%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /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 : Tue Sep 29 09:35:21 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.25s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 32 ( 32 unt; 0 nHn; 3 RR)
% Number of literals : 32 ( 31 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
add(a,multiplicative_identity) != multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_plus_1_is_a) ).
cnf(c2,axiom,
multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id1) ).
cnf(c3,plain,
multiply(add(X2,multiplicative_identity),multiplicative_identity) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(X2,multiplicative_identity) = multiply(add(X2,multiplicative_identity),multiplicative_identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
add(X2,inverse(X2)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiplicative_identity = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
multiply(add(X2,multiplicative_identity),multiplicative_identity) = multiply(add(X2,multiplicative_identity),add(X2,inverse(X2))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
add(X2,Y) = add(Y,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c9,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
add(X3,X2) = add(X2,X3),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(add(X3,multiplicative_identity),add(X3,X2)) = multiply(add(X3,multiplicative_identity),add(X2,X3)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c13,plain,
add(X2,X3) = add(X3,X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(add(X3,multiplicative_identity),add(X2,X3)) = multiply(add(X3,multiplicative_identity),add(X3,X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
add(X2,multiply(Y2,Z)) = multiply(add(X2,Y2),add(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(c16,plain,
add(X3,multiply(multiplicative_identity,X2)) = multiply(add(X3,multiplicative_identity),add(X3,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
multiply(add(X3,multiplicative_identity),add(X3,X2)) = add(X3,multiply(multiplicative_identity,X2)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,axiom,
multiply(multiplicative_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c19,plain,
add(X3,multiply(multiplicative_identity,X2)) = add(X3,X2),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c8]) ).
cnf(c21,plain,
add(X3,multiply(multiplicative_identity,X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
multiply(add(X3,multiplicative_identity),add(X3,X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c17,c21]) ).
cnf(c23,plain,
multiply(add(X3,multiplicative_identity),add(X2,X3)) = add(X2,X3),
inference(transitivity,[status(thm)],[c14,c22]) ).
cnf(c24,plain,
multiply(add(X3,multiplicative_identity),add(X3,X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c11,c23]) ).
cnf(c25,plain,
multiply(add(X2,multiplicative_identity),add(X2,inverse(X2))) = add(inverse(X2),X2),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
add(inverse(X2),X2) = add(X2,inverse(X2)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c27,plain,
add(inverse(X2),X2) = multiplicative_identity,
inference(transitivity,[status(thm)],[c26,c5]) ).
cnf(c28,plain,
multiply(add(X2,multiplicative_identity),add(X2,inverse(X2))) = multiplicative_identity,
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
multiply(add(X2,multiplicative_identity),multiplicative_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[c7,c28]) ).
cnf(c30,plain,
add(X2,multiplicative_identity) = multiplicative_identity,
inference(transitivity,[status(thm)],[c4,c29]) ).
cnf(c31,plain,
add(a,multiplicative_identity) = multiplicative_identity,
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
$false,
inference(resolution,[status(thm)],[c1,c31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n015.cluster.edu
% 0.08/0.16 % Model : x86_64 x86_64
% 0.08/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.16 % Memory : 8046.5625MB
% 0.08/0.16 % OS : Linux 6.8.0-71-generic
% 0.08/0.16 % CPULimit : 300
% 0.08/0.16 % WCLimit : 300
% 0.08/0.16 % DateTime : Mon Sep 28 21:06:46 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.25 Command-line arguments: --flatten --complete-subsets
% 0.08/0.25
% 0.08/0.25 % SZS status Unsatisfiable
% 0.08/0.25
% 0.08/0.25 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------