%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL186-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 08:48:49 AM UTC 2026
% Result : Unsatisfiable 252.45s 252.97s
% Output : Proof 252.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 13
% Syntax : Number of clauses : 88 ( 57 unt; 0 nHn; 83 RR)
% Number of literals : 135 ( 43 equ; 49 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))),
file('LCL004-0.ax',axiom_1_3) ).
cnf(axiom_1_4,axiom,
axiom(implies(or(A,B),or(B,A))),
file('LCL004-0.ax',axiom_1_4) ).
cnf(axiom_1_6,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('LCL004-0.ax',axiom_1_6) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y),
file('LCL004-0.ax',implies_definition) ).
cnf(rule_1,axiom,
( ~ axiom(X)
| theorem(X) ),
file('LCL004-0.ax',rule_1) ).
cnf(rule_2,axiom,
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('LCL004-0.ax',rule_2) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(not(p),implies(p,q))),
file('theBenchmark.p',prove_this) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_2,axiom,
( Eq_x_1 = Eq_x_0
| Eq_x_0 != Eq_x_1 ),
theory(equality,[symmetry]) ).
cnf(equality_4,axiom,
( or(Eq_x_0,Eq_x_1) = or(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( not(Eq_x_0) = not(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( axiom(Eq_y_0)
| ~ axiom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_8,axiom,
( theorem(Eq_y_0)
| ~ theorem(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ theorem(implies(not(p),implies(p,q))),
inference(start,[status(thm),parent(0:0)],[prove_this]) ).
cnf(t2,plain,
( ~ theorem(or(not(not(p)),implies(p,q)))
| or(not(not(p)),implies(p,q)) != implies(not(p),implies(p,q))
| theorem(implies(not(p),implies(p,q))) ),
inference(extension,[status(thm),parent(t1:1)],[equality_8]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( implies(not(p),implies(p,q)) != or(not(not(p)),implies(p,q))
| or(not(not(p)),implies(p,q)) = implies(not(p),implies(p,q)) ),
inference(extension,[status(thm),parent(t2:2)],[equality_2]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
implies(not(p),implies(p,q)) = or(not(not(p)),implies(p,q)),
inference(extension,[status(thm),parent(t4:2)],[implies_definition]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ theorem(or(implies(p,q),not(not(p))))
| ~ theorem(implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q))))
| theorem(or(not(not(p)),implies(p,q))) ),
inference(extension,[status(thm),parent(t2:3)],[rule_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( ~ theorem(or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q))))
| or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q))) != implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q)))
| theorem(implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q)))) ),
inference(extension,[status(thm),parent(t8:2)],[equality_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q))) != or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q)))
| or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q))) = implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q))) ),
inference(extension,[status(thm),parent(t10:2)],[equality_2]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q))) = or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q))),
inference(extension,[status(thm),parent(t12:2)],[implies_definition]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( ~ axiom(or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q))))
| theorem(or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q)))) ),
inference(extension,[status(thm),parent(t10:3)],[rule_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
( ~ axiom(implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q))))
| implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q))) != or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q)))
| axiom(or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q)))) ),
inference(extension,[status(thm),parent(t16:2)],[equality_7]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q))) = or(not(or(implies(p,q),not(not(p)))),or(not(not(p)),implies(p,q))),
inference(extension,[status(thm),parent(t18:2)],[implies_definition]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
axiom(implies(or(implies(p,q),not(not(p))),or(not(not(p)),implies(p,q)))),
inference(extension,[status(thm),parent(t18:3)],[axiom_1_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t18:3]) ).
cnf(t24,plain,
( ~ theorem(or(or(not(p),q),not(not(p))))
| or(or(not(p),q),not(not(p))) != or(implies(p,q),not(not(p)))
| theorem(or(implies(p,q),not(not(p)))) ),
inference(extension,[status(thm),parent(t8:3)],[equality_8]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t8:3]) ).
cnf(t26,plain,
( not(not(p)) != not(not(p))
| or(not(p),q) != implies(p,q)
| or(or(not(p),q),not(not(p))) = or(implies(p,q),not(not(p))) ),
inference(extension,[status(thm),parent(t24:2)],[equality_4]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
( implies(p,q) != or(not(p),q)
| or(not(p),q) = implies(p,q) ),
inference(extension,[status(thm),parent(t26:2)],[equality_2]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t26:2]) ).
cnf(t30,plain,
implies(p,q) = or(not(p),q),
inference(extension,[status(thm),parent(t28:2)],[implies_definition]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
cnf(t32,plain,
( not(p) != not(p)
| not(not(p)) = not(not(p)) ),
inference(extension,[status(thm),parent(t26:3)],[equality_6]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t26:3]) ).
cnf(t34,plain,
( p != p
| not(p) = not(p) ),
inference(extension,[status(thm),parent(t32:2)],[equality_6]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( p != p
| p = p ),
inference(extension,[status(thm),parent(t34:2)],[equality_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t34:2]) ).
cnf(t38,plain,
p = p,
inference(extension,[status(thm),parent(t36:2)],[equality_1]) ).
cnf(t39,plain,
$false,
inference(connection,[status(thm),parent(t38:1)],[t38:1,t36:2]) ).
cnf(t40,plain,
( ~ theorem(or(not(not(p)),or(not(p),q)))
| ~ theorem(implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p)))))
| theorem(or(or(not(p),q),not(not(p)))) ),
inference(extension,[status(thm),parent(t24:3)],[rule_2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t24:3]) ).
cnf(t42,plain,
( ~ theorem(or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p)))))
| or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p)))) != implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p))))
| theorem(implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p))))) ),
inference(extension,[status(thm),parent(t40:2)],[equality_8]) ).
cnf(t43,plain,
$false,
inference(connection,[status(thm),parent(t42:1)],[t42:1,t40:2]) ).
cnf(t44,plain,
( implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p)))) != or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p))))
| or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p)))) = implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p)))) ),
inference(extension,[status(thm),parent(t42:2)],[equality_2]) ).
cnf(t45,plain,
$false,
inference(connection,[status(thm),parent(t44:1)],[t44:1,t42:2]) ).
cnf(t46,plain,
implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p)))) = or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p)))),
inference(extension,[status(thm),parent(t44:2)],[implies_definition]) ).
cnf(t47,plain,
$false,
inference(connection,[status(thm),parent(t46:1)],[t46:1,t44:2]) ).
cnf(t48,plain,
( ~ axiom(or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p)))))
| theorem(or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p))))) ),
inference(extension,[status(thm),parent(t42:3)],[rule_1]) ).
cnf(t49,plain,
$false,
inference(connection,[status(thm),parent(t48:1)],[t48:1,t42:3]) ).
cnf(t50,plain,
( ~ axiom(implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p)))))
| implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p)))) != or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p))))
| axiom(or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p))))) ),
inference(extension,[status(thm),parent(t48:2)],[equality_7]) ).
cnf(t51,plain,
$false,
inference(connection,[status(thm),parent(t50:1)],[t50:1,t48:2]) ).
cnf(t52,plain,
implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p)))) = or(not(or(not(not(p)),or(not(p),q))),or(or(not(p),q),not(not(p)))),
inference(extension,[status(thm),parent(t50:2)],[implies_definition]) ).
cnf(t53,plain,
$false,
inference(connection,[status(thm),parent(t52:1)],[t52:1,t50:2]) ).
cnf(t54,plain,
axiom(implies(or(not(not(p)),or(not(p),q)),or(or(not(p),q),not(not(p))))),
inference(extension,[status(thm),parent(t50:3)],[axiom_1_4]) ).
cnf(t55,plain,
$false,
inference(connection,[status(thm),parent(t54:1)],[t54:1,t50:3]) ).
cnf(t56,plain,
( ~ theorem(or(not(not(p)),or(q,not(p))))
| ~ theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))
| theorem(or(not(not(p)),or(not(p),q))) ),
inference(extension,[status(thm),parent(t40:3)],[rule_2]) ).
cnf(t57,plain,
$false,
inference(connection,[status(thm),parent(t56:1)],[t56:1,t40:3]) ).
cnf(t58,plain,
( ~ theorem(implies(or(q,not(p)),or(not(p),q)))
| ~ theorem(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))))
| theorem(implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))) ),
inference(extension,[status(thm),parent(t56:2)],[rule_2]) ).
cnf(t59,plain,
$false,
inference(connection,[status(thm),parent(t58:1)],[t58:1,t56:2]) ).
cnf(t60,plain,
( ~ axiom(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q)))))
| theorem(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))) ),
inference(extension,[status(thm),parent(t58:2)],[rule_1]) ).
cnf(t61,plain,
$false,
inference(connection,[status(thm),parent(t60:1)],[t60:1,t58:2]) ).
cnf(t62,plain,
axiom(implies(implies(or(q,not(p)),or(not(p),q)),implies(or(not(not(p)),or(q,not(p))),or(not(not(p)),or(not(p),q))))),
inference(extension,[status(thm),parent(t60:2)],[axiom_1_6]) ).
cnf(t63,plain,
$false,
inference(connection,[status(thm),parent(t62:1)],[t62:1,t60:2]) ).
cnf(t64,plain,
( ~ axiom(implies(or(q,not(p)),or(not(p),q)))
| theorem(implies(or(q,not(p)),or(not(p),q))) ),
inference(extension,[status(thm),parent(t58:3)],[rule_1]) ).
cnf(t65,plain,
$false,
inference(connection,[status(thm),parent(t64:1)],[t64:1,t58:3]) ).
cnf(t66,plain,
axiom(implies(or(q,not(p)),or(not(p),q))),
inference(extension,[status(thm),parent(t64:2)],[axiom_1_4]) ).
cnf(t67,plain,
$false,
inference(connection,[status(thm),parent(t66:1)],[t66:1,t64:2]) ).
cnf(t68,plain,
( ~ theorem(implies(not(p),or(q,not(p))))
| implies(not(p),or(q,not(p))) != or(not(not(p)),or(q,not(p)))
| theorem(or(not(not(p)),or(q,not(p)))) ),
inference(extension,[status(thm),parent(t56:3)],[equality_8]) ).
cnf(t69,plain,
$false,
inference(connection,[status(thm),parent(t68:1)],[t68:1,t56:3]) ).
cnf(t70,plain,
implies(not(p),or(q,not(p))) = or(not(not(p)),or(q,not(p))),
inference(extension,[status(thm),parent(t68:2)],[implies_definition]) ).
cnf(t71,plain,
$false,
inference(connection,[status(thm),parent(t70:1)],[t70:1,t68:2]) ).
cnf(t72,plain,
( ~ axiom(implies(not(p),or(q,not(p))))
| theorem(implies(not(p),or(q,not(p)))) ),
inference(extension,[status(thm),parent(t68:3)],[rule_1]) ).
cnf(t73,plain,
$false,
inference(connection,[status(thm),parent(t72:1)],[t72:1,t68:3]) ).
cnf(t74,plain,
axiom(implies(not(p),or(q,not(p)))),
inference(extension,[status(thm),parent(t72:2)],[axiom_1_3]) ).
cnf(t75,plain,
$false,
inference(connection,[status(thm),parent(t74:1)],[t74:1,t72:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL186-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.57 % Computer : n026.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Sat Sep 19 14:21:22 UTC 2026
% 0.12/0.58 % CPUTime :
% 252.45/252.97 % SZS status Unsatisfiable for theBenchmark
% 252.45/252.97 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------