%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT045-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Sun Sep 27 07:49:36 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 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 : 37 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(absorption1,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption1) ).
cnf(c_3,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption1]) ).
fof(commutativity_of_meet,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = meet(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_meet) ).
cnf(c_5,plain,
meet(A,B) = meet(B,A),
inference(clausify,[status(thm)],[commutativity_of_meet]) ).
fof(commutativity_of_join,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',commutativity_of_join) ).
cnf(c_6,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(invertability1,axiom,
! [VAR_0] : join(complement(VAR_0),VAR_0) = n1,
file('theBenchmark.p',invertability1) ).
cnf(c_11,plain,
join(complement(A),A) = n1,
inference(clausify,[status(thm)],[invertability1]) ).
cnf(c_12,plain,
join(A,complement(A)) = n1,
inference(paramod,[status(thm)],[c_6,c_11]) ).
fof(modular_law,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,meet(VAR_1,join(VAR_0,VAR_2))) = meet(join(VAR_0,VAR_1),join(VAR_0,VAR_2)),
file('theBenchmark.p',modular_law) ).
cnf(c_16,plain,
join(A,meet(B,join(A,C))) = meet(join(A,B),join(A,C)),
inference(clausify,[status(thm)],[modular_law]) ).
cnf(c_17,plain,
meet(join(A,B),join(A,C)) = join(A,meet(B,join(A,C))),
inference(copy,[status(thm)],[c_16]) ).
fof(prove_orthomodular_law,axiom,
join(a,meet(complement(a),join(a,b))) != join(a,b),
file('theBenchmark.p',prove_orthomodular_law) ).
cnf(c_18,plain,
join(a,meet(complement(a),join(a,b))) != join(a,b),
inference(clausify,[status(thm)],[prove_orthomodular_law]) ).
cnf(c_37,plain,
meet(A,n1) = A,
inference(paramod,[status(thm)],[c_12,c_3]) ).
cnf(c_58,plain,
meet(n1,join(A,B)) = join(A,meet(complement(A),join(A,B))),
inference(paramod,[status(thm)],[c_12,c_17]) ).
cnf(c_55,plain,
join(A,meet(complement(A),join(A,B))) = meet(n1,join(A,B)),
inference(copy,[status(thm)],[c_58]) ).
cnf(c_59,plain,
meet(join(A,B),n1) = join(A,meet(B,join(A,complement(A)))),
inference(paramod,[status(thm)],[c_12,c_17]) ).
cnf(c_60,plain,
meet(n1,join(A,B)) = join(A,meet(B,join(A,complement(A)))),
inference(paramod,[status(thm)],[c_5,c_59]) ).
cnf(c_61,plain,
meet(n1,join(A,B)) = join(A,meet(B,n1)),
inference(paramod,[status(thm)],[c_12,c_60]) ).
cnf(c_56,plain,
meet(n1,join(A,B)) = join(A,B),
inference(paramod,[status(thm)],[c_37,c_61]) ).
cnf(c_62,plain,
meet(n1,join(a,b)) != join(a,b),
inference(paramod,[status(thm)],[c_55,c_18]) ).
cnf(c_63,plain,
join(a,b) != join(a,b),
inference(paramod,[status(thm)],[c_56,c_62]) ).
cnf(c_57,plain,
$false,
inference(copy,[status(thm)],[c_63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT045-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 20:04:56 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 4097970 was started by sandbox2 on n001,
% 0.10/0.37 % Fri Sep 25 20:04:56 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 0.10/0.40
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.10/0.40 % Length of proof is 12.
% 0.10/0.40 % Level of proof is 4.
% 0.10/0.40 % Maximum clause weight is 35.000.
% 0.10/0.40 % Given clauses 14.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------