%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP177-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 10:09:33 AM UTC 2026
% Result : Unsatisfiable 90.10s 11.87s
% Output : CNFRefutation 91.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 17
% Syntax : Number of clauses : 275 ( 275 unt; 0 nHn; 44 RR)
% Number of literals : 275 ( 274 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 525 ( 22 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) != multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p08a) ).
cnf(c2,axiom,
least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_lub) ).
cnf(c3,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
greatest_lower_bound(X2,Y2) = greatest_lower_bound(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_of_glb) ).
cnf(c5,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(b,X2))) = greatest_lower_bound(greatest_lower_bound(X3,multiply(b,X2)),X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c8,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(b,X2)),X2) = greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(b,X2))),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
greatest_lower_bound(X3,multiply(b,X2)) = greatest_lower_bound(multiply(b,X2),X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c10,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(b,X2))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,X2),X3)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
greatest_lower_bound(greatest_lower_bound(X4,X3),X2) = greatest_lower_bound(X2,greatest_lower_bound(X4,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c12,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(greatest_lower_bound(X2,X4),X3),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c14,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
greatest_lower_bound(X2,greatest_lower_bound(Y2,Z)) = greatest_lower_bound(greatest_lower_bound(X2,Y2),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_glb) ).
cnf(c16,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X4,X2),X3),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c19,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
greatest_lower_bound(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c17,c19]) ).
cnf(c21,plain,
greatest_lower_bound(greatest_lower_bound(X2,X4),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c14,c20]) ).
cnf(c22,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c12,c21]) ).
cnf(c23,plain,
greatest_lower_bound(multiply(b,X2),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(b,X2),X3)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(b,X2),X3)) = greatest_lower_bound(multiply(b,X2),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),multiply(b,X3)) = greatest_lower_bound(multiply(b,X3),greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c26,plain,
greatest_lower_bound(multiply(b,X3),greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X2,X3),multiply(b,X3)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
least_upper_bound(greatest_lower_bound(X2,X3),multiply(b,X3)) = least_upper_bound(multiply(b,X3),greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c28,plain,
least_upper_bound(multiply(b,X3),greatest_lower_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X2,X3),multiply(b,X3)),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c30,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
least_upper_bound(multiply(b,X2),X2) = least_upper_bound(multiply(b,X2),multiply(identity,X2)),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,axiom,
multiply(least_upper_bound(Y2,Z2),X2) = least_upper_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub2) ).
cnf(c33,plain,
multiply(least_upper_bound(X3,X4),X2) = least_upper_bound(multiply(X3,X2),multiply(X4,X2)),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X3,X4),X2),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
multiply(least_upper_bound(X3,X4),X2) = multiply(least_upper_bound(X4,X3),X2),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
least_upper_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(least_upper_bound(X4,X3),X2),
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
least_upper_bound(multiply(b,X2),multiply(identity,X2)) = multiply(least_upper_bound(identity,b),X2),
inference(substitution,[status(thm)],[c37]) ).
cnf(c39,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c40,plain,
multiply(least_upper_bound(identity,b),X2) = multiply(b,X2),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
least_upper_bound(multiply(b,X2),multiply(identity,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c38,c40]) ).
cnf(c42,plain,
least_upper_bound(multiply(b,X2),X2) = multiply(b,X2),
inference(transitivity,[status(thm)],[c31,c41]) ).
cnf(c43,plain,
multiply(b,X2) = least_upper_bound(multiply(b,X2),X2),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
least_upper_bound(greatest_lower_bound(X2,X3),multiply(b,X3)) = least_upper_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(b,X3),X3)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c46,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
least_upper_bound(greatest_lower_bound(X4,X3),least_upper_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X4,X3),least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c46]) ).
cnf(c48,axiom,
least_upper_bound(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(least_upper_bound(X2,Y2),Z2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_lub) ).
cnf(c49,plain,
least_upper_bound(greatest_lower_bound(X4,X3),least_upper_bound(X3,X2)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X4,X3),X3),X2),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(greatest_lower_bound(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = least_upper_bound(X2,greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c53,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = least_upper_bound(X2,greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,axiom,
least_upper_bound(X2,greatest_lower_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lub_absorbtion) ).
cnf(c55,plain,
least_upper_bound(X2,greatest_lower_bound(X2,X3)) = X2,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
least_upper_bound(X2,greatest_lower_bound(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c53,c55]) ).
cnf(c57,plain,
least_upper_bound(greatest_lower_bound(X3,X2),X2) = X2,
inference(transitivity,[status(thm)],[c51,c56]) ).
cnf(c58,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X4,X3),X3),X2) = least_upper_bound(X3,X2),
inference(congruence,[status(thm)],[c57]) ).
cnf(c59,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c60,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X4,X3),X3),X2) = least_upper_bound(X2,X3),
inference(transitivity,[status(thm)],[c58,c59]) ).
cnf(c61,plain,
least_upper_bound(greatest_lower_bound(X4,X3),least_upper_bound(X3,X2)) = least_upper_bound(X2,X3),
inference(transitivity,[status(thm)],[c49,c60]) ).
cnf(c62,plain,
least_upper_bound(greatest_lower_bound(X4,X3),least_upper_bound(X2,X3)) = least_upper_bound(X2,X3),
inference(transitivity,[status(thm)],[c47,c61]) ).
cnf(c63,plain,
least_upper_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(b,X3),X3)) = least_upper_bound(multiply(b,X3),X3),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
least_upper_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(b,X3),X3)) = multiply(b,X3),
inference(transitivity,[status(thm)],[c63,c42]) ).
cnf(c65,plain,
least_upper_bound(greatest_lower_bound(X2,X3),multiply(b,X3)) = multiply(b,X3),
inference(transitivity,[status(thm)],[c44,c64]) ).
cnf(c66,plain,
least_upper_bound(multiply(b,X3),greatest_lower_bound(X2,X3)) = multiply(b,X3),
inference(transitivity,[status(thm)],[c28,c65]) ).
cnf(c67,plain,
multiply(b,X3) = least_upper_bound(multiply(b,X3),greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c66]) ).
cnf(c68,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),multiply(b,X3)) = greatest_lower_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(b,X3),greatest_lower_bound(X2,X3))),
inference(congruence,[status(thm)],[c67]) ).
cnf(c69,plain,
least_upper_bound(X3,X2) = least_upper_bound(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c70,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = greatest_lower_bound(X3,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,axiom,
greatest_lower_bound(X2,least_upper_bound(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',glb_absorbtion) ).
cnf(c73,plain,
greatest_lower_bound(X3,least_upper_bound(X3,X2)) = X3,
inference(substitution,[status(thm)],[c72]) ).
cnf(c74,plain,
greatest_lower_bound(X3,least_upper_bound(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c71,c73]) ).
cnf(c75,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(b,X3),greatest_lower_bound(X2,X3))) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),multiply(b,X3)) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c68,c75]) ).
cnf(c77,plain,
greatest_lower_bound(multiply(b,X3),greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c26,c76]) ).
cnf(c78,plain,
greatest_lower_bound(multiply(b,X2),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(b,X2),X3)) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c24,c78]) ).
cnf(c80,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(b,X2))) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c10,c79]) ).
cnf(c81,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(b,X2)),X2) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c8,c80]) ).
cnf(c82,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c) = greatest_lower_bound(a,c),
inference(substitution,[status(thm)],[c81]) ).
cnf(c83,plain,
greatest_lower_bound(a,c) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c)),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c))),
inference(congruence,[status(thm)],[c84]) ).
cnf(c86,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c87,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X3)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2))) = greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X3))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,axiom,
multiply(X2,greatest_lower_bound(Y2,Z2)) = greatest_lower_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb1) ).
cnf(c91,plain,
multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),X2),multiply(greatest_lower_bound(a,b),X3)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X3))) = greatest_lower_bound(X3,greatest_lower_bound(multiply(greatest_lower_bound(a,b),X2),multiply(greatest_lower_bound(a,b),X3))),
inference(congruence,[status(thm)],[c91]) ).
cnf(c93,plain,
X2 = multiply(identity,X2),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c94,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,axiom,
multiply(greatest_lower_bound(Y2,Z2),X2) = greatest_lower_bound(multiply(Y2,X2),multiply(Z2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_glb2) ).
cnf(c96,plain,
multiply(greatest_lower_bound(identity,X2),X3) = greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c97,plain,
greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(identity,X2),X3),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c4]) ).
cnf(c99,plain,
multiply(greatest_lower_bound(identity,X2),X3) = multiply(greatest_lower_bound(X2,identity),X3),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
greatest_lower_bound(multiply(identity,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c97,c99]) ).
cnf(c101,plain,
greatest_lower_bound(X3,multiply(X2,X3)) = multiply(greatest_lower_bound(X2,identity),X3),
inference(transitivity,[status(thm)],[c94,c100]) ).
cnf(c102,plain,
multiply(greatest_lower_bound(X2,identity),X3) = greatest_lower_bound(X3,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X2,identity),X4),X3) = greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X4)),X3),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
greatest_lower_bound(X4,greatest_lower_bound(multiply(X2,X4),X3)) = greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X4)),X3),
inference(substitution,[status(thm)],[c15]) ).
cnf(c105,plain,
greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X4)),X3) = greatest_lower_bound(X4,greatest_lower_bound(multiply(X2,X4),X3)),
inference(symmetry,[status(thm)],[c104]) ).
cnf(c106,plain,
greatest_lower_bound(multiply(X2,X4),X3) = greatest_lower_bound(X3,multiply(X2,X4)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c107,plain,
greatest_lower_bound(X4,greatest_lower_bound(multiply(X2,X4),X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,multiply(X2,X4))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X4)),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,multiply(X2,X4))),
inference(transitivity,[status(thm)],[c105,c107]) ).
cnf(c109,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X2,identity),X4),X3) = greatest_lower_bound(X4,greatest_lower_bound(X3,multiply(X2,X4))),
inference(transitivity,[status(thm)],[c103,c108]) ).
cnf(c110,plain,
greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a,b),identity),X3),X2) = greatest_lower_bound(X3,greatest_lower_bound(X2,multiply(greatest_lower_bound(a,b),X3))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,multiply(greatest_lower_bound(a,b),X3))) = greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a,b),identity),X3),X2),
inference(symmetry,[status(thm)],[c110]) ).
cnf(c112,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,b)) = greatest_lower_bound(greatest_lower_bound(a,b),identity),
inference(substitution,[status(thm)],[c4]) ).
cnf(c113,plain,
greatest_lower_bound(greatest_lower_bound(a,b),identity) = greatest_lower_bound(identity,greatest_lower_bound(a,b)),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,b)) = greatest_lower_bound(b,greatest_lower_bound(identity,a)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c115,axiom,
least_upper_bound(identity,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c116,plain,
a = least_upper_bound(identity,a),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
greatest_lower_bound(identity,a) = greatest_lower_bound(identity,least_upper_bound(identity,a)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
greatest_lower_bound(identity,least_upper_bound(identity,a)) = identity,
inference(substitution,[status(thm)],[c72]) ).
cnf(c119,plain,
greatest_lower_bound(identity,a) = identity,
inference(transitivity,[status(thm)],[c117,c118]) ).
cnf(c120,plain,
greatest_lower_bound(b,greatest_lower_bound(identity,a)) = greatest_lower_bound(b,identity),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
greatest_lower_bound(b,identity) = greatest_lower_bound(identity,b),
inference(substitution,[status(thm)],[c4]) ).
cnf(c122,plain,
b = least_upper_bound(identity,b),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c123,plain,
greatest_lower_bound(identity,b) = greatest_lower_bound(identity,least_upper_bound(identity,b)),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
greatest_lower_bound(identity,least_upper_bound(identity,b)) = identity,
inference(substitution,[status(thm)],[c72]) ).
cnf(c125,plain,
greatest_lower_bound(identity,b) = identity,
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
greatest_lower_bound(b,identity) = identity,
inference(transitivity,[status(thm)],[c121,c125]) ).
cnf(c127,plain,
greatest_lower_bound(b,greatest_lower_bound(identity,a)) = identity,
inference(transitivity,[status(thm)],[c120,c126]) ).
cnf(c128,plain,
greatest_lower_bound(identity,greatest_lower_bound(a,b)) = identity,
inference(transitivity,[status(thm)],[c114,c127]) ).
cnf(c129,plain,
greatest_lower_bound(greatest_lower_bound(a,b),identity) = identity,
inference(transitivity,[status(thm)],[c113,c128]) ).
cnf(c130,plain,
multiply(greatest_lower_bound(greatest_lower_bound(a,b),identity),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a,b),identity),X3),X2) = greatest_lower_bound(multiply(identity,X3),X2),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
greatest_lower_bound(multiply(identity,X3),X2) = greatest_lower_bound(X3,X2),
inference(congruence,[status(thm)],[c29]) ).
cnf(c133,plain,
greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(a,b),identity),X3),X2) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c131,c132]) ).
cnf(c134,plain,
greatest_lower_bound(X3,greatest_lower_bound(X2,multiply(greatest_lower_bound(a,b),X3))) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c111,c133]) ).
cnf(c135,plain,
greatest_lower_bound(X3,greatest_lower_bound(multiply(greatest_lower_bound(a,b),X2),multiply(greatest_lower_bound(a,b),X3))) = greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),X2)),
inference(substitution,[status(thm)],[c134]) ).
cnf(c136,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X2,X3))) = greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),X2)),
inference(transitivity,[status(thm)],[c92,c135]) ).
cnf(c137,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),greatest_lower_bound(X3,X2))) = greatest_lower_bound(X3,multiply(greatest_lower_bound(a,b),X2)),
inference(transitivity,[status(thm)],[c89,c136]) ).
cnf(c138,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c))) = greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),c)),
inference(substitution,[status(thm)],[c137]) ).
cnf(c139,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X3,X2),X5),greatest_lower_bound(X4,multiply(X2,X5))) = greatest_lower_bound(greatest_lower_bound(X4,multiply(X2,X5)),multiply(greatest_lower_bound(X3,X2),X5)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c140,plain,
greatest_lower_bound(greatest_lower_bound(X5,multiply(X3,X2)),multiply(greatest_lower_bound(X4,X3),X2)) = greatest_lower_bound(multiply(greatest_lower_bound(X4,X3),X2),greatest_lower_bound(X5,multiply(X3,X2))),
inference(symmetry,[status(thm)],[c139]) ).
cnf(c141,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c142,plain,
greatest_lower_bound(X2,X3) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c143,plain,
greatest_lower_bound(X4,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,X4)) = greatest_lower_bound(X4,greatest_lower_bound(X3,X2)),
inference(transitivity,[status(thm)],[c141,c143]) ).
cnf(c145,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X4,X3),X2),greatest_lower_bound(X5,multiply(X3,X2))) = greatest_lower_bound(multiply(X3,X2),greatest_lower_bound(X5,multiply(greatest_lower_bound(X4,X3),X2))),
inference(substitution,[status(thm)],[c144]) ).
cnf(c146,plain,
greatest_lower_bound(multiply(X4,X3),X2) = greatest_lower_bound(X2,multiply(X4,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c147,plain,
greatest_lower_bound(X2,multiply(X4,X3)) = greatest_lower_bound(multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(X2,multiply(X5,X3))) = greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(multiply(X5,X3),X2)),
inference(congruence,[status(thm)],[c147]) ).
cnf(c149,plain,
greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(multiply(X5,X3),X2)) = greatest_lower_bound(greatest_lower_bound(multiply(X4,X3),multiply(X5,X3)),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c150,plain,
multiply(greatest_lower_bound(X4,X2),X3) = greatest_lower_bound(multiply(X4,X3),multiply(X2,X3)),
inference(substitution,[status(thm)],[c95]) ).
cnf(c151,plain,
greatest_lower_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X4,X2),X3),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
greatest_lower_bound(X3,X2) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c153,plain,
multiply(greatest_lower_bound(X4,X2),X3) = multiply(greatest_lower_bound(X2,X4),X3),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
greatest_lower_bound(multiply(X4,X3),multiply(X2,X3)) = multiply(greatest_lower_bound(X2,X4),X3),
inference(transitivity,[status(thm)],[c151,c153]) ).
cnf(c155,plain,
greatest_lower_bound(multiply(X3,X2),multiply(X4,X2)) = multiply(greatest_lower_bound(X4,X3),X2),
inference(substitution,[status(thm)],[c154]) ).
cnf(c156,plain,
greatest_lower_bound(greatest_lower_bound(multiply(X4,X3),multiply(X5,X3)),X2) = greatest_lower_bound(multiply(greatest_lower_bound(X5,X4),X3),X2),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(multiply(X5,X3),X2)) = greatest_lower_bound(multiply(greatest_lower_bound(X5,X4),X3),X2),
inference(transitivity,[status(thm)],[c149,c156]) ).
cnf(c158,plain,
greatest_lower_bound(multiply(X4,X3),greatest_lower_bound(X2,multiply(X5,X3))) = greatest_lower_bound(multiply(greatest_lower_bound(X5,X4),X3),X2),
inference(transitivity,[status(thm)],[c148,c157]) ).
cnf(c159,plain,
greatest_lower_bound(multiply(X5,X4),greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,X5),X4))) = greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(X2,X5),X5),X4),X3),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
X2 = least_upper_bound(greatest_lower_bound(X3,X2),X2),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c161,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),X2) = greatest_lower_bound(greatest_lower_bound(X3,X2),least_upper_bound(greatest_lower_bound(X3,X2),X2)),
inference(congruence,[status(thm)],[c160]) ).
cnf(c162,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),least_upper_bound(greatest_lower_bound(X3,X2),X2)) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c72]) ).
cnf(c163,plain,
greatest_lower_bound(greatest_lower_bound(X3,X2),X2) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c161,c162]) ).
cnf(c164,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),X3) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X2,X4),X4),X3) = multiply(greatest_lower_bound(X2,X4),X3),
inference(congruence,[status(thm)],[c164]) ).
cnf(c166,plain,
greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(X2,X5),X5),X4),X3) = greatest_lower_bound(multiply(greatest_lower_bound(X2,X5),X4),X3),
inference(congruence,[status(thm)],[c165]) ).
cnf(c167,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X2,X5),X4),X3) = greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,X5),X4)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c168,plain,
greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(X2,X5),X5),X4),X3) = greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,X5),X4)),
inference(transitivity,[status(thm)],[c166,c167]) ).
cnf(c169,plain,
greatest_lower_bound(multiply(X5,X4),greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,X5),X4))) = greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,X5),X4)),
inference(transitivity,[status(thm)],[c159,c168]) ).
cnf(c170,plain,
greatest_lower_bound(multiply(X3,X2),greatest_lower_bound(X5,multiply(greatest_lower_bound(X4,X3),X2))) = greatest_lower_bound(X5,multiply(greatest_lower_bound(X4,X3),X2)),
inference(substitution,[status(thm)],[c169]) ).
cnf(c171,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X4,X3),X2),greatest_lower_bound(X5,multiply(X3,X2))) = greatest_lower_bound(X5,multiply(greatest_lower_bound(X4,X3),X2)),
inference(transitivity,[status(thm)],[c145,c170]) ).
cnf(c172,plain,
greatest_lower_bound(greatest_lower_bound(X5,multiply(X3,X2)),multiply(greatest_lower_bound(X4,X3),X2)) = greatest_lower_bound(X5,multiply(greatest_lower_bound(X4,X3),X2)),
inference(transitivity,[status(thm)],[c140,c171]) ).
cnf(c173,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(X2,c)),multiply(greatest_lower_bound(X3,X2),c)) = greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,X2),c)),
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
greatest_lower_bound(multiply(X5,X4),greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,multiply(X5,c)),X4))) = greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(X2,multiply(X5,c)),X5),X4),X3),
inference(substitution,[status(thm)],[c158]) ).
cnf(c175,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(X2,c))) = greatest_lower_bound(greatest_lower_bound(X3,multiply(X2,c)),X2),
inference(substitution,[status(thm)],[c4]) ).
cnf(c176,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(X2,c)),X2) = greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(X2,c))),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
greatest_lower_bound(X3,multiply(X2,c)) = greatest_lower_bound(multiply(X2,c),X3),
inference(substitution,[status(thm)],[c4]) ).
cnf(c178,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(X2,c))) = greatest_lower_bound(X2,greatest_lower_bound(multiply(X2,c),X3)),
inference(congruence,[status(thm)],[c177]) ).
cnf(c179,plain,
greatest_lower_bound(multiply(X2,c),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X2,greatest_lower_bound(multiply(X2,c),X3)),
inference(substitution,[status(thm)],[c22]) ).
cnf(c180,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(X2,c),X3)) = greatest_lower_bound(multiply(X2,c),greatest_lower_bound(X3,X2)),
inference(symmetry,[status(thm)],[c179]) ).
cnf(c181,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),multiply(X3,c)) = greatest_lower_bound(multiply(X3,c),greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c182,plain,
greatest_lower_bound(multiply(X3,c),greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X2,X3),multiply(X3,c)),
inference(symmetry,[status(thm)],[c181]) ).
cnf(c183,plain,
least_upper_bound(greatest_lower_bound(X2,X3),multiply(X3,c)) = least_upper_bound(multiply(X3,c),greatest_lower_bound(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c184,plain,
least_upper_bound(multiply(X3,c),greatest_lower_bound(X2,X3)) = least_upper_bound(greatest_lower_bound(X2,X3),multiply(X3,c)),
inference(symmetry,[status(thm)],[c183]) ).
cnf(c185,axiom,
multiply(multiply(X2,Y2),Z2) = multiply(X2,multiply(Y2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c186,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c189,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c188]) ).
cnf(c190,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c189,c29]) ).
cnf(c191,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c187,c190]) ).
cnf(c192,plain,
X2 = multiply(inverse(X3),multiply(X3,X2)),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(inverse(inverse(X3)),X2) = multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))),
inference(congruence,[status(thm)],[c192]) ).
cnf(c194,plain,
multiply(inverse(inverse(X3)),multiply(inverse(X3),multiply(X3,X2))) = multiply(X3,X2),
inference(substitution,[status(thm)],[c191]) ).
cnf(c195,plain,
multiply(inverse(inverse(X3)),X2) = multiply(X3,X2),
inference(transitivity,[status(thm)],[c193,c194]) ).
cnf(c196,plain,
multiply(inverse(inverse(X2)),identity) = multiply(X2,identity),
inference(substitution,[status(thm)],[c195]) ).
cnf(c197,plain,
multiply(X2,identity) = multiply(inverse(inverse(X2)),identity),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
identity = multiply(inverse(X2),X2),
inference(symmetry,[status(thm)],[c188]) ).
cnf(c199,plain,
multiply(inverse(inverse(X2)),identity) = multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(inverse(inverse(X2)),multiply(inverse(X2),X2)) = X2,
inference(substitution,[status(thm)],[c191]) ).
cnf(c201,plain,
multiply(inverse(inverse(X2)),identity) = X2,
inference(transitivity,[status(thm)],[c199,c200]) ).
cnf(c202,plain,
multiply(X2,identity) = X2,
inference(transitivity,[status(thm)],[c197,c201]) ).
cnf(c203,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c204,plain,
least_upper_bound(multiply(X2,c),X2) = least_upper_bound(multiply(X2,c),multiply(X2,identity)),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,axiom,
multiply(X2,least_upper_bound(Y2,Z2)) = least_upper_bound(multiply(X2,Y2),multiply(X2,Z2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monotony_lub1) ).
cnf(c206,plain,
multiply(X4,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X4,X2),multiply(X4,X3)),
inference(substitution,[status(thm)],[c205]) ).
cnf(c207,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X2,X3)),
inference(symmetry,[status(thm)],[c206]) ).
cnf(c208,plain,
least_upper_bound(X2,X3) = least_upper_bound(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c209,plain,
multiply(X4,least_upper_bound(X2,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
least_upper_bound(multiply(X4,X2),multiply(X4,X3)) = multiply(X4,least_upper_bound(X3,X2)),
inference(transitivity,[status(thm)],[c207,c209]) ).
cnf(c211,plain,
least_upper_bound(multiply(X2,c),multiply(X2,identity)) = multiply(X2,least_upper_bound(identity,c)),
inference(substitution,[status(thm)],[c210]) ).
cnf(c212,axiom,
least_upper_bound(identity,c) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c213,plain,
multiply(X2,least_upper_bound(identity,c)) = multiply(X2,c),
inference(congruence,[status(thm)],[c212]) ).
cnf(c214,plain,
least_upper_bound(multiply(X2,c),multiply(X2,identity)) = multiply(X2,c),
inference(transitivity,[status(thm)],[c211,c213]) ).
cnf(c215,plain,
least_upper_bound(multiply(X2,c),X2) = multiply(X2,c),
inference(transitivity,[status(thm)],[c204,c214]) ).
cnf(c216,plain,
multiply(X2,c) = least_upper_bound(multiply(X2,c),X2),
inference(symmetry,[status(thm)],[c215]) ).
cnf(c217,plain,
least_upper_bound(greatest_lower_bound(X2,X3),multiply(X3,c)) = least_upper_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(X3,c),X3)),
inference(congruence,[status(thm)],[c216]) ).
cnf(c218,plain,
least_upper_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(X3,c),X3)) = least_upper_bound(multiply(X3,c),X3),
inference(substitution,[status(thm)],[c62]) ).
cnf(c219,plain,
least_upper_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(X3,c),X3)) = multiply(X3,c),
inference(transitivity,[status(thm)],[c218,c215]) ).
cnf(c220,plain,
least_upper_bound(greatest_lower_bound(X2,X3),multiply(X3,c)) = multiply(X3,c),
inference(transitivity,[status(thm)],[c217,c219]) ).
cnf(c221,plain,
least_upper_bound(multiply(X3,c),greatest_lower_bound(X2,X3)) = multiply(X3,c),
inference(transitivity,[status(thm)],[c184,c220]) ).
cnf(c222,plain,
multiply(X3,c) = least_upper_bound(multiply(X3,c),greatest_lower_bound(X2,X3)),
inference(symmetry,[status(thm)],[c221]) ).
cnf(c223,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),multiply(X3,c)) = greatest_lower_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(X3,c),greatest_lower_bound(X2,X3))),
inference(congruence,[status(thm)],[c222]) ).
cnf(c224,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),least_upper_bound(multiply(X3,c),greatest_lower_bound(X2,X3))) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c74]) ).
cnf(c225,plain,
greatest_lower_bound(greatest_lower_bound(X2,X3),multiply(X3,c)) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c223,c224]) ).
cnf(c226,plain,
greatest_lower_bound(multiply(X3,c),greatest_lower_bound(X2,X3)) = greatest_lower_bound(X2,X3),
inference(transitivity,[status(thm)],[c182,c225]) ).
cnf(c227,plain,
greatest_lower_bound(multiply(X2,c),greatest_lower_bound(X3,X2)) = greatest_lower_bound(X3,X2),
inference(substitution,[status(thm)],[c226]) ).
cnf(c228,plain,
greatest_lower_bound(X2,greatest_lower_bound(multiply(X2,c),X3)) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c180,c227]) ).
cnf(c229,plain,
greatest_lower_bound(X2,greatest_lower_bound(X3,multiply(X2,c))) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c178,c228]) ).
cnf(c230,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(X2,c)),X2) = greatest_lower_bound(X3,X2),
inference(transitivity,[status(thm)],[c176,c229]) ).
cnf(c231,plain,
greatest_lower_bound(greatest_lower_bound(X2,multiply(X3,c)),X3) = greatest_lower_bound(X2,X3),
inference(substitution,[status(thm)],[c230]) ).
cnf(c232,plain,
multiply(greatest_lower_bound(greatest_lower_bound(X2,multiply(X4,c)),X4),X3) = multiply(greatest_lower_bound(X2,X4),X3),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(X2,multiply(X5,c)),X5),X4),X3) = greatest_lower_bound(multiply(greatest_lower_bound(X2,X5),X4),X3),
inference(congruence,[status(thm)],[c232]) ).
cnf(c234,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X2,X5),X4),X3) = greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,X5),X4)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c235,plain,
greatest_lower_bound(multiply(greatest_lower_bound(greatest_lower_bound(X2,multiply(X5,c)),X5),X4),X3) = greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,X5),X4)),
inference(transitivity,[status(thm)],[c233,c234]) ).
cnf(c236,plain,
greatest_lower_bound(multiply(X5,X4),greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,multiply(X5,c)),X4))) = greatest_lower_bound(X3,multiply(greatest_lower_bound(X2,X5),X4)),
inference(transitivity,[status(thm)],[c174,c235]) ).
cnf(c237,plain,
greatest_lower_bound(multiply(X2,c),greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,multiply(X2,c)),c))) = greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,X2),c)),
inference(substitution,[status(thm)],[c236]) ).
cnf(c238,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,X2),c)) = greatest_lower_bound(multiply(X2,c),greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,multiply(X2,c)),c))),
inference(symmetry,[status(thm)],[c237]) ).
cnf(c239,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X3,multiply(X2,c)),c),greatest_lower_bound(X3,multiply(X2,c))) = greatest_lower_bound(multiply(X2,c),greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,multiply(X2,c)),c))),
inference(substitution,[status(thm)],[c144]) ).
cnf(c240,plain,
greatest_lower_bound(multiply(X2,c),greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,multiply(X2,c)),c))) = greatest_lower_bound(multiply(greatest_lower_bound(X3,multiply(X2,c)),c),greatest_lower_bound(X3,multiply(X2,c))),
inference(symmetry,[status(thm)],[c239]) ).
cnf(c241,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X3,multiply(X2,c)),c),greatest_lower_bound(X3,multiply(X2,c))) = greatest_lower_bound(greatest_lower_bound(X3,multiply(X2,c)),multiply(greatest_lower_bound(X3,multiply(X2,c)),c)),
inference(substitution,[status(thm)],[c4]) ).
cnf(c242,plain,
X2 = multiply(X2,identity),
inference(symmetry,[status(thm)],[c202]) ).
cnf(c243,plain,
greatest_lower_bound(X3,multiply(X3,X2)) = greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)),
inference(congruence,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)),
inference(substitution,[status(thm)],[c90]) ).
cnf(c245,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,greatest_lower_bound(identity,X2)),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
greatest_lower_bound(identity,X2) = greatest_lower_bound(X2,identity),
inference(substitution,[status(thm)],[c4]) ).
cnf(c247,plain,
multiply(X3,greatest_lower_bound(identity,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(congruence,[status(thm)],[c246]) ).
cnf(c248,plain,
greatest_lower_bound(multiply(X3,identity),multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c245,c247]) ).
cnf(c249,plain,
greatest_lower_bound(X3,multiply(X3,X2)) = multiply(X3,greatest_lower_bound(X2,identity)),
inference(transitivity,[status(thm)],[c243,c248]) ).
cnf(c250,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(X2,c)),multiply(greatest_lower_bound(X3,multiply(X2,c)),c)) = multiply(greatest_lower_bound(X3,multiply(X2,c)),greatest_lower_bound(c,identity)),
inference(substitution,[status(thm)],[c249]) ).
cnf(c251,plain,
greatest_lower_bound(c,identity) = greatest_lower_bound(identity,c),
inference(substitution,[status(thm)],[c4]) ).
cnf(c252,plain,
multiply(greatest_lower_bound(X3,multiply(X2,c)),greatest_lower_bound(c,identity)) = multiply(greatest_lower_bound(X3,multiply(X2,c)),greatest_lower_bound(identity,c)),
inference(congruence,[status(thm)],[c251]) ).
cnf(c253,plain,
c = least_upper_bound(identity,c),
inference(symmetry,[status(thm)],[c212]) ).
cnf(c254,plain,
greatest_lower_bound(identity,c) = greatest_lower_bound(identity,least_upper_bound(identity,c)),
inference(congruence,[status(thm)],[c253]) ).
cnf(c255,plain,
greatest_lower_bound(identity,least_upper_bound(identity,c)) = identity,
inference(substitution,[status(thm)],[c72]) ).
cnf(c256,plain,
greatest_lower_bound(identity,c) = identity,
inference(transitivity,[status(thm)],[c254,c255]) ).
cnf(c257,plain,
multiply(greatest_lower_bound(X3,multiply(X2,c)),greatest_lower_bound(identity,c)) = multiply(greatest_lower_bound(X3,multiply(X2,c)),identity),
inference(congruence,[status(thm)],[c256]) ).
cnf(c258,plain,
multiply(greatest_lower_bound(X3,multiply(X2,c)),identity) = greatest_lower_bound(X3,multiply(X2,c)),
inference(substitution,[status(thm)],[c202]) ).
cnf(c259,plain,
multiply(greatest_lower_bound(X3,multiply(X2,c)),greatest_lower_bound(identity,c)) = greatest_lower_bound(X3,multiply(X2,c)),
inference(transitivity,[status(thm)],[c257,c258]) ).
cnf(c260,plain,
multiply(greatest_lower_bound(X3,multiply(X2,c)),greatest_lower_bound(c,identity)) = greatest_lower_bound(X3,multiply(X2,c)),
inference(transitivity,[status(thm)],[c252,c259]) ).
cnf(c261,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(X2,c)),multiply(greatest_lower_bound(X3,multiply(X2,c)),c)) = greatest_lower_bound(X3,multiply(X2,c)),
inference(transitivity,[status(thm)],[c250,c260]) ).
cnf(c262,plain,
greatest_lower_bound(multiply(greatest_lower_bound(X3,multiply(X2,c)),c),greatest_lower_bound(X3,multiply(X2,c))) = greatest_lower_bound(X3,multiply(X2,c)),
inference(transitivity,[status(thm)],[c241,c261]) ).
cnf(c263,plain,
greatest_lower_bound(multiply(X2,c),greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,multiply(X2,c)),c))) = greatest_lower_bound(X3,multiply(X2,c)),
inference(transitivity,[status(thm)],[c240,c262]) ).
cnf(c264,plain,
greatest_lower_bound(X3,multiply(greatest_lower_bound(X3,X2),c)) = greatest_lower_bound(X3,multiply(X2,c)),
inference(transitivity,[status(thm)],[c238,c263]) ).
cnf(c265,plain,
greatest_lower_bound(greatest_lower_bound(X3,multiply(X2,c)),multiply(greatest_lower_bound(X3,X2),c)) = greatest_lower_bound(X3,multiply(X2,c)),
inference(transitivity,[status(thm)],[c173,c264]) ).
cnf(c266,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),c)) = greatest_lower_bound(a,multiply(b,c)),
inference(substitution,[status(thm)],[c265]) ).
cnf(c267,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),c))) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c138,c266]) ).
cnf(c268,plain,
greatest_lower_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c85,c267]) ).
cnf(c269,plain,
greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) = greatest_lower_bound(a,multiply(b,c)),
inference(transitivity,[status(thm)],[c6,c268]) ).
cnf(c270,plain,
greatest_lower_bound(a,multiply(b,c)) = greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))),
inference(symmetry,[status(thm)],[c269]) ).
cnf(c271,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) = least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c)))),
inference(congruence,[status(thm)],[c270]) ).
cnf(c272,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c)))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(substitution,[status(thm)],[c54]) ).
cnf(c273,plain,
least_upper_bound(multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),greatest_lower_bound(a,multiply(b,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(transitivity,[status(thm)],[c271,c272]) ).
cnf(c274,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(transitivity,[status(thm)],[c3,c273]) ).
cnf(c275,plain,
$false,
inference(resolution,[status(thm)],[c1,c274]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP177-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sun Sep 27 09:36:01 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 90.10/11.87 Command-line arguments: --stitch /export/starexec/sandbox/solver/bin/stitch --hint-skel-cost 0 --hint-skel-factor 0.5
% 90.10/11.87
% 90.10/11.87 % SZS status Unsatisfiable
% 90.10/11.87
% 90.10/11.89 % SZS output start CNFRefutation
% See solution above
% 91.70/12.01
% 91.70/12.01 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------