%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO003-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 09:35:20 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.24s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of clauses : 42 ( 42 unt; 0 nHn; 8 RR)
% Number of literals : 42 ( 41 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 53 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(a,a) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_a_is_a) ).
cnf(c2,axiom,
add(additive_identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_id2) ).
cnf(c3,plain,
add(additive_identity,multiply(X2,X2)) = multiply(X2,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X2,X2) = add(additive_identity,multiply(X2,X2)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
add(X2,Y) = add(Y,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c6,plain,
add(multiply(X3,X3),X2) = add(X2,multiply(X3,X3)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
add(X3,multiply(X2,X2)) = add(multiply(X2,X2),X3),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
add(multiply(X2,Y2),Z) = multiply(add(X2,Z),add(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(c9,plain,
add(multiply(X2,X2),X3) = multiply(add(X2,X3),add(X2,X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,axiom,
add(X2,multiply(Y2,Z2)) = multiply(add(X2,Y2),add(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
cnf(c11,plain,
add(X2,multiply(X3,X3)) = multiply(add(X2,X3),add(X2,X3)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
multiply(add(X2,X3),add(X2,X3)) = add(X2,multiply(X3,X3)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
add(multiply(X2,X2),X3) = add(X2,multiply(X3,X3)),
inference(transitivity,[status(thm)],[c9,c12]) ).
cnf(c14,plain,
add(X3,multiply(X2,X2)) = add(X2,multiply(X3,X3)),
inference(transitivity,[status(thm)],[c7,c13]) ).
cnf(c15,plain,
add(X2,multiply(additive_identity,additive_identity)) = add(additive_identity,multiply(X2,X2)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
add(additive_identity,multiply(X2,X2)) = add(X2,multiply(additive_identity,additive_identity)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
add(additive_identity,multiply(additive_identity,additive_identity)) = multiply(additive_identity,additive_identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c18,plain,
multiply(additive_identity,additive_identity) = add(additive_identity,multiply(additive_identity,additive_identity)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
add(multiplicative_identity,X2) = add(X2,multiplicative_identity),
inference(substitution,[status(thm)],[c5]) ).
cnf(c20,plain,
add(X2,multiplicative_identity) = add(multiplicative_identity,X2),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,plain,
multiply(X3,add(X2,multiplicative_identity)) = multiply(X3,add(multiplicative_identity,X2)),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,axiom,
multiply(X2,add(Y2,Z2)) = add(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity4) ).
cnf(c23,plain,
multiply(X3,add(multiplicative_identity,X2)) = add(multiply(X3,multiplicative_identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,axiom,
multiply(X2,multiplicative_identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c25,plain,
add(multiply(X3,multiplicative_identity),multiply(X3,X2)) = add(X3,multiply(X3,X2)),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X3,add(multiplicative_identity,X2)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c23,c25]) ).
cnf(c27,plain,
multiply(X3,add(X2,multiplicative_identity)) = add(X3,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c21,c26]) ).
cnf(c28,plain,
multiply(X2,add(additive_identity,multiplicative_identity)) = add(X2,multiply(X2,additive_identity)),
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
add(X2,multiply(X2,additive_identity)) = multiply(X2,add(additive_identity,multiplicative_identity)),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
add(additive_identity,multiplicative_identity) = multiplicative_identity,
inference(substitution,[status(thm)],[c2]) ).
cnf(c31,plain,
multiply(X2,add(additive_identity,multiplicative_identity)) = multiply(X2,multiplicative_identity),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(X2,add(additive_identity,multiplicative_identity)) = X2,
inference(transitivity,[status(thm)],[c31,c24]) ).
cnf(c33,plain,
add(X2,multiply(X2,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c29,c32]) ).
cnf(c34,plain,
add(additive_identity,multiply(additive_identity,additive_identity)) = additive_identity,
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(additive_identity,additive_identity) = additive_identity,
inference(transitivity,[status(thm)],[c18,c34]) ).
cnf(c36,plain,
add(X2,multiply(additive_identity,additive_identity)) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c38,plain,
add(X2,multiply(additive_identity,additive_identity)) = X2,
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
add(additive_identity,multiply(X2,X2)) = X2,
inference(transitivity,[status(thm)],[c16,c38]) ).
cnf(c40,plain,
multiply(X2,X2) = X2,
inference(transitivity,[status(thm)],[c4,c39]) ).
cnf(c41,plain,
multiply(a,a) = a,
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
$false,
inference(resolution,[status(thm)],[c1,c41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO003-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.16 % Computer : n011.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 21:03:00 UTC 2026
% 0.08/0.16 % CPUTime :
% 0.08/0.16 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.24 Command-line arguments: --flatten --complete-subsets
% 0.08/0.24
% 0.08/0.24 % SZS status Unsatisfiable
% 0.08/0.24
% 0.08/0.24 % SZS output start CNFRefutation
% See solution above
% 0.08/0.25
% 0.08/0.25 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------