%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% 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 09:35:23 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.26s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 3 RR)
% Number of literals : 55 ( 54 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 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 : 78 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
inverse(inverse(x)) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_is_an_involution) ).
cnf(c2,axiom,
add(X,additive_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_id1) ).
cnf(c3,plain,
add(inverse(inverse(X2)),additive_identity) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
inverse(inverse(X2)) = add(inverse(inverse(X2)),additive_identity),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X2,inverse(X2)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
additive_identity = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
add(inverse(inverse(X2)),additive_identity) = add(inverse(inverse(X2)),multiply(X2,inverse(X2))),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
multiply(X2,Y) = multiply(Y,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c9,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
add(inverse(X3),multiply(X2,X3)) = add(inverse(X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
add(X2,multiply(Y2,Z)) = multiply(add(X2,Y2),add(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
cnf(c13,plain,
add(inverse(X3),multiply(X3,X2)) = multiply(add(inverse(X3),X3),add(inverse(X3),X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,axiom,
add(X2,Y2) = add(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c15,plain,
add(X2,inverse(X2)) = add(inverse(X2),X2),
inference(substitution,[status(thm)],[c14]) ).
cnf(c16,plain,
add(inverse(X2),X2) = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,axiom,
add(X2,inverse(X2)) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c18,plain,
add(inverse(X2),X2) = multiplicative_identity,
inference(transitivity,[status(thm)],[c16,c17]) ).
cnf(c19,plain,
multiply(add(inverse(X3),X3),add(inverse(X3),X2)) = multiply(multiplicative_identity,add(inverse(X3),X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
multiply(multiplicative_identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_id2) ).
cnf(c21,plain,
multiply(multiplicative_identity,add(inverse(X3),X2)) = add(inverse(X3),X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c14]) ).
cnf(c23,plain,
multiply(multiplicative_identity,add(inverse(X3),X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
multiply(add(inverse(X3),X3),add(inverse(X3),X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c19,c23]) ).
cnf(c25,plain,
add(inverse(X3),multiply(X3,X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c13,c24]) ).
cnf(c26,plain,
add(inverse(X3),multiply(X2,X3)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c11,c25]) ).
cnf(c27,plain,
add(inverse(inverse(X2)),multiply(X2,inverse(X2))) = add(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
add(inverse(inverse(X2)),X2) = add(X2,inverse(inverse(X2))),
inference(substitution,[status(thm)],[c14]) ).
cnf(c29,plain,
add(X2,inverse(inverse(X2))) = add(inverse(inverse(X2)),X2),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(inverse(X3),X2) = multiply(X2,inverse(X3)),
inference(substitution,[status(thm)],[c8]) ).
cnf(c31,plain,
multiply(X2,inverse(X3)) = multiply(inverse(X3),X2),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
add(X3,multiply(X2,inverse(X3))) = add(X3,multiply(inverse(X3),X2)),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
add(X3,multiply(inverse(X3),X2)) = multiply(add(X3,inverse(X3)),add(X3,X2)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c34,plain,
multiply(add(X3,inverse(X3)),add(X3,X2)) = multiply(multiplicative_identity,add(X3,X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c35,plain,
multiply(multiplicative_identity,add(X3,X2)) = add(X3,X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c36,plain,
add(X3,X2) = add(X2,X3),
inference(substitution,[status(thm)],[c14]) ).
cnf(c37,plain,
multiply(multiplicative_identity,add(X3,X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c35,c36]) ).
cnf(c38,plain,
multiply(add(X3,inverse(X3)),add(X3,X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c34,c37]) ).
cnf(c39,plain,
add(X3,multiply(inverse(X3),X2)) = add(X2,X3),
inference(transitivity,[status(thm)],[c33,c38]) ).
cnf(c40,plain,
add(X3,multiply(X2,inverse(X3))) = add(X2,X3),
inference(transitivity,[status(thm)],[c32,c39]) ).
cnf(c41,plain,
add(X2,multiply(inverse(inverse(X2)),inverse(X2))) = add(inverse(inverse(X2)),X2),
inference(substitution,[status(thm)],[c40]) ).
cnf(c42,plain,
add(inverse(inverse(X2)),X2) = add(X2,multiply(inverse(inverse(X2)),inverse(X2))),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
multiply(X2,inverse(X2)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c8]) ).
cnf(c44,plain,
multiply(inverse(X2),X2) = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,plain,
multiply(inverse(X2),X2) = additive_identity,
inference(transitivity,[status(thm)],[c44,c5]) ).
cnf(c46,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = additive_identity,
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
add(X2,multiply(inverse(inverse(X2)),inverse(X2))) = add(X2,additive_identity),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,plain,
add(X2,multiply(inverse(inverse(X2)),inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c47,c2]) ).
cnf(c49,plain,
add(inverse(inverse(X2)),X2) = X2,
inference(transitivity,[status(thm)],[c42,c48]) ).
cnf(c50,plain,
add(X2,inverse(inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c29,c49]) ).
cnf(c51,plain,
add(inverse(inverse(X2)),multiply(X2,inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c27,c50]) ).
cnf(c52,plain,
add(inverse(inverse(X2)),additive_identity) = X2,
inference(transitivity,[status(thm)],[c7,c51]) ).
cnf(c53,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c4,c52]) ).
cnf(c54,plain,
inverse(inverse(x)) = x,
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
$false,
inference(resolution,[status(thm)],[c1,c54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : BOO012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.15 % Computer : n015.cluster.edu
% 0.11/0.15 % Model : x86_64 x86_64
% 0.11/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.15 % Memory : 8046.5625MB
% 0.11/0.15 % OS : Linux 6.8.0-71-generic
% 0.11/0.15 % CPULimit : 300
% 0.11/0.15 % WCLimit : 300
% 0.11/0.15 % DateTime : Mon Sep 28 21:07:16 UTC 2026
% 0.11/0.15 % CPUTime :
% 0.11/0.15 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.26 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.11/0.26
% 0.11/0.26 % SZS status Unsatisfiable
% 0.11/0.26
% 0.11/0.26 % SZS output start CNFRefutation
% See solution above
% 0.11/0.28
% 0.11/0.28 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------