%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LCL172-3 : 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 : n015.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 08:48:46 AM UTC 2026
% Result : Unsatisfiable 265.48s 266.05s
% Output : Proof 265.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 9
% Syntax : Number of clauses : 46 ( 31 unt; 0 nHn; 43 RR)
% Number of literals : 71 ( 35 equ; 27 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 : 17 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_5,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('LCL004-0.ax',axiom_1_5) ).
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(p,implies(q,r)),implies(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_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(implies(p,implies(q,r)),implies(q,implies(p,r)))),
inference(start,[status(thm),parent(0:0)],[prove_this]) ).
cnf(t2,plain,
( ~ theorem(implies(implies(p,or(not(q),r)),implies(q,or(not(p),r))))
| implies(implies(p,or(not(q),r)),implies(q,or(not(p),r))) != implies(implies(p,implies(q,r)),implies(q,implies(p,r)))
| theorem(implies(implies(p,implies(q,r)),implies(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,
( implies(implies(p,implies(q,r)),implies(q,implies(p,r))) != implies(implies(p,or(not(q),r)),implies(q,or(not(p),r)))
| implies(implies(p,or(not(q),r)),implies(q,or(not(p),r))) = implies(implies(p,implies(q,r)),implies(q,implies(p,r))) ),
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(q,implies(p,r)) != implies(q,or(not(p),r))
| implies(p,implies(q,r)) != implies(p,or(not(q),r))
| implies(implies(p,implies(q,r)),implies(q,implies(p,r))) = implies(implies(p,or(not(q),r)),implies(q,or(not(p),r))) ),
inference(extension,[status(thm),parent(t4:2)],[equality_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( implies(q,r) != or(not(q),r)
| p != p
| implies(p,implies(q,r)) = implies(p,or(not(q),r)) ),
inference(extension,[status(thm),parent(t6:2)],[equality_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
p = p,
inference(extension,[status(thm),parent(t8:2)],[equality_1]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
implies(q,r) = or(not(q),r),
inference(extension,[status(thm),parent(t8:3)],[implies_definition]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
( implies(p,r) != or(not(p),r)
| q != q
| implies(q,implies(p,r)) = implies(q,or(not(p),r)) ),
inference(extension,[status(thm),parent(t6:3)],[equality_5]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
cnf(t16,plain,
q = q,
inference(extension,[status(thm),parent(t14:2)],[equality_1]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
implies(p,r) = or(not(p),r),
inference(extension,[status(thm),parent(t14:3)],[implies_definition]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t14:3]) ).
cnf(t20,plain,
( ~ theorem(implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))))
| implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))) != implies(implies(p,or(not(q),r)),implies(q,or(not(p),r)))
| theorem(implies(implies(p,or(not(q),r)),implies(q,or(not(p),r)))) ),
inference(extension,[status(thm),parent(t2:3)],[equality_8]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t2:3]) ).
cnf(t22,plain,
( implies(implies(p,or(not(q),r)),implies(q,or(not(p),r))) != implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r)))
| implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))) = implies(implies(p,or(not(q),r)),implies(q,or(not(p),r))) ),
inference(extension,[status(thm),parent(t20:2)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t20:2]) ).
cnf(t24,plain,
( implies(q,or(not(p),r)) != or(not(q),or(not(p),r))
| implies(p,or(not(q),r)) != or(not(p),or(not(q),r))
| implies(implies(p,or(not(q),r)),implies(q,or(not(p),r))) = implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))) ),
inference(extension,[status(thm),parent(t22:2)],[equality_5]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
implies(p,or(not(q),r)) = or(not(p),or(not(q),r)),
inference(extension,[status(thm),parent(t24:2)],[implies_definition]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
implies(q,or(not(p),r)) = or(not(q),or(not(p),r)),
inference(extension,[status(thm),parent(t24:3)],[implies_definition]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
( ~ axiom(implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))))
| theorem(implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r)))) ),
inference(extension,[status(thm),parent(t20:3)],[rule_1]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t20:3]) ).
cnf(t32,plain,
( implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))) != implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r)))
| ~ axiom(implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))))
| axiom(implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r)))) ),
inference(extension,[status(thm),parent(t30:2)],[equality_7]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
axiom(implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r)))),
inference(extension,[status(thm),parent(t32:2)],[axiom_1_5]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))) = implies(or(not(p),or(not(q),r)),or(not(q),or(not(p),r))),
inference(extension,[status(thm),parent(t32:3)],[equality_1]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t32:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL172-3 : 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
% 0.10/0.58 % Computer : n015.cluster.edu
% 0.10/0.58 % Model : x86_64 x86_64
% 0.10/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.58 % Memory : 8046.5625MB
% 0.10/0.58 % OS : Linux 6.8.0-71-generic
% 0.10/0.58 % CPULimit : 300
% 0.10/0.58 % WCLimit : 300
% 0.10/0.58 % DateTime : Sat Sep 19 14:19:18 UTC 2026
% 0.10/0.58 % CPUTime :
% 265.48/266.05 % SZS status Unsatisfiable for theBenchmark
% 265.48/266.05 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------