~ is_a_theorem(equivalent(X3,X1)) ),
inference(spm,[status(thm)],[c_0_3,c_0_14]) ).
cnf(c_0_17,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),X3),equivalent(equivalent(X1,X2),X3))),
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_18,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(equivalent(X2,X3),X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_19,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(X3,X2)),equivalent(X1,X3))),
inference(spm,[status(thm)],[c_0_18,c_0_7]) ).
cnf(c_0_20,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X1,X3),equivalent(X2,X3))) ),
inference(spm,[status(thm)],[c_0_3,c_0_19]) ).
cnf(c_0_21,plain,
( is_a_theorem(equivalent(equivalent(X1,X2),equivalent(X3,X2)))
| ~ is_a_theorem(equivalent(X3,X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_8]) ).
cnf(c_0_22,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X2,X1)) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_23,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,X4),equivalent(X3,X4)),X1)) ),
inference(spm,[status(thm)],[c_0_9,c_0_19]) ).
cnf(c_0_24,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(equivalent(X2,X4),equivalent(X3,X4)))),X1)),
inference(spm,[status(thm)],[c_0_22,c_0_4]) ).
cnf(c_0_25,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),equivalent(X4,X3))),equivalent(X1,equivalent(X2,X4)))),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_26,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X4,X2)),equivalent(X1,equivalent(X4,X3)))),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_27,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X3,X2))
| ~ is_a_theorem(equivalent(X1,X3)) ),
inference(spm,[status(thm)],[c_0_3,c_0_21]) ).
cnf(c_0_28,plain,
is_a_theorem(equivalent(equivalent(X1,equivalent(X2,X2)),X1)),
inference(spm,[status(thm)],[c_0_20,c_0_26]) ).
cnf(c_0_29,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(X1,equivalent(X2,equivalent(X3,X3)))) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_30,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(X2,equivalent(X3,X3)),X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_26]) ).
cnf(c_0_31,plain,
( is_a_theorem(equivalent(X1,equivalent(X2,X3)))
| ~ is_a_theorem(equivalent(equivalent(X2,X4),equivalent(X1,equivalent(X4,X3)))) ),
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_32,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,equivalent(X2,X3)),equivalent(X3,X2)),X1)),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_33,plain,
is_a_theorem(equivalent(equivalent(equivalent(X1,X2),equivalent(equivalent(X3,X3),X2)),X1)),
inference(spm,[status(thm)],[c_0_30,c_0_7]) ).
cnf(c_0_34,plain,
is_a_theorem(equivalent(X1,equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X4)),equivalent(X3,X2)),X4))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,plain,
( is_a_theorem(equivalent(X1,X2))
| ~ is_a_theorem(equivalent(equivalent(equivalent(X2,equivalent(equivalent(X3,X3),X4)),X4),X1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_33]) ).
cnf(c_0_36,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(X1,equivalent(equivalent(X2,X3),X4)),equivalent(X3,X2)),X4),X1)),
inference(spm,[status(thm)],[c_0_22,c_0_34]) ).
cnf(c_0_37,negated_conjecture,
~ is_a_theorem(equivalent(a,equivalent(a,equivalent(equivalent(b,equivalent(c,c)),b)))),
prove_lg_1 ).
cnf(c_0_38,plain,
is_a_theorem(equivalent(X1,equivalent(X1,equivalent(equivalent(X2,equivalent(X3,X3)),X2)))),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL121-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n026.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Mon May 4 22:02:08 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 4.09/3.30 % Version : CSE_E---1.7
% 4.09/3.30 % Problem : theBenchmark.p
% 4.09/3.30 % SZS status Unsatisfiable for theBenchmark.p
% 4.09/3.30 % SZS output start CNFRefutation
% See solution above
% 4.09/3.31 % Total time : 2.371s
%------------------------------------------------------------------------------