%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL173-3 : 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:48:47 AM UTC 2026
% Result : Unsatisfiable 240.26s 245.61s
% Output : Proof 240.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 8
% Syntax : Number of clauses : 29 ( 19 unt; 0 nHn; 26 RR)
% Number of literals : 44 ( 22 equ; 17 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(prove_this,negated_conjecture,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
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(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(start,[status(thm),parent(0:0)],[prove_this]) ).
cnf(t2,plain,
( implies(implies(q,r),implies(or(not(p),q),or(not(p),r))) != implies(implies(q,r),implies(implies(p,q),implies(p,r)))
| ~ theorem(implies(implies(q,r),implies(or(not(p),q),or(not(p),r))))
| theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) ),
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,
( ~ axiom(implies(implies(q,r),implies(or(not(p),q),or(not(p),r))))
| theorem(implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))) ),
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(implies(q,r),implies(or(not(p),q),or(not(p),r)))),
inference(extension,[status(thm),parent(t4:2)],[axiom_1_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( implies(implies(q,r),implies(implies(p,q),implies(p,r))) != implies(implies(q,r),implies(or(not(p),q),or(not(p),r)))
| implies(implies(q,r),implies(or(not(p),q),or(not(p),r))) = implies(implies(q,r),implies(implies(p,q),implies(p,r))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_2]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( implies(implies(p,q),implies(p,r)) != implies(or(not(p),q),or(not(p),r))
| implies(q,r) != implies(q,r)
| implies(implies(q,r),implies(implies(p,q),implies(p,r))) = implies(implies(q,r),implies(or(not(p),q),or(not(p),r))) ),
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(q,r) != implies(q,r)
| implies(q,r) = implies(q,r) ),
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(q,r) = implies(q,r),
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(p,r) != or(not(p),r)
| implies(p,q) != or(not(p),q)
| implies(implies(p,q),implies(p,r)) = implies(or(not(p),q),or(not(p),r)) ),
inference(extension,[status(thm),parent(t10:3)],[equality_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t10:3]) ).
cnf(t18,plain,
implies(p,q) = or(not(p),q),
inference(extension,[status(thm),parent(t16:2)],[implies_definition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
implies(p,r) = or(not(p),r),
inference(extension,[status(thm),parent(t16:3)],[implies_definition]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL173-3 : 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
% 0.08/5.44 % Computer : n004.cluster.edu
% 0.08/5.44 % Model : x86_64 x86_64
% 0.08/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.44 % Memory : 8046.5625MB
% 0.08/5.44 % OS : Linux 6.8.0-71-generic
% 0.08/5.44 % CPULimit : 300
% 0.08/5.44 % WCLimit : 300
% 0.08/5.44 % DateTime : Sat Sep 19 14:16:27 UTC 2026
% 0.08/5.44 % CPUTime :
% 240.26/245.61 % SZS status Unsatisfiable for theBenchmark
% 240.26/245.61 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------