%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : RNG010-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 : n002.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 08:54:54 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : Proof 0.09s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(left_additive_identity,axiom,
add(additive_identity,X) = X,
file('RNG004-0.ax',left_additive_identity) ).
cnf(left_multiplicative_zero,axiom,
multiply(additive_identity,X) = additive_identity,
file('RNG004-0.ax',left_multiplicative_zero) ).
cnf(right_multiplicative_zero,axiom,
multiply(X,additive_identity) = additive_identity,
file('RNG004-0.ax',right_multiplicative_zero) ).
cnf(add_inverse,axiom,
add(additive_inverse(X),X) = additive_identity,
file('RNG004-0.ax',add_inverse) ).
cnf(sum_of_inverses,axiom,
additive_inverse(add(X,Y)) = add(additive_inverse(X),additive_inverse(Y)),
file('RNG004-0.ax',sum_of_inverses) ).
cnf(additive_inverse_additive_inverse,axiom,
additive_inverse(additive_inverse(X)) = X,
file('RNG004-0.ax',additive_inverse_additive_inverse) ).
cnf(multiply_over_add1,axiom,
multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('RNG004-0.ax',multiply_over_add1) ).
cnf(multiply_over_add2,axiom,
multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('RNG004-0.ax',multiply_over_add2) ).
cnf(right_alternative,axiom,
multiply(multiply(X,Y),Y) = multiply(X,multiply(Y,Y)),
file('RNG004-0.ax',right_alternative) ).
cnf(left_alternative,axiom,
multiply(multiply(X,X),Y) = multiply(X,multiply(X,Y)),
file('RNG004-0.ax',left_alternative) ).
cnf(inverse_product1,axiom,
multiply(additive_inverse(X),Y) = additive_inverse(multiply(X,Y)),
file('RNG004-0.ax',inverse_product1) ).
cnf(inverse_product2,axiom,
multiply(X,additive_inverse(Y)) = additive_inverse(multiply(X,Y)),
file('RNG004-0.ax',inverse_product2) ).
cnf(inverse_additive_identity,axiom,
additive_inverse(additive_identity) = additive_identity,
file('RNG004-0.ax',inverse_additive_identity) ).
cnf(commutativity_for_addition,axiom,
add(X,Y) = add(Y,X),
file('RNG004-0.ax',commutativity_for_addition) ).
cnf(associativity_for_addition,axiom,
add(X,add(Y,Z)) = add(add(X,Y),Z),
file('RNG004-0.ax',associativity_for_addition) ).
cnf(left_cancellation_for_addition,axiom,
( X = Y
| add(X,Z) != add(Y,Z) ),
file('RNG004-0.ax',left_cancellation_for_addition) ).
cnf(right_cancellation_for_addition,axiom,
( X = Y
| add(Z,X) != add(Z,Y) ),
file('RNG004-0.ax',right_cancellation_for_addition) ).
cnf(associator,axiom,
associator(X,Y,Z) = add(multiply(multiply(X,Y),Z),additive_inverse(multiply(X,multiply(Y,Z)))),
file('theBenchmark.p',associator) ).
cnf(middle_law,axiom,
multiply(multiply(Y,X),Y) != multiply(Y,multiply(X,Y)),
file('theBenchmark.p',middle_law) ).
cnf(associator_skew_symmetry1,axiom,
associator(Y,X,Z) != additive_inverse(associator(X,Y,Z)),
file('theBenchmark.p',associator_skew_symmetry1) ).
cnf(associator_skew_symmetry2,axiom,
associator(Z,Y,X) != additive_inverse(associator(X,Y,Z)),
file('theBenchmark.p',associator_skew_symmetry2) ).
cnf(right_moufang,hypothesis,
multiply(Z,multiply(X,multiply(Y,X))) = multiply(multiply(multiply(Z,X),Y),X),
file('theBenchmark.p',right_moufang) ).
cnf(left_moufang,hypothesis,
multiply(multiply(X,multiply(Y,X)),Z) = multiply(X,multiply(Y,multiply(X,Z))),
file('theBenchmark.p',left_moufang) ).
cnf(prove_skew_symmetry,negated_conjecture,
associator(multiply(cx,cx),cy,cz) != add(multiply(associator(cx,cy,cz),cx),multiply(cx,associator(cx,cy,cz))),
file('theBenchmark.p',prove_skew_symmetry) ).
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_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(equality_5,axiom,
( multiply(Eq_x_0,Eq_x_1) = multiply(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,axiom,
( additive_inverse(Eq_x_0) = additive_inverse(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( associator(Eq_x_0,Eq_x_1,Eq_x_2) = associator(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG010-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 This is a CNF_UNS_RFO_PEQ_NUE problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.38 % Computer : n002.cluster.edu
% 0.09/0.38 % Model : x86_64 x86_64
% 0.09/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.38 % Memory : 8046.5625MB
% 0.09/0.38 % OS : Linux 6.8.0-71-generic
% 0.09/0.38 % CPULimit : 300
% 0.09/0.38 % WCLimit : 300
% 0.09/0.38 % DateTime : Sat Sep 19 20:39:16 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.40 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------