%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL002-1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 12:32:58 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 11
% Syntax : Number of clauses : 95 ( 95 unt; 0 nHn; 12 RR)
% Number of literals : 95 ( 94 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 : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 111 ( 9 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(sk1,top) != top,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
cnf(c2,axiom,
join(A,B) = join(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c3,plain,
join(complement(X),top) = join(top,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(top,complement(X)) = join(complement(X),top),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
join(complement(X),X2) = join(X2,complement(X)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
join(X,complement(X2)) = join(complement(X2),X),
inference(symmetry,[status(thm)],[c5]) ).
cnf(c7,plain,
join(X2,join(X,complement(X2))) = join(X2,join(complement(X2),X)),
inference(congruence,[status(thm)],[c6]) ).
cnf(c8,axiom,
join(A2,join(B2,C)) = join(join(A2,B2),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c9,plain,
join(X2,join(complement(X2),X)) = join(join(X2,complement(X2)),X),
inference(substitution,[status(thm)],[c8]) ).
cnf(c10,axiom,
top = join(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_top_12) ).
cnf(c11,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c11]) ).
cnf(c13,plain,
join(join(X2,complement(X2)),X) = join(top,X),
inference(congruence,[status(thm)],[c12]) ).
cnf(c14,plain,
join(top,X) = join(X,top),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
join(join(X2,complement(X2)),X) = join(X,top),
inference(transitivity,[status(thm)],[c13,c14]) ).
cnf(c16,plain,
join(X2,join(complement(X2),X)) = join(X,top),
inference(transitivity,[status(thm)],[c9,c15]) ).
cnf(c17,plain,
join(X2,join(X,complement(X2))) = join(X,top),
inference(transitivity,[status(thm)],[c7,c16]) ).
cnf(c18,plain,
join(X,join(complement(X),complement(X))) = join(complement(X),top),
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
join(complement(X),top) = join(X,join(complement(X),complement(X))),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
converse(composition(A2,B2)) = composition(converse(B2),converse(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_multiplicativity_10) ).
cnf(c21,plain,
converse(composition(converse(X2),X)) = composition(converse(X),converse(converse(X2))),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,axiom,
converse(converse(A2)) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_idempotence_8) ).
cnf(c23,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c24,plain,
composition(converse(X),converse(converse(X2))) = composition(converse(X),X2),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,plain,
converse(composition(converse(X2),X)) = composition(converse(X),X2),
inference(transitivity,[status(thm)],[c21,c24]) ).
cnf(c26,plain,
converse(composition(converse(X),one)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
composition(converse(one),X) = converse(composition(converse(X),one)),
inference(symmetry,[status(thm)],[c26]) ).
cnf(c28,axiom,
composition(A2,one) = A2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_identity_6) ).
cnf(c29,plain,
composition(converse(X),one) = converse(X),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
converse(composition(converse(X),one)) = converse(converse(X)),
inference(congruence,[status(thm)],[c29]) ).
cnf(c31,plain,
converse(converse(X)) = X,
inference(substitution,[status(thm)],[c22]) ).
cnf(c32,plain,
converse(composition(converse(X),one)) = X,
inference(transitivity,[status(thm)],[c30,c31]) ).
cnf(c33,plain,
composition(converse(one),X) = X,
inference(transitivity,[status(thm)],[c27,c32]) ).
cnf(c34,plain,
composition(converse(one),complement(X)) = complement(X),
inference(substitution,[status(thm)],[c33]) ).
cnf(c35,plain,
complement(X) = composition(converse(one),complement(X)),
inference(symmetry,[status(thm)],[c34]) ).
cnf(c36,plain,
join(complement(X),complement(X)) = join(complement(X),composition(converse(one),complement(X))),
inference(congruence,[status(thm)],[c35]) ).
cnf(c37,plain,
composition(converse(one),composition(one,X)) = composition(one,X),
inference(substitution,[status(thm)],[c33]) ).
cnf(c38,plain,
composition(one,X) = composition(converse(one),composition(one,X)),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,axiom,
composition(A2,composition(B2,C2)) = composition(composition(A2,B2),C2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_associativity_5) ).
cnf(c40,plain,
composition(X2,composition(one,X)) = composition(composition(X2,one),X),
inference(substitution,[status(thm)],[c39]) ).
cnf(c41,plain,
composition(X,one) = X,
inference(substitution,[status(thm)],[c28]) ).
cnf(c42,plain,
composition(composition(X2,one),X) = composition(X2,X),
inference(congruence,[status(thm)],[c41]) ).
cnf(c43,plain,
composition(X2,composition(one,X)) = composition(X2,X),
inference(transitivity,[status(thm)],[c40,c42]) ).
cnf(c44,plain,
composition(converse(one),composition(one,X)) = composition(converse(one),X),
inference(substitution,[status(thm)],[c43]) ).
cnf(c45,plain,
composition(converse(one),composition(one,X)) = X,
inference(transitivity,[status(thm)],[c44,c33]) ).
cnf(c46,plain,
composition(one,X) = X,
inference(transitivity,[status(thm)],[c38,c45]) ).
cnf(c47,plain,
X = composition(one,X),
inference(symmetry,[status(thm)],[c46]) ).
cnf(c48,plain,
complement(X) = complement(composition(one,X)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
composition(converse(one),complement(X)) = composition(converse(one),complement(composition(one,X))),
inference(congruence,[status(thm)],[c48]) ).
cnf(c50,plain,
join(complement(X),composition(converse(one),complement(X))) = join(complement(X),composition(converse(one),complement(composition(one,X)))),
inference(congruence,[status(thm)],[c49]) ).
cnf(c51,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = join(complement(X2),composition(converse(X),complement(composition(X,X2)))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c52,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = join(composition(converse(X),complement(composition(X,X2))),complement(X2)),
inference(symmetry,[status(thm)],[c51]) ).
cnf(c53,axiom,
join(composition(converse(A2),complement(composition(A2,B2))),complement(B2)) = complement(B2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',converse_cancellativity_11) ).
cnf(c54,plain,
join(composition(converse(X),complement(composition(X,X2))),complement(X2)) = complement(X2),
inference(substitution,[status(thm)],[c53]) ).
cnf(c55,plain,
join(complement(X2),composition(converse(X),complement(composition(X,X2)))) = complement(X2),
inference(transitivity,[status(thm)],[c52,c54]) ).
cnf(c56,plain,
join(complement(X),composition(converse(one),complement(composition(one,X)))) = complement(X),
inference(substitution,[status(thm)],[c55]) ).
cnf(c57,plain,
join(complement(X),composition(converse(one),complement(X))) = complement(X),
inference(transitivity,[status(thm)],[c50,c56]) ).
cnf(c58,plain,
join(complement(X),complement(X)) = complement(X),
inference(transitivity,[status(thm)],[c36,c57]) ).
cnf(c59,plain,
join(X,join(complement(X),complement(X))) = join(X,complement(X)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
top = join(X,complement(X)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c61,plain,
join(X,complement(X)) = top,
inference(symmetry,[status(thm)],[c60]) ).
cnf(c62,plain,
join(X,join(complement(X),complement(X))) = top,
inference(transitivity,[status(thm)],[c59,c61]) ).
cnf(c63,plain,
join(complement(X),top) = top,
inference(transitivity,[status(thm)],[c19,c62]) ).
cnf(c64,plain,
join(top,complement(X)) = top,
inference(transitivity,[status(thm)],[c4,c63]) ).
cnf(c65,plain,
top = join(top,complement(X)),
inference(symmetry,[status(thm)],[c64]) ).
cnf(c66,plain,
join(X,top) = join(X,join(top,complement(X))),
inference(congruence,[status(thm)],[c65]) ).
cnf(c67,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c17]) ).
cnf(c68,plain,
join(X,join(top,complement(X))) = join(top,top),
inference(substitution,[status(thm)],[c17]) ).
cnf(c69,plain,
join(top,top) = join(X,join(top,complement(X))),
inference(symmetry,[status(thm)],[c68]) ).
cnf(c70,plain,
join(X,join(top,complement(X))) = join(X,top),
inference(congruence,[status(thm)],[c64]) ).
cnf(c71,plain,
join(top,top) = join(X,top),
inference(transitivity,[status(thm)],[c69,c70]) ).
cnf(c72,plain,
join(X,join(top,complement(X))) = join(X2,top),
inference(transitivity,[status(thm)],[c67,c71]) ).
cnf(c73,plain,
join(X,top) = join(X2,top),
inference(transitivity,[status(thm)],[c66,c72]) ).
cnf(c74,plain,
join(X,top) = join(zero,top),
inference(substitution,[status(thm)],[c73]) ).
cnf(c75,plain,
join(top,zero) = join(zero,top),
inference(substitution,[status(thm)],[c2]) ).
cnf(c76,plain,
join(zero,top) = join(top,zero),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
top = join(complement(X),complement(complement(X))),
inference(substitution,[status(thm)],[c10]) ).
cnf(c78,plain,
complement(top) = complement(join(complement(X),complement(complement(X)))),
inference(congruence,[status(thm)],[c77]) ).
cnf(c79,axiom,
meet(A2,B2) = complement(join(complement(A2),complement(B2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c80,plain,
meet(X,complement(X)) = complement(join(complement(X),complement(complement(X)))),
inference(substitution,[status(thm)],[c79]) ).
cnf(c81,plain,
complement(join(complement(X),complement(complement(X)))) = meet(X,complement(X)),
inference(symmetry,[status(thm)],[c80]) ).
cnf(c82,axiom,
zero = meet(A2,complement(A2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',def_zero_13) ).
cnf(c83,plain,
zero = meet(X,complement(X)),
inference(substitution,[status(thm)],[c82]) ).
cnf(c84,plain,
meet(X,complement(X)) = zero,
inference(symmetry,[status(thm)],[c83]) ).
cnf(c85,plain,
complement(join(complement(X),complement(complement(X)))) = zero,
inference(transitivity,[status(thm)],[c81,c84]) ).
cnf(c86,plain,
complement(top) = zero,
inference(transitivity,[status(thm)],[c78,c85]) ).
cnf(c87,plain,
zero = complement(top),
inference(symmetry,[status(thm)],[c86]) ).
cnf(c88,plain,
join(top,zero) = join(top,complement(top)),
inference(congruence,[status(thm)],[c87]) ).
cnf(c89,plain,
top = join(top,complement(top)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c90,plain,
join(top,complement(top)) = top,
inference(symmetry,[status(thm)],[c89]) ).
cnf(c91,plain,
join(top,zero) = top,
inference(transitivity,[status(thm)],[c88,c90]) ).
cnf(c92,plain,
join(zero,top) = top,
inference(transitivity,[status(thm)],[c76,c91]) ).
cnf(c93,plain,
join(X,top) = top,
inference(transitivity,[status(thm)],[c74,c92]) ).
cnf(c94,plain,
join(sk1,top) = top,
inference(substitution,[status(thm)],[c93]) ).
cnf(c95,plain,
$false,
inference(resolution,[status(thm)],[c1,c94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL002-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sun Sep 27 22:52:56 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.47 Command-line arguments: --no-flatten-goal
% 0.13/0.47
% 0.13/0.47 % SZS status Unsatisfiable
% 0.13/0.47
% 0.13/0.47 % SZS output start CNFRefutation
% See solution above
% 0.13/0.51
% 0.13/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------