%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP002-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 53.78s 7.27s
% Output : CNFRefutation 56.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 17
% Syntax : Number of clauses : 530 ( 530 unt; 0 nHn; 195 RR)
% Number of literals : 530 ( 529 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 782 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
product(k,inverse(b),identity) != true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_k_times_inverse_b_is_e) ).
cnf(c2,axiom,
ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
cnf(c3,plain,
ifeq(true,true,product(k,inverse(b),identity),true) = product(k,inverse(b),identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
product(k,inverse(b),identity) = ifeq(true,true,product(k,inverse(b),identity),true),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
product(identity,X,X) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
cnf(c6,plain,
product(identity,inverse(b),inverse(b)) = true,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
true = product(identity,inverse(b),inverse(b)),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
ifeq(true,true,product(k,inverse(b),identity),true) = ifeq(product(identity,inverse(b),inverse(b)),true,product(k,inverse(b),identity),true),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
ifeq2(A2,A2,B2,C2) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
cnf(c10,plain,
ifeq2(true,true,multiply(inverse(k),b),identity) = multiply(inverse(k),b),
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
multiply(inverse(k),b) = ifeq2(true,true,multiply(inverse(k),b),identity),
inference(symmetry,[status(thm)],[c10]) ).
cnf(c12,plain,
ifeq2(true,true,multiply(inverse(k),d),h) = multiply(inverse(k),d),
inference(substitution,[status(thm)],[c9]) ).
cnf(c13,plain,
multiply(inverse(k),d) = ifeq2(true,true,multiply(inverse(k),d),h),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
ifeq(true,true,product(inverse(k),d,h),true) = product(inverse(k),d,h),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
product(inverse(k),d,h) = ifeq(true,true,product(inverse(k),d,h),true),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,plain,
ifeq2(true,true,j,d) = j,
inference(substitution,[status(thm)],[c9]) ).
cnf(c17,plain,
j = ifeq2(true,true,j,d),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
ifeq(true,true,product(h,b,d),true) = product(h,b,d),
inference(substitution,[status(thm)],[c2]) ).
cnf(c19,plain,
product(h,b,d) = ifeq(true,true,product(h,b,d),true),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
product(d,inverse(b),h) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c21,plain,
true = product(d,inverse(b),h),
inference(symmetry,[status(thm)],[c20]) ).
cnf(c22,plain,
ifeq(true,true,product(h,b,d),true) = ifeq(product(d,inverse(b),h),true,product(h,b,d),true),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,plain,
ifeq(true,true,ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true),true) = ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c24,plain,
ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true) = ifeq(true,true,ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true),true),
inference(symmetry,[status(thm)],[c23]) ).
cnf(c25,axiom,
product(inverse(X2),X2,identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c26,plain,
true = product(inverse(X2),X2,identity),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c27,plain,
ifeq(true,true,ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true),true) = ifeq(product(inverse(X3),X3,identity),true,ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true),true),
inference(congruence,[status(thm)],[c26]) ).
cnf(c28,plain,
ifeq(true,true,ifeq(product(X2,X4,X5),true,product(X5,X3,X2),true),true) = ifeq(product(X2,X4,X5),true,product(X5,X3,X2),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c29,plain,
ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true) = ifeq(true,true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
ifeq(product(X5,X4,identity),true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true) = ifeq(product(X5,X4,identity),true,ifeq(true,true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true),true),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,axiom,
product(X2,identity,X2) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c32,plain,
true = product(X2,identity,X2),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
ifeq(true,true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true) = ifeq(product(X3,identity,X3),true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,plain,
ifeq(product(X5,X4,identity),true,ifeq(true,true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true),true) = ifeq(product(X5,X4,identity),true,ifeq(product(X3,identity,X3),true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true),true),
inference(congruence,[status(thm)],[c33]) ).
cnf(c35,axiom,
ifeq(product(Y,Z,V),true,ifeq(product(X2,V,W),true,ifeq(product(X2,Y,U),true,product(U,Z,W),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
cnf(c36,plain,
ifeq(product(X5,X4,identity),true,ifeq(product(X3,identity,X3),true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c37,plain,
ifeq(product(X5,X4,identity),true,ifeq(true,true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true),true) = true,
inference(transitivity,[status(thm)],[c34,c36]) ).
cnf(c38,plain,
ifeq(product(X5,X4,identity),true,ifeq(product(X3,X5,X2),true,product(X2,X4,X3),true),true) = true,
inference(transitivity,[status(thm)],[c30,c37]) ).
cnf(c39,plain,
ifeq(product(inverse(X3),X3,identity),true,ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true),true) = true,
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
ifeq(true,true,ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true),true) = true,
inference(transitivity,[status(thm)],[c27,c39]) ).
cnf(c41,plain,
ifeq(product(X4,inverse(X3),X2),true,product(X2,X3,X4),true) = true,
inference(transitivity,[status(thm)],[c24,c40]) ).
cnf(c42,plain,
ifeq(product(d,inverse(b),h),true,product(h,b,d),true) = true,
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
ifeq(true,true,product(h,b,d),true) = true,
inference(transitivity,[status(thm)],[c22,c42]) ).
cnf(c44,plain,
product(h,b,d) = true,
inference(transitivity,[status(thm)],[c19,c43]) ).
cnf(c45,plain,
true = product(h,b,d),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
ifeq2(true,true,j,d) = ifeq2(product(h,b,d),true,j,d),
inference(congruence,[status(thm)],[c45]) ).
cnf(c47,plain,
ifeq2(true,true,j,X2) = j,
inference(substitution,[status(thm)],[c9]) ).
cnf(c48,plain,
j = ifeq2(true,true,j,X2),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
ifeq2(product(h,b,X2),true,j,X2) = ifeq2(product(h,b,X2),true,ifeq2(true,true,j,X2),X2),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,axiom,
product(h,b,j) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c51,plain,
true = product(h,b,j),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
ifeq2(true,true,j,X2) = ifeq2(product(h,b,j),true,j,X2),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
ifeq2(product(h,b,X2),true,ifeq2(true,true,j,X2),X2) = ifeq2(product(h,b,X2),true,ifeq2(product(h,b,j),true,j,X2),X2),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,axiom,
ifeq2(product(X2,Y2,W2),true,ifeq2(product(X2,Y2,Z2),true,Z2,W2),W2) = W2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
cnf(c55,plain,
ifeq2(product(h,b,X2),true,ifeq2(product(h,b,j),true,j,X2),X2) = X2,
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
ifeq2(product(h,b,X2),true,ifeq2(true,true,j,X2),X2) = X2,
inference(transitivity,[status(thm)],[c53,c55]) ).
cnf(c57,plain,
ifeq2(product(h,b,X2),true,j,X2) = X2,
inference(transitivity,[status(thm)],[c49,c56]) ).
cnf(c58,plain,
ifeq2(product(h,b,d),true,j,d) = d,
inference(substitution,[status(thm)],[c57]) ).
cnf(c59,plain,
ifeq2(true,true,j,d) = d,
inference(transitivity,[status(thm)],[c46,c58]) ).
cnf(c60,plain,
j = d,
inference(transitivity,[status(thm)],[c17,c59]) ).
cnf(c61,plain,
d = j,
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
product(k,h,d) = product(k,h,j),
inference(congruence,[status(thm)],[c61]) ).
cnf(c63,plain,
ifeq2(true,true,ifeq2(product(identity,X3,X2),true,X2,X3),X3) = ifeq2(product(identity,X3,X2),true,X2,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c64,plain,
ifeq2(product(identity,X3,X2),true,X2,X3) = ifeq2(true,true,ifeq2(product(identity,X3,X2),true,X2,X3),X3),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,plain,
true = product(identity,X2,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c66,plain,
ifeq2(true,true,ifeq2(product(identity,X3,X2),true,X2,X3),X3) = ifeq2(product(identity,X3,X3),true,ifeq2(product(identity,X3,X2),true,X2,X3),X3),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
ifeq2(product(identity,X3,X3),true,ifeq2(product(identity,X3,X2),true,X2,X3),X3) = X3,
inference(substitution,[status(thm)],[c54]) ).
cnf(c68,plain,
ifeq2(true,true,ifeq2(product(identity,X3,X2),true,X2,X3),X3) = X3,
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
ifeq2(product(identity,X3,X2),true,X2,X3) = X3,
inference(transitivity,[status(thm)],[c64,c68]) ).
cnf(c70,plain,
ifeq2(product(identity,inverse(inverse(X2)),X2),true,X2,inverse(inverse(X2))) = inverse(inverse(X2)),
inference(substitution,[status(thm)],[c69]) ).
cnf(c71,plain,
inverse(inverse(X2)) = ifeq2(product(identity,inverse(inverse(X2)),X2),true,X2,inverse(inverse(X2))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
ifeq(true,true,product(identity,inverse(inverse(X2)),X2),true) = product(identity,inverse(inverse(X2)),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c73,plain,
product(identity,inverse(inverse(X2)),X2) = ifeq(true,true,product(identity,inverse(inverse(X2)),X2),true),
inference(symmetry,[status(thm)],[c72]) ).
cnf(c74,axiom,
product(X2,inverse(X2),identity) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c75,plain,
true = product(X2,inverse(X2),identity),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c76,plain,
ifeq(true,true,product(identity,inverse(inverse(X2)),X2),true) = ifeq(product(X2,inverse(X2),identity),true,product(identity,inverse(inverse(X2)),X2),true),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
ifeq(true,true,ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true),true) = ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c78,plain,
ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true) = ifeq(true,true,ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true),true),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
true = product(X2,inverse(X2),identity),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c80,plain,
ifeq(true,true,ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true),true) = ifeq(product(X3,inverse(X3),identity),true,ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true),true),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
ifeq(product(X3,inverse(X3),identity),true,ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true),true) = true,
inference(substitution,[status(thm)],[c38]) ).
cnf(c82,plain,
ifeq(true,true,ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true),true) = true,
inference(transitivity,[status(thm)],[c80,c81]) ).
cnf(c83,plain,
ifeq(product(X4,X3,X2),true,product(X2,inverse(X3),X4),true) = true,
inference(transitivity,[status(thm)],[c78,c82]) ).
cnf(c84,plain,
ifeq(product(X2,inverse(X2),identity),true,product(identity,inverse(inverse(X2)),X2),true) = true,
inference(substitution,[status(thm)],[c83]) ).
cnf(c85,plain,
ifeq(true,true,product(identity,inverse(inverse(X2)),X2),true) = true,
inference(transitivity,[status(thm)],[c76,c84]) ).
cnf(c86,plain,
product(identity,inverse(inverse(X2)),X2) = true,
inference(transitivity,[status(thm)],[c73,c85]) ).
cnf(c87,plain,
ifeq2(product(identity,inverse(inverse(X2)),X2),true,X2,inverse(inverse(X2))) = ifeq2(true,true,X2,inverse(inverse(X2))),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
ifeq2(true,true,X2,inverse(inverse(X2))) = X2,
inference(substitution,[status(thm)],[c9]) ).
cnf(c89,plain,
ifeq2(product(identity,inverse(inverse(X2)),X2),true,X2,inverse(inverse(X2))) = X2,
inference(transitivity,[status(thm)],[c87,c88]) ).
cnf(c90,plain,
inverse(inverse(X2)) = X2,
inference(transitivity,[status(thm)],[c71,c89]) ).
cnf(c91,plain,
inverse(inverse(h)) = h,
inference(substitution,[status(thm)],[c90]) ).
cnf(c92,plain,
h = inverse(inverse(h)),
inference(symmetry,[status(thm)],[c91]) ).
cnf(c93,plain,
product(k,h,j) = product(k,inverse(inverse(h)),j),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
ifeq(true,true,product(k,inverse(inverse(h)),j),true) = product(k,inverse(inverse(h)),j),
inference(substitution,[status(thm)],[c2]) ).
cnf(c95,plain,
product(k,inverse(inverse(h)),j) = ifeq(true,true,product(k,inverse(inverse(h)),j),true),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,axiom,
product(j,inverse(h),k) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c97,plain,
true = product(j,inverse(h),k),
inference(symmetry,[status(thm)],[c96]) ).
cnf(c98,plain,
ifeq(true,true,product(k,inverse(inverse(h)),j),true) = ifeq(product(j,inverse(h),k),true,product(k,inverse(inverse(h)),j),true),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
ifeq(product(j,inverse(h),k),true,product(k,inverse(inverse(h)),j),true) = true,
inference(substitution,[status(thm)],[c83]) ).
cnf(c100,plain,
ifeq(true,true,product(k,inverse(inverse(h)),j),true) = true,
inference(transitivity,[status(thm)],[c98,c99]) ).
cnf(c101,plain,
product(k,inverse(inverse(h)),j) = true,
inference(transitivity,[status(thm)],[c95,c100]) ).
cnf(c102,plain,
product(k,h,j) = true,
inference(transitivity,[status(thm)],[c93,c101]) ).
cnf(c103,plain,
product(k,h,d) = true,
inference(transitivity,[status(thm)],[c62,c102]) ).
cnf(c104,plain,
true = product(k,h,d),
inference(symmetry,[status(thm)],[c103]) ).
cnf(c105,plain,
ifeq(true,true,product(inverse(k),d,h),true) = ifeq(product(k,h,d),true,product(inverse(k),d,h),true),
inference(congruence,[status(thm)],[c104]) ).
cnf(c106,plain,
ifeq(true,true,product(inverse(X4),X2,X3),true) = product(inverse(X4),X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c107,plain,
product(inverse(X4),X2,X3) = ifeq(true,true,product(inverse(X4),X2,X3),true),
inference(symmetry,[status(thm)],[c106]) ).
cnf(c108,plain,
ifeq(product(X4,X3,X2),true,product(inverse(X4),X2,X3),true) = ifeq(product(X4,X3,X2),true,ifeq(true,true,product(inverse(X4),X2,X3),true),true),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,plain,
true = product(inverse(X2),X2,identity),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c110,plain,
ifeq(true,true,product(inverse(X4),X2,X3),true) = ifeq(product(inverse(X4),X4,identity),true,product(inverse(X4),X2,X3),true),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,plain,
ifeq(product(X4,X3,X2),true,ifeq(true,true,product(inverse(X4),X2,X3),true),true) = ifeq(product(X4,X3,X2),true,ifeq(product(inverse(X4),X4,identity),true,product(inverse(X4),X2,X3),true),true),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true) = ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c113,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true) = ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
true = product(identity,X2,X2),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c115,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true) = ifeq(product(identity,X4,X4),true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true),
inference(congruence,[status(thm)],[c114]) ).
cnf(c116,axiom,
ifeq(product(U2,Z2,W2),true,ifeq(product(Y2,Z2,V2),true,ifeq(product(X2,Y2,U2),true,product(X2,V2,W2),true),true),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
cnf(c117,plain,
ifeq(product(identity,X4,X4),true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true) = true,
inference(substitution,[status(thm)],[c116]) ).
cnf(c118,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true),true) = true,
inference(transitivity,[status(thm)],[c115,c117]) ).
cnf(c119,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,identity),true,product(X2,X3,X4),true),true) = true,
inference(transitivity,[status(thm)],[c113,c118]) ).
cnf(c120,plain,
ifeq(product(X4,X3,X2),true,ifeq(product(inverse(X4),X4,identity),true,product(inverse(X4),X2,X3),true),true) = true,
inference(substitution,[status(thm)],[c119]) ).
cnf(c121,plain,
ifeq(product(X4,X3,X2),true,ifeq(true,true,product(inverse(X4),X2,X3),true),true) = true,
inference(transitivity,[status(thm)],[c111,c120]) ).
cnf(c122,plain,
ifeq(product(X4,X3,X2),true,product(inverse(X4),X2,X3),true) = true,
inference(transitivity,[status(thm)],[c108,c121]) ).
cnf(c123,plain,
ifeq(product(k,h,d),true,product(inverse(k),d,h),true) = true,
inference(substitution,[status(thm)],[c122]) ).
cnf(c124,plain,
ifeq(true,true,product(inverse(k),d,h),true) = true,
inference(transitivity,[status(thm)],[c105,c123]) ).
cnf(c125,plain,
product(inverse(k),d,h) = true,
inference(transitivity,[status(thm)],[c15,c124]) ).
cnf(c126,plain,
true = product(inverse(k),d,h),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
ifeq2(true,true,multiply(inverse(k),d),h) = ifeq2(product(inverse(k),d,h),true,multiply(inverse(k),d),h),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
ifeq2(true,true,multiply(X4,X3),X2) = multiply(X4,X3),
inference(substitution,[status(thm)],[c9]) ).
cnf(c129,plain,
multiply(X4,X3) = ifeq2(true,true,multiply(X4,X3),X2),
inference(symmetry,[status(thm)],[c128]) ).
cnf(c130,plain,
ifeq2(product(X4,X3,X2),true,multiply(X4,X3),X2) = ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,axiom,
product(X2,Y2,multiply(X2,Y2)) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
cnf(c132,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c133,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c132]) ).
cnf(c134,plain,
ifeq2(true,true,multiply(X4,X3),X2) = ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),
inference(congruence,[status(thm)],[c133]) ).
cnf(c135,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2) = ifeq2(product(X4,X3,X2),true,ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),X2),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(product(X4,X3,multiply(X4,X3)),true,multiply(X4,X3),X2),X2) = X2,
inference(substitution,[status(thm)],[c54]) ).
cnf(c137,plain,
ifeq2(product(X4,X3,X2),true,ifeq2(true,true,multiply(X4,X3),X2),X2) = X2,
inference(transitivity,[status(thm)],[c135,c136]) ).
cnf(c138,plain,
ifeq2(product(X4,X3,X2),true,multiply(X4,X3),X2) = X2,
inference(transitivity,[status(thm)],[c130,c137]) ).
cnf(c139,plain,
ifeq2(product(inverse(k),d,h),true,multiply(inverse(k),d),h) = h,
inference(substitution,[status(thm)],[c138]) ).
cnf(c140,plain,
ifeq2(true,true,multiply(inverse(k),d),h) = h,
inference(transitivity,[status(thm)],[c127,c139]) ).
cnf(c141,plain,
multiply(inverse(k),d) = h,
inference(transitivity,[status(thm)],[c13,c140]) ).
cnf(c142,plain,
h = multiply(inverse(k),d),
inference(symmetry,[status(thm)],[c141]) ).
cnf(c143,plain,
multiply(h,inverse(d)) = multiply(multiply(inverse(k),d),inverse(d)),
inference(congruence,[status(thm)],[c142]) ).
cnf(c144,plain,
ifeq2(true,true,multiply(multiply(X3,X2),inverse(X2)),X3) = multiply(multiply(X3,X2),inverse(X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c145,plain,
multiply(multiply(X3,X2),inverse(X2)) = ifeq2(true,true,multiply(multiply(X3,X2),inverse(X2)),X3),
inference(symmetry,[status(thm)],[c144]) ).
cnf(c146,plain,
ifeq(true,true,product(multiply(X3,X2),inverse(X2),X3),true) = product(multiply(X3,X2),inverse(X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c147,plain,
product(multiply(X3,X2),inverse(X2),X3) = ifeq(true,true,product(multiply(X3,X2),inverse(X2),X3),true),
inference(symmetry,[status(thm)],[c146]) ).
cnf(c148,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c149,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c148]) ).
cnf(c150,plain,
ifeq(true,true,product(multiply(X3,X2),inverse(X2),X3),true) = ifeq(product(X3,X2,multiply(X3,X2)),true,product(multiply(X3,X2),inverse(X2),X3),true),
inference(congruence,[status(thm)],[c149]) ).
cnf(c151,plain,
ifeq(product(X3,X2,multiply(X3,X2)),true,product(multiply(X3,X2),inverse(X2),X3),true) = true,
inference(substitution,[status(thm)],[c83]) ).
cnf(c152,plain,
ifeq(true,true,product(multiply(X3,X2),inverse(X2),X3),true) = true,
inference(transitivity,[status(thm)],[c150,c151]) ).
cnf(c153,plain,
product(multiply(X3,X2),inverse(X2),X3) = true,
inference(transitivity,[status(thm)],[c147,c152]) ).
cnf(c154,plain,
true = product(multiply(X3,X2),inverse(X2),X3),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,plain,
ifeq2(true,true,multiply(multiply(X3,X2),inverse(X2)),X3) = ifeq2(product(multiply(X3,X2),inverse(X2),X3),true,multiply(multiply(X3,X2),inverse(X2)),X3),
inference(congruence,[status(thm)],[c154]) ).
cnf(c156,plain,
ifeq2(product(multiply(X3,X2),inverse(X2),X3),true,multiply(multiply(X3,X2),inverse(X2)),X3) = X3,
inference(substitution,[status(thm)],[c138]) ).
cnf(c157,plain,
ifeq2(true,true,multiply(multiply(X3,X2),inverse(X2)),X3) = X3,
inference(transitivity,[status(thm)],[c155,c156]) ).
cnf(c158,plain,
multiply(multiply(X3,X2),inverse(X2)) = X3,
inference(transitivity,[status(thm)],[c145,c157]) ).
cnf(c159,plain,
multiply(multiply(inverse(k),d),inverse(d)) = inverse(k),
inference(substitution,[status(thm)],[c158]) ).
cnf(c160,plain,
multiply(h,inverse(d)) = inverse(k),
inference(transitivity,[status(thm)],[c143,c159]) ).
cnf(c161,plain,
inverse(k) = multiply(h,inverse(d)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
product(inverse(k),b,identity) = product(multiply(h,inverse(d)),b,identity),
inference(congruence,[status(thm)],[c161]) ).
cnf(c163,plain,
ifeq2(true,true,multiply(X2,X2),inverse(X2)) = multiply(X2,X2),
inference(substitution,[status(thm)],[c9]) ).
cnf(c164,plain,
multiply(X2,X2) = ifeq2(true,true,multiply(X2,X2),inverse(X2)),
inference(symmetry,[status(thm)],[c163]) ).
cnf(c165,plain,
ifeq(true,true,product(identity,inverse(X2),multiply(X2,X2)),true) = product(identity,inverse(X2),multiply(X2,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c166,plain,
product(identity,inverse(X2),multiply(X2,X2)) = ifeq(true,true,product(identity,inverse(X2),multiply(X2,X2)),true),
inference(symmetry,[status(thm)],[c165]) ).
cnf(c167,plain,
ifeq(true,true,product(multiply(X2,X2),X2,identity),true) = product(multiply(X2,X2),X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c168,plain,
product(multiply(X2,X2),X2,identity) = ifeq(true,true,product(multiply(X2,X2),X2,identity),true),
inference(symmetry,[status(thm)],[c167]) ).
cnf(c169,plain,
product(X2,X2,multiply(X2,X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c170,plain,
true = product(X2,X2,multiply(X2,X2)),
inference(symmetry,[status(thm)],[c169]) ).
cnf(c171,plain,
ifeq(true,true,product(multiply(X2,X2),X2,identity),true) = ifeq(product(X2,X2,multiply(X2,X2)),true,product(multiply(X2,X2),X2,identity),true),
inference(congruence,[status(thm)],[c170]) ).
cnf(c172,hypothesis,
ifeq(product(X2,X2,Y2),true,product(Y2,X2,identity),true) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_cubed_is_identity_2) ).
cnf(c173,plain,
ifeq(product(X2,X2,multiply(X2,X2)),true,product(multiply(X2,X2),X2,identity),true) = true,
inference(substitution,[status(thm)],[c172]) ).
cnf(c174,plain,
ifeq(true,true,product(multiply(X2,X2),X2,identity),true) = true,
inference(transitivity,[status(thm)],[c171,c173]) ).
cnf(c175,plain,
product(multiply(X2,X2),X2,identity) = true,
inference(transitivity,[status(thm)],[c168,c174]) ).
cnf(c176,plain,
true = product(multiply(X2,X2),X2,identity),
inference(symmetry,[status(thm)],[c175]) ).
cnf(c177,plain,
ifeq(true,true,product(identity,inverse(X2),multiply(X2,X2)),true) = ifeq(product(multiply(X2,X2),X2,identity),true,product(identity,inverse(X2),multiply(X2,X2)),true),
inference(congruence,[status(thm)],[c176]) ).
cnf(c178,plain,
ifeq(product(multiply(X2,X2),X2,identity),true,product(identity,inverse(X2),multiply(X2,X2)),true) = true,
inference(substitution,[status(thm)],[c83]) ).
cnf(c179,plain,
ifeq(true,true,product(identity,inverse(X2),multiply(X2,X2)),true) = true,
inference(transitivity,[status(thm)],[c177,c178]) ).
cnf(c180,plain,
product(identity,inverse(X2),multiply(X2,X2)) = true,
inference(transitivity,[status(thm)],[c166,c179]) ).
cnf(c181,plain,
true = product(identity,inverse(X2),multiply(X2,X2)),
inference(symmetry,[status(thm)],[c180]) ).
cnf(c182,plain,
ifeq2(true,true,multiply(X2,X2),inverse(X2)) = ifeq2(product(identity,inverse(X2),multiply(X2,X2)),true,multiply(X2,X2),inverse(X2)),
inference(congruence,[status(thm)],[c181]) ).
cnf(c183,plain,
ifeq2(product(identity,inverse(X2),multiply(X2,X2)),true,multiply(X2,X2),inverse(X2)) = inverse(X2),
inference(substitution,[status(thm)],[c69]) ).
cnf(c184,plain,
ifeq2(true,true,multiply(X2,X2),inverse(X2)) = inverse(X2),
inference(transitivity,[status(thm)],[c182,c183]) ).
cnf(c185,plain,
multiply(X2,X2) = inverse(X2),
inference(transitivity,[status(thm)],[c164,c184]) ).
cnf(c186,plain,
multiply(c,c) = inverse(c),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
inverse(c) = multiply(c,c),
inference(symmetry,[status(thm)],[c186]) ).
cnf(c188,plain,
multiply(inverse(a),inverse(c)) = multiply(inverse(a),multiply(c,c)),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
ifeq2(true,true,multiply(a,multiply(b,X2)),multiply(c,X2)) = multiply(a,multiply(b,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c190,plain,
multiply(a,multiply(b,X2)) = ifeq2(true,true,multiply(a,multiply(b,X2)),multiply(c,X2)),
inference(symmetry,[status(thm)],[c189]) ).
cnf(c191,plain,
ifeq(true,true,product(a,multiply(b,X2),multiply(c,X2)),true) = product(a,multiply(b,X2),multiply(c,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c192,plain,
product(a,multiply(b,X2),multiply(c,X2)) = ifeq(true,true,product(a,multiply(b,X2),multiply(c,X2)),true),
inference(symmetry,[status(thm)],[c191]) ).
cnf(c193,plain,
product(b,X2,multiply(b,X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c194,plain,
true = product(b,X2,multiply(b,X2)),
inference(symmetry,[status(thm)],[c193]) ).
cnf(c195,plain,
ifeq(true,true,product(a,multiply(b,X2),multiply(c,X2)),true) = ifeq(product(b,X2,multiply(b,X2)),true,product(a,multiply(b,X2),multiply(c,X2)),true),
inference(congruence,[status(thm)],[c194]) ).
cnf(c196,plain,
ifeq(true,true,ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true),true) = ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c197,plain,
ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true) = ifeq(true,true,ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true),true),
inference(symmetry,[status(thm)],[c196]) ).
cnf(c198,plain,
product(c,X2,multiply(c,X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c199,plain,
true = product(c,X2,multiply(c,X2)),
inference(symmetry,[status(thm)],[c198]) ).
cnf(c200,plain,
ifeq(true,true,ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true),true) = ifeq(product(c,X3,multiply(c,X3)),true,ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true),true),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
ifeq(true,true,product(a,X2,X3),true) = product(a,X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c202,plain,
product(a,X2,X3) = ifeq(true,true,product(a,X2,X3),true),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
ifeq(product(b,X4,X2),true,product(a,X2,X3),true) = ifeq(product(b,X4,X2),true,ifeq(true,true,product(a,X2,X3),true),true),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
ifeq(product(c,X4,X3),true,ifeq(product(b,X4,X2),true,product(a,X2,X3),true),true) = ifeq(product(c,X4,X3),true,ifeq(product(b,X4,X2),true,ifeq(true,true,product(a,X2,X3),true),true),true),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,axiom,
product(a,b,c) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c206,plain,
true = product(a,b,c),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c207,plain,
ifeq(true,true,product(a,X2,X3),true) = ifeq(product(a,b,c),true,product(a,X2,X3),true),
inference(congruence,[status(thm)],[c206]) ).
cnf(c208,plain,
ifeq(product(b,X4,X2),true,ifeq(true,true,product(a,X2,X3),true),true) = ifeq(product(b,X4,X2),true,ifeq(product(a,b,c),true,product(a,X2,X3),true),true),
inference(congruence,[status(thm)],[c207]) ).
cnf(c209,plain,
ifeq(product(c,X4,X3),true,ifeq(product(b,X4,X2),true,ifeq(true,true,product(a,X2,X3),true),true),true) = ifeq(product(c,X4,X3),true,ifeq(product(b,X4,X2),true,ifeq(product(a,b,c),true,product(a,X2,X3),true),true),true),
inference(congruence,[status(thm)],[c208]) ).
cnf(c210,plain,
ifeq(product(c,X4,X3),true,ifeq(product(b,X4,X2),true,ifeq(product(a,b,c),true,product(a,X2,X3),true),true),true) = true,
inference(substitution,[status(thm)],[c116]) ).
cnf(c211,plain,
ifeq(product(c,X4,X3),true,ifeq(product(b,X4,X2),true,ifeq(true,true,product(a,X2,X3),true),true),true) = true,
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
ifeq(product(c,X4,X3),true,ifeq(product(b,X4,X2),true,product(a,X2,X3),true),true) = true,
inference(transitivity,[status(thm)],[c204,c211]) ).
cnf(c213,plain,
ifeq(product(c,X3,multiply(c,X3)),true,ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true),true) = true,
inference(substitution,[status(thm)],[c212]) ).
cnf(c214,plain,
ifeq(true,true,ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true),true) = true,
inference(transitivity,[status(thm)],[c200,c213]) ).
cnf(c215,plain,
ifeq(product(b,X3,X2),true,product(a,X2,multiply(c,X3)),true) = true,
inference(transitivity,[status(thm)],[c197,c214]) ).
cnf(c216,plain,
ifeq(product(b,X2,multiply(b,X2)),true,product(a,multiply(b,X2),multiply(c,X2)),true) = true,
inference(substitution,[status(thm)],[c215]) ).
cnf(c217,plain,
ifeq(true,true,product(a,multiply(b,X2),multiply(c,X2)),true) = true,
inference(transitivity,[status(thm)],[c195,c216]) ).
cnf(c218,plain,
product(a,multiply(b,X2),multiply(c,X2)) = true,
inference(transitivity,[status(thm)],[c192,c217]) ).
cnf(c219,plain,
true = product(a,multiply(b,X2),multiply(c,X2)),
inference(symmetry,[status(thm)],[c218]) ).
cnf(c220,plain,
ifeq2(true,true,multiply(a,multiply(b,X2)),multiply(c,X2)) = ifeq2(product(a,multiply(b,X2),multiply(c,X2)),true,multiply(a,multiply(b,X2)),multiply(c,X2)),
inference(congruence,[status(thm)],[c219]) ).
cnf(c221,plain,
ifeq2(product(a,multiply(b,X2),multiply(c,X2)),true,multiply(a,multiply(b,X2)),multiply(c,X2)) = multiply(c,X2),
inference(substitution,[status(thm)],[c138]) ).
cnf(c222,plain,
ifeq2(true,true,multiply(a,multiply(b,X2)),multiply(c,X2)) = multiply(c,X2),
inference(transitivity,[status(thm)],[c220,c221]) ).
cnf(c223,plain,
multiply(a,multiply(b,X2)) = multiply(c,X2),
inference(transitivity,[status(thm)],[c190,c222]) ).
cnf(c224,plain,
multiply(c,X2) = multiply(a,multiply(b,X2)),
inference(symmetry,[status(thm)],[c223]) ).
cnf(c225,plain,
multiply(inverse(a),multiply(c,X2)) = multiply(inverse(a),multiply(a,multiply(b,X2))),
inference(congruence,[status(thm)],[c224]) ).
cnf(c226,plain,
ifeq2(true,true,multiply(inverse(X3),multiply(X3,X2)),X2) = multiply(inverse(X3),multiply(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c227,plain,
multiply(inverse(X3),multiply(X3,X2)) = ifeq2(true,true,multiply(inverse(X3),multiply(X3,X2)),X2),
inference(symmetry,[status(thm)],[c226]) ).
cnf(c228,plain,
ifeq(true,true,product(inverse(X3),multiply(X3,X2),X2),true) = product(inverse(X3),multiply(X3,X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c229,plain,
product(inverse(X3),multiply(X3,X2),X2) = ifeq(true,true,product(inverse(X3),multiply(X3,X2),X2),true),
inference(symmetry,[status(thm)],[c228]) ).
cnf(c230,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c231,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c230]) ).
cnf(c232,plain,
ifeq(true,true,product(inverse(X3),multiply(X3,X2),X2),true) = ifeq(product(X3,X2,multiply(X3,X2)),true,product(inverse(X3),multiply(X3,X2),X2),true),
inference(congruence,[status(thm)],[c231]) ).
cnf(c233,plain,
ifeq(product(X3,X2,multiply(X3,X2)),true,product(inverse(X3),multiply(X3,X2),X2),true) = true,
inference(substitution,[status(thm)],[c122]) ).
cnf(c234,plain,
ifeq(true,true,product(inverse(X3),multiply(X3,X2),X2),true) = true,
inference(transitivity,[status(thm)],[c232,c233]) ).
cnf(c235,plain,
product(inverse(X3),multiply(X3,X2),X2) = true,
inference(transitivity,[status(thm)],[c229,c234]) ).
cnf(c236,plain,
true = product(inverse(X3),multiply(X3,X2),X2),
inference(symmetry,[status(thm)],[c235]) ).
cnf(c237,plain,
ifeq2(true,true,multiply(inverse(X3),multiply(X3,X2)),X2) = ifeq2(product(inverse(X3),multiply(X3,X2),X2),true,multiply(inverse(X3),multiply(X3,X2)),X2),
inference(congruence,[status(thm)],[c236]) ).
cnf(c238,plain,
ifeq2(product(inverse(X3),multiply(X3,X2),X2),true,multiply(inverse(X3),multiply(X3,X2)),X2) = X2,
inference(substitution,[status(thm)],[c138]) ).
cnf(c239,plain,
ifeq2(true,true,multiply(inverse(X3),multiply(X3,X2)),X2) = X2,
inference(transitivity,[status(thm)],[c237,c238]) ).
cnf(c240,plain,
multiply(inverse(X3),multiply(X3,X2)) = X2,
inference(transitivity,[status(thm)],[c227,c239]) ).
cnf(c241,plain,
multiply(inverse(a),multiply(a,multiply(b,X2))) = multiply(b,X2),
inference(substitution,[status(thm)],[c240]) ).
cnf(c242,plain,
multiply(inverse(a),multiply(c,X2)) = multiply(b,X2),
inference(transitivity,[status(thm)],[c225,c241]) ).
cnf(c243,plain,
multiply(inverse(a),multiply(c,c)) = multiply(b,c),
inference(substitution,[status(thm)],[c242]) ).
cnf(c244,plain,
multiply(inverse(a),inverse(c)) = multiply(b,c),
inference(transitivity,[status(thm)],[c188,c243]) ).
cnf(c245,plain,
multiply(b,c) = multiply(inverse(a),inverse(c)),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c246,plain,
multiply(inverse(a),multiply(b,c)) = multiply(inverse(a),multiply(inverse(a),inverse(c))),
inference(congruence,[status(thm)],[c245]) ).
cnf(c247,plain,
ifeq2(product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true,multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)) = multiply(multiply(X4,X3),X2),
inference(substitution,[status(thm)],[c138]) ).
cnf(c248,plain,
multiply(multiply(X4,X3),X2) = ifeq2(product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true,multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)),
inference(symmetry,[status(thm)],[c247]) ).
cnf(c249,plain,
ifeq(true,true,product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true) = product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c250,plain,
product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)) = ifeq(true,true,product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true),
inference(symmetry,[status(thm)],[c249]) ).
cnf(c251,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c252,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c251]) ).
cnf(c253,plain,
ifeq(true,true,product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true) = ifeq(product(X4,X3,multiply(X4,X3)),true,product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true),
inference(congruence,[status(thm)],[c252]) ).
cnf(c254,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true),true) = ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c255,plain,
ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true) = ifeq(true,true,ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true),true),
inference(symmetry,[status(thm)],[c254]) ).
cnf(c256,plain,
product(X3,X2,multiply(X3,X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c257,plain,
true = product(X3,X2,multiply(X3,X2)),
inference(symmetry,[status(thm)],[c256]) ).
cnf(c258,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true),true) = ifeq(product(X4,X2,multiply(X4,X2)),true,ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true),true),
inference(congruence,[status(thm)],[c257]) ).
cnf(c259,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,X6),true,product(X2,X3,multiply(X6,X4)),true),true),true) = ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,X6),true,product(X2,X3,multiply(X6,X4)),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c260,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X3,X4,multiply(X2,X5)),true),true) = ifeq(true,true,ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X3,X4,multiply(X2,X5)),true),true),true),
inference(symmetry,[status(thm)],[c259]) ).
cnf(c261,plain,
product(X2,X3,multiply(X2,X3)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c262,plain,
true = product(X2,X3,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c261]) ).
cnf(c263,plain,
ifeq(true,true,ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X3,X4,multiply(X2,X5)),true),true),true) = ifeq(product(X2,X5,multiply(X2,X5)),true,ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X3,X4,multiply(X2,X5)),true),true),true),
inference(congruence,[status(thm)],[c262]) ).
cnf(c264,plain,
ifeq(product(X2,X5,multiply(X2,X5)),true,ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X3,X4,multiply(X2,X5)),true),true),true) = true,
inference(substitution,[status(thm)],[c116]) ).
cnf(c265,plain,
ifeq(true,true,ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X3,X4,multiply(X2,X5)),true),true),true) = true,
inference(transitivity,[status(thm)],[c263,c264]) ).
cnf(c266,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X3,X4,multiply(X2,X5)),true),true) = true,
inference(transitivity,[status(thm)],[c260,c265]) ).
cnf(c267,plain,
ifeq(product(X4,X2,multiply(X4,X2)),true,ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true),true) = true,
inference(substitution,[status(thm)],[c266]) ).
cnf(c268,plain,
ifeq(true,true,ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true),true) = true,
inference(transitivity,[status(thm)],[c258,c267]) ).
cnf(c269,plain,
ifeq(product(X5,X4,X3),true,product(X5,multiply(X4,X2),multiply(X3,X2)),true) = true,
inference(transitivity,[status(thm)],[c255,c268]) ).
cnf(c270,plain,
ifeq(product(X4,X3,multiply(X4,X3)),true,product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true) = true,
inference(substitution,[status(thm)],[c269]) ).
cnf(c271,plain,
ifeq(true,true,product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true) = true,
inference(transitivity,[status(thm)],[c253,c270]) ).
cnf(c272,plain,
product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)) = true,
inference(transitivity,[status(thm)],[c250,c271]) ).
cnf(c273,plain,
ifeq2(product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true,multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)) = ifeq2(true,true,multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)),
inference(congruence,[status(thm)],[c272]) ).
cnf(c274,plain,
ifeq2(true,true,multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)) = multiply(X4,multiply(X3,X2)),
inference(substitution,[status(thm)],[c9]) ).
cnf(c275,plain,
ifeq2(product(X4,multiply(X3,X2),multiply(multiply(X4,X3),X2)),true,multiply(X4,multiply(X3,X2)),multiply(multiply(X4,X3),X2)) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c273,c274]) ).
cnf(c276,plain,
multiply(multiply(X4,X3),X2) = multiply(X4,multiply(X3,X2)),
inference(transitivity,[status(thm)],[c248,c275]) ).
cnf(c277,plain,
multiply(multiply(X3,X3),X2) = multiply(X3,multiply(X3,X2)),
inference(substitution,[status(thm)],[c276]) ).
cnf(c278,plain,
multiply(X3,multiply(X3,X2)) = multiply(multiply(X3,X3),X2),
inference(symmetry,[status(thm)],[c277]) ).
cnf(c279,plain,
multiply(multiply(X3,X3),X2) = multiply(inverse(X3),X2),
inference(congruence,[status(thm)],[c185]) ).
cnf(c280,plain,
multiply(X3,multiply(X3,X2)) = multiply(inverse(X3),X2),
inference(transitivity,[status(thm)],[c278,c279]) ).
cnf(c281,plain,
multiply(inverse(a),multiply(inverse(a),inverse(c))) = multiply(inverse(inverse(a)),inverse(c)),
inference(substitution,[status(thm)],[c280]) ).
cnf(c282,plain,
inverse(inverse(a)) = a,
inference(substitution,[status(thm)],[c90]) ).
cnf(c283,plain,
multiply(inverse(inverse(a)),inverse(c)) = multiply(a,inverse(c)),
inference(congruence,[status(thm)],[c282]) ).
cnf(c284,plain,
ifeq2(true,true,multiply(inverse(d),c),a) = multiply(inverse(d),c),
inference(substitution,[status(thm)],[c9]) ).
cnf(c285,plain,
multiply(inverse(d),c) = ifeq2(true,true,multiply(inverse(d),c),a),
inference(symmetry,[status(thm)],[c284]) ).
cnf(c286,plain,
ifeq(true,true,product(inverse(d),c,a),true) = product(inverse(d),c,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c287,plain,
product(inverse(d),c,a) = ifeq(true,true,product(inverse(d),c,a),true),
inference(symmetry,[status(thm)],[c286]) ).
cnf(c288,plain,
inverse(inverse(a)) = a,
inference(substitution,[status(thm)],[c90]) ).
cnf(c289,plain,
a = inverse(inverse(a)),
inference(symmetry,[status(thm)],[c288]) ).
cnf(c290,plain,
product(d,a,c) = product(d,inverse(inverse(a)),c),
inference(congruence,[status(thm)],[c289]) ).
cnf(c291,plain,
ifeq(true,true,product(d,inverse(inverse(a)),c),true) = product(d,inverse(inverse(a)),c),
inference(substitution,[status(thm)],[c2]) ).
cnf(c292,plain,
product(d,inverse(inverse(a)),c) = ifeq(true,true,product(d,inverse(inverse(a)),c),true),
inference(symmetry,[status(thm)],[c291]) ).
cnf(c293,axiom,
product(c,inverse(a),d) = true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c294,plain,
true = product(c,inverse(a),d),
inference(symmetry,[status(thm)],[c293]) ).
cnf(c295,plain,
ifeq(true,true,product(d,inverse(inverse(a)),c),true) = ifeq(product(c,inverse(a),d),true,product(d,inverse(inverse(a)),c),true),
inference(congruence,[status(thm)],[c294]) ).
cnf(c296,plain,
ifeq(product(c,inverse(a),d),true,product(d,inverse(inverse(a)),c),true) = true,
inference(substitution,[status(thm)],[c83]) ).
cnf(c297,plain,
ifeq(true,true,product(d,inverse(inverse(a)),c),true) = true,
inference(transitivity,[status(thm)],[c295,c296]) ).
cnf(c298,plain,
product(d,inverse(inverse(a)),c) = true,
inference(transitivity,[status(thm)],[c292,c297]) ).
cnf(c299,plain,
product(d,a,c) = true,
inference(transitivity,[status(thm)],[c290,c298]) ).
cnf(c300,plain,
true = product(d,a,c),
inference(symmetry,[status(thm)],[c299]) ).
cnf(c301,plain,
ifeq(true,true,product(inverse(d),c,a),true) = ifeq(product(d,a,c),true,product(inverse(d),c,a),true),
inference(congruence,[status(thm)],[c300]) ).
cnf(c302,plain,
ifeq(product(d,a,c),true,product(inverse(d),c,a),true) = true,
inference(substitution,[status(thm)],[c122]) ).
cnf(c303,plain,
ifeq(true,true,product(inverse(d),c,a),true) = true,
inference(transitivity,[status(thm)],[c301,c302]) ).
cnf(c304,plain,
product(inverse(d),c,a) = true,
inference(transitivity,[status(thm)],[c287,c303]) ).
cnf(c305,plain,
true = product(inverse(d),c,a),
inference(symmetry,[status(thm)],[c304]) ).
cnf(c306,plain,
ifeq2(true,true,multiply(inverse(d),c),a) = ifeq2(product(inverse(d),c,a),true,multiply(inverse(d),c),a),
inference(congruence,[status(thm)],[c305]) ).
cnf(c307,plain,
ifeq2(product(inverse(d),c,a),true,multiply(inverse(d),c),a) = a,
inference(substitution,[status(thm)],[c138]) ).
cnf(c308,plain,
ifeq2(true,true,multiply(inverse(d),c),a) = a,
inference(transitivity,[status(thm)],[c306,c307]) ).
cnf(c309,plain,
multiply(inverse(d),c) = a,
inference(transitivity,[status(thm)],[c285,c308]) ).
cnf(c310,plain,
a = multiply(inverse(d),c),
inference(symmetry,[status(thm)],[c309]) ).
cnf(c311,plain,
multiply(a,inverse(c)) = multiply(multiply(inverse(d),c),inverse(c)),
inference(congruence,[status(thm)],[c310]) ).
cnf(c312,plain,
multiply(multiply(inverse(d),c),inverse(c)) = inverse(d),
inference(substitution,[status(thm)],[c158]) ).
cnf(c313,plain,
multiply(a,inverse(c)) = inverse(d),
inference(transitivity,[status(thm)],[c311,c312]) ).
cnf(c314,plain,
multiply(inverse(inverse(a)),inverse(c)) = inverse(d),
inference(transitivity,[status(thm)],[c283,c313]) ).
cnf(c315,plain,
multiply(inverse(a),multiply(inverse(a),inverse(c))) = inverse(d),
inference(transitivity,[status(thm)],[c281,c314]) ).
cnf(c316,plain,
multiply(inverse(a),multiply(b,c)) = inverse(d),
inference(transitivity,[status(thm)],[c246,c315]) ).
cnf(c317,plain,
inverse(d) = multiply(inverse(a),multiply(b,c)),
inference(symmetry,[status(thm)],[c316]) ).
cnf(c318,plain,
multiply(h,inverse(d)) = multiply(h,multiply(inverse(a),multiply(b,c))),
inference(congruence,[status(thm)],[c317]) ).
cnf(c319,plain,
product(multiply(h,inverse(d)),b,identity) = product(multiply(h,multiply(inverse(a),multiply(b,c))),b,identity),
inference(congruence,[status(thm)],[c318]) ).
cnf(c320,plain,
inverse(inverse(h)) = h,
inference(substitution,[status(thm)],[c90]) ).
cnf(c321,plain,
h = inverse(inverse(h)),
inference(symmetry,[status(thm)],[c320]) ).
cnf(c322,plain,
multiply(h,multiply(inverse(a),multiply(b,c))) = multiply(inverse(inverse(h)),multiply(inverse(a),multiply(b,c))),
inference(congruence,[status(thm)],[c321]) ).
cnf(c323,plain,
product(multiply(h,multiply(inverse(a),multiply(b,c))),b,identity) = product(multiply(inverse(inverse(h)),multiply(inverse(a),multiply(b,c))),b,identity),
inference(congruence,[status(thm)],[c322]) ).
cnf(c324,plain,
multiply(multiply(inverse(inverse(h)),inverse(a)),multiply(b,c)) = multiply(inverse(inverse(h)),multiply(inverse(a),multiply(b,c))),
inference(substitution,[status(thm)],[c276]) ).
cnf(c325,plain,
multiply(inverse(inverse(h)),multiply(inverse(a),multiply(b,c))) = multiply(multiply(inverse(inverse(h)),inverse(a)),multiply(b,c)),
inference(symmetry,[status(thm)],[c324]) ).
cnf(c326,plain,
product(multiply(inverse(inverse(h)),multiply(inverse(a),multiply(b,c))),b,identity) = product(multiply(multiply(inverse(inverse(h)),inverse(a)),multiply(b,c)),b,identity),
inference(congruence,[status(thm)],[c325]) ).
cnf(c327,plain,
multiply(inverse(X2),multiply(X2,X3)) = X3,
inference(substitution,[status(thm)],[c240]) ).
cnf(c328,plain,
X3 = multiply(inverse(X2),multiply(X2,X3)),
inference(symmetry,[status(thm)],[c327]) ).
cnf(c329,plain,
multiply(X3,inverse(multiply(X2,X3))) = multiply(multiply(inverse(X2),multiply(X2,X3)),inverse(multiply(X2,X3))),
inference(congruence,[status(thm)],[c328]) ).
cnf(c330,plain,
multiply(multiply(inverse(X2),multiply(X2,X3)),inverse(multiply(X2,X3))) = inverse(X2),
inference(substitution,[status(thm)],[c158]) ).
cnf(c331,plain,
multiply(X3,inverse(multiply(X2,X3))) = inverse(X2),
inference(transitivity,[status(thm)],[c329,c330]) ).
cnf(c332,plain,
multiply(inverse(X2),inverse(multiply(multiply(X3,X2),inverse(X2)))) = inverse(multiply(X3,X2)),
inference(substitution,[status(thm)],[c331]) ).
cnf(c333,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),inverse(multiply(multiply(X3,X2),inverse(X2)))),
inference(symmetry,[status(thm)],[c332]) ).
cnf(c334,plain,
inverse(multiply(multiply(X3,X2),inverse(X2))) = inverse(X3),
inference(congruence,[status(thm)],[c158]) ).
cnf(c335,plain,
multiply(inverse(X2),inverse(multiply(multiply(X3,X2),inverse(X2)))) = multiply(inverse(X2),inverse(X3)),
inference(congruence,[status(thm)],[c334]) ).
cnf(c336,plain,
inverse(multiply(X3,X2)) = multiply(inverse(X2),inverse(X3)),
inference(transitivity,[status(thm)],[c333,c335]) ).
cnf(c337,plain,
inverse(multiply(a,inverse(h))) = multiply(inverse(inverse(h)),inverse(a)),
inference(substitution,[status(thm)],[c336]) ).
cnf(c338,plain,
multiply(inverse(inverse(h)),inverse(a)) = inverse(multiply(a,inverse(h))),
inference(symmetry,[status(thm)],[c337]) ).
cnf(c339,plain,
multiply(multiply(inverse(inverse(h)),inverse(a)),multiply(b,c)) = multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),
inference(congruence,[status(thm)],[c338]) ).
cnf(c340,plain,
product(multiply(multiply(inverse(inverse(h)),inverse(a)),multiply(b,c)),b,identity) = product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity),
inference(congruence,[status(thm)],[c339]) ).
cnf(c341,plain,
ifeq(true,true,product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity),true) = product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c342,plain,
product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity) = ifeq(true,true,product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity),true),
inference(symmetry,[status(thm)],[c341]) ).
cnf(c343,plain,
multiply(a,multiply(b,inverse(d))) = multiply(c,inverse(d)),
inference(substitution,[status(thm)],[c223]) ).
cnf(c344,plain,
multiply(c,inverse(d)) = multiply(a,multiply(b,inverse(d))),
inference(symmetry,[status(thm)],[c343]) ).
cnf(c345,plain,
ifeq2(true,true,multiply(inverse(h),d),b) = multiply(inverse(h),d),
inference(substitution,[status(thm)],[c9]) ).
cnf(c346,plain,
multiply(inverse(h),d) = ifeq2(true,true,multiply(inverse(h),d),b),
inference(symmetry,[status(thm)],[c345]) ).
cnf(c347,plain,
ifeq(true,true,product(inverse(h),d,b),true) = product(inverse(h),d,b),
inference(substitution,[status(thm)],[c2]) ).
cnf(c348,plain,
product(inverse(h),d,b) = ifeq(true,true,product(inverse(h),d,b),true),
inference(symmetry,[status(thm)],[c347]) ).
cnf(c349,plain,
product(inverse(h),h,identity) = true,
inference(substitution,[status(thm)],[c25]) ).
cnf(c350,plain,
true = product(inverse(h),h,identity),
inference(symmetry,[status(thm)],[c349]) ).
cnf(c351,plain,
ifeq(true,true,product(inverse(h),d,b),true) = ifeq(product(inverse(h),h,identity),true,product(inverse(h),d,b),true),
inference(congruence,[status(thm)],[c350]) ).
cnf(c352,plain,
d = j,
inference(symmetry,[status(thm)],[c60]) ).
cnf(c353,plain,
product(X2,d,b) = product(X2,j,b),
inference(congruence,[status(thm)],[c352]) ).
cnf(c354,plain,
ifeq(product(X2,h,identity),true,product(X2,d,b),true) = ifeq(product(X2,h,identity),true,product(X2,j,b),true),
inference(congruence,[status(thm)],[c353]) ).
cnf(c355,plain,
ifeq(true,true,ifeq(product(X2,h,identity),true,product(X2,j,b),true),true) = ifeq(product(X2,h,identity),true,product(X2,j,b),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c356,plain,
ifeq(product(X2,h,identity),true,product(X2,j,b),true) = ifeq(true,true,ifeq(product(X2,h,identity),true,product(X2,j,b),true),true),
inference(symmetry,[status(thm)],[c355]) ).
cnf(c357,plain,
true = product(h,b,j),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c358,plain,
ifeq(true,true,ifeq(product(X2,h,identity),true,product(X2,j,b),true),true) = ifeq(product(h,b,j),true,ifeq(product(X2,h,identity),true,product(X2,j,b),true),true),
inference(congruence,[status(thm)],[c357]) ).
cnf(c359,plain,
ifeq(product(h,b,j),true,ifeq(product(X2,h,identity),true,product(X2,j,b),true),true) = true,
inference(substitution,[status(thm)],[c119]) ).
cnf(c360,plain,
ifeq(true,true,ifeq(product(X2,h,identity),true,product(X2,j,b),true),true) = true,
inference(transitivity,[status(thm)],[c358,c359]) ).
cnf(c361,plain,
ifeq(product(X2,h,identity),true,product(X2,j,b),true) = true,
inference(transitivity,[status(thm)],[c356,c360]) ).
cnf(c362,plain,
ifeq(product(X2,h,identity),true,product(X2,d,b),true) = true,
inference(transitivity,[status(thm)],[c354,c361]) ).
cnf(c363,plain,
ifeq(product(inverse(h),h,identity),true,product(inverse(h),d,b),true) = true,
inference(substitution,[status(thm)],[c362]) ).
cnf(c364,plain,
ifeq(true,true,product(inverse(h),d,b),true) = true,
inference(transitivity,[status(thm)],[c351,c363]) ).
cnf(c365,plain,
product(inverse(h),d,b) = true,
inference(transitivity,[status(thm)],[c348,c364]) ).
cnf(c366,plain,
true = product(inverse(h),d,b),
inference(symmetry,[status(thm)],[c365]) ).
cnf(c367,plain,
ifeq2(true,true,multiply(inverse(h),d),b) = ifeq2(product(inverse(h),d,b),true,multiply(inverse(h),d),b),
inference(congruence,[status(thm)],[c366]) ).
cnf(c368,plain,
ifeq2(product(inverse(h),d,b),true,multiply(inverse(h),d),b) = b,
inference(substitution,[status(thm)],[c138]) ).
cnf(c369,plain,
ifeq2(true,true,multiply(inverse(h),d),b) = b,
inference(transitivity,[status(thm)],[c367,c368]) ).
cnf(c370,plain,
multiply(inverse(h),d) = b,
inference(transitivity,[status(thm)],[c346,c369]) ).
cnf(c371,plain,
b = multiply(inverse(h),d),
inference(symmetry,[status(thm)],[c370]) ).
cnf(c372,plain,
multiply(b,inverse(d)) = multiply(multiply(inverse(h),d),inverse(d)),
inference(congruence,[status(thm)],[c371]) ).
cnf(c373,plain,
multiply(multiply(inverse(h),d),inverse(d)) = inverse(h),
inference(substitution,[status(thm)],[c158]) ).
cnf(c374,plain,
multiply(b,inverse(d)) = inverse(h),
inference(transitivity,[status(thm)],[c372,c373]) ).
cnf(c375,plain,
multiply(a,multiply(b,inverse(d))) = multiply(a,inverse(h)),
inference(congruence,[status(thm)],[c374]) ).
cnf(c376,plain,
multiply(c,inverse(d)) = multiply(a,inverse(h)),
inference(transitivity,[status(thm)],[c344,c375]) ).
cnf(c377,plain,
multiply(a,inverse(h)) = multiply(c,inverse(d)),
inference(symmetry,[status(thm)],[c376]) ).
cnf(c378,plain,
product(multiply(b,c),b,multiply(a,inverse(h))) = product(multiply(b,c),b,multiply(c,inverse(d))),
inference(congruence,[status(thm)],[c377]) ).
cnf(c379,plain,
inverse(d) = multiply(a,inverse(c)),
inference(symmetry,[status(thm)],[c313]) ).
cnf(c380,plain,
multiply(c,inverse(d)) = multiply(c,multiply(a,inverse(c))),
inference(congruence,[status(thm)],[c379]) ).
cnf(c381,plain,
product(multiply(b,c),b,multiply(c,inverse(d))) = product(multiply(b,c),b,multiply(c,multiply(a,inverse(c)))),
inference(congruence,[status(thm)],[c380]) ).
cnf(c382,plain,
multiply(multiply(c,a),inverse(c)) = multiply(c,multiply(a,inverse(c))),
inference(substitution,[status(thm)],[c276]) ).
cnf(c383,plain,
multiply(c,multiply(a,inverse(c))) = multiply(multiply(c,a),inverse(c)),
inference(symmetry,[status(thm)],[c382]) ).
cnf(c384,plain,
product(multiply(b,c),b,multiply(c,multiply(a,inverse(c)))) = product(multiply(b,c),b,multiply(multiply(c,a),inverse(c))),
inference(congruence,[status(thm)],[c383]) ).
cnf(c385,plain,
multiply(b,c) = multiply(inverse(a),inverse(c)),
inference(symmetry,[status(thm)],[c244]) ).
cnf(c386,plain,
product(multiply(b,c),b,multiply(multiply(c,a),inverse(c))) = product(multiply(inverse(a),inverse(c)),b,multiply(multiply(c,a),inverse(c))),
inference(congruence,[status(thm)],[c385]) ).
cnf(c387,plain,
inverse(multiply(c,a)) = multiply(inverse(a),inverse(c)),
inference(substitution,[status(thm)],[c336]) ).
cnf(c388,plain,
multiply(inverse(a),inverse(c)) = inverse(multiply(c,a)),
inference(symmetry,[status(thm)],[c387]) ).
cnf(c389,plain,
product(multiply(inverse(a),inverse(c)),b,multiply(multiply(c,a),inverse(c))) = product(inverse(multiply(c,a)),b,multiply(multiply(c,a),inverse(c))),
inference(congruence,[status(thm)],[c388]) ).
cnf(c390,plain,
multiply(multiply(c,a),multiply(c,a)) = inverse(multiply(c,a)),
inference(substitution,[status(thm)],[c185]) ).
cnf(c391,plain,
inverse(multiply(c,a)) = multiply(multiply(c,a),multiply(c,a)),
inference(symmetry,[status(thm)],[c390]) ).
cnf(c392,plain,
product(inverse(multiply(c,a)),b,multiply(multiply(c,a),inverse(c))) = product(multiply(multiply(c,a),multiply(c,a)),b,multiply(multiply(c,a),inverse(c))),
inference(congruence,[status(thm)],[c391]) ).
cnf(c393,plain,
multiply(c,c) = inverse(c),
inference(substitution,[status(thm)],[c185]) ).
cnf(c394,plain,
inverse(c) = multiply(c,c),
inference(symmetry,[status(thm)],[c393]) ).
cnf(c395,plain,
multiply(X2,inverse(c)) = multiply(X2,multiply(c,c)),
inference(congruence,[status(thm)],[c394]) ).
cnf(c396,plain,
product(multiply(X2,multiply(c,a)),b,multiply(X2,inverse(c))) = product(multiply(X2,multiply(c,a)),b,multiply(X2,multiply(c,c))),
inference(congruence,[status(thm)],[c395]) ).
cnf(c397,plain,
ifeq(true,true,product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))),true) = product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c398,plain,
product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))) = ifeq(true,true,product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))),true),
inference(symmetry,[status(thm)],[c397]) ).
cnf(c399,plain,
ifeq(true,true,product(multiply(X2,a),b,multiply(X2,c)),true) = product(multiply(X2,a),b,multiply(X2,c)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c400,plain,
product(multiply(X2,a),b,multiply(X2,c)) = ifeq(true,true,product(multiply(X2,a),b,multiply(X2,c)),true),
inference(symmetry,[status(thm)],[c399]) ).
cnf(c401,plain,
product(X2,a,multiply(X2,a)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c402,plain,
true = product(X2,a,multiply(X2,a)),
inference(symmetry,[status(thm)],[c401]) ).
cnf(c403,plain,
ifeq(true,true,product(multiply(X2,a),b,multiply(X2,c)),true) = ifeq(product(X2,a,multiply(X2,a)),true,product(multiply(X2,a),b,multiply(X2,c)),true),
inference(congruence,[status(thm)],[c402]) ).
cnf(c404,plain,
ifeq(true,true,ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true),true) = ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c405,plain,
ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true) = ifeq(true,true,ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true),true),
inference(symmetry,[status(thm)],[c404]) ).
cnf(c406,plain,
product(X2,c,multiply(X2,c)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c407,plain,
true = product(X2,c,multiply(X2,c)),
inference(symmetry,[status(thm)],[c406]) ).
cnf(c408,plain,
ifeq(true,true,ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true),true) = ifeq(product(X3,c,multiply(X3,c)),true,ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true),true),
inference(congruence,[status(thm)],[c407]) ).
cnf(c409,plain,
ifeq(true,true,ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true),true) = ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c410,plain,
ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true) = ifeq(true,true,ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true),true),
inference(symmetry,[status(thm)],[c409]) ).
cnf(c411,plain,
true = product(a,b,c),
inference(symmetry,[status(thm)],[c205]) ).
cnf(c412,plain,
ifeq(true,true,ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true),true) = ifeq(product(a,b,c),true,ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true),true),
inference(congruence,[status(thm)],[c411]) ).
cnf(c413,plain,
ifeq(product(a,b,c),true,ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c414,plain,
ifeq(true,true,ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true),true) = true,
inference(transitivity,[status(thm)],[c412,c413]) ).
cnf(c415,plain,
ifeq(product(X4,c,X3),true,ifeq(product(X4,a,X2),true,product(X2,b,X3),true),true) = true,
inference(transitivity,[status(thm)],[c410,c414]) ).
cnf(c416,plain,
ifeq(product(X3,c,multiply(X3,c)),true,ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true),true) = true,
inference(substitution,[status(thm)],[c415]) ).
cnf(c417,plain,
ifeq(true,true,ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true),true) = true,
inference(transitivity,[status(thm)],[c408,c416]) ).
cnf(c418,plain,
ifeq(product(X3,a,X2),true,product(X2,b,multiply(X3,c)),true) = true,
inference(transitivity,[status(thm)],[c405,c417]) ).
cnf(c419,plain,
ifeq(product(X2,a,multiply(X2,a)),true,product(multiply(X2,a),b,multiply(X2,c)),true) = true,
inference(substitution,[status(thm)],[c418]) ).
cnf(c420,plain,
ifeq(true,true,product(multiply(X2,a),b,multiply(X2,c)),true) = true,
inference(transitivity,[status(thm)],[c403,c419]) ).
cnf(c421,plain,
product(multiply(X2,a),b,multiply(X2,c)) = true,
inference(transitivity,[status(thm)],[c400,c420]) ).
cnf(c422,plain,
true = product(multiply(X2,a),b,multiply(X2,c)),
inference(symmetry,[status(thm)],[c421]) ).
cnf(c423,plain,
ifeq(true,true,product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))),true) = ifeq(product(multiply(X2,a),b,multiply(X2,c)),true,product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))),true),
inference(congruence,[status(thm)],[c422]) ).
cnf(c424,plain,
ifeq(true,true,product(multiply(X2,X5),X4,multiply(X2,X3)),true) = product(multiply(X2,X5),X4,multiply(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c425,plain,
product(multiply(X2,X5),X4,multiply(X2,X3)) = ifeq(true,true,product(multiply(X2,X5),X4,multiply(X2,X3)),true),
inference(symmetry,[status(thm)],[c424]) ).
cnf(c426,plain,
ifeq(product(X5,X4,X3),true,product(multiply(X2,X5),X4,multiply(X2,X3)),true) = ifeq(product(X5,X4,X3),true,ifeq(true,true,product(multiply(X2,X5),X4,multiply(X2,X3)),true),true),
inference(congruence,[status(thm)],[c425]) ).
cnf(c427,plain,
product(X2,X3,multiply(X2,X3)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c428,plain,
true = product(X2,X3,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c427]) ).
cnf(c429,plain,
ifeq(true,true,product(multiply(X2,X5),X4,multiply(X2,X3)),true) = ifeq(product(X2,X5,multiply(X2,X5)),true,product(multiply(X2,X5),X4,multiply(X2,X3)),true),
inference(congruence,[status(thm)],[c428]) ).
cnf(c430,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,product(multiply(X2,X5),X4,multiply(X2,X3)),true),true) = ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,multiply(X2,X5)),true,product(multiply(X2,X5),X4,multiply(X2,X3)),true),true),
inference(congruence,[status(thm)],[c429]) ).
cnf(c431,plain,
ifeq(true,true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true) = ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c432,plain,
ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true) = ifeq(true,true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true),
inference(symmetry,[status(thm)],[c431]) ).
cnf(c433,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true) = ifeq(product(X6,X5,X4),true,ifeq(true,true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true),true),
inference(congruence,[status(thm)],[c432]) ).
cnf(c434,plain,
product(X2,X3,multiply(X2,X3)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c435,plain,
true = product(X2,X3,multiply(X2,X3)),
inference(symmetry,[status(thm)],[c434]) ).
cnf(c436,plain,
ifeq(true,true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true) = ifeq(product(X3,X4,multiply(X3,X4)),true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true),
inference(congruence,[status(thm)],[c435]) ).
cnf(c437,plain,
ifeq(product(X6,X5,X4),true,ifeq(true,true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true),true) = ifeq(product(X6,X5,X4),true,ifeq(product(X3,X4,multiply(X3,X4)),true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true),true),
inference(congruence,[status(thm)],[c436]) ).
cnf(c438,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(X3,X4,multiply(X3,X4)),true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c439,plain,
ifeq(product(X6,X5,X4),true,ifeq(true,true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true),true) = true,
inference(transitivity,[status(thm)],[c437,c438]) ).
cnf(c440,plain,
ifeq(product(X6,X5,X4),true,ifeq(product(X3,X6,X2),true,product(X2,X5,multiply(X3,X4)),true),true) = true,
inference(transitivity,[status(thm)],[c433,c439]) ).
cnf(c441,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(X2,X5,multiply(X2,X5)),true,product(multiply(X2,X5),X4,multiply(X2,X3)),true),true) = true,
inference(substitution,[status(thm)],[c440]) ).
cnf(c442,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,product(multiply(X2,X5),X4,multiply(X2,X3)),true),true) = true,
inference(transitivity,[status(thm)],[c430,c441]) ).
cnf(c443,plain,
ifeq(product(X5,X4,X3),true,product(multiply(X2,X5),X4,multiply(X2,X3)),true) = true,
inference(transitivity,[status(thm)],[c426,c442]) ).
cnf(c444,plain,
ifeq(product(multiply(X2,a),b,multiply(X2,c)),true,product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))),true) = true,
inference(substitution,[status(thm)],[c443]) ).
cnf(c445,plain,
ifeq(true,true,product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))),true) = true,
inference(transitivity,[status(thm)],[c423,c444]) ).
cnf(c446,plain,
product(multiply(X3,multiply(X2,a)),b,multiply(X3,multiply(X2,c))) = true,
inference(transitivity,[status(thm)],[c398,c445]) ).
cnf(c447,plain,
product(multiply(X2,multiply(c,a)),b,multiply(X2,multiply(c,c))) = true,
inference(substitution,[status(thm)],[c446]) ).
cnf(c448,plain,
product(multiply(X2,multiply(c,a)),b,multiply(X2,inverse(c))) = true,
inference(transitivity,[status(thm)],[c396,c447]) ).
cnf(c449,plain,
product(multiply(multiply(c,a),multiply(c,a)),b,multiply(multiply(c,a),inverse(c))) = true,
inference(substitution,[status(thm)],[c448]) ).
cnf(c450,plain,
product(inverse(multiply(c,a)),b,multiply(multiply(c,a),inverse(c))) = true,
inference(transitivity,[status(thm)],[c392,c449]) ).
cnf(c451,plain,
product(multiply(inverse(a),inverse(c)),b,multiply(multiply(c,a),inverse(c))) = true,
inference(transitivity,[status(thm)],[c389,c450]) ).
cnf(c452,plain,
product(multiply(b,c),b,multiply(multiply(c,a),inverse(c))) = true,
inference(transitivity,[status(thm)],[c386,c451]) ).
cnf(c453,plain,
product(multiply(b,c),b,multiply(c,multiply(a,inverse(c)))) = true,
inference(transitivity,[status(thm)],[c384,c452]) ).
cnf(c454,plain,
product(multiply(b,c),b,multiply(c,inverse(d))) = true,
inference(transitivity,[status(thm)],[c381,c453]) ).
cnf(c455,plain,
product(multiply(b,c),b,multiply(a,inverse(h))) = true,
inference(transitivity,[status(thm)],[c378,c454]) ).
cnf(c456,plain,
true = product(multiply(b,c),b,multiply(a,inverse(h))),
inference(symmetry,[status(thm)],[c455]) ).
cnf(c457,plain,
ifeq(true,true,product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity),true) = ifeq(product(multiply(b,c),b,multiply(a,inverse(h))),true,product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity),true),
inference(congruence,[status(thm)],[c456]) ).
cnf(c458,plain,
ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true) = product(multiply(inverse(X2),X4),X3,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c459,plain,
product(multiply(inverse(X2),X4),X3,identity) = ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true),
inference(symmetry,[status(thm)],[c458]) ).
cnf(c460,plain,
ifeq(product(X4,X3,X2),true,product(multiply(inverse(X2),X4),X3,identity),true) = ifeq(product(X4,X3,X2),true,ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true),true),
inference(congruence,[status(thm)],[c459]) ).
cnf(c461,plain,
product(inverse(X2),X3,multiply(inverse(X2),X3)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c462,plain,
true = product(inverse(X2),X3,multiply(inverse(X2),X3)),
inference(symmetry,[status(thm)],[c461]) ).
cnf(c463,plain,
ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true) = ifeq(product(inverse(X2),X4,multiply(inverse(X2),X4)),true,product(multiply(inverse(X2),X4),X3,identity),true),
inference(congruence,[status(thm)],[c462]) ).
cnf(c464,plain,
ifeq(product(X4,X3,X2),true,ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true),true) = ifeq(product(X4,X3,X2),true,ifeq(product(inverse(X2),X4,multiply(inverse(X2),X4)),true,product(multiply(inverse(X2),X4),X3,identity),true),true),
inference(congruence,[status(thm)],[c463]) ).
cnf(c465,plain,
ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true) = ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c466,plain,
ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true) = ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),
inference(symmetry,[status(thm)],[c465]) ).
cnf(c467,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true) = ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true),
inference(congruence,[status(thm)],[c466]) ).
cnf(c468,plain,
true = product(inverse(X2),X2,identity),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c469,plain,
ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true) = ifeq(product(inverse(X3),X3,identity),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),
inference(congruence,[status(thm)],[c468]) ).
cnf(c470,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true) = ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X3),X3,identity),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true),
inference(congruence,[status(thm)],[c469]) ).
cnf(c471,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X3),X3,identity),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true) = true,
inference(substitution,[status(thm)],[c35]) ).
cnf(c472,plain,
ifeq(product(X5,X4,X3),true,ifeq(true,true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true),true) = true,
inference(transitivity,[status(thm)],[c470,c471]) ).
cnf(c473,plain,
ifeq(product(X5,X4,X3),true,ifeq(product(inverse(X3),X5,X2),true,product(X2,X4,identity),true),true) = true,
inference(transitivity,[status(thm)],[c467,c472]) ).
cnf(c474,plain,
ifeq(product(X4,X3,X2),true,ifeq(product(inverse(X2),X4,multiply(inverse(X2),X4)),true,product(multiply(inverse(X2),X4),X3,identity),true),true) = true,
inference(substitution,[status(thm)],[c473]) ).
cnf(c475,plain,
ifeq(product(X4,X3,X2),true,ifeq(true,true,product(multiply(inverse(X2),X4),X3,identity),true),true) = true,
inference(transitivity,[status(thm)],[c464,c474]) ).
cnf(c476,plain,
ifeq(product(X4,X3,X2),true,product(multiply(inverse(X2),X4),X3,identity),true) = true,
inference(transitivity,[status(thm)],[c460,c475]) ).
cnf(c477,plain,
ifeq(product(multiply(b,c),b,multiply(a,inverse(h))),true,product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity),true) = true,
inference(substitution,[status(thm)],[c476]) ).
cnf(c478,plain,
ifeq(true,true,product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity),true) = true,
inference(transitivity,[status(thm)],[c457,c477]) ).
cnf(c479,plain,
product(multiply(inverse(multiply(a,inverse(h))),multiply(b,c)),b,identity) = true,
inference(transitivity,[status(thm)],[c342,c478]) ).
cnf(c480,plain,
product(multiply(multiply(inverse(inverse(h)),inverse(a)),multiply(b,c)),b,identity) = true,
inference(transitivity,[status(thm)],[c340,c479]) ).
cnf(c481,plain,
product(multiply(inverse(inverse(h)),multiply(inverse(a),multiply(b,c))),b,identity) = true,
inference(transitivity,[status(thm)],[c326,c480]) ).
cnf(c482,plain,
product(multiply(h,multiply(inverse(a),multiply(b,c))),b,identity) = true,
inference(transitivity,[status(thm)],[c323,c481]) ).
cnf(c483,plain,
product(multiply(h,inverse(d)),b,identity) = true,
inference(transitivity,[status(thm)],[c319,c482]) ).
cnf(c484,plain,
product(inverse(k),b,identity) = true,
inference(transitivity,[status(thm)],[c162,c483]) ).
cnf(c485,plain,
true = product(inverse(k),b,identity),
inference(symmetry,[status(thm)],[c484]) ).
cnf(c486,plain,
ifeq2(true,true,multiply(inverse(k),b),identity) = ifeq2(product(inverse(k),b,identity),true,multiply(inverse(k),b),identity),
inference(congruence,[status(thm)],[c485]) ).
cnf(c487,plain,
ifeq2(product(inverse(k),b,identity),true,multiply(inverse(k),b),identity) = identity,
inference(substitution,[status(thm)],[c138]) ).
cnf(c488,plain,
ifeq2(true,true,multiply(inverse(k),b),identity) = identity,
inference(transitivity,[status(thm)],[c486,c487]) ).
cnf(c489,plain,
multiply(inverse(k),b) = identity,
inference(transitivity,[status(thm)],[c11,c488]) ).
cnf(c490,plain,
identity = multiply(inverse(k),b),
inference(symmetry,[status(thm)],[c489]) ).
cnf(c491,plain,
product(identity,inverse(b),inverse(b)) = product(multiply(inverse(k),b),inverse(b),inverse(b)),
inference(congruence,[status(thm)],[c490]) ).
cnf(c492,plain,
ifeq(product(identity,inverse(b),inverse(b)),true,product(k,inverse(b),identity),true) = ifeq(product(multiply(inverse(k),b),inverse(b),inverse(b)),true,product(k,inverse(b),identity),true),
inference(congruence,[status(thm)],[c491]) ).
cnf(c493,plain,
ifeq(true,true,product(X3,X2,identity),true) = product(X3,X2,identity),
inference(substitution,[status(thm)],[c2]) ).
cnf(c494,plain,
product(X3,X2,identity) = ifeq(true,true,product(X3,X2,identity),true),
inference(symmetry,[status(thm)],[c493]) ).
cnf(c495,plain,
ifeq(product(multiply(inverse(X4),X3),inverse(X3),X2),true,product(X4,X2,identity),true) = ifeq(product(multiply(inverse(X4),X3),inverse(X3),X2),true,ifeq(true,true,product(X4,X2,identity),true),true),
inference(congruence,[status(thm)],[c494]) ).
cnf(c496,plain,
ifeq(true,true,product(X3,multiply(inverse(X3),X2),X2),true) = product(X3,multiply(inverse(X3),X2),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c497,plain,
product(X3,multiply(inverse(X3),X2),X2) = ifeq(true,true,product(X3,multiply(inverse(X3),X2),X2),true),
inference(symmetry,[status(thm)],[c496]) ).
cnf(c498,plain,
product(inverse(X3),X2,multiply(inverse(X3),X2)) = true,
inference(substitution,[status(thm)],[c131]) ).
cnf(c499,plain,
true = product(inverse(X3),X2,multiply(inverse(X3),X2)),
inference(symmetry,[status(thm)],[c498]) ).
cnf(c500,plain,
ifeq(true,true,product(X3,multiply(inverse(X3),X2),X2),true) = ifeq(product(inverse(X3),X2,multiply(inverse(X3),X2)),true,product(X3,multiply(inverse(X3),X2),X2),true),
inference(congruence,[status(thm)],[c499]) ).
cnf(c501,plain,
ifeq(true,true,product(X4,X2,X3),true) = product(X4,X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c502,plain,
product(X4,X2,X3) = ifeq(true,true,product(X4,X2,X3),true),
inference(symmetry,[status(thm)],[c501]) ).
cnf(c503,plain,
ifeq(product(inverse(X4),X3,X2),true,product(X4,X2,X3),true) = ifeq(product(inverse(X4),X3,X2),true,ifeq(true,true,product(X4,X2,X3),true),true),
inference(congruence,[status(thm)],[c502]) ).
cnf(c504,plain,
true = product(X2,inverse(X2),identity),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c505,plain,
ifeq(true,true,product(X4,X2,X3),true) = ifeq(product(X4,inverse(X4),identity),true,product(X4,X2,X3),true),
inference(congruence,[status(thm)],[c504]) ).
cnf(c506,plain,
ifeq(product(inverse(X4),X3,X2),true,ifeq(true,true,product(X4,X2,X3),true),true) = ifeq(product(inverse(X4),X3,X2),true,ifeq(product(X4,inverse(X4),identity),true,product(X4,X2,X3),true),true),
inference(congruence,[status(thm)],[c505]) ).
cnf(c507,plain,
ifeq(product(inverse(X4),X3,X2),true,ifeq(product(X4,inverse(X4),identity),true,product(X4,X2,X3),true),true) = true,
inference(substitution,[status(thm)],[c119]) ).
cnf(c508,plain,
ifeq(product(inverse(X4),X3,X2),true,ifeq(true,true,product(X4,X2,X3),true),true) = true,
inference(transitivity,[status(thm)],[c506,c507]) ).
cnf(c509,plain,
ifeq(product(inverse(X4),X3,X2),true,product(X4,X2,X3),true) = true,
inference(transitivity,[status(thm)],[c503,c508]) ).
cnf(c510,plain,
ifeq(product(inverse(X3),X2,multiply(inverse(X3),X2)),true,product(X3,multiply(inverse(X3),X2),X2),true) = true,
inference(substitution,[status(thm)],[c509]) ).
cnf(c511,plain,
ifeq(true,true,product(X3,multiply(inverse(X3),X2),X2),true) = true,
inference(transitivity,[status(thm)],[c500,c510]) ).
cnf(c512,plain,
product(X3,multiply(inverse(X3),X2),X2) = true,
inference(transitivity,[status(thm)],[c497,c511]) ).
cnf(c513,plain,
true = product(X3,multiply(inverse(X3),X2),X2),
inference(symmetry,[status(thm)],[c512]) ).
cnf(c514,plain,
ifeq(true,true,product(X4,X2,identity),true) = ifeq(product(X4,multiply(inverse(X4),X3),X3),true,product(X4,X2,identity),true),
inference(congruence,[status(thm)],[c513]) ).
cnf(c515,plain,
ifeq(product(multiply(inverse(X4),X3),inverse(X3),X2),true,ifeq(true,true,product(X4,X2,identity),true),true) = ifeq(product(multiply(inverse(X4),X3),inverse(X3),X2),true,ifeq(product(X4,multiply(inverse(X4),X3),X3),true,product(X4,X2,identity),true),true),
inference(congruence,[status(thm)],[c514]) ).
cnf(c516,plain,
ifeq(true,true,ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true),true) = ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true),
inference(substitution,[status(thm)],[c2]) ).
cnf(c517,plain,
ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true) = ifeq(true,true,ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true),true),
inference(symmetry,[status(thm)],[c516]) ).
cnf(c518,plain,
true = product(X2,inverse(X2),identity),
inference(symmetry,[status(thm)],[c74]) ).
cnf(c519,plain,
ifeq(true,true,ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true),true) = ifeq(product(X4,inverse(X4),identity),true,ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true),true),
inference(congruence,[status(thm)],[c518]) ).
cnf(c520,plain,
ifeq(product(X4,inverse(X4),identity),true,ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true),true) = true,
inference(substitution,[status(thm)],[c116]) ).
cnf(c521,plain,
ifeq(true,true,ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true),true) = true,
inference(transitivity,[status(thm)],[c519,c520]) ).
cnf(c522,plain,
ifeq(product(X5,inverse(X4),X3),true,ifeq(product(X2,X5,X4),true,product(X2,X3,identity),true),true) = true,
inference(transitivity,[status(thm)],[c517,c521]) ).
cnf(c523,plain,
ifeq(product(multiply(inverse(X4),X3),inverse(X3),X2),true,ifeq(product(X4,multiply(inverse(X4),X3),X3),true,product(X4,X2,identity),true),true) = true,
inference(substitution,[status(thm)],[c522]) ).
cnf(c524,plain,
ifeq(product(multiply(inverse(X4),X3),inverse(X3),X2),true,ifeq(true,true,product(X4,X2,identity),true),true) = true,
inference(transitivity,[status(thm)],[c515,c523]) ).
cnf(c525,plain,
ifeq(product(multiply(inverse(X4),X3),inverse(X3),X2),true,product(X4,X2,identity),true) = true,
inference(transitivity,[status(thm)],[c495,c524]) ).
cnf(c526,plain,
ifeq(product(multiply(inverse(k),b),inverse(b),inverse(b)),true,product(k,inverse(b),identity),true) = true,
inference(substitution,[status(thm)],[c525]) ).
cnf(c527,plain,
ifeq(product(identity,inverse(b),inverse(b)),true,product(k,inverse(b),identity),true) = true,
inference(transitivity,[status(thm)],[c492,c526]) ).
cnf(c528,plain,
ifeq(true,true,product(k,inverse(b),identity),true) = true,
inference(transitivity,[status(thm)],[c8,c527]) ).
cnf(c529,plain,
product(k,inverse(b),identity) = true,
inference(transitivity,[status(thm)],[c4,c528]) ).
cnf(c530,plain,
$false,
inference(resolution,[status(thm)],[c1,c529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP002-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sun Sep 27 09:12:44 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 53.78/7.27 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 53.78/7.27
% 53.78/7.27 % SZS status Unsatisfiable
% 53.78/7.27
% 54.59/7.30 % SZS output start CNFRefutation
% See solution above
% 56.95/7.60
% 56.95/7.60 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------