%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : ALG007-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 09:06:54 AM UTC 2026
% Result : Unsatisfiable 0.48s 0.29s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of clauses : 70 ( 70 unt; 0 nHn; 7 RR)
% Number of literals : 70 ( 69 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 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 : 187 ( 8 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
difference(difference(a,b),c) != difference(difference(a,c),difference(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_set_difference_3) ).
cnf(c2,axiom,
difference(difference(X,Y),Z) = difference(difference(X,Z),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_3_simplified) ).
cnf(c3,plain,
difference(difference(a,c),b) = difference(difference(a,b),c),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
difference(difference(a,b),c) = difference(difference(a,c),b),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
difference(difference(X4,difference(X2,X3)),X3) = difference(difference(X4,X3),difference(X2,X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
difference(difference(X4,X3),difference(X2,X3)) = difference(difference(X4,difference(X2,X3)),X3),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
difference(difference(X4,difference(X4,X2)),X3) = difference(difference(X4,X3),difference(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c8,plain,
difference(difference(X4,X3),difference(X4,X2)) = difference(difference(X4,difference(X4,X2)),X3),
inference(symmetry,[status(thm)],[c7]) ).
cnf(c9,plain,
difference(difference(difference(X4,X3),difference(X5,X4)),X2) = difference(difference(difference(X4,X3),X2),difference(X5,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
difference(difference(difference(X5,X4),X3),difference(X2,X5)) = difference(difference(difference(X5,X4),difference(X2,X5)),X3),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
difference(difference(X4,difference(X2,X4)),X3) = difference(difference(X4,X3),difference(X2,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c12,plain,
difference(difference(X4,X3),difference(X2,X4)) = difference(difference(X4,difference(X2,X4)),X3),
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,axiom,
difference(X2,difference(Y2,X2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_1) ).
cnf(c14,plain,
difference(X3,difference(X2,X3)) = X3,
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
difference(difference(X4,difference(X2,X4)),X3) = difference(X4,X3),
inference(congruence,[status(thm)],[c14]) ).
cnf(c16,plain,
difference(difference(X4,X3),difference(X2,X4)) = difference(X4,X3),
inference(transitivity,[status(thm)],[c12,c15]) ).
cnf(c17,plain,
difference(difference(difference(X5,X4),difference(X2,X5)),X3) = difference(difference(X5,X4),X3),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
difference(difference(difference(X5,X4),X3),difference(X2,X5)) = difference(difference(X5,X4),X3),
inference(transitivity,[status(thm)],[c10,c17]) ).
cnf(c19,plain,
difference(difference(difference(X4,difference(X4,X2)),X3),difference(difference(X2,X3),X4)) = difference(difference(X4,difference(X4,X2)),X3),
inference(substitution,[status(thm)],[c18]) ).
cnf(c20,plain,
difference(difference(X4,difference(X4,X2)),X3) = difference(difference(difference(X4,difference(X4,X2)),X3),difference(difference(X2,X3),X4)),
inference(symmetry,[status(thm)],[c19]) ).
cnf(c21,axiom,
difference(X2,difference(X2,Y2)) = difference(Y2,difference(Y2,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_difference_2) ).
cnf(c22,plain,
difference(X3,difference(X3,X2)) = difference(X2,difference(X2,X3)),
inference(substitution,[status(thm)],[c21]) ).
cnf(c23,plain,
difference(X2,difference(X2,X3)) = difference(X3,difference(X3,X2)),
inference(symmetry,[status(thm)],[c22]) ).
cnf(c24,plain,
difference(difference(X2,difference(X2,X4)),X3) = difference(difference(X4,difference(X4,X2)),X3),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
difference(difference(X4,difference(X4,X2)),X3) = difference(difference(X4,X3),difference(X4,X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c26,plain,
difference(difference(X2,difference(X2,X4)),X3) = difference(difference(X4,X3),difference(X4,X2)),
inference(transitivity,[status(thm)],[c24,c25]) ).
cnf(c27,plain,
difference(difference(X4,difference(X4,X2)),X3) = difference(difference(X2,X3),difference(X2,X4)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c28,plain,
difference(difference(difference(X4,difference(X4,X2)),X3),difference(difference(X2,X3),X4)) = difference(difference(difference(X2,X3),difference(X2,X4)),difference(difference(X2,X3),X4)),
inference(congruence,[status(thm)],[c27]) ).
cnf(c29,plain,
difference(difference(X2,difference(X2,X4)),difference(X3,X2)) = difference(difference(X4,difference(X3,X2)),difference(X4,X2)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c30,plain,
difference(difference(X4,difference(X3,X2)),difference(X4,X2)) = difference(difference(X2,difference(X2,X4)),difference(X3,X2)),
inference(symmetry,[status(thm)],[c29]) ).
cnf(c31,plain,
difference(difference(X2,difference(X2,X4)),difference(X3,X2)) = difference(X2,difference(X2,X4)),
inference(substitution,[status(thm)],[c16]) ).
cnf(c32,plain,
difference(difference(X4,difference(X3,X2)),difference(X4,X2)) = difference(X2,difference(X2,X4)),
inference(transitivity,[status(thm)],[c30,c31]) ).
cnf(c33,plain,
difference(difference(difference(X2,X3),difference(X2,X4)),difference(difference(X2,X3),X4)) = difference(X4,difference(X4,difference(X2,X3))),
inference(substitution,[status(thm)],[c32]) ).
cnf(c34,plain,
difference(difference(difference(X4,difference(X4,X2)),X3),difference(difference(X2,X3),X4)) = difference(X4,difference(X4,difference(X2,X3))),
inference(transitivity,[status(thm)],[c28,c33]) ).
cnf(c35,plain,
difference(difference(X4,difference(X4,X2)),X3) = difference(X4,difference(X4,difference(X2,X3))),
inference(transitivity,[status(thm)],[c20,c34]) ).
cnf(c36,plain,
difference(difference(X4,X3),difference(X4,X2)) = difference(X4,difference(X4,difference(X2,X3))),
inference(transitivity,[status(thm)],[c8,c35]) ).
cnf(c37,plain,
difference(difference(X4,X2),difference(X4,difference(X4,X3))) = difference(X4,difference(X4,difference(difference(X4,X3),X2))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
difference(X4,difference(X4,difference(difference(X4,X3),X2))) = difference(difference(X4,X2),difference(X4,difference(X4,X3))),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
difference(difference(difference(X4,X3),difference(difference(X4,X3),X4)),X2) = difference(difference(X4,X2),difference(X4,difference(X4,X3))),
inference(substitution,[status(thm)],[c26]) ).
cnf(c40,plain,
difference(difference(X4,X2),difference(X4,difference(X4,X3))) = difference(difference(difference(X4,X3),difference(difference(X4,X3),X4)),X2),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
difference(difference(X3,X2),difference(difference(X3,X2),X3)) = difference(X3,X2),
inference(substitution,[status(thm)],[c16]) ).
cnf(c42,plain,
difference(difference(difference(X4,X3),difference(difference(X4,X3),X4)),X2) = difference(difference(X4,X3),X2),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
difference(difference(X4,X2),difference(X4,difference(X4,X3))) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
difference(X4,difference(X4,difference(difference(X4,X3),X2))) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c38,c43]) ).
cnf(c45,plain,
difference(X4,difference(X4,difference(difference(X4,difference(X2,X3)),X3))) = difference(difference(X4,difference(X2,X3)),X3),
inference(substitution,[status(thm)],[c44]) ).
cnf(c46,plain,
difference(difference(X4,difference(X2,X3)),X3) = difference(X4,difference(X4,difference(difference(X4,difference(X2,X3)),X3))),
inference(symmetry,[status(thm)],[c45]) ).
cnf(c47,plain,
difference(difference(X4,X3),difference(X4,difference(X4,difference(X2,X3)))) = difference(X4,difference(X4,difference(difference(X4,difference(X2,X3)),X3))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c48,plain,
difference(X4,difference(X4,difference(difference(X4,difference(X2,X3)),X3))) = difference(difference(X4,X3),difference(X4,difference(X4,difference(X2,X3)))),
inference(symmetry,[status(thm)],[c47]) ).
cnf(c49,plain,
difference(X4,difference(X4,difference(X2,X3))) = difference(difference(X4,X3),difference(X4,X2)),
inference(symmetry,[status(thm)],[c36]) ).
cnf(c50,plain,
difference(difference(X4,X3),difference(X4,difference(X4,difference(X2,X3)))) = difference(difference(X4,X3),difference(difference(X4,X3),difference(X4,X2))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
difference(difference(X4,X2),difference(X4,X3)) = difference(difference(X4,difference(X4,X3)),X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
difference(difference(X4,difference(X4,X3)),X2) = difference(difference(X4,X2),difference(X4,X3)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,plain,
difference(difference(X4,X2),difference(X4,X3)) = difference(X4,difference(X4,difference(X3,X2))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c54,plain,
difference(difference(X4,difference(X4,X3)),X2) = difference(X4,difference(X4,difference(X3,X2))),
inference(transitivity,[status(thm)],[c52,c53]) ).
cnf(c55,plain,
difference(difference(X3,difference(X3,X4)),X2) = difference(X3,difference(X3,difference(X4,X2))),
inference(substitution,[status(thm)],[c54]) ).
cnf(c56,plain,
difference(X3,difference(X3,difference(X4,X2))) = difference(difference(X3,difference(X3,X4)),X2),
inference(symmetry,[status(thm)],[c55]) ).
cnf(c57,plain,
difference(difference(X3,difference(X3,X4)),X2) = difference(difference(X4,X2),difference(X4,X3)),
inference(substitution,[status(thm)],[c26]) ).
cnf(c58,plain,
difference(difference(X4,X2),difference(X4,X3)) = difference(X4,difference(X4,difference(X3,X2))),
inference(substitution,[status(thm)],[c36]) ).
cnf(c59,plain,
difference(difference(X3,difference(X3,X4)),X2) = difference(X4,difference(X4,difference(X3,X2))),
inference(transitivity,[status(thm)],[c57,c58]) ).
cnf(c60,plain,
difference(X3,difference(X3,difference(X4,X2))) = difference(X4,difference(X4,difference(X3,X2))),
inference(transitivity,[status(thm)],[c56,c59]) ).
cnf(c61,plain,
difference(difference(X4,X3),difference(difference(X4,X3),difference(X4,X2))) = difference(X4,difference(X4,difference(difference(X4,X3),X2))),
inference(substitution,[status(thm)],[c60]) ).
cnf(c62,plain,
difference(difference(X4,X3),difference(difference(X4,X3),difference(X4,X2))) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c61,c44]) ).
cnf(c63,plain,
difference(difference(X4,X3),difference(X4,difference(X4,difference(X2,X3)))) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c50,c62]) ).
cnf(c64,plain,
difference(X4,difference(X4,difference(difference(X4,difference(X2,X3)),X3))) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c48,c63]) ).
cnf(c65,plain,
difference(difference(X4,difference(X2,X3)),X3) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c46,c64]) ).
cnf(c66,plain,
difference(difference(X4,X3),difference(X2,X3)) = difference(difference(X4,X3),X2),
inference(transitivity,[status(thm)],[c6,c65]) ).
cnf(c67,plain,
difference(difference(a,c),difference(b,c)) = difference(difference(a,c),b),
inference(substitution,[status(thm)],[c66]) ).
cnf(c68,plain,
difference(difference(a,c),b) = difference(difference(a,c),difference(b,c)),
inference(symmetry,[status(thm)],[c67]) ).
cnf(c69,plain,
difference(difference(a,b),c) = difference(difference(a,c),difference(b,c)),
inference(transitivity,[status(thm)],[c4,c68]) ).
cnf(c70,plain,
$false,
inference(resolution,[status(thm)],[c1,c69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG007-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n017.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Mon Sep 28 19:12:21 UTC 2026
% 0.10/0.17 % CPUTime :
% 0.10/0.17 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.48/0.29 Command-line arguments: --no-flatten-goal
% 0.48/0.29
% 0.48/0.29 % SZS status Unsatisfiable
% 0.48/0.29
% 0.48/0.30 % SZS output start CNFRefutation
% See solution above
% 0.48/0.33
% 0.48/0.33 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------