%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : LDA003-1 : TPTP v9.3.1. Released v1.0.0.
% 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 : n001.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 08:50:25 AM UTC 2026
% Result : Unsatisfiable 246.34s 246.69s
% Output : Proof 246.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 10
% Syntax : Number of clauses : 51 ( 37 unt; 0 nHn; 48 RR)
% Number of literals : 76 ( 44 equ; 27 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 16 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(a1,axiom,
f(X,f(Y,Z)) = f(f(X,Y),f(X,Z)),
file('theBenchmark.p',a1) ).
cnf(a2,axiom,
left(X,f(X,Y)),
file('theBenchmark.p',a2) ).
cnf(clause_4,axiom,
n2 = f(n1,n1),
file('theBenchmark.p',clause_4) ).
cnf(clause_5,axiom,
n3 = f(n2,n1),
file('theBenchmark.p',clause_5) ).
cnf(clause_6,axiom,
u = f(n2,n2),
file('theBenchmark.p',clause_6) ).
cnf(prove_equation,negated_conjecture,
~ left(n3,u),
file('theBenchmark.p',prove_equation) ).
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,
( f(Eq_x_0,Eq_x_1) = f(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_5,axiom,
( left(Eq_y_0,Eq_y_1)
| ~ left(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ left(n3,u),
inference(start,[status(thm),parent(0:0)],[prove_equation]) ).
cnf(t2,plain,
( ~ left(f(n2,n1),f(n2,n2))
| f(n2,n1) != n3
| f(n2,n2) != u
| left(n3,u) ),
inference(extension,[status(thm),parent(t1:1)],[equality_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( u != f(n2,n2)
| f(n2,n2) = u ),
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,
u = f(n2,n2),
inference(extension,[status(thm),parent(t4:2)],[clause_6]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( n3 != f(n2,n1)
| f(n2,n1) = n3 ),
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,
n3 = f(n2,n1),
inference(extension,[status(thm),parent(t8:2)],[clause_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
( ~ left(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1)))
| f(f(n1,n1),n1) != f(n2,n1)
| f(f(n1,n1),f(n1,n1)) != f(n2,n2)
| left(f(n2,n1),f(n2,n2)) ),
inference(extension,[status(thm),parent(t2:4)],[equality_5]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:4]) ).
cnf(t14,plain,
( f(n2,n2) != f(f(n1,n1),f(n1,n1))
| f(f(n1,n1),f(n1,n1)) = f(n2,n2) ),
inference(extension,[status(thm),parent(t12:2)],[equality_2]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(t16,plain,
( n2 != f(n1,n1)
| n2 != f(n1,n1)
| f(n2,n2) = f(f(n1,n1),f(n1,n1)) ),
inference(extension,[status(thm),parent(t14:2)],[equality_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
cnf(t18,plain,
n2 = f(n1,n1),
inference(extension,[status(thm),parent(t16:2)],[clause_4]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
n2 = f(n1,n1),
inference(extension,[status(thm),parent(t16:3)],[clause_4]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( f(n2,n1) != f(f(n1,n1),n1)
| f(f(n1,n1),n1) = f(n2,n1) ),
inference(extension,[status(thm),parent(t12:3)],[equality_2]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t12:3]) ).
cnf(t24,plain,
( n2 != f(n1,n1)
| n1 != n1
| f(n2,n1) = f(f(n1,n1),n1) ),
inference(extension,[status(thm),parent(t22:2)],[equality_4]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
n1 = n1,
inference(extension,[status(thm),parent(t24:2)],[equality_1]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t24:2]) ).
cnf(t28,plain,
n2 = f(n1,n1),
inference(extension,[status(thm),parent(t24:3)],[clause_4]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t24:3]) ).
cnf(t30,plain,
( ~ left(f(f(n1,n1),n1),f(f(f(n1,n1),n1),f(f(n1,n1),n1)))
| f(f(n1,n1),n1) != f(f(n1,n1),n1)
| f(f(f(n1,n1),n1),f(f(n1,n1),n1)) != f(f(n1,n1),f(n1,n1))
| left(f(f(n1,n1),n1),f(f(n1,n1),f(n1,n1))) ),
inference(extension,[status(thm),parent(t12:4)],[equality_5]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t12:4]) ).
cnf(t32,plain,
( f(f(n1,n1),f(n1,n1)) != f(f(f(n1,n1),n1),f(f(n1,n1),n1))
| f(f(f(n1,n1),n1),f(f(n1,n1),n1)) = f(f(n1,n1),f(n1,n1)) ),
inference(extension,[status(thm),parent(t30:2)],[equality_2]) ).
cnf(t33,plain,
$false,
inference(connection,[status(thm),parent(t32:1)],[t32:1,t30:2]) ).
cnf(t34,plain,
f(f(n1,n1),f(n1,n1)) = f(f(f(n1,n1),n1),f(f(n1,n1),n1)),
inference(extension,[status(thm),parent(t32:2)],[a1]) ).
cnf(t35,plain,
$false,
inference(connection,[status(thm),parent(t34:1)],[t34:1,t32:2]) ).
cnf(t36,plain,
( f(f(n1,n1),n1) != f(f(n1,n1),n1)
| f(f(n1,n1),n1) = f(f(n1,n1),n1) ),
inference(extension,[status(thm),parent(t30:3)],[equality_2]) ).
cnf(t37,plain,
$false,
inference(connection,[status(thm),parent(t36:1)],[t36:1,t30:3]) ).
cnf(t38,plain,
f(f(n1,n1),n1) = f(f(n1,n1),n1),
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,
left(f(f(n1,n1),n1),f(f(f(n1,n1),n1),f(f(n1,n1),n1))),
inference(extension,[status(thm),parent(t30:4)],[a2]) ).
cnf(t41,plain,
$false,
inference(connection,[status(thm),parent(t40:1)],[t40:1,t30:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LDA003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_HRN problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 16:08:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 246.34/246.69 % SZS status Unsatisfiable for theBenchmark
% 246.34/246.69 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------