%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL098-1 : 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 : n012.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 08:48:39 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.35s
% Output : Proof 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 3
% Syntax : Number of clauses : 30 ( 23 unt; 0 nHn; 29 RR)
% Number of literals : 44 ( 0 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 7 ( 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(lg_3,axiom,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(X,Y),equivalent(X,Z)),U),equivalent(equivalent(Y,Z),U)),V),V)),
file('theBenchmark.p',lg_3) ).
cnf(prove_lg_4,negated_conjecture,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
file('theBenchmark.p',prove_lg_4) ).
cnf(t1,plain,
~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),
inference(start,[status(thm),parent(0:0)],[prove_lg_4]) ).
cnf(t2,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))) ),
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(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))) ),
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(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),
inference(extension,[status(thm),parent(t4:2)],[lg_3]) ).
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(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))) ),
inference(extension,[status(thm),parent(t4:3)],[condensed_detachment]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))) ),
inference(extension,[status(thm),parent(t8:2)],[condensed_detachment]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))))),
inference(extension,[status(thm),parent(t10:2)],[lg_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))))),
inference(extension,[status(thm),parent(t10:3)],[lg_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(a,b),c),e),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),
inference(extension,[status(thm),parent(t8:3)],[lg_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t8:3]) ).
cnf(t18,plain,
( ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))) ),
inference(extension,[status(thm),parent(t2:3)],[condensed_detachment]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t2:3]) ).
cnf(t20,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),
inference(extension,[status(thm),parent(t18:2)],[lg_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(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))))
| ~ is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))))
| is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))) ),
inference(extension,[status(thm),parent(t18:3)],[condensed_detachment]) ).
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(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))),
inference(extension,[status(thm),parent(t22:2)],[lg_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
is_a_theorem(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e)))))),equivalent(equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e),equivalent(equivalent(b,falsehood),e)),equivalent(equivalent(equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),equivalent(equivalent(a,b),c)),equivalent(equivalent(equivalent(a,b),equivalent(a,falsehood)),e)),equivalent(equivalent(equivalent(a,falsehood),c),equivalent(equivalent(b,falsehood),e))))))),
inference(extension,[status(thm),parent(t22:3)],[lg_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL098-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.01 This is a CNF_UNS_RFO_NEQ_HRN problem
% 0.00/0.02 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Sat Sep 19 14:05:57 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.08/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.35 % SZS output start Proof for theBenchmark
% See solution above
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