%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG024-7 : TPTP v9.3.1. Released v1.0.0.
% 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 08:54:56 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.42s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 7
% Syntax : Number of clauses : 22 ( 17 unt; 0 nHn; 18 RR)
% Number of literals : 32 ( 25 equ; 12 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 14 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(right_additive_inverse,axiom,
add(X,additive_inverse(X)) = additive_identity,
file('RNG003-0.ax',right_additive_inverse) ).
cnf(right_alternative,axiom,
multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
file('RNG003-0.ax',right_alternative) ).
cnf(associator,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('RNG003-0.ax',associator) ).
cnf(prove_right_alternative,negated_conjecture,
associator(x,y,y) != additive_identity,
file('theBenchmark.p',prove_right_alternative) ).
cnf(equality_1,axiom,
Eq_x_0 = Eq_x_0,
theory(equality,[reflexivity]) ).
cnf(equality_3,axiom,
( Eq_x_0 = Eq_x_2
| Eq_x_1 != Eq_x_2
| Eq_x_0 != Eq_x_1 ),
theory(equality,[transitivity]) ).
cnf(equality_4,axiom,
( add(Eq_x_0,Eq_x_1) = add(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(t1,plain,
associator(x,y,y) != additive_identity,
inference(start,[status(thm),parent(0:0)],[prove_right_alternative]) ).
cnf(t2,plain,
( add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))) != additive_identity
| associator(x,y,y) != add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y))))
| associator(x,y,y) = additive_identity ),
inference(extension,[status(thm),parent(t1:1)],[equality_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
associator(x,y,y) = add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))),
inference(extension,[status(thm),parent(t2:2)],[associator]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( add(multiply(x,multiply(y,y)),additive_inverse(multiply(x,multiply(y,y)))) != additive_identity
| add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))) != add(multiply(x,multiply(y,y)),additive_inverse(multiply(x,multiply(y,y))))
| add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))) = additive_identity ),
inference(extension,[status(thm),parent(t2:3)],[equality_3]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
( additive_inverse(multiply(x,multiply(y,y))) != additive_inverse(multiply(x,multiply(y,y)))
| multiply(multiply(x,y),y) != multiply(x,multiply(y,y))
| add(multiply(multiply(x,y),y),additive_inverse(multiply(x,multiply(y,y)))) = add(multiply(x,multiply(y,y)),additive_inverse(multiply(x,multiply(y,y)))) ),
inference(extension,[status(thm),parent(t6:2)],[equality_4]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
multiply(multiply(x,y),y) = multiply(x,multiply(y,y)),
inference(extension,[status(thm),parent(t8:2)],[right_alternative]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
additive_inverse(multiply(x,multiply(y,y))) = additive_inverse(multiply(x,multiply(y,y))),
inference(extension,[status(thm),parent(t8:3)],[equality_1]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
add(multiply(x,multiply(y,y)),additive_inverse(multiply(x,multiply(y,y)))) = additive_identity,
inference(extension,[status(thm),parent(t6:3)],[right_additive_inverse]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t6:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG024-7 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_UEQ 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
% 0.08/0.36 % Computer : n015.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 20:42:33 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.42 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.42 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------