%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:48:40 AM UTC 2026
% Result : Unsatisfiable 26.78s 27.11s
% Output : Proof 26.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 4
% Syntax : Number of clauses : 51 ( 39 unt; 0 nHn; 49 RR)
% Number of literals : 75 ( 0 equ; 26 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(condensed_detachment,axiom,
( is_a_theorem(Y)
| ~ is_a_theorem(X)
| ~ is_a_theorem(equivalent(X,Y)) ),
file('theBenchmark.p',condensed_detachment) ).
cnf(p_4,axiom,
is_a_theorem(equivalent(X,equivalent(equivalent(equivalent(equivalent(Y,Z),equivalent(Y,U)),equivalent(Z,U)),X))),
file('theBenchmark.p',p_4) ).
cnf(q_3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(X,Y),equivalent(equivalent(Y,X),Z)),Z)),
file('theBenchmark.p',q_3) ).
cnf(prove_p_1,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
file('theBenchmark.p',prove_p_1) ).
cnf(t1,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(start,[status(thm),parent(0:0)],[prove_p_1]) ).
cnf(t2,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))) ),
inference(extension,[status(thm),parent(t1:1)],[condensed_detachment]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))) ),
inference(extension,[status(thm),parent(t2:2)],[condensed_detachment]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))) ),
inference(extension,[status(thm),parent(t4:2)],[condensed_detachment]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))),
inference(extension,[status(thm),parent(t6:2)],[q_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))),
inference(extension,[status(thm),parent(t6:3)],[p_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),
inference(extension,[status(thm),parent(t4:3)],[q_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))) ),
inference(extension,[status(thm),parent(t2:3)],[condensed_detachment]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t2:3]) ).
cnf(t16,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))) ),
inference(extension,[status(thm),parent(t14:2)],[condensed_detachment]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))) ),
inference(extension,[status(thm),parent(t16:2)],[condensed_detachment]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))))),
inference(extension,[status(thm),parent(t18:2)],[q_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))))),
inference(extension,[status(thm),parent(t18:3)],[p_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(e,b)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),
inference(extension,[status(thm),parent(t16:3)],[p_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t16:3]) ).
cnf(t26,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))) ),
inference(extension,[status(thm),parent(t14:3)],[condensed_detachment]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t14:3]) ).
cnf(t28,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))) ),
inference(extension,[status(thm),parent(t26:2)],[condensed_detachment]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))) ),
inference(extension,[status(thm),parent(t28:2)],[condensed_detachment]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))),
inference(extension,[status(thm),parent(t30:2)],[q_3]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))))),
inference(extension,[status(thm),parent(t30:3)],[p_4]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t30:3]) ).
cnf(t36,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))) ),
inference(extension,[status(thm),parent(t28:3)],[condensed_detachment]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t28:3]) ).
cnf(t38,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))))),
inference(extension,[status(thm),parent(t36:2)],[q_3]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c)))),equivalent(equivalent(equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(equivalent(e,b),equivalent(equivalent(a,e),equivalent(a,b))),equivalent(equivalent(e,b),equivalent(equivalent(a,e),c))))))),
inference(extension,[status(thm),parent(t36:3)],[p_4]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t36:3]) ).
cnf(t42,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)))) ),
inference(extension,[status(thm),parent(t26:3)],[condensed_detachment]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t26:3]) ).
cnf(t44,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))))),
inference(extension,[status(thm),parent(t42:2)],[q_3]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c))),equivalent(equivalent(equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,e),equivalent(a,b)),equivalent(equivalent(a,e),c)))))),
inference(extension,[status(thm),parent(t42:3)],[p_4]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t42:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL104-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 19 14:06:49 UTC 2026
% 0.09/0.34 % CPUTime :
% 26.78/27.11 % SZS status Unsatisfiable for theBenchmark
% 26.78/27.11 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------