%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% 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 : n017.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 08:48:54 AM UTC 2026
% Result : Unsatisfiable 262.40s 272.78s
% Output : Proof 262.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 34 ( 22 unt; 0 nHn; 31 RR)
% Number of literals : 53 ( 20 equ; 21 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 : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))),
file('LCL004-0.ax',axiom_1_3) ).
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(q,implies(implies(p,q),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_5,axiom,
( implies(Eq_x_0,Eq_x_1) = implies(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
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(q,implies(implies(p,q),q)))),
inference(start,[status(thm),parent(0:0)],[prove_this]) ).
cnf(t2,plain,
( ~ theorem(implies(implies(q,or(not(implies(p,q)),q)),implies(not(p),implies(q,implies(implies(p,q),q)))))
| ~ theorem(implies(q,or(not(implies(p,q)),q)))
| theorem(implies(not(p),implies(q,implies(implies(p,q),q)))) ),
inference(extension,[status(thm),parent(t1:1)],[rule_2]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ axiom(implies(q,or(not(implies(p,q)),q)))
| theorem(implies(q,or(not(implies(p,q)),q))) ),
inference(extension,[status(thm),parent(t2:2)],[rule_1]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
axiom(implies(q,or(not(implies(p,q)),q))),
inference(extension,[status(thm),parent(t4:2)],[axiom_1_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ theorem(implies(implies(q,implies(implies(p,q),q)),or(not(not(p)),implies(q,implies(implies(p,q),q)))))
| implies(implies(q,implies(implies(p,q),q)),or(not(not(p)),implies(q,implies(implies(p,q),q)))) != implies(implies(q,or(not(implies(p,q)),q)),implies(not(p),implies(q,implies(implies(p,q),q))))
| theorem(implies(implies(q,or(not(implies(p,q)),q)),implies(not(p),implies(q,implies(implies(p,q),q))))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_8]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( or(not(not(p)),implies(q,implies(implies(p,q),q))) != implies(not(p),implies(q,implies(implies(p,q),q)))
| implies(q,implies(implies(p,q),q)) != implies(q,or(not(implies(p,q)),q))
| implies(implies(q,implies(implies(p,q),q)),or(not(not(p)),implies(q,implies(implies(p,q),q)))) = implies(implies(q,or(not(implies(p,q)),q)),implies(not(p),implies(q,implies(implies(p,q),q)))) ),
inference(extension,[status(thm),parent(t8:2)],[equality_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( implies(implies(p,q),q) != or(not(implies(p,q)),q)
| q != q
| implies(q,implies(implies(p,q),q)) = implies(q,or(not(implies(p,q)),q)) ),
inference(extension,[status(thm),parent(t10:2)],[equality_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
q = q,
inference(extension,[status(thm),parent(t12:2)],[equality_1]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
implies(implies(p,q),q) = or(not(implies(p,q)),q),
inference(extension,[status(thm),parent(t12:3)],[implies_definition]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t12:3]) ).
cnf(t18,plain,
( implies(not(p),implies(q,implies(implies(p,q),q))) != or(not(not(p)),implies(q,implies(implies(p,q),q)))
| or(not(not(p)),implies(q,implies(implies(p,q),q))) = implies(not(p),implies(q,implies(implies(p,q),q))) ),
inference(extension,[status(thm),parent(t10:3)],[equality_2]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t10:3]) ).
cnf(t20,plain,
implies(not(p),implies(q,implies(implies(p,q),q))) = or(not(not(p)),implies(q,implies(implies(p,q),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(implies(q,implies(implies(p,q),q)),or(not(not(p)),implies(q,implies(implies(p,q),q)))))
| theorem(implies(implies(q,implies(implies(p,q),q)),or(not(not(p)),implies(q,implies(implies(p,q),q))))) ),
inference(extension,[status(thm),parent(t8:3)],[rule_1]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t8:3]) ).
cnf(t24,plain,
axiom(implies(implies(q,implies(implies(p,q),q)),or(not(not(p)),implies(q,implies(implies(p,q),q))))),
inference(extension,[status(thm),parent(t22:2)],[axiom_1_3]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL212-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.39 % Computer : n017.cluster.edu
% 0.10/10.39 % Model : x86_64 x86_64
% 0.10/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.39 % Memory : 8046.5625MB
% 0.10/10.39 % OS : Linux 6.8.0-71-generic
% 0.10/10.39 % CPULimit : 300
% 0.10/10.39 % WCLimit : 300
% 0.10/10.39 % DateTime : Sat Sep 19 14:18:21 UTC 2026
% 0.10/10.39 % CPUTime :
% 262.40/272.78 % SZS status Unsatisfiable for theBenchmark
% 262.40/272.78 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------