%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.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 0.06s 0.25s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of clauses : 34 ( 34 unt; 0 nHn; 3 RR)
% Number of literals : 34 ( 33 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 : 49 ( 6 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(X2,additive_identity) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c3,plain,
X2 = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X2,add(X2,X3)) = multiply(add(X2,additive_identity),add(X2,X3)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,axiom,
add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
cnf(c6,plain,
add(X3,multiply(additive_identity,X2)) = multiply(add(X3,additive_identity),add(X3,X2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = add(X3,multiply(additive_identity,X2)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(X2,Y2) = multiply(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c9,plain,
multiply(X2,additive_identity) = multiply(additive_identity,X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(additive_identity,X2) = multiply(X2,additive_identity),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(c12,plain,
multiply(X3,add(X2,inverse(X3))) = add(multiply(X3,X2),multiply(X3,inverse(X3))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,axiom,
multiply(X2,inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c14,plain,
add(multiply(X3,X2),multiply(X3,inverse(X3))) = add(multiply(X3,X2),additive_identity),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,plain,
add(multiply(X3,X2),additive_identity) = multiply(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
add(multiply(X3,X2),multiply(X3,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
multiply(X3,add(X2,inverse(X3))) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c12,c16]) ).
cnf(c18,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,additive_identity),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X2,additive_identity) = multiply(X2,add(additive_identity,inverse(X2))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
add(X2,Y2) = add(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c21,plain,
add(X2,additive_identity) = add(additive_identity,X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
add(additive_identity,X2) = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
add(additive_identity,X2) = X2,
inference(transitivity,[status(thm)],[c22,c2]) ).
cnf(c24,plain,
add(additive_identity,inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
multiply(X2,add(additive_identity,inverse(X2))) = multiply(X2,inverse(X2)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X2,add(additive_identity,inverse(X2))) = additive_identity,
inference(transitivity,[status(thm)],[c25,c13]) ).
cnf(c27,plain,
multiply(X2,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c19,c26]) ).
cnf(c28,plain,
multiply(additive_identity,X2) = additive_identity,
inference(transitivity,[status(thm)],[c10,c27]) ).
cnf(c29,plain,
add(X3,multiply(additive_identity,X2)) = add(X3,additive_identity),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
add(X3,multiply(additive_identity,X2)) = X3,
inference(transitivity,[status(thm)],[c29,c2]) ).
cnf(c31,plain,
multiply(add(X3,additive_identity),add(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c7,c30]) ).
cnf(c32,plain,
multiply(X3,add(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c4,c31]) ).
cnf(c33,plain,
multiply(a,add(a,b)) = a,
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
$false,
inference(resolution,[status(thm)],[c1,c33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.17 % Computer : n012.cluster.edu
% 0.06/0.17 % Model : x86_64 x86_64
% 0.06/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.17 % Memory : 8046.5625MB
% 0.06/0.17 % OS : Linux 6.8.0-71-generic
% 0.06/0.17 % CPULimit : 300
% 0.06/0.17 % WCLimit : 300
% 0.06/0.17 % DateTime : Mon Sep 28 21:03:18 UTC 2026
% 0.06/0.17 % CPUTime :
% 0.06/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.25 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.06/0.25
% 0.06/0.25 % SZS status Unsatisfiable
% 0.06/0.25
% 0.23/0.26 % SZS output start CNFRefutation
% See solution above
% 0.23/0.26
% 0.23/0.26 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------