%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : LAT045-1 : TPTP v9.3.1. Released v2.5.0.
% 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 11:42:54 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.50s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of clauses : 33 ( 33 unt; 0 nHn; 12 RR)
% Number of literals : 33 ( 32 equ; 1 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 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 : 36 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c1,negated_conjecture,
join(a,meet(complement(a),join(a,b))) != join(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_orthomodular_law) ).
cnf(c2,axiom,
join(X,Y) = join(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_join) ).
cnf(c3,plain,
join(a,b) = join(b,a),
inference(substitution,[status(thm)],[c2]) ).
cnf(c4,plain,
meet(complement(a),join(a,b)) = meet(complement(a),join(b,a)),
inference(congruence,[status(thm)],[c3]) ).
cnf(c5,plain,
join(a,meet(complement(a),join(a,b))) = join(a,meet(complement(a),join(b,a))),
inference(congruence,[status(thm)],[c4]) ).
cnf(c6,plain,
join(X3,X2) = join(X2,X3),
inference(substitution,[status(thm)],[c2]) ).
cnf(c7,plain,
join(X2,X3) = join(X3,X2),
inference(symmetry,[status(thm)],[c6]) ).
cnf(c8,plain,
meet(X4,join(X2,X3)) = meet(X4,join(X3,X2)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
join(X4,meet(X3,join(X2,X4))) = join(X4,meet(X3,join(X4,X2))),
inference(congruence,[status(thm)],[c8]) ).
cnf(c10,axiom,
join(X2,meet(Y2,join(X2,Z))) = meet(join(X2,Y2),join(X2,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular_law) ).
cnf(c11,plain,
join(X4,meet(X3,join(X4,X2))) = meet(join(X4,X3),join(X4,X2)),
inference(substitution,[status(thm)],[c10]) ).
cnf(c12,plain,
join(X4,meet(X3,join(X2,X4))) = meet(join(X4,X3),join(X4,X2)),
inference(transitivity,[status(thm)],[c9,c11]) ).
cnf(c13,plain,
join(a,meet(complement(a),join(b,a))) = meet(join(a,complement(a)),join(a,b)),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
join(complement(X2),X2) = join(X2,complement(X2)),
inference(substitution,[status(thm)],[c2]) ).
cnf(c15,plain,
join(X2,complement(X2)) = join(complement(X2),X2),
inference(symmetry,[status(thm)],[c14]) ).
cnf(c16,axiom,
join(complement(X2),X2) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',step) ).
cnf(c17,plain,
join(X2,complement(X2)) = n1,
inference(transitivity,[status(thm)],[c15,c16]) ).
cnf(c18,plain,
join(a,complement(a)) = n1,
inference(substitution,[status(thm)],[c17]) ).
cnf(c19,plain,
meet(join(a,complement(a)),join(a,b)) = meet(n1,join(a,b)),
inference(congruence,[status(thm)],[c18]) ).
cnf(c20,axiom,
meet(X2,Y2) = meet(Y2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_meet) ).
cnf(c21,plain,
meet(X2,n1) = meet(n1,X2),
inference(substitution,[status(thm)],[c20]) ).
cnf(c22,plain,
meet(n1,X2) = meet(X2,n1),
inference(symmetry,[status(thm)],[c21]) ).
cnf(c23,plain,
n1 = join(X2,complement(X2)),
inference(symmetry,[status(thm)],[c17]) ).
cnf(c24,plain,
meet(X2,n1) = meet(X2,join(X2,complement(X2))),
inference(congruence,[status(thm)],[c23]) ).
cnf(c25,axiom,
meet(X2,join(X2,Y2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',absorption1) ).
cnf(c26,plain,
meet(X2,join(X2,complement(X2))) = X2,
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
meet(X2,n1) = X2,
inference(transitivity,[status(thm)],[c24,c26]) ).
cnf(c28,plain,
meet(n1,X2) = X2,
inference(transitivity,[status(thm)],[c22,c27]) ).
cnf(c29,plain,
meet(n1,join(a,b)) = join(a,b),
inference(substitution,[status(thm)],[c28]) ).
cnf(c30,plain,
meet(join(a,complement(a)),join(a,b)) = join(a,b),
inference(transitivity,[status(thm)],[c19,c29]) ).
cnf(c31,plain,
join(a,meet(complement(a),join(b,a))) = join(a,b),
inference(transitivity,[status(thm)],[c13,c30]) ).
cnf(c32,plain,
join(a,meet(complement(a),join(a,b))) = join(a,b),
inference(transitivity,[status(thm)],[c5,c31]) ).
cnf(c33,plain,
$false,
inference(resolution,[status(thm)],[c1,c32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT045-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 14:00:41 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_twee /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.50 Command-line arguments: --no-flatten-goal
% 0.12/0.50
% 0.12/0.50 % SZS status Unsatisfiable
% 0.12/0.50
% 0.12/0.50 % SZS output start CNFRefutation
% See solution above
% 0.63/0.51
% 0.63/0.51 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------