%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 10:11:58 AM UTC 2026
% Result : Unsatisfiable 59.20s 7.94s
% Output : CNFRefutation 60.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 18
% Syntax : Number of clauses : 219 ( 219 unt; 0 nHn; 3 RR)
% Number of literals : 219 ( 218 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 506 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
a(x0,x1,x1) != a(x1,x1,x0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
a(j(A),B,C) = a(B,C,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos32) ).
cnf(c3,plain,
a(j(i(X)),X3,X2) = a(X3,X2,i(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
a(X3,X2,i(X)) = a(j(i(X)),X3,X2),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
j(A2) = quotient(one,A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos10) ).
cnf(c6,plain,
j(i(X)) = quotient(one,i(X)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,axiom,
i(A2) = difference(A2,one),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos09) ).
cnf(c8,plain,
i(X) = difference(X,one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
product(X,i(X)) = product(X,difference(X,one)),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
product(A2,difference(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos03) ).
cnf(c11,plain,
product(X,difference(X,one)) = one,
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
product(X,i(X)) = one,
inference(transitivity,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
one = product(X,i(X)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
quotient(one,i(X)) = quotient(product(X,i(X)),i(X)),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
quotient(product(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos05) ).
cnf(c16,plain,
quotient(product(X,i(X)),i(X)) = X,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
quotient(one,i(X)) = X,
inference(transitivity,[status(thm)],[c14,c16]) ).
cnf(c18,plain,
j(i(X)) = X,
inference(transitivity,[status(thm)],[c6,c17]) ).
cnf(c19,plain,
a(j(i(X)),X3,X2) = a(X,X3,X2),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,plain,
a(X3,X2,i(X)) = a(X,X3,X2),
inference(transitivity,[status(thm)],[c4,c19]) ).
cnf(c21,plain,
a(X,j(X3),i(X2)) = a(X2,X,j(X3)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
a(X2,X,j(X3)) = a(X,j(X3),i(X2)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
a(A2,i(B2),C2) = a(A2,j(B2),C2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos30) ).
cnf(c24,plain,
a(X,i(X3),i(X2)) = a(X,j(X3),i(X2)),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
a(X,j(X3),i(X2)) = a(X,i(X3),i(X2)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
a(X,i(X3),i(X2)) = a(X2,X,i(X3)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c27,plain,
a(X2,X,i(X3)) = a(X3,X2,X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c28,plain,
a(X,i(X3),i(X2)) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c26,c27]) ).
cnf(c29,plain,
a(X,j(X3),i(X2)) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c25,c28]) ).
cnf(c30,plain,
a(X2,X,j(X3)) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c22,c29]) ).
cnf(c31,plain,
a(X2,X2,j(X)) = a(X,X2,X2),
inference(substitution,[status(thm)],[c30]) ).
cnf(c32,plain,
a(X,X2,X2) = a(X2,X2,j(X)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
a(X2,j(X),j(X2)) = a(X2,X2,j(X)),
inference(substitution,[status(thm)],[c30]) ).
cnf(c34,plain,
a(X2,X2,j(X)) = a(X2,j(X),j(X2)),
inference(symmetry,[status(thm)],[c33]) ).
cnf(c35,plain,
a(j(X),j(X3),X2) = a(j(X3),X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c36,plain,
a(j(X3),X2,X) = a(j(X),j(X3),X2),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
a(X,i(X3),X2) = a(X,j(X3),X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c38,plain,
a(X,j(X3),X2) = a(X,i(X3),X2),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
a(j(X2),j(X),X3) = a(j(X),X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c40,plain,
a(j(X),X3,X2) = a(X3,X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c41,plain,
a(j(X2),j(X),X3) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c39,c40]) ).
cnf(c42,plain,
a(j(i(X3)),j(X2),X) = a(X,i(X3),X2),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
a(X,i(X3),X2) = a(j(i(X3)),j(X2),X),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
a(j(i(X3)),j(X2),X) = a(X3,j(X2),X),
inference(congruence,[status(thm)],[c18]) ).
cnf(c45,plain,
a(X,i(X3),X2) = a(X3,j(X2),X),
inference(transitivity,[status(thm)],[c43,c44]) ).
cnf(c46,plain,
a(X,j(X3),X2) = a(X3,j(X2),X),
inference(transitivity,[status(thm)],[c38,c45]) ).
cnf(c47,plain,
a(j(X),j(X3),X2) = a(X3,j(X2),j(X)),
inference(substitution,[status(thm)],[c46]) ).
cnf(c48,plain,
a(j(X3),X2,X) = a(X3,j(X2),j(X)),
inference(transitivity,[status(thm)],[c36,c47]) ).
cnf(c49,plain,
a(j(X2),X,X2) = a(X2,j(X),j(X2)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
a(X2,j(X),j(X2)) = a(j(X2),X,X2),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,axiom,
product(A2,one) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos01) ).
cnf(c52,plain,
product(eta(X),one) = eta(X),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
eta(X) = product(eta(X),one),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
product(X,eta(X)) = product(X,product(eta(X),one)),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,axiom,
product(A2,product(eta(A2),B2)) = product(j(j(A2)),B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos14) ).
cnf(c56,plain,
product(X,product(eta(X),one)) = product(j(j(X)),one),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
product(j(j(X)),one) = j(j(X)),
inference(substitution,[status(thm)],[c51]) ).
cnf(c58,plain,
product(X,product(eta(X),one)) = j(j(X)),
inference(transitivity,[status(thm)],[c56,c57]) ).
cnf(c59,plain,
product(X,eta(X)) = j(j(X)),
inference(transitivity,[status(thm)],[c54,c58]) ).
cnf(c60,plain,
product(a(X3,X2,X),eta(a(X3,X2,X))) = j(j(a(X3,X2,X))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,plain,
j(j(a(X3,X2,X))) = product(a(X3,X2,X),eta(a(X3,X2,X))),
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,axiom,
difference(A2,product(A2,B2)) = B2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos04) ).
cnf(c63,plain,
difference(j(j(X)),product(j(j(X)),j(product(X2,X)))) = j(product(X2,X)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c64,plain,
j(product(X2,X)) = difference(j(j(X)),product(j(j(X)),j(product(X2,X)))),
inference(symmetry,[status(thm)],[c63]) ).
cnf(c65,axiom,
product(j(j(A2)),j(product(B2,A2))) = j(B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos22) ).
cnf(c66,plain,
product(j(j(X)),j(product(X2,X))) = j(X2),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
difference(j(j(X)),product(j(j(X)),j(product(X2,X)))) = difference(j(j(X)),j(X2)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
j(product(X2,X)) = difference(j(j(X)),j(X2)),
inference(transitivity,[status(thm)],[c64,c67]) ).
cnf(c69,plain,
j(product(X,X2)) = difference(j(j(X2)),j(X)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
difference(j(j(X2)),j(X)) = j(product(X,X2)),
inference(symmetry,[status(thm)],[c69]) ).
cnf(c71,plain,
i(difference(j(j(X2)),j(X))) = i(j(product(X,X2))),
inference(congruence,[status(thm)],[c70]) ).
cnf(c72,plain,
i(j(X)) = difference(j(X),one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c73,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c74,plain,
product(j(X),X) = product(quotient(one,X),X),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,axiom,
product(quotient(A2,B2),B2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos06) ).
cnf(c76,plain,
product(quotient(one,X),X) = one,
inference(substitution,[status(thm)],[c75]) ).
cnf(c77,plain,
product(j(X),X) = one,
inference(transitivity,[status(thm)],[c74,c76]) ).
cnf(c78,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c77]) ).
cnf(c79,plain,
difference(j(X),one) = difference(j(X),product(j(X),X)),
inference(congruence,[status(thm)],[c78]) ).
cnf(c80,plain,
difference(j(X),product(j(X),X)) = X,
inference(substitution,[status(thm)],[c62]) ).
cnf(c81,plain,
difference(j(X),one) = X,
inference(transitivity,[status(thm)],[c79,c80]) ).
cnf(c82,plain,
i(j(X)) = X,
inference(transitivity,[status(thm)],[c72,c81]) ).
cnf(c83,plain,
i(j(product(X,X2))) = product(X,X2),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
i(difference(j(j(X2)),j(X))) = product(X,X2),
inference(transitivity,[status(thm)],[c71,c83]) ).
cnf(c85,plain,
i(difference(j(j(eta(a(X3,X2,X)))),j(a(X3,X2,X)))) = product(a(X3,X2,X),eta(a(X3,X2,X))),
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
product(a(X3,X2,X),eta(a(X3,X2,X))) = i(difference(j(j(eta(a(X3,X2,X)))),j(a(X3,X2,X)))),
inference(symmetry,[status(thm)],[c85]) ).
cnf(c87,plain,
X = j(i(X)),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c88,plain,
difference(j(j(X)),X) = difference(j(j(X)),j(i(X))),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
j(product(i(X),X)) = difference(j(j(X)),j(i(X))),
inference(substitution,[status(thm)],[c68]) ).
cnf(c90,plain,
difference(j(j(X)),j(i(X))) = j(product(i(X),X)),
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,axiom,
eta(A2) = product(i(A2),A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos12) ).
cnf(c92,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c91]) ).
cnf(c93,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c92]) ).
cnf(c94,plain,
j(product(i(X),X)) = j(eta(X)),
inference(congruence,[status(thm)],[c93]) ).
cnf(c95,plain,
difference(j(j(X)),j(i(X))) = j(eta(X)),
inference(transitivity,[status(thm)],[c90,c94]) ).
cnf(c96,plain,
difference(j(j(X)),X) = j(eta(X)),
inference(transitivity,[status(thm)],[c88,c95]) ).
cnf(c97,plain,
difference(j(j(a(X3,X2,X))),a(X3,X2,X)) = j(eta(a(X3,X2,X))),
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
j(eta(a(X3,X2,X))) = difference(j(j(a(X3,X2,X))),a(X3,X2,X)),
inference(symmetry,[status(thm)],[c97]) ).
cnf(c99,plain,
j(j(eta(a(X3,X2,X)))) = j(difference(j(j(a(X3,X2,X))),a(X3,X2,X))),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
difference(j(j(eta(a(X3,X2,X)))),j(a(X3,X2,X))) = difference(j(difference(j(j(a(X3,X2,X))),a(X3,X2,X))),j(a(X3,X2,X))),
inference(congruence,[status(thm)],[c99]) ).
cnf(c101,plain,
i(difference(j(j(eta(a(X3,X2,X)))),j(a(X3,X2,X)))) = i(difference(j(difference(j(j(a(X3,X2,X))),a(X3,X2,X))),j(a(X3,X2,X)))),
inference(congruence,[status(thm)],[c100]) ).
cnf(c102,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c103,plain,
i(X) = i(i(j(X))),
inference(congruence,[status(thm)],[c102]) ).
cnf(c104,plain,
product(X2,i(X)) = product(X2,i(i(j(X)))),
inference(congruence,[status(thm)],[c103]) ).
cnf(c105,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c106,plain,
product(X2,i(i(X))) = product(i(j(X2)),i(i(X))),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
product(X,difference(X,X2)) = X2,
inference(substitution,[status(thm)],[c10]) ).
cnf(c108,plain,
X2 = product(X,difference(X,X2)),
inference(symmetry,[status(thm)],[c107]) ).
cnf(c109,plain,
i(X2) = i(product(X,difference(X,X2))),
inference(congruence,[status(thm)],[c108]) ).
cnf(c110,plain,
product(i(X2),i(i(X))) = product(i(product(X,difference(X,X2))),i(i(X))),
inference(congruence,[status(thm)],[c109]) ).
cnf(c111,axiom,
product(i(product(A2,B2)),i(i(A2))) = i(B2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos21) ).
cnf(c112,plain,
product(i(product(X,difference(X,X2))),i(i(X))) = i(difference(X,X2)),
inference(substitution,[status(thm)],[c111]) ).
cnf(c113,plain,
product(i(X2),i(i(X))) = i(difference(X,X2)),
inference(transitivity,[status(thm)],[c110,c112]) ).
cnf(c114,plain,
product(i(j(X2)),i(i(X))) = i(difference(X,j(X2))),
inference(substitution,[status(thm)],[c113]) ).
cnf(c115,plain,
product(X2,i(i(X))) = i(difference(X,j(X2))),
inference(transitivity,[status(thm)],[c106,c114]) ).
cnf(c116,plain,
product(X2,i(i(j(X)))) = i(difference(j(X),j(X2))),
inference(substitution,[status(thm)],[c115]) ).
cnf(c117,plain,
product(X2,i(X)) = i(difference(j(X),j(X2))),
inference(transitivity,[status(thm)],[c104,c116]) ).
cnf(c118,plain,
product(a(X2,X,X4),i(difference(j(j(X3)),a(X2,X,X4)))) = i(difference(j(difference(j(j(X3)),a(X2,X,X4))),j(a(X2,X,X4)))),
inference(substitution,[status(thm)],[c117]) ).
cnf(c119,plain,
i(difference(j(difference(j(j(X4)),a(X3,X2,X))),j(a(X3,X2,X)))) = product(a(X3,X2,X),i(difference(j(j(X4)),a(X3,X2,X)))),
inference(symmetry,[status(thm)],[c118]) ).
cnf(c120,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c121,plain,
product(i(X2),X) = product(i(X2),i(j(X))),
inference(congruence,[status(thm)],[c120]) ).
cnf(c122,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c82]) ).
cnf(c123,plain,
i(X) = i(i(j(X))),
inference(congruence,[status(thm)],[c122]) ).
cnf(c124,plain,
product(i(X2),i(X)) = product(i(X2),i(i(j(X)))),
inference(congruence,[status(thm)],[c123]) ).
cnf(c125,plain,
product(i(X2),i(i(j(X)))) = i(difference(j(X),X2)),
inference(substitution,[status(thm)],[c113]) ).
cnf(c126,plain,
product(i(X2),i(X)) = i(difference(j(X),X2)),
inference(transitivity,[status(thm)],[c124,c125]) ).
cnf(c127,plain,
product(i(X2),i(j(X))) = i(difference(j(j(X)),X2)),
inference(substitution,[status(thm)],[c126]) ).
cnf(c128,plain,
product(i(X2),X) = i(difference(j(j(X)),X2)),
inference(transitivity,[status(thm)],[c121,c127]) ).
cnf(c129,plain,
product(i(a(X3,X2,X)),X4) = i(difference(j(j(X4)),a(X3,X2,X))),
inference(substitution,[status(thm)],[c128]) ).
cnf(c130,plain,
i(difference(j(j(X4)),a(X3,X2,X))) = product(i(a(X3,X2,X)),X4),
inference(symmetry,[status(thm)],[c129]) ).
cnf(c131,plain,
product(a(X3,X2,X),i(difference(j(j(X4)),a(X3,X2,X)))) = product(a(X3,X2,X),product(i(a(X3,X2,X)),X4)),
inference(congruence,[status(thm)],[c130]) ).
cnf(c132,axiom,
product(a(A2,B2,C2),product(D,E)) = product(product(a(A2,B2,C2),D),E),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos27) ).
cnf(c133,plain,
product(a(X3,X2,X),product(i(a(X3,X2,X)),X4)) = product(product(a(X3,X2,X),i(a(X3,X2,X))),X4),
inference(substitution,[status(thm)],[c132]) ).
cnf(c134,plain,
product(a(X3,X2,X),i(a(X3,X2,X))) = one,
inference(substitution,[status(thm)],[c12]) ).
cnf(c135,plain,
product(product(a(X3,X2,X),i(a(X3,X2,X))),X4) = product(one,X4),
inference(congruence,[status(thm)],[c134]) ).
cnf(c136,axiom,
product(one,A2) = A2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos02) ).
cnf(c137,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c136]) ).
cnf(c138,plain,
product(product(a(X3,X2,X),i(a(X3,X2,X))),X4) = X4,
inference(transitivity,[status(thm)],[c135,c137]) ).
cnf(c139,plain,
product(a(X3,X2,X),product(i(a(X3,X2,X)),X4)) = X4,
inference(transitivity,[status(thm)],[c133,c138]) ).
cnf(c140,plain,
product(a(X3,X2,X),i(difference(j(j(X4)),a(X3,X2,X)))) = X4,
inference(transitivity,[status(thm)],[c131,c139]) ).
cnf(c141,plain,
i(difference(j(difference(j(j(X4)),a(X3,X2,X))),j(a(X3,X2,X)))) = X4,
inference(transitivity,[status(thm)],[c119,c140]) ).
cnf(c142,plain,
i(difference(j(difference(j(j(a(X3,X2,X))),a(X3,X2,X))),j(a(X3,X2,X)))) = a(X3,X2,X),
inference(substitution,[status(thm)],[c141]) ).
cnf(c143,plain,
i(difference(j(j(eta(a(X3,X2,X)))),j(a(X3,X2,X)))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c101,c142]) ).
cnf(c144,plain,
product(a(X3,X2,X),eta(a(X3,X2,X))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c86,c143]) ).
cnf(c145,plain,
j(j(a(X3,X2,X))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c61,c144]) ).
cnf(c146,plain,
a(X3,X2,X) = j(j(a(X3,X2,X))),
inference(symmetry,[status(thm)],[c145]) ).
cnf(c147,plain,
i(a(X3,X2,X)) = i(j(j(a(X3,X2,X)))),
inference(congruence,[status(thm)],[c146]) ).
cnf(c148,plain,
i(j(j(a(X3,X2,X)))) = j(a(X3,X2,X)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c149,plain,
i(a(X3,X2,X)) = j(a(X3,X2,X)),
inference(transitivity,[status(thm)],[c147,c148]) ).
cnf(c150,plain,
i(a(X3,j(X2),j(X))) = j(a(X3,j(X2),j(X))),
inference(substitution,[status(thm)],[c149]) ).
cnf(c151,plain,
j(a(X3,j(X2),j(X))) = i(a(X3,j(X2),j(X))),
inference(symmetry,[status(thm)],[c150]) ).
cnf(c152,plain,
t(X3,j(a(X3,j(X2),j(X)))) = t(X3,i(a(X3,j(X2),j(X)))),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
difference(a(X2,X,X3),product(a(X2,X,X3),difference(X3,product(a(X3,X2,X),X3)))) = difference(X3,product(a(X3,X2,X),X3)),
inference(substitution,[status(thm)],[c62]) ).
cnf(c154,plain,
difference(X3,product(a(X3,X2,X),X3)) = difference(a(X2,X,X3),product(a(X2,X,X3),difference(X3,product(a(X3,X2,X),X3)))),
inference(symmetry,[status(thm)],[c153]) ).
cnf(c155,axiom,
product(a(A2,B2,C2),difference(C2,product(a(C2,A2,B2),C2))) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos29) ).
cnf(c156,plain,
product(a(X2,X,X3),difference(X3,product(a(X3,X2,X),X3))) = one,
inference(substitution,[status(thm)],[c155]) ).
cnf(c157,plain,
difference(a(X2,X,X3),product(a(X2,X,X3),difference(X3,product(a(X3,X2,X),X3)))) = difference(a(X2,X,X3),one),
inference(congruence,[status(thm)],[c156]) ).
cnf(c158,plain,
i(a(X2,X,X3)) = difference(a(X2,X,X3),one),
inference(substitution,[status(thm)],[c7]) ).
cnf(c159,plain,
difference(a(X2,X,X3),one) = i(a(X2,X,X3)),
inference(symmetry,[status(thm)],[c158]) ).
cnf(c160,plain,
a(X3,j(j(X2)),X) = a(j(X2),j(X),X3),
inference(substitution,[status(thm)],[c46]) ).
cnf(c161,plain,
a(X3,j(j(X2)),X) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c160,c41]) ).
cnf(c162,plain,
a(X2,j(j(X)),X3) = a(X2,X,X3),
inference(substitution,[status(thm)],[c161]) ).
cnf(c163,plain,
a(X2,X,X3) = a(X2,j(j(X)),X3),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
a(j(X3),X2,j(j(X))) = a(X2,j(j(X)),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c165,plain,
a(X2,j(j(X)),X3) = a(j(X3),X2,j(j(X))),
inference(symmetry,[status(thm)],[c164]) ).
cnf(c166,plain,
a(X3,j(j(X2)),j(j(X))) = a(X3,X2,j(j(X))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c167,plain,
a(X3,X2,j(j(X))) = a(X3,j(j(X2)),j(j(X))),
inference(symmetry,[status(thm)],[c166]) ).
cnf(c168,plain,
a(j(X3),j(X2),j(X)) = a(X3,j(j(X2)),j(j(X))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c169,plain,
a(X3,j(j(X2)),j(j(X))) = a(j(X3),j(X2),j(X)),
inference(symmetry,[status(thm)],[c168]) ).
cnf(c170,plain,
a(j(X3),j(X2),j(X)) = a(j(X),X3,X2),
inference(substitution,[status(thm)],[c41]) ).
cnf(c171,plain,
a(j(X),X3,X2) = a(X3,X2,X),
inference(substitution,[status(thm)],[c2]) ).
cnf(c172,plain,
a(j(X3),j(X2),j(X)) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c170,c171]) ).
cnf(c173,plain,
a(X3,j(j(X2)),j(j(X))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c169,c172]) ).
cnf(c174,plain,
a(X3,X2,j(j(X))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c167,c173]) ).
cnf(c175,plain,
a(j(X3),X2,j(j(X))) = a(j(X3),X2,X),
inference(substitution,[status(thm)],[c174]) ).
cnf(c176,plain,
a(j(X3),X2,j(j(X))) = a(X3,j(X2),j(X)),
inference(transitivity,[status(thm)],[c175,c48]) ).
cnf(c177,plain,
a(X2,j(j(X)),X3) = a(X3,j(X2),j(X)),
inference(transitivity,[status(thm)],[c165,c176]) ).
cnf(c178,plain,
a(X2,X,X3) = a(X3,j(X2),j(X)),
inference(transitivity,[status(thm)],[c163,c177]) ).
cnf(c179,plain,
i(a(X2,X,X3)) = i(a(X3,j(X2),j(X))),
inference(congruence,[status(thm)],[c178]) ).
cnf(c180,plain,
difference(a(X2,X,X3),one) = i(a(X3,j(X2),j(X))),
inference(transitivity,[status(thm)],[c159,c179]) ).
cnf(c181,plain,
difference(a(X2,X,X3),product(a(X2,X,X3),difference(X3,product(a(X3,X2,X),X3)))) = i(a(X3,j(X2),j(X))),
inference(transitivity,[status(thm)],[c157,c180]) ).
cnf(c182,plain,
difference(X3,product(a(X3,X2,X),X3)) = i(a(X3,j(X2),j(X))),
inference(transitivity,[status(thm)],[c154,c181]) ).
cnf(c183,plain,
i(a(X3,j(X2),j(X))) = difference(X3,product(a(X3,X2,X),X3)),
inference(symmetry,[status(thm)],[c182]) ).
cnf(c184,plain,
t(X3,i(a(X3,j(X2),j(X)))) = t(X3,difference(X3,product(a(X3,X2,X),X3))),
inference(congruence,[status(thm)],[c183]) ).
cnf(c185,axiom,
t(A2,B2) = quotient(product(A2,B2),A2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos19) ).
cnf(c186,plain,
t(X2,difference(X2,X)) = quotient(product(X2,difference(X2,X)),X2),
inference(substitution,[status(thm)],[c185]) ).
cnf(c187,plain,
product(X2,difference(X2,X)) = X,
inference(substitution,[status(thm)],[c10]) ).
cnf(c188,plain,
quotient(product(X2,difference(X2,X)),X2) = quotient(X,X2),
inference(congruence,[status(thm)],[c187]) ).
cnf(c189,plain,
t(X2,difference(X2,X)) = quotient(X,X2),
inference(transitivity,[status(thm)],[c186,c188]) ).
cnf(c190,plain,
t(X3,difference(X3,product(a(X3,X2,X),X3))) = quotient(product(a(X3,X2,X),X3),X3),
inference(substitution,[status(thm)],[c189]) ).
cnf(c191,plain,
quotient(product(a(X3,X2,X),X3),X3) = a(X3,X2,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c192,plain,
t(X3,difference(X3,product(a(X3,X2,X),X3))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c190,c191]) ).
cnf(c193,plain,
t(X3,i(a(X3,j(X2),j(X)))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c184,c192]) ).
cnf(c194,plain,
t(X3,j(a(X3,j(X2),j(X)))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c152,c193]) ).
cnf(c195,plain,
t(j(X2),j(a(j(X2),j(X),j(X2)))) = a(j(X2),X,X2),
inference(substitution,[status(thm)],[c194]) ).
cnf(c196,plain,
a(j(X2),X,X2) = t(j(X2),j(a(j(X2),j(X),j(X2)))),
inference(symmetry,[status(thm)],[c195]) ).
cnf(c197,plain,
a(X2,j(j(X)),X3) = a(X2,X,X3),
inference(substitution,[status(thm)],[c161]) ).
cnf(c198,plain,
a(X2,X,X3) = a(X2,j(j(X)),X3),
inference(symmetry,[status(thm)],[c197]) ).
cnf(c199,plain,
j(a(X2,X,X3)) = j(a(X2,j(j(X)),X3)),
inference(congruence,[status(thm)],[c198]) ).
cnf(c200,plain,
t(X3,j(a(X2,X,X3))) = t(X3,j(a(X2,j(j(X)),X3))),
inference(congruence,[status(thm)],[c199]) ).
cnf(c201,plain,
a(X3,j(X2),j(X)) = a(X2,j(j(X)),X3),
inference(substitution,[status(thm)],[c46]) ).
cnf(c202,plain,
a(X2,j(j(X)),X3) = a(X3,j(X2),j(X)),
inference(symmetry,[status(thm)],[c201]) ).
cnf(c203,plain,
j(a(X2,j(j(X)),X3)) = j(a(X3,j(X2),j(X))),
inference(congruence,[status(thm)],[c202]) ).
cnf(c204,plain,
t(X3,j(a(X2,j(j(X)),X3))) = t(X3,j(a(X3,j(X2),j(X)))),
inference(congruence,[status(thm)],[c203]) ).
cnf(c205,plain,
t(X3,j(a(X2,j(j(X)),X3))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c204,c194]) ).
cnf(c206,plain,
t(X3,j(a(X2,X,X3))) = a(X3,X2,X),
inference(transitivity,[status(thm)],[c200,c205]) ).
cnf(c207,plain,
t(j(X2),j(a(j(X2),j(X),j(X2)))) = a(j(X2),j(X2),j(X)),
inference(substitution,[status(thm)],[c206]) ).
cnf(c208,plain,
a(j(X2),j(X2),j(X)) = a(X2,j(j(X2)),j(j(X))),
inference(substitution,[status(thm)],[c48]) ).
cnf(c209,plain,
a(X2,j(j(X2)),j(j(X))) = a(X2,X2,j(j(X))),
inference(substitution,[status(thm)],[c161]) ).
cnf(c210,plain,
a(X2,X2,j(j(X))) = a(X2,X2,X),
inference(substitution,[status(thm)],[c174]) ).
cnf(c211,plain,
a(X2,j(j(X2)),j(j(X))) = a(X2,X2,X),
inference(transitivity,[status(thm)],[c209,c210]) ).
cnf(c212,plain,
a(j(X2),j(X2),j(X)) = a(X2,X2,X),
inference(transitivity,[status(thm)],[c208,c211]) ).
cnf(c213,plain,
t(j(X2),j(a(j(X2),j(X),j(X2)))) = a(X2,X2,X),
inference(transitivity,[status(thm)],[c207,c212]) ).
cnf(c214,plain,
a(j(X2),X,X2) = a(X2,X2,X),
inference(transitivity,[status(thm)],[c196,c213]) ).
cnf(c215,plain,
a(X2,j(X),j(X2)) = a(X2,X2,X),
inference(transitivity,[status(thm)],[c50,c214]) ).
cnf(c216,plain,
a(X2,X2,j(X)) = a(X2,X2,X),
inference(transitivity,[status(thm)],[c34,c215]) ).
cnf(c217,plain,
a(X,X2,X2) = a(X2,X2,X),
inference(transitivity,[status(thm)],[c32,c216]) ).
cnf(c218,plain,
a(x0,x1,x1) = a(x1,x1,x0),
inference(substitution,[status(thm)],[c217]) ).
cnf(c219,plain,
$false,
inference(resolution,[status(thm)],[c1,c218]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP772-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n010.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 10:44:01 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 59.20/7.94 Command-line arguments: --no-flatten-goal
% 59.20/7.94
% 59.20/7.94 % SZS status Unsatisfiable
% 59.20/7.94
% 59.20/7.95 % SZS output start CNFRefutation
% See solution above
% 60.02/8.13
% 60.02/8.13 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------