%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT044-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/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 11:42:54 AM UTC 2026
% Result : Unsatisfiable 2.75s 0.89s
% Output : CNFRefutation 3.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of clauses : 89 ( 89 unt; 0 nHn; 3 RR)
% Number of literals : 89 ( 88 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 : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 186 ( 14 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_weak_orthomodular_law) ).
cnf(c2,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c3,plain,
join(join(X2,X4),X3) = join(X3,join(X2,X4)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
join(X3,join(X2,X4)) = join(join(X2,X4),X3),
inference(symmetry,[status(thm)],[c3]) ).
cnf(c5,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c6,plain,
join(join(X2,X4),X3) = join(join(X4,X2),X3),
inference(congruence,[status(thm)],[c5]) ).
cnf(c7,axiom,
join(join(X2,Y2),Z) = join(X2,join(Y2,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_join) ).
cnf(c8,plain,
join(join(X4,X2),X3) = join(X4,join(X2,X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c9,plain,
join(X2,X3) = join(X3,X2),
inference(substitution,[status(thm)],[c2]) ).
cnf(c10,plain,
join(X4,join(X2,X3)) = join(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c9]) ).
cnf(c11,plain,
join(join(X4,X2),X3) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c8,c10]) ).
cnf(c12,plain,
join(join(X2,X4),X3) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c6,c11]) ).
cnf(c13,plain,
join(X3,join(X2,X4)) = join(X4,join(X3,X2)),
inference(transitivity,[status(thm)],[c4,c12]) ).
cnf(c14,plain,
join(meet(complement(X3),join(X3,X2)),join(complement(X2),meet(X3,X2))) = join(meet(X3,X2),join(meet(complement(X3),join(X3,X2)),complement(X2))),
inference(substitution,[status(thm)],[c13]) ).
cnf(c15,plain,
join(complement(join(X2,X4)),X3) = join(X3,complement(join(X2,X4))),
inference(substitution,[status(thm)],[c2]) ).
cnf(c16,plain,
join(X3,complement(join(X2,X4))) = join(complement(join(X2,X4)),X3),
inference(symmetry,[status(thm)],[c15]) ).
cnf(c17,plain,
join(complement(X4),join(X3,complement(join(X2,X4)))) = join(complement(X4),join(complement(join(X2,X4)),X3)),
inference(congruence,[status(thm)],[c16]) ).
cnf(c18,plain,
join(join(complement(X4),complement(join(X2,X4))),X3) = join(complement(X4),join(complement(join(X2,X4)),X3)),
inference(substitution,[status(thm)],[c7]) ).
cnf(c19,plain,
join(complement(X4),join(complement(join(X2,X4)),X3)) = join(join(complement(X4),complement(join(X2,X4))),X3),
inference(symmetry,[status(thm)],[c18]) ).
cnf(c20,axiom,
complement(join(X2,Y2)) = meet(complement(X2),complement(Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility1) ).
cnf(c21,plain,
complement(join(X2,X3)) = meet(complement(X2),complement(X3)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
join(complement(X3),complement(join(X2,X3))) = join(complement(X3),meet(complement(X2),complement(X3))),
inference(congruence,[status(thm)],[c21]) ).
cnf(c23,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c24,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c23]) ).
cnf(c25,plain,
meet(X2,X3) = meet(X3,X2),
inference(symmetry,[status(thm)],[c24]) ).
cnf(c26,plain,
join(X3,meet(X2,X3)) = join(X3,meet(X3,X2)),
inference(congruence,[status(thm)],[c25]) ).
cnf(c27,axiom,
join(X2,meet(X2,Y2)) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',absorption2) ).
cnf(c28,plain,
join(X3,meet(X3,X2)) = X3,
inference(substitution,[status(thm)],[c27]) ).
cnf(c29,plain,
join(X3,meet(X2,X3)) = X3,
inference(transitivity,[status(thm)],[c26,c28]) ).
cnf(c30,plain,
join(complement(X3),meet(complement(X2),complement(X3))) = complement(X3),
inference(substitution,[status(thm)],[c29]) ).
cnf(c31,plain,
join(complement(X3),complement(join(X2,X3))) = complement(X3),
inference(transitivity,[status(thm)],[c22,c30]) ).
cnf(c32,plain,
join(join(complement(X4),complement(join(X2,X4))),X3) = join(complement(X4),X3),
inference(congruence,[status(thm)],[c31]) ).
cnf(c33,plain,
join(complement(X3),X2) = join(X2,complement(X3)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c34,plain,
join(join(complement(X4),complement(join(X2,X4))),X3) = join(X3,complement(X4)),
inference(transitivity,[status(thm)],[c32,c33]) ).
cnf(c35,plain,
join(complement(X4),join(complement(join(X2,X4)),X3)) = join(X3,complement(X4)),
inference(transitivity,[status(thm)],[c19,c34]) ).
cnf(c36,plain,
join(complement(X4),join(X3,complement(join(X2,X4)))) = join(X3,complement(X4)),
inference(transitivity,[status(thm)],[c17,c35]) ).
cnf(c37,plain,
join(complement(X2),join(meet(complement(X3),join(X3,X2)),complement(join(X3,X2)))) = join(meet(complement(X3),join(X3,X2)),complement(X2)),
inference(substitution,[status(thm)],[c36]) ).
cnf(c38,plain,
join(meet(complement(X3),join(X3,X2)),complement(X2)) = join(complement(X2),join(meet(complement(X3),join(X3,X2)),complement(join(X3,X2)))),
inference(symmetry,[status(thm)],[c37]) ).
cnf(c39,plain,
meet(complement(meet(complement(X3),join(X3,X2))),complement(X3)) = meet(complement(X3),complement(meet(complement(X3),join(X3,X2)))),
inference(substitution,[status(thm)],[c23]) ).
cnf(c40,plain,
meet(complement(X3),complement(meet(complement(X3),join(X3,X2)))) = meet(complement(meet(complement(X3),join(X3,X2))),complement(X3)),
inference(symmetry,[status(thm)],[c39]) ).
cnf(c41,plain,
complement(join(meet(complement(X3),join(X3,X2)),X3)) = meet(complement(meet(complement(X3),join(X3,X2))),complement(X3)),
inference(substitution,[status(thm)],[c20]) ).
cnf(c42,plain,
meet(complement(meet(complement(X3),join(X3,X2))),complement(X3)) = complement(join(meet(complement(X3),join(X3,X2)),X3)),
inference(symmetry,[status(thm)],[c41]) ).
cnf(c43,plain,
join(X3,meet(complement(X3),join(X3,X2))) = join(meet(complement(X3),join(X3,X2)),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c44,plain,
join(meet(complement(X3),join(X3,X2)),X3) = join(X3,meet(complement(X3),join(X3,X2))),
inference(symmetry,[status(thm)],[c43]) ).
cnf(c45,axiom,
join(X2,meet(complement(X2),join(X2,Y2))) = join(X2,Y2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',orthomodular_law) ).
cnf(c46,plain,
join(X3,meet(complement(X3),join(X3,X2))) = join(X3,X2),
inference(substitution,[status(thm)],[c45]) ).
cnf(c47,plain,
join(meet(complement(X3),join(X3,X2)),X3) = join(X3,X2),
inference(transitivity,[status(thm)],[c44,c46]) ).
cnf(c48,plain,
complement(join(meet(complement(X3),join(X3,X2)),X3)) = complement(join(X3,X2)),
inference(congruence,[status(thm)],[c47]) ).
cnf(c49,plain,
meet(complement(meet(complement(X3),join(X3,X2))),complement(X3)) = complement(join(X3,X2)),
inference(transitivity,[status(thm)],[c42,c48]) ).
cnf(c50,plain,
meet(complement(X3),complement(meet(complement(X3),join(X3,X2)))) = complement(join(X3,X2)),
inference(transitivity,[status(thm)],[c40,c49]) ).
cnf(c51,plain,
complement(join(X3,X2)) = meet(complement(X3),complement(meet(complement(X3),join(X3,X2)))),
inference(symmetry,[status(thm)],[c50]) ).
cnf(c52,plain,
join(meet(complement(X3),join(X3,X2)),complement(join(X3,X2))) = join(meet(complement(X3),join(X3,X2)),meet(complement(X3),complement(meet(complement(X3),join(X3,X2))))),
inference(congruence,[status(thm)],[c51]) ).
cnf(c53,plain,
meet(complement(meet(complement(X3),join(X3,X2))),complement(X3)) = meet(complement(X3),complement(meet(complement(X3),join(X3,X2)))),
inference(substitution,[status(thm)],[c23]) ).
cnf(c54,plain,
meet(complement(X3),complement(meet(complement(X3),join(X3,X2)))) = meet(complement(meet(complement(X3),join(X3,X2))),complement(X3)),
inference(symmetry,[status(thm)],[c53]) ).
cnf(c55,plain,
join(meet(complement(X3),join(X3,X2)),meet(complement(X3),complement(meet(complement(X3),join(X3,X2))))) = join(meet(complement(X3),join(X3,X2)),meet(complement(meet(complement(X3),join(X3,X2))),complement(X3))),
inference(congruence,[status(thm)],[c54]) ).
cnf(c56,plain,
join(X3,meet(X3,X2)) = join(meet(X3,X2),X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c57,plain,
join(meet(X3,X2),X3) = join(X3,meet(X3,X2)),
inference(symmetry,[status(thm)],[c56]) ).
cnf(c58,plain,
meet(X3,X2) = meet(X2,X3),
inference(substitution,[status(thm)],[c23]) ).
cnf(c59,plain,
join(X3,meet(X3,X2)) = join(X3,meet(X2,X3)),
inference(congruence,[status(thm)],[c58]) ).
cnf(c60,plain,
join(X3,meet(X3,X2)) = X3,
inference(transitivity,[status(thm)],[c59,c29]) ).
cnf(c61,plain,
join(meet(X3,X2),X3) = X3,
inference(transitivity,[status(thm)],[c57,c60]) ).
cnf(c62,plain,
join(meet(complement(X3),join(X3,X2)),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c63,plain,
complement(X3) = join(meet(complement(X3),join(X3,X2)),complement(X3)),
inference(symmetry,[status(thm)],[c62]) ).
cnf(c64,plain,
meet(complement(meet(complement(X3),join(X3,X2))),complement(X3)) = meet(complement(meet(complement(X3),join(X3,X2))),join(meet(complement(X3),join(X3,X2)),complement(X3))),
inference(congruence,[status(thm)],[c63]) ).
cnf(c65,plain,
join(meet(complement(X3),join(X3,X2)),meet(complement(meet(complement(X3),join(X3,X2))),complement(X3))) = join(meet(complement(X3),join(X3,X2)),meet(complement(meet(complement(X3),join(X3,X2))),join(meet(complement(X3),join(X3,X2)),complement(X3)))),
inference(congruence,[status(thm)],[c64]) ).
cnf(c66,plain,
join(meet(complement(X3),join(X3,X2)),meet(complement(meet(complement(X3),join(X3,X2))),join(meet(complement(X3),join(X3,X2)),complement(X3)))) = join(meet(complement(X3),join(X3,X2)),complement(X3)),
inference(substitution,[status(thm)],[c45]) ).
cnf(c67,plain,
join(meet(complement(X3),join(X3,X2)),complement(X3)) = complement(X3),
inference(substitution,[status(thm)],[c61]) ).
cnf(c68,plain,
join(meet(complement(X3),join(X3,X2)),meet(complement(meet(complement(X3),join(X3,X2))),join(meet(complement(X3),join(X3,X2)),complement(X3)))) = complement(X3),
inference(transitivity,[status(thm)],[c66,c67]) ).
cnf(c69,plain,
join(meet(complement(X3),join(X3,X2)),meet(complement(meet(complement(X3),join(X3,X2))),complement(X3))) = complement(X3),
inference(transitivity,[status(thm)],[c65,c68]) ).
cnf(c70,plain,
join(meet(complement(X3),join(X3,X2)),meet(complement(X3),complement(meet(complement(X3),join(X3,X2))))) = complement(X3),
inference(transitivity,[status(thm)],[c55,c69]) ).
cnf(c71,plain,
join(meet(complement(X3),join(X3,X2)),complement(join(X3,X2))) = complement(X3),
inference(transitivity,[status(thm)],[c52,c70]) ).
cnf(c72,plain,
join(complement(X2),join(meet(complement(X3),join(X3,X2)),complement(join(X3,X2)))) = join(complement(X2),complement(X3)),
inference(congruence,[status(thm)],[c71]) ).
cnf(c73,plain,
join(complement(X2),complement(X3)) = join(complement(X3),complement(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c74,axiom,
complement(meet(X2,Y2)) = join(complement(X2),complement(Y2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',compatibility2) ).
cnf(c75,plain,
complement(meet(X3,X2)) = join(complement(X3),complement(X2)),
inference(substitution,[status(thm)],[c74]) ).
cnf(c76,plain,
join(complement(X3),complement(X2)) = complement(meet(X3,X2)),
inference(symmetry,[status(thm)],[c75]) ).
cnf(c77,plain,
join(complement(X2),complement(X3)) = complement(meet(X3,X2)),
inference(transitivity,[status(thm)],[c73,c76]) ).
cnf(c78,plain,
join(complement(X2),join(meet(complement(X3),join(X3,X2)),complement(join(X3,X2)))) = complement(meet(X3,X2)),
inference(transitivity,[status(thm)],[c72,c77]) ).
cnf(c79,plain,
join(meet(complement(X3),join(X3,X2)),complement(X2)) = complement(meet(X3,X2)),
inference(transitivity,[status(thm)],[c38,c78]) ).
cnf(c80,plain,
join(meet(X3,X2),join(meet(complement(X3),join(X3,X2)),complement(X2))) = join(meet(X3,X2),complement(meet(X3,X2))),
inference(congruence,[status(thm)],[c79]) ).
cnf(c81,plain,
join(complement(X2),X2) = join(X2,complement(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c82,plain,
join(X2,complement(X2)) = join(complement(X2),X2),
inference(symmetry,[status(thm)],[c81]) ).
cnf(c83,axiom,
join(complement(X2),X2) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',step) ).
cnf(c84,plain,
join(X2,complement(X2)) = n1,
inference(transitivity,[status(thm)],[c82,c83]) ).
cnf(c85,plain,
join(meet(X3,X2),complement(meet(X3,X2))) = n1,
inference(substitution,[status(thm)],[c84]) ).
cnf(c86,plain,
join(meet(X3,X2),join(meet(complement(X3),join(X3,X2)),complement(X2))) = n1,
inference(transitivity,[status(thm)],[c80,c85]) ).
cnf(c87,plain,
join(meet(complement(X3),join(X3,X2)),join(complement(X2),meet(X3,X2))) = n1,
inference(transitivity,[status(thm)],[c14,c86]) ).
cnf(c88,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) = n1,
inference(substitution,[status(thm)],[c87]) ).
cnf(c89,plain,
$false,
inference(resolution,[status(thm)],[c1,c88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT044-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sun Sep 27 14:00:41 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.75/0.89 Command-line arguments: --flatten --complete-subsets
% 2.75/0.89
% 2.75/0.89 % SZS status Unsatisfiable
% 2.75/0.89
% 2.75/0.90 % SZS output start CNFRefutation
% See solution above
% 3.49/0.92
% 3.49/0.92 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------