%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 : Tue Sep 29 09:35:22 AM UTC 2026
% Result : Unsatisfiable 0.21s 0.26s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 43 ( 43 unt; 0 nHn; 6 RR)
% Number of literals : 43 ( 42 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_operation) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c3,plain,
add(a,b) = add(b,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(a,add(a,b)) = multiply(a,add(b,a)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(X3,add(X2,X3)) = multiply(X3,add(X3,X2)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
X2 = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X3,add(X3,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
add(X2,multiply(Y2,Z)) = multiply(add(X2,Y2),add(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(c12,plain,
add(X3,multiply(additive_identity,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = add(X3,multiply(additive_identity,X2)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,axiom,
multiply(X2,Y2) = multiply(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c15,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
add(X3,multiply(additive_identity,X2)) = add(X3,multiply(X2,additive_identity)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c13,c16]) ).
cnf(c18,plain,
multiply(X3,add(X3,X2)) = add(X3,multiply(X2,additive_identity)),
inference(transitivity,[status(thm)],[c10,c17]) ).
cnf(c19,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c20,plain,
add(X2,inverse(X3)) = add(inverse(X3),X2),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,add(inverse(X3),X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity4) ).
cnf(c23,plain,
multiply(X3,add(inverse(X3),X2)) = add(multiply(X3,inverse(X3)),multiply(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,axiom,
multiply(X2,inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c25,plain,
add(multiply(X3,inverse(X3)),multiply(X3,X2)) = add(additive_identity,multiply(X3,X2)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,axiom,
add(additive_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id2) ).
cnf(c27,plain,
add(additive_identity,multiply(X3,X2)) = multiply(X3,X2),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
add(multiply(X3,inverse(X3)),multiply(X3,X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
multiply(X3,add(inverse(X3),X2)) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c23,c28]) ).
cnf(c30,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c21,c29]) ).
cnf(c31,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X2,additive_identity) = multiply(X2,add(additive_identity,inverse(X2))),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
add(additive_identity,inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c26]) ).
cnf(c34,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,inverse(X2)),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(X2,add(additive_identity,inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c34,c24]) ).
cnf(c36,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c32,c35]) ).
cnf(c37,plain,
add(X3,multiply(X2,additive_identity)) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
add(X3,multiply(X2,additive_identity)) = X3,
inference(transitivity,[status(thm)],[c37,c8]) ).
cnf(c39,plain,
multiply(X3,add(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c18,c38]) ).
cnf(c40,plain,
multiply(X3,add(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c7,c39]) ).
cnf(c41,plain,
multiply(a,add(b,a)) = a,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(a,add(a,b)) = a,
inference(transitivity,[status(thm)],[c4,c41]) ).
cnf(c43,plain,
$false,
inference(resolution,[status(thm)],[c1,c42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.18 % Computer : n010.cluster.edu
% 0.06/0.18 % Model : x86_64 x86_64
% 0.06/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.18 % Memory : 8046.5625MB
% 0.06/0.18 % OS : Linux 6.8.0-71-generic
% 0.06/0.18 % CPULimit : 300
% 0.06/0.18 % WCLimit : 300
% 0.06/0.18 % DateTime : Mon Sep 28 21:04:02 UTC 2026
% 0.06/0.18 % CPUTime :
% 0.06/0.18 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.26 Command-line arguments: --no-flatten-goal
% 0.21/0.26
% 0.21/0.26 % SZS status Unsatisfiable
% 0.21/0.26
% 0.21/0.26 % SZS output start CNFRefutation
% See solution above
% 0.21/0.27
% 0.21/0.27 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------