%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP769-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 62.91s 8.45s
% Output : CNFRefutation 63.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 14
% Syntax : Number of clauses : 117 ( 117 unt; 0 nHn; 4 RR)
% Number of literals : 117 ( 116 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 : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 236 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
product(product(x0,x1),x2) != product(product(x0,x2),difference(x2,product(x1,x2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
i(A) = difference(A,one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos09) ).
cnf(c3,plain,
i(j(X)) = difference(j(X),one),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,axiom,
j(A2) = quotient(one,A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos10) ).
cnf(c5,plain,
j(X) = quotient(one,X),
inference(substitution,[status(thm)],[c4]) ).
cnf(c6,plain,
product(j(X),X) = product(quotient(one,X),X),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
product(quotient(A2,B),B) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(c8,plain,
product(quotient(one,X),X) = one,
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
product(j(X),X) = one,
inference(transitivity,[status(thm)],[c6,c8]) ).
cnf(c10,plain,
one = product(j(X),X),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
difference(j(X),one) = difference(j(X),product(j(X),X)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
difference(A2,product(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(c13,plain,
difference(j(X),product(j(X),X)) = X,
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
difference(j(X),one) = X,
inference(transitivity,[status(thm)],[c11,c13]) ).
cnf(c15,plain,
i(j(X)) = X,
inference(transitivity,[status(thm)],[c3,c14]) ).
cnf(c16,plain,
i(j(difference(X2,product(X,X2)))) = difference(X2,product(X,X2)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
difference(X2,product(X,X2)) = i(j(difference(X2,product(X,X2)))),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
product(product(X3,X2),difference(X2,product(X,X2))) = product(product(X3,X2),i(j(difference(X2,product(X,X2))))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
product(quotient(product(j(product(product(X3,X2),X)),product(X3,X)),X),X) = product(j(product(product(X3,X2),X)),product(X3,X)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c20,plain,
product(j(product(product(X3,X2),X)),product(X3,X)) = product(quotient(product(j(product(product(X3,X2),X)),product(X3,X)),X),X),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
difference(A2,product(product(A2,B2),C)) = quotient(product(B2,product(C,A2)),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(c22,plain,
difference(X,product(product(X,j(product(product(X3,X2),X))),X3)) = quotient(product(j(product(product(X3,X2),X)),product(X3,X)),X),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
quotient(product(j(product(product(X3,X2),X)),product(X3,X)),X) = difference(X,product(product(X,j(product(product(X3,X2),X))),X3)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c25,plain,
product(X2,j(product(X,X2))) = product(i(j(X2)),j(product(X,X2))),
inference(congruence,[status(thm)],[c24]) ).
cnf(c26,plain,
product(product(X3,j(product(X2,X3))),X) = product(product(i(j(X3)),j(product(X2,X3))),X),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
i(j(j(X))) = j(X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c28,plain,
j(X) = i(j(j(X))),
inference(symmetry,[status(thm)],[c27]) ).
cnf(c29,plain,
i(j(X)) = i(i(j(j(X)))),
inference(congruence,[status(thm)],[c28]) ).
cnf(c30,plain,
product(i(j(X2)),j(product(X,X2))) = product(i(i(j(j(X2)))),j(product(X,X2))),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
product(product(i(j(X3)),j(product(X2,X3))),X) = product(product(i(i(j(j(X3)))),j(product(X2,X3))),X),
inference(congruence,[status(thm)],[c30]) ).
cnf(c32,axiom,
product(eta(A2),product(B2,C2)) = product(product(eta(A2),B2),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
cnf(c33,plain,
product(eta(X3),product(product(X3,X2),X)) = product(product(eta(X3),product(X3,X2)),X),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,axiom,
product(i(i(A2)),B2) = product(eta(A2),product(A2,B2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos13) ).
cnf(c35,plain,
product(i(i(X2)),X) = product(eta(X2),product(X2,X)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
product(eta(X2),product(X2,X)) = product(i(i(X2)),X),
inference(symmetry,[status(thm)],[c35]) ).
cnf(c37,plain,
product(product(eta(X3),product(X3,X2)),X) = product(product(i(i(X3)),X2),X),
inference(congruence,[status(thm)],[c36]) ).
cnf(c38,plain,
product(eta(X3),product(product(X3,X2),X)) = product(product(i(i(X3)),X2),X),
inference(transitivity,[status(thm)],[c33,c37]) ).
cnf(c39,plain,
product(eta(j(j(X3))),product(product(j(j(X3)),j(product(X2,X3))),X)) = product(product(i(i(j(j(X3)))),j(product(X2,X3))),X),
inference(substitution,[status(thm)],[c38]) ).
cnf(c40,plain,
product(product(i(i(j(j(X3)))),j(product(X2,X3))),X) = product(eta(j(j(X3))),product(product(j(j(X3)),j(product(X2,X3))),X)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,axiom,
product(j(j(A2)),j(product(B2,A2))) = j(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos22) ).
cnf(c42,plain,
product(j(j(X2)),j(product(X,X2))) = j(X),
inference(substitution,[status(thm)],[c41]) ).
cnf(c43,plain,
product(product(j(j(X3)),j(product(X2,X3))),X) = product(j(X2),X),
inference(congruence,[status(thm)],[c42]) ).
cnf(c44,plain,
product(eta(j(j(X3))),product(product(j(j(X3)),j(product(X2,X3))),X)) = product(eta(j(j(X3))),product(j(X2),X)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,axiom,
eta(A2) = product(i(A2),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos12) ).
cnf(c46,plain,
eta(j(X)) = product(i(j(X)),j(X)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
product(i(j(X)),j(X)) = product(X,j(X)),
inference(congruence,[status(thm)],[c15]) ).
cnf(c48,axiom,
product(i(A2),A2) = product(A2,j(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos11) ).
cnf(c49,plain,
product(i(X),X) = product(X,j(X)),
inference(substitution,[status(thm)],[c48]) ).
cnf(c50,plain,
product(X,j(X)) = product(i(X),X),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c51,plain,
eta(X) = product(i(X),X),
inference(substitution,[status(thm)],[c45]) ).
cnf(c52,plain,
product(i(X),X) = eta(X),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
product(X,j(X)) = eta(X),
inference(transitivity,[status(thm)],[c50,c52]) ).
cnf(c54,plain,
product(i(j(X)),j(X)) = eta(X),
inference(transitivity,[status(thm)],[c47,c53]) ).
cnf(c55,plain,
eta(j(X)) = eta(X),
inference(transitivity,[status(thm)],[c46,c54]) ).
cnf(c56,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
product(eta(j(j(X3))),product(j(X2),X)) = product(eta(j(X3)),product(j(X2),X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
product(eta(j(X3)),product(j(X2),X)) = product(eta(X3),product(j(X2),X)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c59,plain,
product(eta(j(j(X3))),product(j(X2),X)) = product(eta(X3),product(j(X2),X)),
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
product(eta(j(j(X3))),product(product(j(j(X3)),j(product(X2,X3))),X)) = product(eta(X3),product(j(X2),X)),
inference(transitivity,[status(thm)],[c44,c59]) ).
cnf(c61,plain,
product(product(i(i(j(j(X3)))),j(product(X2,X3))),X) = product(eta(X3),product(j(X2),X)),
inference(transitivity,[status(thm)],[c40,c60]) ).
cnf(c62,plain,
product(product(i(j(X3)),j(product(X2,X3))),X) = product(eta(X3),product(j(X2),X)),
inference(transitivity,[status(thm)],[c31,c61]) ).
cnf(c63,plain,
product(product(X3,j(product(X2,X3))),X) = product(eta(X3),product(j(X2),X)),
inference(transitivity,[status(thm)],[c26,c62]) ).
cnf(c64,plain,
product(product(X3,j(product(product(X2,X),X3))),X2) = product(eta(X3),product(j(product(X2,X)),X2)),
inference(substitution,[status(thm)],[c63]) ).
cnf(c65,axiom,
product(j(product(A2,B2)),A2) = j(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos24) ).
cnf(c66,plain,
product(j(product(X2,X)),X2) = j(X),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
product(eta(X3),product(j(product(X2,X)),X2)) = product(eta(X3),j(X)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
X = i(j(X)),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c69,plain,
product(X2,j(product(X,X2))) = product(i(j(X2)),j(product(X,X2))),
inference(congruence,[status(thm)],[c68]) ).
cnf(c70,plain,
i(j(j(X))) = j(X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c71,plain,
j(X) = i(j(j(X))),
inference(symmetry,[status(thm)],[c70]) ).
cnf(c72,plain,
i(j(X)) = i(i(j(j(X)))),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
product(i(j(X2)),j(product(X,X2))) = product(i(i(j(j(X2)))),j(product(X,X2))),
inference(congruence,[status(thm)],[c72]) ).
cnf(c74,plain,
product(i(i(j(j(X2)))),j(product(X,X2))) = product(eta(j(j(X2))),product(j(j(X2)),j(product(X,X2)))),
inference(substitution,[status(thm)],[c34]) ).
cnf(c75,plain,
product(j(j(X2)),j(product(X,X2))) = j(X),
inference(substitution,[status(thm)],[c41]) ).
cnf(c76,plain,
product(eta(j(j(X2))),product(j(j(X2)),j(product(X,X2)))) = product(eta(j(j(X2))),j(X)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
eta(j(j(X))) = eta(j(X)),
inference(substitution,[status(thm)],[c55]) ).
cnf(c78,plain,
product(eta(j(j(X2))),j(X)) = product(eta(j(X2)),j(X)),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,plain,
product(eta(j(X2)),j(X)) = product(eta(X2),j(X)),
inference(congruence,[status(thm)],[c55]) ).
cnf(c80,plain,
product(eta(j(j(X2))),j(X)) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
product(eta(j(j(X2))),product(j(j(X2)),j(product(X,X2)))) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c76,c80]) ).
cnf(c82,plain,
product(i(i(j(j(X2)))),j(product(X,X2))) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c74,c81]) ).
cnf(c83,plain,
product(i(j(X2)),j(product(X,X2))) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c73,c82]) ).
cnf(c84,plain,
product(X2,j(product(X,X2))) = product(eta(X2),j(X)),
inference(transitivity,[status(thm)],[c69,c83]) ).
cnf(c85,plain,
product(eta(X2),j(X)) = product(X2,j(product(X,X2))),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
product(eta(X3),product(j(product(X2,X)),X2)) = product(X3,j(product(X,X3))),
inference(transitivity,[status(thm)],[c67,c85]) ).
cnf(c87,plain,
product(product(X3,j(product(product(X2,X),X3))),X2) = product(X3,j(product(X,X3))),
inference(transitivity,[status(thm)],[c64,c86]) ).
cnf(c88,plain,
product(product(X,j(product(product(X3,X2),X))),X3) = product(X,j(product(X2,X))),
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
difference(X,product(product(X,j(product(product(X3,X2),X))),X3)) = difference(X,product(X,j(product(X2,X)))),
inference(congruence,[status(thm)],[c88]) ).
cnf(c90,plain,
difference(X,product(X,j(product(X2,X)))) = j(product(X2,X)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c91,plain,
difference(X,product(product(X,j(product(product(X3,X2),X))),X3)) = j(product(X2,X)),
inference(transitivity,[status(thm)],[c89,c90]) ).
cnf(c92,plain,
quotient(product(j(product(product(X3,X2),X)),product(X3,X)),X) = j(product(X2,X)),
inference(transitivity,[status(thm)],[c23,c91]) ).
cnf(c93,plain,
product(quotient(product(j(product(product(X3,X2),X)),product(X3,X)),X),X) = product(j(product(X2,X)),X),
inference(congruence,[status(thm)],[c92]) ).
cnf(c94,plain,
product(j(product(X,difference(X,X2))),X) = j(difference(X,X2)),
inference(substitution,[status(thm)],[c65]) ).
cnf(c95,plain,
j(difference(X,X2)) = product(j(product(X,difference(X,X2))),X),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,axiom,
product(A2,difference(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(c97,plain,
product(X,difference(X,X2)) = X2,
inference(substitution,[status(thm)],[c96]) ).
cnf(c98,plain,
j(product(X,difference(X,X2))) = j(X2),
inference(congruence,[status(thm)],[c97]) ).
cnf(c99,plain,
product(j(product(X,difference(X,X2))),X) = product(j(X2),X),
inference(congruence,[status(thm)],[c98]) ).
cnf(c100,plain,
j(difference(X,X2)) = product(j(X2),X),
inference(transitivity,[status(thm)],[c95,c99]) ).
cnf(c101,plain,
j(difference(X,product(X2,X))) = product(j(product(X2,X)),X),
inference(substitution,[status(thm)],[c100]) ).
cnf(c102,plain,
product(j(product(X2,X)),X) = j(difference(X,product(X2,X))),
inference(symmetry,[status(thm)],[c101]) ).
cnf(c103,plain,
product(quotient(product(j(product(product(X3,X2),X)),product(X3,X)),X),X) = j(difference(X,product(X2,X))),
inference(transitivity,[status(thm)],[c93,c102]) ).
cnf(c104,plain,
product(j(product(product(X3,X2),X)),product(X3,X)) = j(difference(X,product(X2,X))),
inference(transitivity,[status(thm)],[c20,c103]) ).
cnf(c105,plain,
product(j(product(product(X3,X),X2)),product(X3,X2)) = j(difference(X2,product(X,X2))),
inference(substitution,[status(thm)],[c104]) ).
cnf(c106,plain,
j(difference(X2,product(X,X2))) = product(j(product(product(X3,X),X2)),product(X3,X2)),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c107,plain,
i(j(difference(X2,product(X,X2)))) = i(product(j(product(product(X3,X),X2)),product(X3,X2))),
inference(congruence,[status(thm)],[c106]) ).
cnf(c108,plain,
product(product(X3,X2),i(j(difference(X2,product(X,X2))))) = product(product(X3,X2),i(product(j(product(product(X3,X),X2)),product(X3,X2)))),
inference(congruence,[status(thm)],[c107]) ).
cnf(c109,axiom,
product(A2,i(product(B2,A2))) = i(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos23) ).
cnf(c110,plain,
product(product(X3,X2),i(product(j(product(product(X3,X),X2)),product(X3,X2)))) = i(j(product(product(X3,X),X2))),
inference(substitution,[status(thm)],[c109]) ).
cnf(c111,plain,
i(j(product(product(X3,X),X2))) = product(product(X3,X),X2),
inference(substitution,[status(thm)],[c15]) ).
cnf(c112,plain,
product(product(X3,X2),i(product(j(product(product(X3,X),X2)),product(X3,X2)))) = product(product(X3,X),X2),
inference(transitivity,[status(thm)],[c110,c111]) ).
cnf(c113,plain,
product(product(X3,X2),i(j(difference(X2,product(X,X2))))) = product(product(X3,X),X2),
inference(transitivity,[status(thm)],[c108,c112]) ).
cnf(c114,plain,
product(product(X3,X2),difference(X2,product(X,X2))) = product(product(X3,X),X2),
inference(transitivity,[status(thm)],[c18,c113]) ).
cnf(c115,plain,
product(product(x0,x2),difference(x2,product(x1,x2))) = product(product(x0,x1),x2),
inference(substitution,[status(thm)],[c114]) ).
cnf(c116,plain,
product(product(x0,x1),x2) = product(product(x0,x2),difference(x2,product(x1,x2))),
inference(symmetry,[status(thm)],[c115]) ).
cnf(c117,plain,
$false,
inference(resolution,[status(thm)],[c1,c116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP769-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n015.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 10:45:59 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 62.91/8.45 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
% 62.91/8.45
% 62.91/8.45 % SZS status Unsatisfiable
% 62.91/8.45
% 62.91/8.46 % SZS output start CNFRefutation
% See solution above
% 63.71/8.51
% 63.71/8.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------