%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LAT045-1 : TPTP v8.1.0. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 05:59:07 EDT 2022
% Result : Unsatisfiable 0.19s 0.49s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of clauses : 38 ( 23 unt; 0 nHn; 20 RR)
% Number of literals : 60 ( 59 equ; 24 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 1 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absorption1,axiom,
meet(X,join(X,Y)) = X ).
cnf(commutativity_of_meet,axiom,
meet(X,Y) = meet(Y,X) ).
cnf(commutativity_of_join,axiom,
join(X,Y) = join(Y,X) ).
cnf(invertability1,axiom,
join(complement(X),X) = n1 ).
cnf(modular_law,axiom,
join(X,meet(Y,join(X,Z))) = meet(join(X,Y),join(X,Z)) ).
cnf(prove_orthomodular_law,negated_conjecture,
join(a,meet(complement(a),join(a,b))) != join(a,b) ).
cnf(refute_0_0,plain,
join(X_51,meet(complement(X_51),join(X_51,X_53))) = meet(join(X_51,complement(X_51)),join(X_51,X_53)),
inference(subst,[],[modular_law:[bind(X,$fot(X_51)),bind(Y,$fot(complement(X_51))),bind(Z,$fot(X_53))]]) ).
cnf(refute_0_1,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_2,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_3,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( join(X,Y) != join(Y,X)
| join(Y,X) = join(X,Y) ),
inference(subst,[],[refute_0_3:[bind(X0,$fot(join(X,Y))),bind(Y0,$fot(join(Y,X)))]]) ).
cnf(refute_0_5,plain,
join(Y,X) = join(X,Y),
inference(resolve,[$cnf( $equal(join(X,Y),join(Y,X)) )],[commutativity_of_join,refute_0_4]) ).
cnf(refute_0_6,plain,
join(complement(X),X) = join(X,complement(X)),
inference(subst,[],[refute_0_5:[bind(Y,$fot(complement(X)))]]) ).
cnf(refute_0_7,plain,
( join(complement(X),X) != join(X,complement(X))
| join(complement(X),X) != n1
| join(X,complement(X)) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X),X),n1) ),[0],$fot(join(X,complement(X)))]]) ).
cnf(refute_0_8,plain,
( join(complement(X),X) != n1
| join(X,complement(X)) = n1 ),
inference(resolve,[$cnf( $equal(join(complement(X),X),join(X,complement(X))) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
join(X,complement(X)) = n1,
inference(resolve,[$cnf( $equal(join(complement(X),X),n1) )],[invertability1,refute_0_8]) ).
cnf(refute_0_10,plain,
join(X_51,complement(X_51)) = n1,
inference(subst,[],[refute_0_9:[bind(X,$fot(X_51))]]) ).
cnf(refute_0_11,plain,
( join(X_51,complement(X_51)) != n1
| join(X_51,meet(complement(X_51),join(X_51,X_53))) != meet(join(X_51,complement(X_51)),join(X_51,X_53))
| join(X_51,meet(complement(X_51),join(X_51,X_53))) = meet(n1,join(X_51,X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(join(X_51,meet(complement(X_51),join(X_51,X_53))),meet(join(X_51,complement(X_51)),join(X_51,X_53))) ),[1,0],$fot(n1)]]) ).
cnf(refute_0_12,plain,
( join(X_51,meet(complement(X_51),join(X_51,X_53))) != meet(join(X_51,complement(X_51)),join(X_51,X_53))
| join(X_51,meet(complement(X_51),join(X_51,X_53))) = meet(n1,join(X_51,X_53)) ),
inference(resolve,[$cnf( $equal(join(X_51,complement(X_51)),n1) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
join(X_51,meet(complement(X_51),join(X_51,X_53))) = meet(n1,join(X_51,X_53)),
inference(resolve,[$cnf( $equal(join(X_51,meet(complement(X_51),join(X_51,X_53))),meet(join(X_51,complement(X_51)),join(X_51,X_53))) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
meet(X,join(X,complement(X))) = X,
inference(subst,[],[absorption1:[bind(Y,$fot(complement(X)))]]) ).
cnf(refute_0_15,plain,
( join(X,complement(X)) != n1
| meet(X,join(X,complement(X))) != X
| meet(X,n1) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,join(X,complement(X))),X) ),[0,1],$fot(n1)]]) ).
cnf(refute_0_16,plain,
( meet(X,join(X,complement(X))) != X
| meet(X,n1) = X ),
inference(resolve,[$cnf( $equal(join(X,complement(X)),n1) )],[refute_0_9,refute_0_15]) ).
cnf(refute_0_17,plain,
meet(X,n1) = X,
inference(resolve,[$cnf( $equal(meet(X,join(X,complement(X))),X) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
meet(X,n1) = meet(n1,X),
inference(subst,[],[commutativity_of_meet:[bind(Y,$fot(n1))]]) ).
cnf(refute_0_19,plain,
( meet(X,n1) != X
| meet(X,n1) != meet(n1,X)
| meet(n1,X) = X ),
introduced(tautology,[equality,[$cnf( $equal(meet(X,n1),X) ),[0],$fot(meet(n1,X))]]) ).
cnf(refute_0_20,plain,
( meet(X,n1) != X
| meet(n1,X) = X ),
inference(resolve,[$cnf( $equal(meet(X,n1),meet(n1,X)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
meet(n1,X) = X,
inference(resolve,[$cnf( $equal(meet(X,n1),X) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
meet(n1,join(X_51,X_53)) = join(X_51,X_53),
inference(subst,[],[refute_0_21:[bind(X,$fot(join(X_51,X_53)))]]) ).
cnf(refute_0_23,plain,
( join(X_51,meet(complement(X_51),join(X_51,X_53))) != meet(n1,join(X_51,X_53))
| meet(n1,join(X_51,X_53)) != join(X_51,X_53)
| join(X_51,meet(complement(X_51),join(X_51,X_53))) = join(X_51,X_53) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_51,meet(complement(X_51),join(X_51,X_53))),join(X_51,X_53)) ),[0],$fot(meet(n1,join(X_51,X_53)))]]) ).
cnf(refute_0_24,plain,
( join(X_51,meet(complement(X_51),join(X_51,X_53))) != meet(n1,join(X_51,X_53))
| join(X_51,meet(complement(X_51),join(X_51,X_53))) = join(X_51,X_53) ),
inference(resolve,[$cnf( $equal(meet(n1,join(X_51,X_53)),join(X_51,X_53)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
join(X_51,meet(complement(X_51),join(X_51,X_53))) = join(X_51,X_53),
inference(resolve,[$cnf( $equal(join(X_51,meet(complement(X_51),join(X_51,X_53))),meet(n1,join(X_51,X_53))) )],[refute_0_13,refute_0_24]) ).
cnf(refute_0_26,plain,
join(a,meet(complement(a),join(a,b))) = join(a,b),
inference(subst,[],[refute_0_25:[bind(X_51,$fot(a)),bind(X_53,$fot(b))]]) ).
cnf(refute_0_27,plain,
( join(a,b) != join(a,b)
| join(a,meet(complement(a),join(a,b))) != join(a,b)
| join(a,meet(complement(a),join(a,b))) = join(a,b) ),
introduced(tautology,[equality,[$cnf( $equal(join(a,meet(complement(a),join(a,b))),join(a,b)) ),[0,1,1],$fot(join(a,b))]]) ).
cnf(refute_0_28,plain,
( join(a,b) != join(a,b)
| join(a,meet(complement(a),join(a,b))) = join(a,b) ),
inference(resolve,[$cnf( $equal(join(a,meet(complement(a),join(a,b))),join(a,b)) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
join(a,b) != join(a,b),
inference(resolve,[$cnf( $equal(join(a,meet(complement(a),join(a,b))),join(a,b)) )],[refute_0_28,prove_orthomodular_law]) ).
cnf(refute_0_30,plain,
join(a,b) = join(a,b),
introduced(tautology,[refl,[$fot(join(a,b))]]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( $equal(join(a,b),join(a,b)) )],[refute_0_30,refute_0_29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT045-1 : TPTP v8.1.0. Released v2.5.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Wed Jun 29 21:08:02 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.49
% 0.19/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.50
%------------------------------------------------------------------------------