%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : GRP768-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 10:11:57 AM UTC 2026
% Result : Unsatisfiable 14.99s 2.37s
% Output : CNFRefutation 15.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 10
% Syntax : Number of clauses : 96 ( 96 unt; 0 nHn; 4 RR)
% Number of literals : 96 ( 95 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 231 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
t(eta(x0),product(x1,x2)) != product(t(eta(x0),x1),t(eta(x0),x2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c2,axiom,
product(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos01) ).
cnf(c3,plain,
product(product(t(eta(X3),X2),t(eta(X3),X)),one) = product(t(eta(X3),X2),t(eta(X3),X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
product(t(eta(X3),X2),t(eta(X3),X)) = product(product(t(eta(X3),X2),t(eta(X3),X)),one),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,axiom,
product(one,A2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos02) ).
cnf(c6,plain,
product(one,X) = X,
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
X = product(one,X),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
quotient(X,X) = quotient(product(one,X),X),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,axiom,
quotient(product(A2,B),B) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos05) ).
cnf(c10,plain,
quotient(product(one,X),X) = one,
inference(substitution,[status(thm)],[c9]) ).
cnf(c11,plain,
quotient(X,X) = one,
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
quotient(eta(X),eta(X)) = one,
inference(substitution,[status(thm)],[c11]) ).
cnf(c13,plain,
one = quotient(eta(X),eta(X)),
inference(symmetry,[status(thm)],[c12]) ).
cnf(c14,plain,
product(product(t(eta(X3),X2),t(eta(X3),X)),one) = product(product(t(eta(X3),X2),t(eta(X3),X)),quotient(eta(X3),eta(X3))),
inference(congruence,[status(thm)],[c13]) ).
cnf(c15,axiom,
product(quotient(A2,B2),B2) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos06) ).
cnf(c16,plain,
product(quotient(X2,eta(X)),eta(X)) = X2,
inference(substitution,[status(thm)],[c15]) ).
cnf(c17,plain,
X2 = product(quotient(X2,eta(X)),eta(X)),
inference(symmetry,[status(thm)],[c16]) ).
cnf(c18,plain,
product(X3,X2) = product(X3,product(quotient(X2,eta(X)),eta(X))),
inference(congruence,[status(thm)],[c17]) ).
cnf(c19,plain,
quotient(product(X3,X2),eta(X)) = quotient(product(X3,product(quotient(X2,eta(X)),eta(X))),eta(X)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
difference(A2,product(product(A2,B2),C)) = quotient(product(B2,product(C,A2)),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos07) ).
cnf(c21,plain,
difference(eta(X),product(product(eta(X),X3),X2)) = quotient(product(X3,product(X2,eta(X))),eta(X)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
quotient(product(X3,product(X2,eta(X))),eta(X)) = difference(eta(X),product(product(eta(X),X3),X2)),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,axiom,
product(eta(A2),product(B2,C2)) = product(product(eta(A2),B2),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos16) ).
cnf(c24,plain,
product(eta(X),product(X3,X2)) = product(product(eta(X),X3),X2),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
product(product(eta(X),X3),X2) = product(eta(X),product(X3,X2)),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
difference(eta(X),product(product(eta(X),X3),X2)) = difference(eta(X),product(eta(X),product(X3,X2))),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,plain,
product(eta(X3),product(difference(eta(X3),X2),X)) = product(product(eta(X3),difference(eta(X3),X2)),X),
inference(substitution,[status(thm)],[c23]) ).
cnf(c28,axiom,
product(A2,difference(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos03) ).
cnf(c29,plain,
product(eta(X2),difference(eta(X2),X)) = X,
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
product(product(eta(X3),difference(eta(X3),X2)),X) = product(X2,X),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
product(eta(X3),product(difference(eta(X3),X2),X)) = product(X2,X),
inference(transitivity,[status(thm)],[c27,c30]) ).
cnf(c32,plain,
product(X2,X) = product(eta(X3),product(difference(eta(X3),X2),X)),
inference(symmetry,[status(thm)],[c31]) ).
cnf(c33,plain,
difference(eta(X3),product(X2,X)) = difference(eta(X3),product(eta(X3),product(difference(eta(X3),X2),X))),
inference(congruence,[status(thm)],[c32]) ).
cnf(c34,axiom,
difference(A2,product(A2,B2)) = B2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos04) ).
cnf(c35,plain,
difference(eta(X3),product(eta(X3),product(difference(eta(X3),X2),X))) = product(difference(eta(X3),X2),X),
inference(substitution,[status(thm)],[c34]) ).
cnf(c36,plain,
difference(eta(X3),product(X2,X)) = product(difference(eta(X3),X2),X),
inference(transitivity,[status(thm)],[c33,c35]) ).
cnf(c37,plain,
difference(eta(X),product(eta(X),product(X3,X2))) = product(difference(eta(X),eta(X)),product(X3,X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
product(X,one) = X,
inference(substitution,[status(thm)],[c2]) ).
cnf(c39,plain,
X = product(X,one),
inference(symmetry,[status(thm)],[c38]) ).
cnf(c40,plain,
difference(X,X) = difference(X,product(X,one)),
inference(congruence,[status(thm)],[c39]) ).
cnf(c41,plain,
difference(X,product(X,one)) = one,
inference(substitution,[status(thm)],[c34]) ).
cnf(c42,plain,
difference(X,X) = one,
inference(transitivity,[status(thm)],[c40,c41]) ).
cnf(c43,plain,
difference(eta(X),eta(X)) = one,
inference(substitution,[status(thm)],[c42]) ).
cnf(c44,plain,
product(difference(eta(X),eta(X)),product(X3,X2)) = product(one,product(X3,X2)),
inference(congruence,[status(thm)],[c43]) ).
cnf(c45,plain,
product(one,product(X2,X)) = product(X2,X),
inference(substitution,[status(thm)],[c5]) ).
cnf(c46,plain,
product(difference(eta(X),eta(X)),product(X3,X2)) = product(X3,X2),
inference(transitivity,[status(thm)],[c44,c45]) ).
cnf(c47,plain,
difference(eta(X),product(eta(X),product(X3,X2))) = product(X3,X2),
inference(transitivity,[status(thm)],[c37,c46]) ).
cnf(c48,plain,
difference(eta(X),product(product(eta(X),X3),X2)) = product(X3,X2),
inference(transitivity,[status(thm)],[c26,c47]) ).
cnf(c49,plain,
quotient(product(X3,product(X2,eta(X))),eta(X)) = product(X3,X2),
inference(transitivity,[status(thm)],[c22,c48]) ).
cnf(c50,plain,
quotient(product(X3,product(quotient(X2,eta(X)),eta(X))),eta(X)) = product(X3,quotient(X2,eta(X))),
inference(substitution,[status(thm)],[c49]) ).
cnf(c51,plain,
quotient(product(X3,X2),eta(X)) = product(X3,quotient(X2,eta(X))),
inference(transitivity,[status(thm)],[c19,c50]) ).
cnf(c52,plain,
quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),eta(X3)) = product(product(t(eta(X3),X2),t(eta(X3),X)),quotient(eta(X3),eta(X3))),
inference(substitution,[status(thm)],[c51]) ).
cnf(c53,plain,
product(product(t(eta(X3),X2),t(eta(X3),X)),quotient(eta(X3),eta(X3))) = quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),eta(X3)),
inference(symmetry,[status(thm)],[c52]) ).
cnf(c54,plain,
product(quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),X),X) = product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),
inference(substitution,[status(thm)],[c15]) ).
cnf(c55,plain,
product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)) = product(quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),X),X),
inference(symmetry,[status(thm)],[c54]) ).
cnf(c56,plain,
product(X3,X2) = quotient(product(X3,product(X2,eta(X))),eta(X)),
inference(symmetry,[status(thm)],[c49]) ).
cnf(c57,plain,
product(product(X3,X2),eta(X)) = product(quotient(product(X3,product(X2,eta(X))),eta(X)),eta(X)),
inference(congruence,[status(thm)],[c56]) ).
cnf(c58,plain,
product(quotient(product(X3,product(X2,eta(X))),eta(X)),eta(X)) = product(X3,product(X2,eta(X))),
inference(substitution,[status(thm)],[c15]) ).
cnf(c59,plain,
product(product(X3,X2),eta(X)) = product(X3,product(X2,eta(X))),
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
product(product(X3,t(eta(X2),X)),eta(X2)) = product(X3,product(t(eta(X2),X),eta(X2))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c61,axiom,
t(A2,B2) = quotient(product(A2,B2),A2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos19) ).
cnf(c62,plain,
t(X2,X) = quotient(product(X2,X),X2),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
product(t(X2,X),X2) = product(quotient(product(X2,X),X2),X2),
inference(congruence,[status(thm)],[c62]) ).
cnf(c64,plain,
product(quotient(product(X2,X),X2),X2) = product(X2,X),
inference(substitution,[status(thm)],[c15]) ).
cnf(c65,plain,
product(t(X2,X),X2) = product(X2,X),
inference(transitivity,[status(thm)],[c63,c64]) ).
cnf(c66,plain,
product(t(eta(X2),X),eta(X2)) = product(eta(X2),X),
inference(substitution,[status(thm)],[c65]) ).
cnf(c67,plain,
product(X3,product(t(eta(X2),X),eta(X2))) = product(X3,product(eta(X2),X)),
inference(congruence,[status(thm)],[c66]) ).
cnf(c68,plain,
product(product(X3,t(eta(X2),X)),eta(X2)) = product(X3,product(eta(X2),X)),
inference(transitivity,[status(thm)],[c60,c67]) ).
cnf(c69,plain,
product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)) = product(t(eta(X3),X2),product(eta(X3),X)),
inference(substitution,[status(thm)],[c68]) ).
cnf(c70,plain,
quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),X) = quotient(product(t(eta(X3),X2),product(eta(X3),X)),X),
inference(congruence,[status(thm)],[c69]) ).
cnf(c71,plain,
difference(X,product(product(X,X3),eta(X2))) = quotient(product(X3,product(eta(X2),X)),X),
inference(substitution,[status(thm)],[c20]) ).
cnf(c72,plain,
quotient(product(X3,product(eta(X2),X)),X) = difference(X,product(product(X,X3),eta(X2))),
inference(symmetry,[status(thm)],[c71]) ).
cnf(c73,plain,
product(product(X,X3),eta(X2)) = product(X,product(X3,eta(X2))),
inference(substitution,[status(thm)],[c59]) ).
cnf(c74,plain,
difference(X,product(product(X,X3),eta(X2))) = difference(X,product(X,product(X3,eta(X2)))),
inference(congruence,[status(thm)],[c73]) ).
cnf(c75,plain,
difference(X,product(X,product(X3,eta(X2)))) = product(X3,eta(X2)),
inference(substitution,[status(thm)],[c34]) ).
cnf(c76,plain,
difference(X,product(product(X,X3),eta(X2))) = product(X3,eta(X2)),
inference(transitivity,[status(thm)],[c74,c75]) ).
cnf(c77,plain,
quotient(product(X3,product(eta(X2),X)),X) = product(X3,eta(X2)),
inference(transitivity,[status(thm)],[c72,c76]) ).
cnf(c78,plain,
quotient(product(t(eta(X3),X2),product(eta(X3),X)),X) = product(t(eta(X3),X2),eta(X3)),
inference(substitution,[status(thm)],[c77]) ).
cnf(c79,plain,
product(t(eta(X2),X),eta(X2)) = product(eta(X2),X),
inference(substitution,[status(thm)],[c65]) ).
cnf(c80,plain,
quotient(product(t(eta(X3),X2),product(eta(X3),X)),X) = product(eta(X3),X2),
inference(transitivity,[status(thm)],[c78,c79]) ).
cnf(c81,plain,
quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),X) = product(eta(X3),X2),
inference(transitivity,[status(thm)],[c70,c80]) ).
cnf(c82,plain,
product(quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),X),X) = product(product(eta(X3),X2),X),
inference(congruence,[status(thm)],[c81]) ).
cnf(c83,plain,
product(eta(X3),product(X2,X)) = product(product(eta(X3),X2),X),
inference(substitution,[status(thm)],[c23]) ).
cnf(c84,plain,
product(product(eta(X3),X2),X) = product(eta(X3),product(X2,X)),
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
product(quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),X),X) = product(eta(X3),product(X2,X)),
inference(transitivity,[status(thm)],[c82,c84]) ).
cnf(c86,plain,
product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)) = product(eta(X3),product(X2,X)),
inference(transitivity,[status(thm)],[c55,c85]) ).
cnf(c87,plain,
quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),eta(X3)) = quotient(product(eta(X3),product(X2,X)),eta(X3)),
inference(congruence,[status(thm)],[c86]) ).
cnf(c88,plain,
t(eta(X3),product(X2,X)) = quotient(product(eta(X3),product(X2,X)),eta(X3)),
inference(substitution,[status(thm)],[c61]) ).
cnf(c89,plain,
quotient(product(eta(X3),product(X2,X)),eta(X3)) = t(eta(X3),product(X2,X)),
inference(symmetry,[status(thm)],[c88]) ).
cnf(c90,plain,
quotient(product(product(t(eta(X3),X2),t(eta(X3),X)),eta(X3)),eta(X3)) = t(eta(X3),product(X2,X)),
inference(transitivity,[status(thm)],[c87,c89]) ).
cnf(c91,plain,
product(product(t(eta(X3),X2),t(eta(X3),X)),quotient(eta(X3),eta(X3))) = t(eta(X3),product(X2,X)),
inference(transitivity,[status(thm)],[c53,c90]) ).
cnf(c92,plain,
product(product(t(eta(X3),X2),t(eta(X3),X)),one) = t(eta(X3),product(X2,X)),
inference(transitivity,[status(thm)],[c14,c91]) ).
cnf(c93,plain,
product(t(eta(X3),X2),t(eta(X3),X)) = t(eta(X3),product(X2,X)),
inference(transitivity,[status(thm)],[c4,c92]) ).
cnf(c94,plain,
product(t(eta(x0),x1),t(eta(x0),x2)) = t(eta(x0),product(x1,x2)),
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
t(eta(x0),product(x1,x2)) = product(t(eta(x0),x1),t(eta(x0),x2)),
inference(symmetry,[status(thm)],[c94]) ).
cnf(c96,plain,
$false,
inference(resolution,[status(thm)],[c1,c95]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP768-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 10:43:34 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.99/2.37 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 14.99/2.37
% 14.99/2.37 % SZS status Unsatisfiable
% 14.99/2.37
% 14.99/2.38 % SZS output start CNFRefutation
% See solution above
% 15.67/2.42
% 15.67/2.42 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------