%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.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 09:35:24 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.27s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 26 RR)
% Number of literals : 72 ( 71 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
b != inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_inverse_is_b) ).
cnf(c2,axiom,
add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_add) ).
cnf(c3,plain,
add(multiply(a,b),X2) = add(X2,multiply(a,b)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
add(X2,multiply(a,b)) = add(multiply(a,b),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
add(multiply(a,b),X2) = add(additive_identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,plain,
add(X2,additive_identity) = add(additive_identity,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
add(additive_identity,X2) = add(X2,additive_identity),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,axiom,
add(X2,additive_identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c10,plain,
add(additive_identity,X2) = X2,
inference(transitivity,[status(thm)],[c8,c9]) ).
cnf(c11,plain,
add(multiply(a,b),X2) = X2,
inference(transitivity,[status(thm)],[c6,c10]) ).
cnf(c12,plain,
add(X2,multiply(a,b)) = X2,
inference(transitivity,[status(thm)],[c4,c11]) ).
cnf(c13,plain,
add(inverse(a),multiply(a,b)) = inverse(a),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
inverse(a) = add(inverse(a),multiply(a,b)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,axiom,
multiply(X2,Y2) = multiply(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_multiply) ).
cnf(c16,plain,
multiply(a,b) = multiply(b,a),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
add(inverse(a),multiply(a,b)) = add(inverse(a),multiply(b,a)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c19,plain,
multiply(X2,X3) = multiply(X3,X2),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,plain,
add(inverse(X3),multiply(X2,X3)) = add(inverse(X3),multiply(X3,X2)),
inference(congruence,[status(thm)],[c19]) ).
cnf(c21,axiom,
add(X2,multiply(Y2,Z)) = multiply(add(X2,Y2),add(X2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
cnf(c22,plain,
add(inverse(X3),multiply(X3,X2)) = multiply(add(inverse(X3),X3),add(inverse(X3),X2)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
add(X2,inverse(X2)) = add(inverse(X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
add(inverse(X2),X2) = add(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,axiom,
add(X2,inverse(X2)) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c26,axiom,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c27,plain,
multiplicative_identity = add(a,b),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
add(X2,inverse(X2)) = add(a,b),
inference(transitivity,[status(thm)],[c25,c27]) ).
cnf(c29,plain,
add(inverse(X2),X2) = add(a,b),
inference(transitivity,[status(thm)],[c24,c28]) ).
cnf(c30,plain,
multiply(add(inverse(X3),X3),add(inverse(X3),X2)) = multiply(add(a,b),add(inverse(X3),X2)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
multiply(X2,add(a,b)) = multiply(add(a,b),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c32,plain,
multiply(add(a,b),X2) = multiply(X2,add(a,b)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(X2,add(a,b)) = multiply(X2,multiplicative_identity),
inference(congruence,[status(thm)],[c26]) ).
cnf(c34,axiom,
multiply(X2,multiplicative_identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c35,plain,
multiply(X2,add(a,b)) = X2,
inference(transitivity,[status(thm)],[c33,c34]) ).
cnf(c36,plain,
multiply(add(a,b),X2) = X2,
inference(transitivity,[status(thm)],[c32,c35]) ).
cnf(c37,plain,
multiply(add(a,b),add(inverse(X3),X2)) = add(inverse(X3),X2),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
add(inverse(X3),X2) = add(X2,inverse(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
multiply(add(a,b),add(inverse(X3),X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c37,c38]) ).
cnf(c40,plain,
multiply(add(inverse(X3),X3),add(inverse(X3),X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c30,c39]) ).
cnf(c41,plain,
add(inverse(X3),multiply(X3,X2)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c22,c40]) ).
cnf(c42,plain,
add(inverse(X3),multiply(X2,X3)) = add(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c20,c41]) ).
cnf(c43,plain,
add(inverse(a),multiply(b,a)) = add(b,inverse(a)),
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
add(b,inverse(a)) = add(inverse(a),b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c45,plain,
add(b,multiply(X2,a)) = multiply(add(b,X2),add(b,a)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c46,plain,
add(a,b) = add(b,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c47,plain,
add(b,a) = add(a,b),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
multiply(add(b,X2),add(b,a)) = multiply(add(b,X2),add(a,b)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
multiply(add(b,X2),add(a,b)) = add(b,X2),
inference(substitution,[status(thm)],[c35]) ).
cnf(c50,plain,
add(b,X2) = add(X2,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
multiply(add(b,X2),add(a,b)) = add(X2,b),
inference(transitivity,[status(thm)],[c49,c50]) ).
cnf(c52,plain,
multiply(add(b,X2),add(b,a)) = add(X2,b),
inference(transitivity,[status(thm)],[c48,c51]) ).
cnf(c53,plain,
add(b,multiply(X2,a)) = add(X2,b),
inference(transitivity,[status(thm)],[c45,c52]) ).
cnf(c54,plain,
add(b,multiply(inverse(a),a)) = add(inverse(a),b),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
add(inverse(a),b) = add(b,multiply(inverse(a),a)),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
multiply(X2,inverse(X2)) = multiply(inverse(X2),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c57,plain,
multiply(inverse(X2),X2) = multiply(X2,inverse(X2)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,axiom,
multiply(X2,inverse(X2)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c59,plain,
additive_identity = multiply(a,b),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c60,plain,
multiply(X2,inverse(X2)) = multiply(a,b),
inference(transitivity,[status(thm)],[c58,c59]) ).
cnf(c61,plain,
multiply(inverse(X2),X2) = multiply(a,b),
inference(transitivity,[status(thm)],[c57,c60]) ).
cnf(c62,plain,
multiply(inverse(a),a) = multiply(a,b),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
add(b,multiply(inverse(a),a)) = add(b,multiply(a,b)),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
add(b,multiply(a,b)) = b,
inference(substitution,[status(thm)],[c12]) ).
cnf(c65,plain,
add(b,multiply(inverse(a),a)) = b,
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
add(inverse(a),b) = b,
inference(transitivity,[status(thm)],[c55,c65]) ).
cnf(c67,plain,
add(b,inverse(a)) = b,
inference(transitivity,[status(thm)],[c44,c66]) ).
cnf(c68,plain,
add(inverse(a),multiply(b,a)) = b,
inference(transitivity,[status(thm)],[c43,c67]) ).
cnf(c69,plain,
add(inverse(a),multiply(a,b)) = b,
inference(transitivity,[status(thm)],[c17,c68]) ).
cnf(c70,plain,
inverse(a) = b,
inference(transitivity,[status(thm)],[c14,c69]) ).
cnf(c71,plain,
b = inverse(a),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
$false,
inference(resolution,[status(thm)],[c1,c71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.17 % Computer : n008.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Mon Sep 28 21:04:39 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.27 Command-line arguments: --flatten --complete-subsets
% 0.07/0.27
% 0.07/0.27 % SZS status Unsatisfiable
% 0.07/0.27
% 0.20/0.28 % SZS output start CNFRefutation
% See solution above
% 0.20/0.31
% 0.20/0.31 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------