%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP173-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 10:09:32 AM UTC 2026
% Result : Unsatisfiable 0.14s 0.46s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of clauses : 72 ( 72 unt; 0 nHn; 36 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 : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
identity != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_p05a) ).
cnf(c2,axiom,
multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
cnf(c3,plain,
multiply(inverse(a),a) = identity,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
identity = multiply(inverse(a),a),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
greatest_lower_bound(X2,Y) = greatest_lower_bound(Y,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c6,plain,
greatest_lower_bound(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
greatest_lower_bound(identity,inverse(a)) = greatest_lower_bound(inverse(a),identity),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,axiom,
least_upper_bound(identity,inverse(a)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c9,plain,
identity = least_upper_bound(identity,inverse(a)),
inference(symmetry,[status(thm)],[c8]) ).
cnf(c10,plain,
greatest_lower_bound(inverse(a),identity) = greatest_lower_bound(inverse(a),least_upper_bound(identity,inverse(a))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,axiom,
least_upper_bound(X2,Y2) = least_upper_bound(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c12,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c16,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c14,c16]) ).
cnf(c18,plain,
greatest_lower_bound(inverse(a),least_upper_bound(identity,inverse(a))) = inverse(a),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
greatest_lower_bound(inverse(a),identity) = inverse(a),
inference(transitivity,[status(thm)],[c10,c18]) ).
cnf(c20,plain,
greatest_lower_bound(identity,inverse(a)) = inverse(a),
inference(transitivity,[status(thm)],[c7,c19]) ).
cnf(c21,plain,
inverse(a) = greatest_lower_bound(identity,inverse(a)),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
greatest_lower_bound(inverse(a),identity) = greatest_lower_bound(identity,inverse(a)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c23,plain,
greatest_lower_bound(identity,inverse(a)) = greatest_lower_bound(inverse(a),identity),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,axiom,
multiply(multiply(X2,Y2),Z) = multiply(X2,multiply(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c25,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c2]) ).
cnf(c28,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c29,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c27,c28]) ).
cnf(c30,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c26,c29]) ).
cnf(c31,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c30]) ).
cnf(c32,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c34,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = multiply(X2,inverse(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
multiply(X2,inverse(X2)) = multiply(inverse(inverse(X2)),inverse(X2)),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
multiply(inverse(inverse(X2)),inverse(X2)) = identity,
inference(substitution,[status(thm)],[c2]) ).
cnf(c38,plain,
multiply(X2,inverse(X2)) = identity,
inference(transitivity,[status(thm)],[c36,c37]) ).
cnf(c39,plain,
multiply(a,inverse(a)) = identity,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
identity = multiply(a,inverse(a)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
greatest_lower_bound(inverse(a),identity) = greatest_lower_bound(inverse(a),multiply(a,inverse(a))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c5]) ).
cnf(c43,plain,
greatest_lower_bound(X2,identity) = greatest_lower_bound(identity,X2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(greatest_lower_bound(X3,identity),X2) = multiply(greatest_lower_bound(identity,X3),X2),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c46,plain,
multiply(greatest_lower_bound(identity,X3),X2) = greatest_lower_bound(multiply(identity,X2),multiply(X3,X2)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
greatest_lower_bound(multiply(identity,X2),multiply(X3,X2)) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(congruence,[status(thm)],[c28]) ).
cnf(c48,plain,
multiply(greatest_lower_bound(identity,X3),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c46,c47]) ).
cnf(c49,plain,
multiply(greatest_lower_bound(X3,identity),X2) = greatest_lower_bound(X2,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c44,c48]) ).
cnf(c50,plain,
multiply(greatest_lower_bound(a,identity),X2) = greatest_lower_bound(X2,multiply(a,X2)),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
greatest_lower_bound(X2,multiply(a,X2)) = multiply(greatest_lower_bound(a,identity),X2),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
least_upper_bound(identity,a) = least_upper_bound(a,identity),
inference(substitution,[status(thm)],[c11]) ).
cnf(c53,plain,
least_upper_bound(a,identity) = least_upper_bound(identity,a),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,axiom,
least_upper_bound(identity,a) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c55,plain,
least_upper_bound(a,identity) = identity,
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
identity = least_upper_bound(a,identity),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
greatest_lower_bound(a,identity) = greatest_lower_bound(a,least_upper_bound(a,identity)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
greatest_lower_bound(a,least_upper_bound(a,identity)) = a,
inference(substitution,[status(thm)],[c15]) ).
cnf(c59,plain,
greatest_lower_bound(a,identity) = a,
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
multiply(greatest_lower_bound(a,identity),X2) = multiply(a,X2),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
greatest_lower_bound(X2,multiply(a,X2)) = multiply(a,X2),
inference(transitivity,[status(thm)],[c51,c60]) ).
cnf(c62,plain,
greatest_lower_bound(inverse(a),multiply(a,inverse(a))) = multiply(a,inverse(a)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
multiply(a,inverse(a)) = identity,
inference(substitution,[status(thm)],[c38]) ).
cnf(c64,plain,
greatest_lower_bound(inverse(a),multiply(a,inverse(a))) = identity,
inference(transitivity,[status(thm)],[c62,c63]) ).
cnf(c65,plain,
greatest_lower_bound(inverse(a),identity) = identity,
inference(transitivity,[status(thm)],[c41,c64]) ).
cnf(c66,plain,
greatest_lower_bound(identity,inverse(a)) = identity,
inference(transitivity,[status(thm)],[c23,c65]) ).
cnf(c67,plain,
inverse(a) = identity,
inference(transitivity,[status(thm)],[c21,c66]) ).
cnf(c68,plain,
multiply(inverse(a),a) = multiply(identity,a),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(identity,a) = a,
inference(substitution,[status(thm)],[c28]) ).
cnf(c70,plain,
multiply(inverse(a),a) = a,
inference(transitivity,[status(thm)],[c68,c69]) ).
cnf(c71,plain,
identity = a,
inference(transitivity,[status(thm)],[c4,c70]) ).
cnf(c72,plain,
$false,
inference(resolution,[status(thm)],[c1,c71]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP173-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 09:35:30 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.46 Command-line arguments: --no-flatten-goal
% 0.14/0.46
% 0.14/0.46 % SZS status Unsatisfiable
% 0.14/0.46
% 0.14/0.46 % SZS output start CNFRefutation
% See solution above
% 0.14/0.48
% 0.14/0.48 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------