%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 08:48:31 AM UTC 2026
% Result : Unsatisfiable 2.55s 13.08s
% Output : Proof 2.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 90 ( 68 unt; 0 nHn; 89 RR)
% Number of literals : 134 ( 0 equ; 46 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 10 ( 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 : 5 ( 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(yql,axiom,
is_a_theorem(equivalent(equivalent(X,Y),equivalent(equivalent(Z,Y),equivalent(X,Z)))),
file('theBenchmark.p',yql) ).
cnf(prove_ec_5,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
file('theBenchmark.p',prove_ec_5) ).
cnf(t1,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))),
inference(start,[status(thm),parent(0:0)],[prove_ec_5]) ).
cnf(t2,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,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(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,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(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,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(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))))),
inference(extension,[status(thm),parent(t6:2)],[yql]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( ~ is_a_theorem(equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a)))) ),
inference(extension,[status(thm),parent(t6:3)],[condensed_detachment]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))))),
inference(extension,[status(thm),parent(t10:2)],[yql]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
is_a_theorem(equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))))),
inference(extension,[status(thm),parent(t10:3)],[yql]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a)))) ),
inference(extension,[status(thm),parent(t4:3)],[condensed_detachment]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:3]) ).
cnf(t18,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))))) ),
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(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a)))))) ),
inference(extension,[status(thm),parent(t18:2)],[condensed_detachment]) ).
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(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))))))),
inference(extension,[status(thm),parent(t20:2)],[yql]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))))),
inference(extension,[status(thm),parent(t20:3)],[yql]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t20:3]) ).
cnf(t26,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c)))))) ),
inference(extension,[status(thm),parent(t18:3)],[condensed_detachment]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t18:3]) ).
cnf(t28,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,b),c),equivalent(a,equivalent(b,c))))))),
inference(extension,[status(thm),parent(t26:2)],[yql]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),a)))),
inference(extension,[status(thm),parent(t26:3)],[yql]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t26:3]) ).
cnf(t32,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))))
| is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))) ),
inference(extension,[status(thm),parent(t16:3)],[condensed_detachment]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t16:3]) ).
cnf(t34,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))) ),
inference(extension,[status(thm),parent(t32:2)],[condensed_detachment]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))),equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))))),
inference(extension,[status(thm),parent(t34:2)],[yql]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,b),c),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a)))),
inference(extension,[status(thm),parent(t34:3)],[yql]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t34:3]) ).
cnf(t40,plain,
( ~ is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,c),equivalent(a,b))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a)))) ),
inference(extension,[status(thm),parent(t32:3)],[condensed_detachment]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t32:3]) ).
cnf(t42,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,c),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))),equivalent(equivalent(a,c),equivalent(equivalent(a,b),a))))),
inference(extension,[status(thm),parent(t40:2)],[yql]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
is_a_theorem(equivalent(equivalent(a,c),equivalent(equivalent(b,c),equivalent(a,b)))),
inference(extension,[status(thm),parent(t40:3)],[yql]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t40:3]) ).
cnf(t46,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))),equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))))))
| is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))))) ),
inference(extension,[status(thm),parent(t2:3)],[condensed_detachment]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t2:3]) ).
cnf(t48,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))),equivalent(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))),equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))),equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c)))))) ),
inference(extension,[status(thm),parent(t46:2)],[condensed_detachment]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t46:2]) ).
cnf(t50,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))),equivalent(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))),equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))))))),
inference(extension,[status(thm),parent(t48:2)],[yql]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))))
| is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))) ),
inference(extension,[status(thm),parent(t48:3)],[condensed_detachment]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t48:3]) ).
cnf(t54,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))))) ),
inference(extension,[status(thm),parent(t52:2)],[condensed_detachment]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t52:2]) ).
cnf(t56,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))))),
inference(extension,[status(thm),parent(t54:2)],[yql]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t54:2]) ).
cnf(t58,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),a),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))),
inference(extension,[status(thm),parent(t54:3)],[yql]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t54:3]) ).
cnf(t60,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))) ),
inference(extension,[status(thm),parent(t52:3)],[condensed_detachment]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t52:3]) ).
cnf(t62,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))),
inference(extension,[status(thm),parent(t60:2)],[yql]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
is_a_theorem(equivalent(equivalent(equivalent(b,c),a),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))),
inference(extension,[status(thm),parent(t60:3)],[yql]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t60:3]) ).
cnf(t66,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))) ),
inference(extension,[status(thm),parent(t46:3)],[condensed_detachment]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t46:3]) ).
cnf(t68,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b))))))) ),
inference(extension,[status(thm),parent(t66:2)],[condensed_detachment]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t66:2]) ).
cnf(t70,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))))))),
inference(extension,[status(thm),parent(t68:2)],[yql]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))),
inference(extension,[status(thm),parent(t68:3)],[yql]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t68:3]) ).
cnf(t74,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))) ),
inference(extension,[status(thm),parent(t66:3)],[condensed_detachment]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t66:3]) ).
cnf(t76,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))))) ),
inference(extension,[status(thm),parent(t74:2)],[condensed_detachment]) ).
cnf(t77,plain,
$false,
inference(connection,[status(thm),parent(t76:1)],[t76:1,t74:2]) ).
cnf(t78,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))))),
inference(extension,[status(thm),parent(t76:2)],[yql]) ).
cnf(t79,plain,
$false,
inference(connection,[status(thm),parent(t78:1)],[t78:1,t76:2]) ).
cnf(t80,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c)))))),
inference(extension,[status(thm),parent(t76:3)],[yql]) ).
cnf(t81,plain,
$false,
inference(connection,[status(thm),parent(t80:1)],[t80:1,t76:3]) ).
cnf(t82,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c)))))) ),
inference(extension,[status(thm),parent(t74:3)],[condensed_detachment]) ).
cnf(t83,plain,
$false,
inference(connection,[status(thm),parent(t82:1)],[t82:1,t74:3]) ).
cnf(t84,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c)),equivalent(a,equivalent(b,c))))))),
inference(extension,[status(thm),parent(t82:2)],[yql]) ).
cnf(t85,plain,
$false,
inference(connection,[status(thm),parent(t84:1)],[t84:1,t82:2]) ).
cnf(t86,plain,
is_a_theorem(equivalent(equivalent(equivalent(a,equivalent(b,c)),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(equivalent(b,c),equivalent(equivalent(equivalent(a,b),a),equivalent(equivalent(b,c),equivalent(a,b)))),equivalent(equivalent(a,equivalent(b,c)),equivalent(b,c))))),
inference(extension,[status(thm),parent(t82:3)],[yql]) ).
cnf(t87,plain,
$false,
inference(connection,[status(thm),parent(t86:1)],[t86:1,t82:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL009-1 : 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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.59 % Computer : n013.cluster.edu
% 0.10/10.59 % Model : x86_64 x86_64
% 0.10/10.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.59 % Memory : 8046.5625MB
% 0.10/10.59 % OS : Linux 6.8.0-71-generic
% 0.10/10.59 % CPULimit : 300
% 0.10/10.59 % WCLimit : 300
% 0.10/10.59 % DateTime : Sat Sep 19 13:54:54 UTC 2026
% 0.10/10.60 % CPUTime :
% 2.55/13.08 % SZS status Unsatisfiable for theBenchmark
% 2.55/13.08 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------