%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT043-1 : 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 : n012.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 0.09s 5.49s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 11
% Syntax : Number of formulae : 97 ( 97 unt; 0 def)
% Number of atoms : 97 ( 96 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 185 ( 24 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_of_join,axiom,
! [VAR_0] : join(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_join) ).
cnf(c_2,plain,
join(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_join]) ).
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_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(distributivity,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,VAR_2)) = join(meet(VAR_0,VAR_1),meet(VAR_0,VAR_2)),
file('theBenchmark.p',distributivity) ).
cnf(c_9,plain,
meet(A,join(B,C)) = join(meet(A,B),meet(A,C)),
inference(clausify,[status(thm)],[distributivity]) ).
cnf(c_10,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_9]) ).
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(invertability2,axiom,
! [VAR_0] : meet(complement(VAR_0),VAR_0) = n0,
file('theBenchmark.p',invertability2) ).
cnf(c_13,plain,
meet(complement(A),A) = n0,
inference(clausify,[status(thm)],[invertability2]) ).
cnf(c_14,plain,
meet(A,complement(A)) = n0,
inference(paramod,[status(thm)],[c_5,c_13]) ).
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(prove_compatability_law,axiom,
complement(join(c,d)) != meet(complement(c),complement(d)),
file('theBenchmark.p',prove_compatability_law) ).
cnf(c_16,plain,
complement(join(c,d)) != meet(complement(c),complement(d)),
inference(clausify,[status(thm)],[prove_compatability_law]) ).
cnf(c_17,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_18,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_594,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_27,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_594]) ).
cnf(c_595,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_28,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_6,c_595]) ).
cnf(c_596,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_31,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_596]) ).
cnf(c_35,plain,
join(meet(A,B),meet(B,C)) = meet(B,join(A,C)),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_38,plain,
meet(A,n1) = A,
inference(paramod,[status(thm)],[c_12,c_3]) ).
cnf(c_41,plain,
join(A,n0) = A,
inference(paramod,[status(thm)],[c_14,c_4]) ).
cnf(c_597,plain,
join(A,B) = join(A,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_17,c_8]) ).
cnf(c_47,plain,
join(A,join(meet(B,A),C)) = join(A,C),
inference(copy,[status(thm)],[c_597]) ).
cnf(c_598,plain,
A = meet(n1,A),
inference(paramod,[status(thm)],[c_38,c_5]) ).
cnf(c_59,plain,
meet(n1,A) = A,
inference(copy,[status(thm)],[c_598]) ).
cnf(c_599,plain,
A = join(n0,A),
inference(paramod,[status(thm)],[c_41,c_6]) ).
cnf(c_64,plain,
join(n0,A) = A,
inference(copy,[status(thm)],[c_599]) ).
cnf(c_69,plain,
complement(n1) = n0,
inference(paramod,[status(thm)],[c_59,c_14]) ).
cnf(c_70,plain,
join(A,n1) = n1,
inference(paramod,[status(thm)],[c_59,c_18]) ).
cnf(c_71,plain,
complement(n0) = n1,
inference(paramod,[status(thm)],[c_69,c_15]) ).
cnf(c_91,plain,
join(meet(A,B),meet(C,B)) = meet(B,join(A,C)),
inference(paramod,[status(thm)],[c_5,c_35]) ).
cnf(c_600,plain,
join(n0,meet(complement(A),B)) = meet(complement(A),join(A,B)),
inference(paramod,[status(thm)],[c_14,c_35]) ).
cnf(c_601,plain,
meet(complement(A),B) = meet(complement(A),join(A,B)),
inference(paramod,[status(thm)],[c_64,c_600]) ).
cnf(c_93,plain,
meet(complement(A),join(A,B)) = meet(complement(A),B),
inference(copy,[status(thm)],[c_601]) ).
cnf(c_97,plain,
meet(complement(A),B) = meet(join(A,B),complement(A)),
inference(paramod,[status(thm)],[c_93,c_5]) ).
cnf(c_98,plain,
meet(complement(A),join(B,A)) = meet(complement(A),B),
inference(paramod,[status(thm)],[c_6,c_93]) ).
cnf(c_124,plain,
meet(join(A,B),complement(A)) = meet(B,complement(A)),
inference(paramod,[status(thm)],[c_97,c_5]) ).
cnf(c_602,plain,
meet(complement(join(A,B)),join(A,B)) = meet(complement(join(A,B)),B),
inference(paramod,[status(thm)],[c_28,c_98]) ).
cnf(c_603,plain,
meet(join(A,B),complement(join(A,B))) = meet(complement(join(A,B)),B),
inference(paramod,[status(thm)],[c_5,c_602]) ).
cnf(c_604,plain,
n0 = meet(complement(join(A,B)),B),
inference(paramod,[status(thm)],[c_14,c_603]) ).
cnf(c_605,plain,
n0 = meet(B,complement(join(A,B))),
inference(paramod,[status(thm)],[c_5,c_604]) ).
cnf(c_140,plain,
meet(A,complement(join(B,A))) = n0,
inference(copy,[status(thm)],[c_605]) ).
cnf(c_606,plain,
join(A,n1) = join(A,complement(meet(A,B))),
inference(paramod,[status(thm)],[c_12,c_31]) ).
cnf(c_607,plain,
n1 = join(A,complement(meet(A,B))),
inference(paramod,[status(thm)],[c_70,c_606]) ).
cnf(c_175,plain,
join(A,complement(meet(A,B))) = n1,
inference(copy,[status(thm)],[c_607]) ).
cnf(c_178,plain,
join(A,meet(B,join(A,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_35,c_31]) ).
cnf(c_608,plain,
join(A,meet(B,join(A,C))) = meet(join(A,C),join(A,B)),
inference(paramod,[status(thm)],[c_3,c_91]) ).
cnf(c_216,plain,
join(A,meet(B,C)) = meet(join(A,C),join(A,B)),
inference(paramod,[status(thm)],[c_178,c_608]) ).
cnf(c_609,plain,
meet(complement(A),n1) = meet(complement(A),complement(meet(A,B))),
inference(paramod,[status(thm)],[c_175,c_93]) ).
cnf(c_610,plain,
meet(n1,complement(A)) = meet(complement(A),complement(meet(A,B))),
inference(paramod,[status(thm)],[c_5,c_609]) ).
cnf(c_611,plain,
complement(A) = meet(complement(A),complement(meet(A,B))),
inference(paramod,[status(thm)],[c_59,c_610]) ).
cnf(c_255,plain,
meet(complement(A),complement(meet(A,B))) = complement(A),
inference(copy,[status(thm)],[c_611]) ).
cnf(c_612,plain,
meet(join(A,B),join(A,C)) = join(meet(C,B),A),
inference(paramod,[status(thm)],[c_216,c_6]) ).
cnf(c_258,plain,
join(meet(A,B),C) = meet(join(C,B),join(C,A)),
inference(copy,[status(thm)],[c_612]) ).
cnf(c_613,plain,
join(A,n0) = meet(join(A,complement(B)),join(A,B)),
inference(paramod,[status(thm)],[c_14,c_216]) ).
cnf(c_614,plain,
A = meet(join(A,complement(B)),join(A,B)),
inference(paramod,[status(thm)],[c_41,c_613]) ).
cnf(c_615,plain,
A = meet(join(A,B),join(A,complement(B))),
inference(paramod,[status(thm)],[c_5,c_614]) ).
cnf(c_260,plain,
meet(join(A,B),join(A,complement(B))) = A,
inference(copy,[status(thm)],[c_615]) ).
cnf(c_616,plain,
meet(join(join(meet(A,B),C),B),join(join(meet(A,B),C),A)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_258,c_27]) ).
cnf(c_617,plain,
meet(join(B,join(meet(A,B),C)),join(join(meet(A,B),C),A)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_6,c_616]) ).
cnf(c_618,plain,
meet(join(B,C),join(join(meet(A,B),C),A)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_47,c_617]) ).
cnf(c_619,plain,
meet(join(B,C),join(A,join(meet(A,B),C))) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_6,c_618]) ).
cnf(c_620,plain,
meet(join(B,C),join(A,C)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_31,c_619]) ).
cnf(c_343,plain,
join(meet(A,B),C) = meet(join(B,C),join(A,C)),
inference(copy,[status(thm)],[c_620]) ).
cnf(c_621,plain,
meet(join(meet(A,B),complement(A)),complement(meet(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_255,c_124]) ).
cnf(c_622,plain,
meet(meet(join(B,complement(A)),join(A,complement(A))),complement(meet(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_343,c_621]) ).
cnf(c_623,plain,
meet(meet(join(B,complement(A)),n1),complement(meet(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_12,c_622]) ).
cnf(c_624,plain,
meet(meet(n1,join(B,complement(A))),complement(meet(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_5,c_623]) ).
cnf(c_450,plain,
meet(join(A,complement(B)),complement(meet(B,A))) = complement(B),
inference(paramod,[status(thm)],[c_59,c_624]) ).
cnf(c_625,plain,
meet(join(complement(join(A,B)),complement(B)),complement(n0)) = complement(B),
inference(paramod,[status(thm)],[c_140,c_450]) ).
cnf(c_626,plain,
meet(join(complement(B),complement(join(A,B))),complement(n0)) = complement(B),
inference(paramod,[status(thm)],[c_6,c_625]) ).
cnf(c_627,plain,
meet(join(complement(B),complement(join(A,B))),n1) = complement(B),
inference(paramod,[status(thm)],[c_71,c_626]) ).
cnf(c_628,plain,
meet(n1,join(complement(B),complement(join(A,B)))) = complement(B),
inference(paramod,[status(thm)],[c_5,c_627]) ).
cnf(c_564,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_59,c_628]) ).
cnf(c_629,plain,
meet(join(join(A,complement(B)),complement(join(A,B))),complement(A)) = complement(join(A,B)),
inference(paramod,[status(thm)],[c_260,c_450]) ).
cnf(c_630,plain,
meet(join(A,join(complement(B),complement(join(A,B)))),complement(A)) = complement(join(A,B)),
inference(paramod,[status(thm)],[c_8,c_629]) ).
cnf(c_631,plain,
meet(join(A,complement(B)),complement(A)) = complement(join(A,B)),
inference(paramod,[status(thm)],[c_564,c_630]) ).
cnf(c_632,plain,
meet(complement(B),complement(A)) = complement(join(A,B)),
inference(paramod,[status(thm)],[c_124,c_631]) ).
cnf(c_570,plain,
complement(join(A,B)) = meet(complement(B),complement(A)),
inference(copy,[status(thm)],[c_632]) ).
cnf(c_633,plain,
meet(complement(d),complement(c)) != meet(complement(c),complement(d)),
inference(paramod,[status(thm)],[c_570,c_16]) ).
cnf(c_634,plain,
meet(complement(c),complement(d)) != meet(complement(c),complement(d)),
inference(paramod,[status(thm)],[c_5,c_633]) ).
cnf(c_593,plain,
$false,
inference(copy,[status(thm)],[c_634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LAT043-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/5.33 % Computer : n012.cluster.edu
% 0.06/5.33 % Model : x86_64 x86_64
% 0.06/5.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/5.33 % Memory : 8046.5625MB
% 0.06/5.33 % OS : Linux 6.8.0-71-generic
% 0.06/5.33 % CPULimit : 300
% 0.06/5.33 % WCLimit : 300
% 0.06/5.33 % DateTime : Fri Sep 25 19:58:40 UTC 2026
% 0.06/5.33 % CPUTime :
% 0.06/5.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/5.34 % Process 2856363 was started by sandbox2 on n012,
% 0.06/5.34 % Fri Sep 25 19:58:40 2026
% 0.06/5.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.06/5.34
% 0.06/5.34 % From the command line: assign(max_seconds, 300).
% 0.09/5.49
% 0.09/5.49 % SZS status Unsatisfiable for theBenchmark
% 0.09/5.49
% 0.09/5.49 % Proof 1 at 0.10 (+ 0.04) seconds.
% 0.09/5.49 % Length of proof is 45.
% 0.09/5.49 % Level of proof is 10.
% 0.09/5.49 % Maximum clause weight is 36.000.
% 0.09/5.49 % Given clauses 75.
% 0.09/5.49
% 0.09/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------