%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 10:08:50 AM UTC 2026
% Result : Unsatisfiable 0.19s 0.54s
% Output : CNFRefutation 1.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 12
% Syntax : Number of clauses : 213 ( 213 unt; 0 nHn; 106 RR)
% Number of literals : 213 ( 212 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 : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 148 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
multiply(k,inverse(b)) != identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(c2,axiom,
multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(c3,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(X3,multiply(inverse(X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
multiply(X3,multiply(inverse(X3),X2)) = multiply(multiply(X3,inverse(X3)),X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
multiply(X2,inverse(X2)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c6,plain,
multiply(multiply(X3,inverse(X3)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
multiply(identity,X2) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c8,plain,
multiply(multiply(X3,inverse(X3)),X2) = X2,
inference(transitivity,[status(thm)],[c6,c7]) ).
cnf(c9,plain,
multiply(X3,multiply(inverse(X3),X2)) = X2,
inference(transitivity,[status(thm)],[c4,c8]) ).
cnf(c10,plain,
multiply(X2,multiply(inverse(X2),multiply(inverse(X2),inverse(X2)))) = multiply(inverse(X2),inverse(X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(inverse(X2),inverse(X2)) = multiply(X2,multiply(inverse(X2),multiply(inverse(X2),inverse(X2)))),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,hypothesis,
multiply(X2,multiply(X2,X2)) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity) ).
cnf(c13,plain,
multiply(inverse(X2),multiply(inverse(X2),inverse(X2))) = identity,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
multiply(X2,multiply(inverse(X2),multiply(inverse(X2),inverse(X2)))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
multiply(X2,identity) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c16,plain,
multiply(X2,multiply(inverse(X2),multiply(inverse(X2),inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c14,c15]) ).
cnf(c17,plain,
multiply(inverse(X2),inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c11,c16]) ).
cnf(c18,plain,
X2 = multiply(inverse(X2),inverse(X2)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
multiply(X2,X2) = multiply(X2,multiply(inverse(X2),inverse(X2))),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
multiply(X2,multiply(inverse(X2),inverse(X2))) = inverse(X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c21,plain,
multiply(X2,X2) = inverse(X2),
inference(transitivity,[status(thm)],[c19,c20]) ).
cnf(c22,plain,
multiply(b,b) = inverse(b),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
inverse(b) = multiply(b,b),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,axiom,
multiply(h,b) = j,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c25,plain,
j = multiply(h,b),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c27,plain,
inverse(inverse(X2)) = multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
multiply(inverse(X2),inverse(inverse(X2))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c29,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = multiply(X2,identity),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
multiply(X2,multiply(inverse(X2),inverse(inverse(X2)))) = X2,
inference(transitivity,[status(thm)],[c29,c15]) ).
cnf(c31,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c27,c30]) ).
cnf(c32,plain,
inverse(inverse(b)) = b,
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
b = inverse(inverse(b)),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
multiply(h,b) = multiply(h,inverse(inverse(b))),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,plain,
multiply(multiply(d,inverse(b)),X2) = multiply(d,multiply(inverse(b),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
multiply(d,multiply(inverse(b),X2)) = multiply(multiply(d,inverse(b)),X2),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,axiom,
multiply(d,inverse(b)) = h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c38,plain,
multiply(multiply(d,inverse(b)),X2) = multiply(h,X2),
inference(congruence,[status(thm)],[c37]) ).
cnf(c39,plain,
multiply(d,multiply(inverse(b),X2)) = multiply(h,X2),
inference(transitivity,[status(thm)],[c36,c38]) ).
cnf(c40,plain,
multiply(d,multiply(inverse(b),inverse(inverse(b)))) = multiply(h,inverse(inverse(b))),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
multiply(h,inverse(inverse(b))) = multiply(d,multiply(inverse(b),inverse(inverse(b)))),
inference(symmetry,[status(thm)],[c40]) ).
cnf(c42,plain,
multiply(inverse(b),inverse(inverse(b))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c43,plain,
multiply(d,multiply(inverse(b),inverse(inverse(b)))) = multiply(d,identity),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
multiply(d,identity) = d,
inference(substitution,[status(thm)],[c15]) ).
cnf(c45,plain,
multiply(d,multiply(inverse(b),inverse(inverse(b)))) = d,
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
multiply(h,inverse(inverse(b))) = d,
inference(transitivity,[status(thm)],[c41,c45]) ).
cnf(c47,plain,
multiply(h,b) = d,
inference(transitivity,[status(thm)],[c34,c46]) ).
cnf(c48,plain,
j = d,
inference(transitivity,[status(thm)],[c25,c47]) ).
cnf(c49,plain,
d = j,
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
multiply(d,X2) = multiply(j,X2),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
multiply(inverse(h),multiply(d,X2)) = multiply(inverse(h),multiply(j,X2)),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
multiply(multiply(h,b),X2) = multiply(h,multiply(b,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c53,plain,
multiply(h,multiply(b,X2)) = multiply(multiply(h,b),X2),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
multiply(multiply(h,b),X2) = multiply(j,X2),
inference(congruence,[status(thm)],[c24]) ).
cnf(c55,plain,
multiply(h,multiply(b,X2)) = multiply(j,X2),
inference(transitivity,[status(thm)],[c53,c54]) ).
cnf(c56,plain,
multiply(j,X2) = multiply(h,multiply(b,X2)),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
multiply(inverse(h),multiply(j,X2)) = multiply(inverse(h),multiply(h,multiply(b,X2))),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c59,plain,
multiply(inverse(X3),multiply(X3,X2)) = multiply(multiply(inverse(X3),X3),X2),
inference(symmetry,[status(thm)],[c58]) ).
cnf(c60,axiom,
multiply(inverse(X2),X2) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c61,plain,
multiply(multiply(inverse(X3),X3),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c60]) ).
cnf(c62,plain,
multiply(multiply(inverse(X3),X3),X2) = X2,
inference(transitivity,[status(thm)],[c61,c7]) ).
cnf(c63,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c59,c62]) ).
cnf(c64,plain,
multiply(inverse(h),multiply(h,multiply(b,X2))) = multiply(b,X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,plain,
multiply(inverse(h),multiply(j,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c57,c64]) ).
cnf(c66,plain,
multiply(inverse(h),multiply(d,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c51,c65]) ).
cnf(c67,plain,
multiply(inverse(h),multiply(d,b)) = multiply(b,b),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
multiply(b,b) = multiply(inverse(h),multiply(d,b)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
multiply(d,d) = inverse(d),
inference(substitution,[status(thm)],[c21]) ).
cnf(c70,plain,
inverse(d) = multiply(d,d),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
multiply(inverse(h),inverse(d)) = multiply(inverse(h),multiply(d,d)),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
multiply(inverse(h),multiply(d,d)) = multiply(b,d),
inference(substitution,[status(thm)],[c66]) ).
cnf(c73,plain,
multiply(inverse(h),inverse(d)) = multiply(b,d),
inference(transitivity,[status(thm)],[c71,c72]) ).
cnf(c74,plain,
multiply(b,d) = multiply(inverse(h),inverse(d)),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
d = j,
inference(symmetry,[status(thm)],[c48]) ).
cnf(c76,plain,
multiply(d,multiply(inverse(h),X2)) = multiply(j,multiply(inverse(h),X2)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
multiply(multiply(j,inverse(h)),X2) = multiply(j,multiply(inverse(h),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c78,plain,
multiply(j,multiply(inverse(h),X2)) = multiply(multiply(j,inverse(h)),X2),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,axiom,
multiply(j,inverse(h)) = k,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c80,plain,
multiply(multiply(j,inverse(h)),X2) = multiply(k,X2),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
multiply(j,multiply(inverse(h),X2)) = multiply(k,X2),
inference(transitivity,[status(thm)],[c78,c80]) ).
cnf(c82,plain,
multiply(d,multiply(inverse(h),X2)) = multiply(k,X2),
inference(transitivity,[status(thm)],[c76,c81]) ).
cnf(c83,plain,
multiply(k,X2) = multiply(d,multiply(inverse(h),X2)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c84,plain,
multiply(inverse(d),multiply(k,X2)) = multiply(inverse(d),multiply(d,multiply(inverse(h),X2))),
inference(congruence,[status(thm)],[c83]) ).
cnf(c85,plain,
multiply(inverse(d),multiply(d,multiply(inverse(h),X2))) = multiply(inverse(h),X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c86,plain,
multiply(inverse(d),multiply(k,X2)) = multiply(inverse(h),X2),
inference(transitivity,[status(thm)],[c84,c85]) ).
cnf(c87,plain,
multiply(inverse(d),multiply(k,inverse(k))) = multiply(inverse(h),inverse(k)),
inference(substitution,[status(thm)],[c86]) ).
cnf(c88,plain,
multiply(inverse(h),inverse(k)) = multiply(inverse(d),multiply(k,inverse(k))),
inference(symmetry,[status(thm)],[c87]) ).
cnf(c89,plain,
multiply(k,inverse(k)) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c90,plain,
multiply(inverse(d),multiply(k,inverse(k))) = multiply(inverse(d),identity),
inference(congruence,[status(thm)],[c89]) ).
cnf(c91,plain,
multiply(inverse(d),identity) = inverse(d),
inference(substitution,[status(thm)],[c15]) ).
cnf(c92,plain,
multiply(inverse(d),multiply(k,inverse(k))) = inverse(d),
inference(transitivity,[status(thm)],[c90,c91]) ).
cnf(c93,plain,
multiply(inverse(h),inverse(k)) = inverse(d),
inference(transitivity,[status(thm)],[c88,c92]) ).
cnf(c94,plain,
inverse(d) = multiply(inverse(h),inverse(k)),
inference(symmetry,[status(thm)],[c93]) ).
cnf(c95,plain,
multiply(inverse(h),inverse(d)) = multiply(inverse(h),multiply(inverse(h),inverse(k))),
inference(congruence,[status(thm)],[c94]) ).
cnf(c96,plain,
X2 = multiply(X3,multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c97,plain,
multiply(X3,X2) = multiply(X3,multiply(X3,multiply(inverse(X3),X2))),
inference(congruence,[status(thm)],[c96]) ).
cnf(c98,plain,
multiply(X3,multiply(X3,X2)) = multiply(X3,multiply(X3,multiply(X3,multiply(inverse(X3),X2)))),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
multiply(multiply(X3,X3),X2) = multiply(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c100,plain,
multiply(X3,multiply(X3,X2)) = multiply(multiply(X3,X3),X2),
inference(symmetry,[status(thm)],[c99]) ).
cnf(c101,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = multiply(X3,multiply(multiply(X3,X3),X2)),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
multiply(multiply(X3,multiply(X3,X3)),X2) = multiply(X3,multiply(multiply(X3,X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c103,plain,
multiply(X3,multiply(multiply(X3,X3),X2)) = multiply(multiply(X3,multiply(X3,X3)),X2),
inference(symmetry,[status(thm)],[c102]) ).
cnf(c104,plain,
multiply(multiply(X3,multiply(X3,X3)),X2) = multiply(identity,X2),
inference(congruence,[status(thm)],[c12]) ).
cnf(c105,plain,
multiply(multiply(X3,multiply(X3,X3)),X2) = X2,
inference(transitivity,[status(thm)],[c104,c7]) ).
cnf(c106,plain,
multiply(X3,multiply(multiply(X3,X3),X2)) = X2,
inference(transitivity,[status(thm)],[c103,c105]) ).
cnf(c107,plain,
multiply(X3,multiply(X3,multiply(X3,X2))) = X2,
inference(transitivity,[status(thm)],[c101,c106]) ).
cnf(c108,plain,
multiply(X3,multiply(X3,multiply(X3,multiply(inverse(X3),X2)))) = multiply(inverse(X3),X2),
inference(substitution,[status(thm)],[c107]) ).
cnf(c109,plain,
multiply(X3,multiply(X3,X2)) = multiply(inverse(X3),X2),
inference(transitivity,[status(thm)],[c98,c108]) ).
cnf(c110,plain,
multiply(inverse(h),multiply(inverse(h),inverse(k))) = multiply(inverse(inverse(h)),inverse(k)),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
inverse(inverse(h)) = h,
inference(substitution,[status(thm)],[c31]) ).
cnf(c112,plain,
multiply(inverse(inverse(h)),inverse(k)) = multiply(h,inverse(k)),
inference(congruence,[status(thm)],[c111]) ).
cnf(c113,plain,
multiply(inverse(h),multiply(inverse(h),inverse(k))) = multiply(h,inverse(k)),
inference(transitivity,[status(thm)],[c110,c112]) ).
cnf(c114,plain,
multiply(inverse(h),inverse(d)) = multiply(h,inverse(k)),
inference(transitivity,[status(thm)],[c95,c113]) ).
cnf(c115,plain,
multiply(b,d) = multiply(h,inverse(k)),
inference(transitivity,[status(thm)],[c74,c114]) ).
cnf(c116,plain,
multiply(h,inverse(k)) = multiply(b,d),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
multiply(multiply(a,b),X2) = multiply(a,multiply(b,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c118,plain,
multiply(a,multiply(b,X2)) = multiply(multiply(a,b),X2),
inference(symmetry,[status(thm)],[c117]) ).
cnf(c119,axiom,
multiply(a,b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c120,plain,
multiply(multiply(a,b),X2) = multiply(c,X2),
inference(congruence,[status(thm)],[c119]) ).
cnf(c121,plain,
multiply(a,multiply(b,X2)) = multiply(c,X2),
inference(transitivity,[status(thm)],[c118,c120]) ).
cnf(c122,plain,
multiply(c,X2) = multiply(a,multiply(b,X2)),
inference(symmetry,[status(thm)],[c121]) ).
cnf(c123,plain,
multiply(inverse(a),multiply(c,X2)) = multiply(inverse(a),multiply(a,multiply(b,X2))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
multiply(inverse(a),multiply(a,multiply(b,X2))) = multiply(b,X2),
inference(substitution,[status(thm)],[c63]) ).
cnf(c125,plain,
multiply(inverse(a),multiply(c,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c123,c124]) ).
cnf(c126,plain,
multiply(inverse(a),multiply(c,d)) = multiply(b,d),
inference(substitution,[status(thm)],[c125]) ).
cnf(c127,plain,
multiply(b,d) = multiply(inverse(a),multiply(c,d)),
inference(symmetry,[status(thm)],[c126]) ).
cnf(c128,plain,
inverse(inverse(a)) = a,
inference(substitution,[status(thm)],[c31]) ).
cnf(c129,plain,
a = inverse(inverse(a)),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
multiply(a,X2) = multiply(inverse(inverse(a)),X2),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
multiply(d,multiply(a,X2)) = multiply(d,multiply(inverse(inverse(a)),X2)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,plain,
multiply(multiply(c,inverse(a)),X2) = multiply(c,multiply(inverse(a),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c133,plain,
multiply(c,multiply(inverse(a),X2)) = multiply(multiply(c,inverse(a)),X2),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,axiom,
multiply(c,inverse(a)) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c135,plain,
multiply(multiply(c,inverse(a)),X2) = multiply(d,X2),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
multiply(c,multiply(inverse(a),X2)) = multiply(d,X2),
inference(transitivity,[status(thm)],[c133,c135]) ).
cnf(c137,plain,
multiply(c,multiply(inverse(a),multiply(inverse(inverse(a)),X2))) = multiply(d,multiply(inverse(inverse(a)),X2)),
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
multiply(d,multiply(inverse(inverse(a)),X2)) = multiply(c,multiply(inverse(a),multiply(inverse(inverse(a)),X2))),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
multiply(inverse(a),multiply(inverse(inverse(a)),X2)) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c140,plain,
multiply(c,multiply(inverse(a),multiply(inverse(inverse(a)),X2))) = multiply(c,X2),
inference(congruence,[status(thm)],[c139]) ).
cnf(c141,plain,
multiply(d,multiply(inverse(inverse(a)),X2)) = multiply(c,X2),
inference(transitivity,[status(thm)],[c138,c140]) ).
cnf(c142,plain,
multiply(d,multiply(a,X2)) = multiply(c,X2),
inference(transitivity,[status(thm)],[c131,c141]) ).
cnf(c143,plain,
multiply(d,multiply(a,multiply(a,c))) = multiply(c,multiply(a,c)),
inference(substitution,[status(thm)],[c142]) ).
cnf(c144,plain,
multiply(c,multiply(a,c)) = multiply(d,multiply(a,multiply(a,c))),
inference(symmetry,[status(thm)],[c143]) ).
cnf(c145,plain,
c = multiply(a,b),
inference(symmetry,[status(thm)],[c119]) ).
cnf(c146,plain,
multiply(a,c) = multiply(a,multiply(a,b)),
inference(congruence,[status(thm)],[c145]) ).
cnf(c147,plain,
multiply(a,multiply(a,c)) = multiply(a,multiply(a,multiply(a,b))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
multiply(a,multiply(a,multiply(a,b))) = b,
inference(substitution,[status(thm)],[c107]) ).
cnf(c149,plain,
multiply(a,multiply(a,c)) = b,
inference(transitivity,[status(thm)],[c147,c148]) ).
cnf(c150,plain,
multiply(d,multiply(a,multiply(a,c))) = multiply(d,b),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
multiply(c,multiply(a,c)) = multiply(d,b),
inference(transitivity,[status(thm)],[c144,c150]) ).
cnf(c152,plain,
multiply(d,b) = multiply(c,multiply(a,c)),
inference(symmetry,[status(thm)],[c151]) ).
cnf(c153,plain,
multiply(a,multiply(d,b)) = multiply(a,multiply(c,multiply(a,c))),
inference(congruence,[status(thm)],[c152]) ).
cnf(c154,plain,
d = multiply(c,inverse(a)),
inference(symmetry,[status(thm)],[c134]) ).
cnf(c155,plain,
multiply(c,d) = multiply(c,multiply(c,inverse(a))),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
multiply(c,multiply(c,d)) = multiply(c,multiply(c,multiply(c,inverse(a)))),
inference(congruence,[status(thm)],[c155]) ).
cnf(c157,plain,
multiply(c,multiply(c,multiply(c,inverse(a)))) = inverse(a),
inference(substitution,[status(thm)],[c107]) ).
cnf(c158,plain,
multiply(c,multiply(c,d)) = inverse(a),
inference(transitivity,[status(thm)],[c156,c157]) ).
cnf(c159,plain,
inverse(a) = multiply(c,multiply(c,d)),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(inverse(c),inverse(a)) = multiply(inverse(c),multiply(c,multiply(c,d))),
inference(congruence,[status(thm)],[c159]) ).
cnf(c161,plain,
multiply(inverse(c),multiply(c,multiply(c,d))) = multiply(c,d),
inference(substitution,[status(thm)],[c63]) ).
cnf(c162,plain,
multiply(inverse(c),inverse(a)) = multiply(c,d),
inference(transitivity,[status(thm)],[c160,c161]) ).
cnf(c163,plain,
multiply(c,d) = multiply(inverse(c),inverse(a)),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
inverse(multiply(c,d)) = inverse(multiply(inverse(c),inverse(a))),
inference(congruence,[status(thm)],[c163]) ).
cnf(c165,plain,
multiply(X2,multiply(inverse(X2),inverse(multiply(X3,inverse(X2))))) = inverse(multiply(X3,inverse(X2))),
inference(substitution,[status(thm)],[c9]) ).
cnf(c166,plain,
inverse(multiply(X3,inverse(X2))) = multiply(X2,multiply(inverse(X2),inverse(multiply(X3,inverse(X2))))),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))) = multiply(X3,inverse(multiply(X2,X3))),
inference(substitution,[status(thm)],[c63]) ).
cnf(c168,plain,
multiply(X3,inverse(multiply(X2,X3))) = multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
multiply(multiply(X3,X2),inverse(multiply(X3,X2))) = multiply(X3,multiply(X2,inverse(multiply(X3,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c170,plain,
multiply(X3,multiply(X2,inverse(multiply(X3,X2)))) = multiply(multiply(X3,X2),inverse(multiply(X3,X2))),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
multiply(multiply(X3,X2),inverse(multiply(X3,X2))) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c172,plain,
multiply(X3,multiply(X2,inverse(multiply(X3,X2)))) = identity,
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
multiply(X2,multiply(X3,inverse(multiply(X2,X3)))) = identity,
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))) = multiply(inverse(X2),identity),
inference(congruence,[status(thm)],[c173]) ).
cnf(c175,plain,
multiply(inverse(X2),identity) = inverse(X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c176,plain,
multiply(inverse(X2),multiply(X2,multiply(X3,inverse(multiply(X2,X3))))) = inverse(X2),
inference(transitivity,[status(thm)],[c174,c175]) ).
cnf(c177,plain,
multiply(X3,inverse(multiply(X2,X3))) = inverse(X2),
inference(transitivity,[status(thm)],[c168,c176]) ).
cnf(c178,plain,
multiply(inverse(X2),inverse(multiply(X3,inverse(X2)))) = inverse(X3),
inference(substitution,[status(thm)],[c177]) ).
cnf(c179,plain,
multiply(X2,multiply(inverse(X2),inverse(multiply(X3,inverse(X2))))) = multiply(X2,inverse(X3)),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
inverse(multiply(X3,inverse(X2))) = multiply(X2,inverse(X3)),
inference(transitivity,[status(thm)],[c166,c179]) ).
cnf(c181,plain,
inverse(multiply(inverse(c),inverse(a))) = multiply(a,inverse(inverse(c))),
inference(substitution,[status(thm)],[c180]) ).
cnf(c182,plain,
inverse(inverse(c)) = c,
inference(substitution,[status(thm)],[c31]) ).
cnf(c183,plain,
multiply(a,inverse(inverse(c))) = multiply(a,c),
inference(congruence,[status(thm)],[c182]) ).
cnf(c184,plain,
inverse(multiply(inverse(c),inverse(a))) = multiply(a,c),
inference(transitivity,[status(thm)],[c181,c183]) ).
cnf(c185,plain,
inverse(multiply(c,d)) = multiply(a,c),
inference(transitivity,[status(thm)],[c164,c184]) ).
cnf(c186,plain,
multiply(a,c) = inverse(multiply(c,d)),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c187,plain,
multiply(c,multiply(a,c)) = multiply(c,inverse(multiply(c,d))),
inference(congruence,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(a,multiply(c,multiply(a,c))) = multiply(a,multiply(c,inverse(multiply(c,d)))),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
multiply(multiply(a,c),inverse(multiply(c,d))) = multiply(a,multiply(c,inverse(multiply(c,d)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c190,plain,
multiply(a,multiply(c,inverse(multiply(c,d)))) = multiply(multiply(a,c),inverse(multiply(c,d))),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
multiply(a,c) = inverse(multiply(c,d)),
inference(symmetry,[status(thm)],[c185]) ).
cnf(c192,plain,
multiply(multiply(a,c),inverse(multiply(c,d))) = multiply(inverse(multiply(c,d)),inverse(multiply(c,d))),
inference(congruence,[status(thm)],[c191]) ).
cnf(c193,plain,
multiply(inverse(multiply(c,d)),inverse(multiply(c,d))) = multiply(c,d),
inference(substitution,[status(thm)],[c17]) ).
cnf(c194,plain,
multiply(multiply(a,c),inverse(multiply(c,d))) = multiply(c,d),
inference(transitivity,[status(thm)],[c192,c193]) ).
cnf(c195,plain,
multiply(a,multiply(c,inverse(multiply(c,d)))) = multiply(c,d),
inference(transitivity,[status(thm)],[c190,c194]) ).
cnf(c196,plain,
multiply(a,multiply(c,multiply(a,c))) = multiply(c,d),
inference(transitivity,[status(thm)],[c188,c195]) ).
cnf(c197,plain,
multiply(a,multiply(d,b)) = multiply(c,d),
inference(transitivity,[status(thm)],[c153,c196]) ).
cnf(c198,plain,
multiply(c,d) = multiply(a,multiply(d,b)),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
multiply(inverse(a),multiply(c,d)) = multiply(inverse(a),multiply(a,multiply(d,b))),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
multiply(inverse(a),multiply(a,multiply(d,b))) = multiply(d,b),
inference(substitution,[status(thm)],[c63]) ).
cnf(c201,plain,
multiply(inverse(a),multiply(c,d)) = multiply(d,b),
inference(transitivity,[status(thm)],[c199,c200]) ).
cnf(c202,plain,
multiply(b,d) = multiply(d,b),
inference(transitivity,[status(thm)],[c127,c201]) ).
cnf(c203,plain,
multiply(h,inverse(k)) = multiply(d,b),
inference(transitivity,[status(thm)],[c116,c202]) ).
cnf(c204,plain,
multiply(d,b) = multiply(h,inverse(k)),
inference(symmetry,[status(thm)],[c203]) ).
cnf(c205,plain,
multiply(inverse(h),multiply(d,b)) = multiply(inverse(h),multiply(h,inverse(k))),
inference(congruence,[status(thm)],[c204]) ).
cnf(c206,plain,
multiply(inverse(h),multiply(h,inverse(k))) = inverse(k),
inference(substitution,[status(thm)],[c63]) ).
cnf(c207,plain,
multiply(inverse(h),multiply(d,b)) = inverse(k),
inference(transitivity,[status(thm)],[c205,c206]) ).
cnf(c208,plain,
multiply(b,b) = inverse(k),
inference(transitivity,[status(thm)],[c68,c207]) ).
cnf(c209,plain,
inverse(b) = inverse(k),
inference(transitivity,[status(thm)],[c23,c208]) ).
cnf(c210,plain,
multiply(k,inverse(b)) = multiply(k,inverse(k)),
inference(congruence,[status(thm)],[c209]) ).
cnf(c211,plain,
multiply(k,inverse(k)) = identity,
inference(substitution,[status(thm)],[c5]) ).
cnf(c212,plain,
multiply(k,inverse(b)) = identity,
inference(transitivity,[status(thm)],[c210,c211]) ).
cnf(c213,plain,
$false,
inference(resolution,[status(thm)],[c1,c212]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 09:18:01 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.54 Command-line arguments: --no-flatten-goal
% 0.19/0.54
% 0.19/0.54 % SZS status Unsatisfiable
% 0.19/0.54
% 0.19/0.54 % SZS output start CNFRefutation
% See solution above
% 1.18/0.63
% 1.18/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------