%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT044-1 : 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 : n006.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 10.01s 1.75s
% Output : CNFRefutation 10.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 129 ( 8 sgn 22 !; 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(absorption2,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption2) ).
cnf(c_4,plain,
join(A,meet(A,B)) = A,
inference(clausify,[status(thm)],[absorption2]) ).
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(associativity_of_meet,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(VAR_0,VAR_1),VAR_2) = meet(VAR_0,meet(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_meet) ).
cnf(c_7,plain,
meet(meet(A,B),C) = meet(A,meet(B,C)),
inference(clausify,[status(thm)],[associativity_of_meet]) ).
fof(associativity_of_join,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(VAR_0,VAR_1),VAR_2) = join(VAR_0,join(VAR_1,VAR_2)),
file('theBenchmark.p',associativity_of_join) ).
cnf(c_8,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[associativity_of_join]) ).
fof(compatibility1,axiom,
! [VAR_0,VAR_1] : complement(join(VAR_0,VAR_1)) = meet(complement(VAR_0),complement(VAR_1)),
file('theBenchmark.p',compatibility1) ).
cnf(c_9,plain,
complement(join(A,B)) = meet(complement(A),complement(B)),
inference(clausify,[status(thm)],[compatibility1]) ).
fof(compatibility2,axiom,
! [VAR_0,VAR_1] : complement(meet(VAR_0,VAR_1)) = join(complement(VAR_0),complement(VAR_1)),
file('theBenchmark.p',compatibility2) ).
cnf(c_10,plain,
complement(meet(A,B)) = join(complement(A),complement(B)),
inference(clausify,[status(thm)],[compatibility2]) ).
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(invertability3,axiom,
! [VAR_0] : complement(complement(VAR_0)) = VAR_0,
file('theBenchmark.p',invertability3) ).
cnf(c_15,plain,
complement(complement(A)) = A,
inference(clausify,[status(thm)],[invertability3]) ).
fof(orthomodular_law,axiom,
! [VAR_0,VAR_1] : join(VAR_0,meet(complement(VAR_0),join(VAR_0,VAR_1))) = join(VAR_0,VAR_1),
file('theBenchmark.p',orthomodular_law) ).
cnf(c_16,plain,
join(A,meet(complement(A),join(A,B))) = join(A,B),
inference(clausify,[status(thm)],[orthomodular_law]) ).
fof(prove_weak_orthomodular_law,axiom,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1,
file('theBenchmark.p',prove_weak_orthomodular_law) ).
cnf(c_17,plain,
join(meet(complement(a),join(a,b)),join(complement(b),meet(a,b))) != n1,
inference(clausify,[status(thm)],[prove_weak_orthomodular_law]) ).
cnf(c_2392,plain,
join(join(complement(b),meet(a,b)),meet(complement(a),join(a,b))) != n1,
inference(paramod,[status(thm)],[c_6,c_17]) ).
cnf(c_18,plain,
join(complement(b),join(meet(a,b),meet(complement(a),join(a,b)))) != n1,
inference(paramod,[status(thm)],[c_8,c_2392]) ).
cnf(c_19,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_20,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_2393,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_36,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_8,c_2393]) ).
cnf(c_2394,plain,
join(meet(A,B),join(complement(A),complement(B))) = n1,
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_2395,plain,
join(join(complement(A),complement(B)),meet(A,B)) = n1,
inference(paramod,[status(thm)],[c_6,c_2394]) ).
cnf(c_43,plain,
join(complement(A),join(complement(B),meet(A,B))) = n1,
inference(paramod,[status(thm)],[c_8,c_2395]) ).
cnf(c_49,plain,
join(A,meet(complement(A),join(B,A))) = join(A,B),
inference(paramod,[status(thm)],[c_6,c_16]) ).
cnf(c_2396,plain,
join(A,B) = join(A,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_19,c_8]) ).
cnf(c_56,plain,
join(A,join(meet(B,A),C)) = join(A,C),
inference(copy,[status(thm)],[c_2396]) ).
cnf(c_2397,plain,
meet(A,B) = meet(A,meet(join(C,A),B)),
inference(paramod,[status(thm)],[c_20,c_7]) ).
cnf(c_68,plain,
meet(A,meet(join(B,A),C)) = meet(A,C),
inference(copy,[status(thm)],[c_2397]) ).
cnf(c_2398,plain,
join(meet(A,B),meet(complement(meet(A,B)),A)) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_4,c_49]) ).
cnf(c_2399,plain,
join(meet(A,B),meet(join(complement(A),complement(B)),A)) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_10,c_2398]) ).
cnf(c_2400,plain,
join(meet(A,B),meet(A,join(complement(A),complement(B)))) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_5,c_2399]) ).
cnf(c_2401,plain,
join(meet(A,B),meet(A,join(complement(A),complement(B)))) = join(A,meet(A,B)),
inference(paramod,[status(thm)],[c_6,c_2400]) ).
cnf(c_94,plain,
join(meet(A,B),meet(A,join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_4,c_2401]) ).
cnf(c_2402,plain,
complement(A) = meet(complement(meet(A,B)),complement(meet(A,join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_94,c_9]) ).
cnf(c_2403,plain,
complement(A) = meet(join(complement(A),complement(B)),complement(meet(A,join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_10,c_2402]) ).
cnf(c_2404,plain,
complement(A) = meet(join(complement(A),complement(B)),join(complement(A),complement(join(complement(A),complement(B))))),
inference(paramod,[status(thm)],[c_10,c_2403]) ).
cnf(c_2405,plain,
complement(A) = meet(join(complement(A),complement(B)),join(complement(A),meet(complement(complement(A)),complement(complement(B))))),
inference(paramod,[status(thm)],[c_9,c_2404]) ).
cnf(c_2406,plain,
complement(A) = meet(join(complement(A),complement(B)),join(complement(A),meet(A,complement(complement(B))))),
inference(paramod,[status(thm)],[c_15,c_2405]) ).
cnf(c_2407,plain,
complement(A) = meet(join(complement(A),complement(B)),join(complement(A),meet(A,B))),
inference(paramod,[status(thm)],[c_15,c_2406]) ).
cnf(c_1921,plain,
meet(join(complement(A),complement(B)),join(complement(A),meet(A,B))) = complement(A),
inference(copy,[status(thm)],[c_2407]) ).
cnf(c_2408,plain,
join(A,B) = join(A,meet(B,join(complement(B),complement(A)))),
inference(paramod,[status(thm)],[c_94,c_56]) ).
cnf(c_1934,plain,
join(A,meet(B,join(complement(B),complement(A)))) = join(A,B),
inference(copy,[status(thm)],[c_2408]) ).
cnf(c_2409,plain,
meet(complement(A),complement(B)) = meet(complement(A),join(complement(B),meet(B,A))),
inference(paramod,[status(thm)],[c_1921,c_68]) ).
cnf(c_1961,plain,
meet(complement(A),join(complement(B),meet(B,A))) = meet(complement(A),complement(B)),
inference(copy,[status(thm)],[c_2409]) ).
cnf(c_2410,plain,
join(meet(complement(A),complement(B)),meet(complement(A),join(complement(complement(A)),complement(join(complement(B),meet(B,A)))))) = complement(A),
inference(paramod,[status(thm)],[c_1961,c_94]) ).
cnf(c_2411,plain,
join(meet(complement(A),complement(B)),meet(complement(A),join(A,complement(join(complement(B),meet(B,A)))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_2410]) ).
cnf(c_2412,plain,
join(meet(complement(A),complement(B)),meet(complement(A),join(A,meet(complement(complement(B)),complement(meet(B,A)))))) = complement(A),
inference(paramod,[status(thm)],[c_9,c_2411]) ).
cnf(c_2413,plain,
join(meet(complement(A),complement(B)),meet(complement(A),join(A,meet(B,complement(meet(B,A)))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_2412]) ).
cnf(c_2414,plain,
join(meet(complement(A),complement(B)),meet(complement(A),join(A,meet(B,join(complement(B),complement(A)))))) = complement(A),
inference(paramod,[status(thm)],[c_10,c_2413]) ).
cnf(c_2175,plain,
join(meet(complement(A),complement(B)),meet(complement(A),join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_1934,c_2414]) ).
cnf(c_2415,plain,
join(complement(A),complement(B)) = join(complement(A),meet(complement(B),join(B,A))),
inference(paramod,[status(thm)],[c_2175,c_56]) ).
cnf(c_2245,plain,
join(complement(A),meet(complement(B),join(B,A))) = join(complement(A),complement(B)),
inference(copy,[status(thm)],[c_2415]) ).
cnf(c_2416,plain,
join(A,join(complement(B),complement(C))) = join(complement(B),join(A,meet(complement(C),join(C,B)))),
inference(paramod,[status(thm)],[c_2245,c_36]) ).
cnf(c_2373,plain,
join(complement(A),join(B,meet(complement(C),join(C,A)))) = join(B,join(complement(A),complement(C))),
inference(copy,[status(thm)],[c_2416]) ).
cnf(c_2417,plain,
join(meet(a,b),join(complement(b),complement(a))) != n1,
inference(paramod,[status(thm)],[c_2373,c_18]) ).
cnf(c_2418,plain,
join(meet(a,b),join(complement(a),complement(b))) != n1,
inference(paramod,[status(thm)],[c_6,c_2417]) ).
cnf(c_2419,plain,
join(join(complement(a),complement(b)),meet(a,b)) != n1,
inference(paramod,[status(thm)],[c_6,c_2418]) ).
cnf(c_2420,plain,
join(complement(a),join(complement(b),meet(a,b))) != n1,
inference(paramod,[status(thm)],[c_8,c_2419]) ).
cnf(c_2421,plain,
n1 != n1,
inference(paramod,[status(thm)],[c_43,c_2420]) ).
cnf(c_2391,plain,
$false,
inference(copy,[status(thm)],[c_2421]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT044-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n006.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:58:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.35 % Process 3598642 was started by sandbox2 on n006,
% 0.13/0.35 % Fri Sep 25 19:58:55 2026
% 0.13/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 10.01/1.75
% 10.01/1.75 % Assigning unary symbol complement kb_weight 0 and highest precedence (8).
% 10.01/1.75
% 10.01/1.75 % SZS status Unsatisfiable for theBenchmark
% 10.01/1.75
% 10.01/1.75 % Proof 1 at 1.09 (+ 0.28) seconds.
% 10.01/1.75 % Length of proof is 29.
% 10.01/1.75 % Level of proof is 8.
% 10.01/1.75 % Maximum clause weight is 54.000.
% 10.01/1.75 % Given clauses 137.
% 10.01/1.75
% 10.01/1.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------