%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 09:06:53 AM UTC 2026
% Result : Unsatisfiable 0.49s 0.28s
% Output : CNFRefutation 0.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 50
% Number of leaves : 4
% Syntax : Number of clauses : 166 ( 166 unt; 0 nHn; 3 RR)
% Number of literals : 166 ( 165 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 418 ( 37 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
difference(difference(a,c),b) != difference(difference(a,b),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_set_difference_3_simplified) ).
cnf(c2,axiom,
difference(X,difference(Y,X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_1) ).
cnf(c3,plain,
difference(X2,difference(X3,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
X2 = difference(X2,difference(X3,X2)),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
difference(X4,X2) = difference(X4,difference(X2,difference(X3,X2))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
difference(difference(X4,X3),difference(X2,X3)) = difference(difference(X4,X3),difference(X2,difference(X3,difference(X4,X3)))),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
difference(difference(X2,Y2),Z) = difference(difference(X2,Z),difference(Y2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_3) ).
cnf(c8,plain,
difference(difference(X4,X3),difference(X2,X4)) = difference(difference(X4,difference(X2,X4)),difference(X3,difference(X2,X4))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
difference(X3,difference(X2,X3)) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
difference(difference(X4,difference(X2,X4)),difference(X3,difference(X2,X4))) = difference(X4,difference(X3,difference(X2,X4))),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
difference(difference(X4,X3),difference(X2,X4)) = difference(X4,difference(X3,difference(X2,X4))),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
difference(X4,difference(X3,difference(X2,X4))) = difference(difference(X4,X3),difference(X2,X4)),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
difference(X2,difference(X3,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c14,plain,
X2 = difference(X2,difference(X3,X2)),
inference(symmetry,[status(thm)],[c13]) ).
cnf(c15,plain,
difference(difference(X3,X2),X2) = difference(difference(X3,X2),difference(X2,difference(X3,X2))),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
difference(difference(X3,X2),difference(X2,difference(X3,X2))) = difference(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c17,plain,
difference(difference(X3,X2),X2) = difference(X3,X2),
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
difference(X3,X2) = difference(difference(X3,X2),X2),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c19,plain,
difference(difference(X3,X2),difference(X3,X2)) = difference(difference(X3,X2),difference(difference(X3,X2),X2)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
difference(X2,difference(X2,Y2)) = difference(Y2,difference(Y2,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',set_difference_2) ).
cnf(c21,plain,
difference(difference(X3,X2),difference(difference(X3,X2),X2)) = difference(X2,difference(X2,difference(X3,X2))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
difference(X2,difference(X3,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c23,plain,
difference(X2,difference(X2,difference(X3,X2))) = difference(X2,X2),
inference(congruence,[status(thm)],[c22]) ).
cnf(c24,plain,
difference(difference(X3,X2),difference(difference(X3,X2),X2)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c21,c23]) ).
cnf(c25,plain,
difference(difference(X3,X2),difference(X3,X2)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c19,c24]) ).
cnf(c26,plain,
difference(difference(difference(X2,X2),X3),difference(difference(X2,X2),X3)) = difference(X3,X3),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
difference(X3,X3) = difference(difference(difference(X2,X2),X3),difference(difference(X2,X2),X3)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,plain,
difference(difference(difference(X2,X2),difference(difference(X2,X2),X3)),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(difference(difference(X2,X2),X3),difference(difference(X2,X2),X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c29,plain,
difference(difference(difference(X2,X2),X3),difference(difference(X2,X2),X3)) = difference(difference(difference(X2,X2),difference(difference(X2,X2),X3)),difference(difference(X2,X2),difference(difference(X2,X2),X3))),
inference(symmetry,[status(thm)],[c28]) ).
cnf(c30,plain,
difference(difference(X3,X3),X2) = difference(difference(X3,X2),difference(X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c31,plain,
difference(difference(X3,X3),X2) = difference(X2,X2),
inference(transitivity,[status(thm)],[c30,c25]) ).
cnf(c32,plain,
difference(difference(X2,X2),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(difference(difference(X2,X2),difference(difference(X2,X2),X3)),difference(difference(X2,X2),difference(difference(X2,X2),X3))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c33,plain,
difference(difference(difference(X2,X2),difference(difference(X2,X2),X3)),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(difference(X2,X2),difference(difference(X2,X2),difference(difference(X2,X2),X3))),
inference(symmetry,[status(thm)],[c32]) ).
cnf(c34,plain,
difference(X3,difference(X3,X2)) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c35,plain,
difference(X2,difference(X2,X3)) = difference(X3,difference(X3,X2)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
difference(X3,difference(X2,difference(X2,X3))) = difference(X3,difference(X3,difference(X3,X2))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
difference(X3,difference(X3,difference(X3,X2))) = difference(difference(X3,X2),difference(difference(X3,X2),X3)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c38,plain,
difference(difference(X3,X2),difference(difference(X3,X2),X3)) = difference(X3,difference(X2,difference(difference(X3,X2),X3))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c39,plain,
difference(X2,difference(X3,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c40,plain,
X2 = difference(X2,difference(X3,X2)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
difference(difference(X4,difference(X3,X2)),X2) = difference(difference(X4,difference(X3,X2)),difference(X2,difference(X3,X2))),
inference(congruence,[status(thm)],[c40]) ).
cnf(c42,plain,
difference(difference(X4,X2),difference(X3,X2)) = difference(difference(X4,difference(X3,X2)),difference(X2,difference(X3,X2))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c43,plain,
difference(difference(X4,difference(X3,X2)),difference(X2,difference(X3,X2))) = difference(difference(X4,X2),difference(X3,X2)),
inference(symmetry,[status(thm)],[c42]) ).
cnf(c44,plain,
difference(difference(X4,X3),X2) = difference(difference(X4,X2),difference(X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c45,plain,
difference(difference(X4,X2),difference(X3,X2)) = difference(difference(X4,X3),X2),
inference(symmetry,[status(thm)],[c44]) ).
cnf(c46,plain,
difference(difference(X4,difference(X3,X2)),difference(X2,difference(X3,X2))) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c43,c45]) ).
cnf(c47,plain,
difference(difference(X4,difference(X3,X2)),X2) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c41,c46]) ).
cnf(c48,plain,
difference(difference(X3,difference(X2,X3)),X3) = difference(difference(X3,X2),X3),
inference(substitution,[status(thm)],[c47]) ).
cnf(c49,plain,
difference(difference(X3,X2),X3) = difference(difference(X3,difference(X2,X3)),X3),
inference(symmetry,[status(thm)],[c48]) ).
cnf(c50,plain,
difference(X3,difference(X2,X3)) = X3,
inference(substitution,[status(thm)],[c2]) ).
cnf(c51,plain,
difference(difference(X3,difference(X2,X3)),X3) = difference(X3,X3),
inference(congruence,[status(thm)],[c50]) ).
cnf(c52,plain,
difference(difference(X3,X2),X3) = difference(X3,X3),
inference(transitivity,[status(thm)],[c49,c51]) ).
cnf(c53,plain,
difference(X2,difference(difference(X3,X2),X3)) = difference(X2,difference(X3,X3)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c54,plain,
difference(X3,difference(X2,difference(difference(X3,X2),X3))) = difference(X3,difference(X2,difference(X3,X3))),
inference(congruence,[status(thm)],[c53]) ).
cnf(c55,plain,
difference(difference(X3,X2),difference(difference(X3,X2),X3)) = difference(X3,difference(X2,difference(X3,X3))),
inference(transitivity,[status(thm)],[c38,c54]) ).
cnf(c56,plain,
difference(X3,difference(X3,difference(X3,X2))) = difference(X3,difference(X2,difference(X3,X3))),
inference(transitivity,[status(thm)],[c37,c55]) ).
cnf(c57,plain,
difference(X3,difference(X2,difference(X2,X3))) = difference(X3,difference(X2,difference(X3,X3))),
inference(transitivity,[status(thm)],[c36,c56]) ).
cnf(c58,plain,
difference(X3,difference(X2,difference(X3,X3))) = difference(X3,difference(X2,difference(X2,X3))),
inference(symmetry,[status(thm)],[c57]) ).
cnf(c59,plain,
difference(X2,difference(X2,X3)) = difference(X3,difference(X3,X2)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c60,plain,
difference(X3,difference(X2,difference(X2,X3))) = difference(X3,difference(X3,difference(X3,X2))),
inference(congruence,[status(thm)],[c59]) ).
cnf(c61,plain,
difference(X3,difference(X2,difference(X3,X3))) = difference(X3,difference(X3,difference(X3,X2))),
inference(transitivity,[status(thm)],[c58,c60]) ).
cnf(c62,plain,
difference(difference(X2,X2),difference(X3,difference(difference(X2,X2),difference(X2,X2)))) = difference(difference(X2,X2),difference(difference(X2,X2),difference(difference(X2,X2),X3))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
difference(difference(X2,X2),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(difference(X2,X2),difference(X3,difference(difference(X2,X2),difference(X2,X2)))),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
difference(difference(X2,X2),X3) = difference(difference(X2,X3),difference(X2,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c65,plain,
difference(difference(X2,X3),difference(X2,X3)) = difference(X3,X3),
inference(substitution,[status(thm)],[c25]) ).
cnf(c66,plain,
difference(X2,X2) = difference(difference(X3,X2),difference(X3,X2)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c67,plain,
difference(difference(X3,X3),X2) = difference(difference(X3,X2),difference(X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c68,plain,
difference(difference(X3,X2),difference(X3,X2)) = difference(difference(X3,X3),X2),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
difference(X2,X2) = difference(difference(X3,X3),X2),
inference(transitivity,[status(thm)],[c66,c68]) ).
cnf(c70,plain,
difference(difference(X2,X3),difference(X2,X3)) = difference(difference(X4,X4),X3),
inference(transitivity,[status(thm)],[c65,c69]) ).
cnf(c71,plain,
difference(difference(X2,X2),X3) = difference(difference(X4,X4),X3),
inference(transitivity,[status(thm)],[c64,c70]) ).
cnf(c72,plain,
difference(difference(X4,X4),difference(X3,X2)) = difference(difference(difference(X3,X2),difference(X3,X2)),difference(X3,X2)),
inference(substitution,[status(thm)],[c71]) ).
cnf(c73,plain,
difference(difference(X2,X3),X3) = difference(X2,X3),
inference(substitution,[status(thm)],[c17]) ).
cnf(c74,plain,
difference(X2,X3) = difference(difference(X2,X3),X3),
inference(symmetry,[status(thm)],[c73]) ).
cnf(c75,plain,
difference(difference(X2,X3),difference(X2,X3)) = difference(difference(X2,X3),difference(difference(X2,X3),X3)),
inference(congruence,[status(thm)],[c74]) ).
cnf(c76,plain,
difference(difference(difference(X2,X3),difference(X2,X3)),difference(X2,X3)) = difference(difference(difference(X2,X3),difference(difference(X2,X3),X3)),difference(X2,X3)),
inference(congruence,[status(thm)],[c75]) ).
cnf(c77,plain,
difference(difference(difference(X2,X3),difference(difference(X2,X3),X3)),difference(X2,X3)) = difference(difference(X2,X3),difference(X2,X3)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c78,plain,
difference(difference(X2,X3),difference(X2,X3)) = difference(X3,X3),
inference(substitution,[status(thm)],[c25]) ).
cnf(c79,plain,
difference(X2,X2) = difference(difference(X3,X2),difference(X3,X2)),
inference(symmetry,[status(thm)],[c25]) ).
cnf(c80,plain,
difference(difference(difference(X3,X2),difference(difference(X3,X2),X2)),difference(X3,X2)) = difference(difference(X3,X2),difference(X3,X2)),
inference(substitution,[status(thm)],[c52]) ).
cnf(c81,plain,
difference(difference(X3,X2),difference(X3,X2)) = difference(difference(difference(X3,X2),difference(difference(X3,X2),X2)),difference(X3,X2)),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,plain,
difference(difference(X3,X2),difference(difference(X3,X2),X2)) = difference(difference(X3,X2),difference(X3,X2)),
inference(congruence,[status(thm)],[c17]) ).
cnf(c83,plain,
difference(difference(difference(X3,X2),difference(difference(X3,X2),X2)),difference(X3,X2)) = difference(difference(difference(X3,X2),difference(X3,X2)),difference(X3,X2)),
inference(congruence,[status(thm)],[c82]) ).
cnf(c84,plain,
difference(difference(X4,X4),difference(X3,X2)) = difference(difference(difference(X3,X2),difference(X3,X2)),difference(X3,X2)),
inference(substitution,[status(thm)],[c71]) ).
cnf(c85,plain,
difference(difference(difference(X3,X2),difference(X3,X2)),difference(X3,X2)) = difference(difference(X4,X4),difference(X3,X2)),
inference(symmetry,[status(thm)],[c84]) ).
cnf(c86,plain,
difference(difference(difference(X3,X2),difference(difference(X3,X2),X2)),difference(X3,X2)) = difference(difference(X4,X4),difference(X3,X2)),
inference(transitivity,[status(thm)],[c83,c85]) ).
cnf(c87,plain,
difference(difference(X3,X2),difference(X3,X2)) = difference(difference(X4,X4),difference(X3,X2)),
inference(transitivity,[status(thm)],[c81,c86]) ).
cnf(c88,plain,
difference(X2,X2) = difference(difference(X4,X4),difference(X3,X2)),
inference(transitivity,[status(thm)],[c79,c87]) ).
cnf(c89,plain,
difference(difference(X2,X3),difference(X2,X3)) = difference(difference(X5,X5),difference(X4,X3)),
inference(transitivity,[status(thm)],[c78,c88]) ).
cnf(c90,plain,
difference(difference(difference(X2,X3),difference(difference(X2,X3),X3)),difference(X2,X3)) = difference(difference(X5,X5),difference(X4,X3)),
inference(transitivity,[status(thm)],[c77,c89]) ).
cnf(c91,plain,
difference(difference(difference(X2,X3),difference(X2,X3)),difference(X2,X3)) = difference(difference(X5,X5),difference(X4,X3)),
inference(transitivity,[status(thm)],[c76,c90]) ).
cnf(c92,plain,
difference(difference(X3,X3),difference(X2,X4)) = difference(difference(X6,X6),difference(X5,X4)),
inference(transitivity,[status(thm)],[c72,c91]) ).
cnf(c93,plain,
difference(difference(X2,X2),difference(X3,difference(difference(X2,X2),difference(X2,X2)))) = difference(difference(X2,X2),difference(X4,difference(difference(X2,X2),difference(X2,X2)))),
inference(substitution,[status(thm)],[c92]) ).
cnf(c94,plain,
difference(difference(X2,X2),difference(X3,difference(difference(X2,X2),difference(X2,X2)))) = difference(difference(X2,X2),difference(difference(X2,X2),difference(difference(X2,X2),X3))),
inference(substitution,[status(thm)],[c61]) ).
cnf(c95,plain,
difference(difference(X2,X2),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(difference(difference(X2,X2),difference(difference(X2,X2),X3)),difference(difference(X2,X2),difference(difference(X2,X2),X3))),
inference(substitution,[status(thm)],[c31]) ).
cnf(c96,plain,
difference(difference(difference(X2,X2),difference(difference(X2,X2),X3)),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(difference(difference(X2,X2),X3),difference(difference(X2,X2),X3)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c97,plain,
difference(difference(difference(X2,X2),X3),difference(difference(X2,X2),X3)) = difference(X3,X3),
inference(substitution,[status(thm)],[c25]) ).
cnf(c98,plain,
difference(difference(difference(X2,X2),difference(difference(X2,X2),X3)),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(X3,X3),
inference(transitivity,[status(thm)],[c96,c97]) ).
cnf(c99,plain,
difference(difference(X2,X2),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(X3,X3),
inference(transitivity,[status(thm)],[c95,c98]) ).
cnf(c100,plain,
difference(difference(X2,X2),difference(X3,difference(difference(X2,X2),difference(X2,X2)))) = difference(X3,X3),
inference(transitivity,[status(thm)],[c94,c99]) ).
cnf(c101,plain,
difference(difference(X2,X2),difference(X3,difference(difference(X2,X2),difference(X2,X2)))) = difference(X4,X4),
inference(transitivity,[status(thm)],[c93,c100]) ).
cnf(c102,plain,
difference(difference(X2,X2),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(X4,X4),
inference(transitivity,[status(thm)],[c63,c101]) ).
cnf(c103,plain,
difference(difference(difference(X2,X2),difference(difference(X2,X2),X3)),difference(difference(X2,X2),difference(difference(X2,X2),X3))) = difference(X4,X4),
inference(transitivity,[status(thm)],[c33,c102]) ).
cnf(c104,plain,
difference(difference(difference(X2,X2),X3),difference(difference(X2,X2),X3)) = difference(X4,X4),
inference(transitivity,[status(thm)],[c29,c103]) ).
cnf(c105,plain,
difference(X2,X2) = difference(X3,X3),
inference(transitivity,[status(thm)],[c27,c104]) ).
cnf(c106,plain,
difference(X3,difference(X2,X2)) = difference(X3,difference(X3,X3)),
inference(congruence,[status(thm)],[c105]) ).
cnf(c107,plain,
difference(X2,difference(X2,X2)) = X2,
inference(substitution,[status(thm)],[c2]) ).
cnf(c108,plain,
difference(X3,difference(X2,X2)) = X3,
inference(transitivity,[status(thm)],[c106,c107]) ).
cnf(c109,plain,
difference(difference(X2,X4),difference(difference(X4,X3),difference(X4,X3))) = difference(X2,X4),
inference(substitution,[status(thm)],[c108]) ).
cnf(c110,plain,
difference(X2,X4) = difference(difference(X2,X4),difference(difference(X4,X3),difference(X4,X3))),
inference(symmetry,[status(thm)],[c109]) ).
cnf(c111,plain,
difference(difference(X4,X3),difference(X2,X4)) = difference(difference(X4,X3),difference(difference(X2,X4),difference(difference(X4,X3),difference(X4,X3)))),
inference(congruence,[status(thm)],[c110]) ).
cnf(c112,plain,
difference(difference(X4,X3),difference(difference(X2,X4),difference(difference(X2,X4),difference(X4,X3)))) = difference(difference(X4,X3),difference(difference(X2,X4),difference(difference(X4,X3),difference(X4,X3)))),
inference(substitution,[status(thm)],[c57]) ).
cnf(c113,plain,
difference(difference(X4,X3),difference(difference(X2,X4),difference(difference(X4,X3),difference(X4,X3)))) = difference(difference(X4,X3),difference(difference(X2,X4),difference(difference(X2,X4),difference(X4,X3)))),
inference(symmetry,[status(thm)],[c112]) ).
cnf(c114,plain,
difference(difference(X4,X3),difference(X3,difference(X3,X2))) = difference(difference(X4,difference(X3,difference(X3,X2))),difference(X3,difference(X3,difference(X3,X2)))),
inference(substitution,[status(thm)],[c7]) ).
cnf(c115,plain,
difference(X3,difference(X3,difference(X3,X2))) = difference(X3,difference(X2,difference(X3,X3))),
inference(symmetry,[status(thm)],[c61]) ).
cnf(c116,plain,
difference(X3,X3) = difference(X2,X2),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c117,plain,
difference(X3,difference(X4,X4)) = difference(X3,difference(X2,X2)),
inference(congruence,[status(thm)],[c116]) ).
cnf(c118,plain,
difference(X4,difference(X3,difference(X4,X4))) = difference(X4,difference(X3,difference(X2,X2))),
inference(congruence,[status(thm)],[c117]) ).
cnf(c119,plain,
difference(X4,difference(X3,difference(X2,X2))) = difference(X4,X3),
inference(congruence,[status(thm)],[c108]) ).
cnf(c120,plain,
difference(X3,difference(X2,difference(X3,X3))) = difference(X3,X2),
inference(transitivity,[status(thm)],[c118,c119]) ).
cnf(c121,plain,
difference(X3,difference(X3,difference(X3,X2))) = difference(X3,X2),
inference(transitivity,[status(thm)],[c115,c120]) ).
cnf(c122,plain,
difference(difference(X4,difference(X3,difference(X3,X2))),difference(X3,difference(X3,difference(X3,X2)))) = difference(difference(X4,difference(X3,difference(X3,X2))),difference(X3,X2)),
inference(congruence,[status(thm)],[c121]) ).
cnf(c123,plain,
difference(difference(X4,difference(X3,difference(X3,X2))),difference(X3,X2)) = difference(difference(X4,X3),difference(X3,X2)),
inference(substitution,[status(thm)],[c47]) ).
cnf(c124,plain,
difference(difference(X4,difference(X3,difference(X3,X2))),difference(X3,difference(X3,difference(X3,X2)))) = difference(difference(X4,X3),difference(X3,X2)),
inference(transitivity,[status(thm)],[c122,c123]) ).
cnf(c125,plain,
difference(difference(X4,X3),difference(X3,difference(X3,X2))) = difference(difference(X4,X3),difference(X3,X2)),
inference(transitivity,[status(thm)],[c114,c124]) ).
cnf(c126,plain,
difference(difference(X4,X3),difference(X3,X2)) = difference(difference(X4,X3),difference(X3,difference(X3,X2))),
inference(symmetry,[status(thm)],[c125]) ).
cnf(c127,plain,
difference(difference(X4,X3),difference(difference(X4,X3),difference(X3,X2))) = difference(difference(X4,X3),difference(difference(X4,X3),difference(X3,difference(X3,X2)))),
inference(congruence,[status(thm)],[c126]) ).
cnf(c128,plain,
difference(difference(X4,X3),difference(difference(X4,X3),difference(X3,difference(X3,X2)))) = difference(difference(X3,difference(X3,X2)),difference(difference(X3,difference(X3,X2)),difference(X4,X3))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c129,plain,
difference(difference(X3,difference(X3,X2)),difference(X4,X3)) = difference(X3,difference(difference(X3,X2),difference(X4,X3))),
inference(substitution,[status(thm)],[c11]) ).
cnf(c130,plain,
difference(difference(X3,difference(X3,X2)),difference(difference(X3,difference(X3,X2)),difference(X4,X3))) = difference(difference(X3,difference(X3,X2)),difference(X3,difference(difference(X3,X2),difference(X4,X3)))),
inference(congruence,[status(thm)],[c129]) ).
cnf(c131,plain,
difference(difference(X4,difference(X3,X2)),X3) = difference(difference(X4,X3),difference(difference(X3,X2),X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c132,plain,
difference(difference(X4,X3),difference(difference(X3,X2),X3)) = difference(difference(X4,X3),difference(X3,X3)),
inference(congruence,[status(thm)],[c52]) ).
cnf(c133,plain,
difference(difference(X3,X2),X2) = difference(difference(X3,X2),difference(X2,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c134,plain,
difference(difference(X3,X2),difference(X2,X2)) = difference(difference(X3,X2),X2),
inference(symmetry,[status(thm)],[c133]) ).
cnf(c135,plain,
difference(difference(X3,X2),difference(X2,X2)) = difference(X3,X2),
inference(transitivity,[status(thm)],[c134,c17]) ).
cnf(c136,plain,
difference(difference(X4,X3),difference(difference(X3,X2),X3)) = difference(X4,X3),
inference(transitivity,[status(thm)],[c132,c135]) ).
cnf(c137,plain,
difference(difference(X4,difference(X3,X2)),X3) = difference(X4,X3),
inference(transitivity,[status(thm)],[c131,c136]) ).
cnf(c138,plain,
difference(X4,X3) = difference(difference(X4,difference(X3,X2)),X3),
inference(symmetry,[status(thm)],[c137]) ).
cnf(c139,plain,
difference(difference(X4,X3),difference(X4,difference(X3,X2))) = difference(difference(difference(X4,difference(X3,X2)),X3),difference(X4,difference(X3,X2))),
inference(congruence,[status(thm)],[c138]) ).
cnf(c140,plain,
difference(difference(difference(X4,difference(X3,X2)),X3),difference(X4,difference(X3,X2))) = difference(difference(X4,difference(X3,X2)),difference(X4,difference(X3,X2))),
inference(substitution,[status(thm)],[c52]) ).
cnf(c141,plain,
difference(difference(X4,difference(X3,X2)),difference(X4,difference(X3,X2))) = difference(difference(X3,X2),difference(X3,X2)),
inference(substitution,[status(thm)],[c25]) ).
cnf(c142,plain,
difference(X3,X3) = difference(X2,X2),
inference(symmetry,[status(thm)],[c105]) ).
cnf(c143,plain,
difference(difference(X4,X3),difference(X4,X3)) = difference(X2,X2),
inference(transitivity,[status(thm)],[c25,c142]) ).
cnf(c144,plain,
difference(difference(X5,difference(X4,X3)),difference(X5,difference(X4,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c141,c143]) ).
cnf(c145,plain,
difference(difference(difference(X5,difference(X4,X3)),X4),difference(X5,difference(X4,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c140,c144]) ).
cnf(c146,plain,
difference(difference(X5,X4),difference(X5,difference(X4,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c139,c145]) ).
cnf(c147,plain,
difference(difference(X4,difference(X4,X3)),difference(X4,difference(difference(X4,X3),difference(X5,X4)))) = difference(X2,X2),
inference(substitution,[status(thm)],[c146]) ).
cnf(c148,plain,
difference(difference(X4,difference(X4,X3)),difference(difference(X4,difference(X4,X3)),difference(X5,X4))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c130,c147]) ).
cnf(c149,plain,
difference(difference(X5,X4),difference(difference(X5,X4),difference(X4,difference(X4,X3)))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c128,c148]) ).
cnf(c150,plain,
difference(difference(X5,X4),difference(difference(X5,X4),difference(X4,X3))) = difference(X2,X2),
inference(transitivity,[status(thm)],[c127,c149]) ).
cnf(c151,plain,
difference(difference(X3,X5),difference(difference(X3,X5),difference(X5,X4))) = difference(X2,X2),
inference(substitution,[status(thm)],[c150]) ).
cnf(c152,plain,
difference(difference(X5,X4),difference(difference(X3,X5),difference(difference(X3,X5),difference(X5,X4)))) = difference(difference(X5,X4),difference(X2,X2)),
inference(congruence,[status(thm)],[c151]) ).
cnf(c153,plain,
difference(difference(X4,X3),difference(X2,X2)) = difference(X4,X3),
inference(substitution,[status(thm)],[c108]) ).
cnf(c154,plain,
difference(difference(X4,X3),difference(difference(X2,X4),difference(difference(X2,X4),difference(X4,X3)))) = difference(X4,X3),
inference(transitivity,[status(thm)],[c152,c153]) ).
cnf(c155,plain,
difference(difference(X4,X3),difference(difference(X2,X4),difference(difference(X4,X3),difference(X4,X3)))) = difference(X4,X3),
inference(transitivity,[status(thm)],[c113,c154]) ).
cnf(c156,plain,
difference(difference(X4,X3),difference(X2,X4)) = difference(X4,X3),
inference(transitivity,[status(thm)],[c111,c155]) ).
cnf(c157,plain,
difference(X4,difference(X3,difference(X2,X4))) = difference(X4,X3),
inference(transitivity,[status(thm)],[c12,c156]) ).
cnf(c158,plain,
difference(difference(X4,X3),difference(X2,difference(X3,difference(X4,X3)))) = difference(difference(X4,X3),X2),
inference(substitution,[status(thm)],[c157]) ).
cnf(c159,plain,
difference(difference(X4,X3),difference(X2,X3)) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c6,c158]) ).
cnf(c160,plain,
difference(difference(X4,X2),difference(X3,X2)) = difference(difference(X4,X2),X3),
inference(substitution,[status(thm)],[c159]) ).
cnf(c161,plain,
difference(difference(X4,X2),X3) = difference(difference(X4,X2),difference(X3,X2)),
inference(symmetry,[status(thm)],[c160]) ).
cnf(c162,plain,
difference(difference(X4,X3),X2) = difference(difference(X4,X2),difference(X3,X2)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c163,plain,
difference(difference(X4,X2),difference(X3,X2)) = difference(difference(X4,X3),X2),
inference(symmetry,[status(thm)],[c162]) ).
cnf(c164,plain,
difference(difference(X4,X2),X3) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c161,c163]) ).
cnf(c165,plain,
difference(difference(a,c),b) = difference(difference(a,b),c),
inference(substitution,[status(thm)],[c164]) ).
cnf(c166,plain,
$false,
inference(resolution,[status(thm)],[c1,c165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG006-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.14 % Computer : n002.cluster.edu
% 0.10/0.14 % Model : x86_64 x86_64
% 0.10/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.14 % Memory : 8046.5625MB
% 0.10/0.14 % OS : Linux 6.8.0-71-generic
% 0.10/0.15 % CPULimit : 300
% 0.10/0.15 % WCLimit : 300
% 0.10/0.15 % DateTime : Mon Sep 28 19:19:36 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.49/0.28 Command-line arguments: --no-flatten-goal
% 0.49/0.28
% 0.49/0.28 % SZS status Unsatisfiable
% 0.49/0.28
% 0.49/0.29 % SZS output start CNFRefutation
% See solution above
% 0.49/0.34
% 0.49/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------