%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 07:49:32 AM UTC 2026
% Result : Unsatisfiable 0.90s 0.54s
% Output : CNFRefutation 0.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 10
% Syntax : Number of formulae : 138 ( 138 unt; 0 def)
% Number of atoms : 138 ( 137 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 : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 373 ( 29 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_of_meet,axiom,
! [VAR_0] : meet(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_meet) ).
cnf(c_1,plain,
meet(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_meet]) ).
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_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(distributivity_dual,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(join(meet(VAR_0,VAR_1),VAR_2),VAR_1),meet(VAR_2,VAR_0)) = meet(join(meet(join(VAR_0,VAR_1),VAR_2),VAR_1),join(VAR_2,VAR_0)),
file('theBenchmark.p',distributivity_dual) ).
cnf(c_9,plain,
join(meet(join(meet(A,B),C),B),meet(C,A)) = meet(join(meet(join(A,B),C),B),join(C,A)),
inference(clausify,[status(thm)],[distributivity_dual]) ).
cnf(c_681,plain,
join(meet(B,join(meet(A,B),C)),meet(C,A)) = meet(join(meet(join(A,B),C),B),join(C,A)),
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_682,plain,
join(meet(B,join(meet(A,B),C)),meet(C,A)) = meet(join(B,meet(join(A,B),C)),join(C,A)),
inference(paramod,[status(thm)],[c_6,c_681]) ).
cnf(c_683,plain,
join(meet(B,join(meet(A,B),C)),meet(C,A)) = meet(join(C,A),join(B,meet(join(A,B),C))),
inference(paramod,[status(thm)],[c_5,c_682]) ).
cnf(c_10,plain,
meet(join(A,B),join(C,meet(join(B,C),A))) = join(meet(C,join(meet(B,C),A)),meet(A,B)),
inference(copy,[status(thm)],[c_683]) ).
fof(prove_distributivity,axiom,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('theBenchmark.p',prove_distributivity) ).
cnf(c_11,plain,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
inference(clausify,[status(thm)],[prove_distributivity]) ).
cnf(c_12,plain,
meet(join(a,b),join(a,c)) != join(a,meet(b,c)),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_14,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_684,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_16,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_684]) ).
cnf(c_685,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_17,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_5,c_685]) ).
cnf(c_686,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_19,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_686]) ).
cnf(c_687,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_22,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_687]) ).
cnf(c_688,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_24,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_688]) ).
cnf(c_689,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_25,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_6,c_689]) ).
cnf(c_26,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_690,plain,
meet(join(A,B),join(join(B,C),meet(join(B,join(B,C)),A))) = join(meet(join(B,C),join(B,A)),meet(A,B)),
inference(paramod,[status(thm)],[c_3,c_10]) ).
cnf(c_691,plain,
meet(join(A,B),join(join(B,C),meet(join(B,C),A))) = join(meet(join(B,C),join(B,A)),meet(A,B)),
inference(paramod,[status(thm)],[c_24,c_690]) ).
cnf(c_692,plain,
meet(join(A,B),join(B,C)) = join(meet(join(B,C),join(B,A)),meet(A,B)),
inference(paramod,[status(thm)],[c_4,c_691]) ).
cnf(c_33,plain,
join(meet(join(A,B),join(A,C)),meet(C,A)) = meet(join(C,A),join(A,B)),
inference(copy,[status(thm)],[c_692]) ).
cnf(c_693,plain,
meet(join(A,join(A,B)),join(C,meet(join(join(A,B),C),A))) = join(meet(C,join(meet(join(A,B),C),A)),A),
inference(paramod,[status(thm)],[c_3,c_10]) ).
cnf(c_694,plain,
meet(join(A,B),join(C,meet(join(join(A,B),C),A))) = join(meet(C,join(meet(join(A,B),C),A)),A),
inference(paramod,[status(thm)],[c_24,c_693]) ).
cnf(c_695,plain,
meet(join(A,B),join(C,meet(join(A,join(B,C)),A))) = join(meet(C,join(meet(join(A,B),C),A)),A),
inference(paramod,[status(thm)],[c_8,c_694]) ).
cnf(c_696,plain,
meet(join(A,B),join(C,meet(A,join(A,join(B,C))))) = join(meet(C,join(meet(join(A,B),C),A)),A),
inference(paramod,[status(thm)],[c_5,c_695]) ).
cnf(c_697,plain,
meet(join(A,B),join(C,A)) = join(meet(C,join(meet(join(A,B),C),A)),A),
inference(paramod,[status(thm)],[c_3,c_696]) ).
cnf(c_698,plain,
meet(join(A,B),join(C,A)) = join(meet(C,join(A,meet(join(A,B),C))),A),
inference(paramod,[status(thm)],[c_6,c_697]) ).
cnf(c_699,plain,
meet(join(A,B),join(C,A)) = join(A,meet(C,join(A,meet(join(A,B),C)))),
inference(paramod,[status(thm)],[c_6,c_698]) ).
cnf(c_34,plain,
join(A,meet(B,join(A,meet(join(A,C),B)))) = meet(join(A,C),join(B,A)),
inference(copy,[status(thm)],[c_699]) ).
cnf(c_50,plain,
join(A,meet(B,meet(C,A))) = A,
inference(paramod,[status(thm)],[c_7,c_13]) ).
cnf(c_700,plain,
meet(A,B) = meet(A,meet(join(C,A),B)),
inference(paramod,[status(thm)],[c_14,c_7]) ).
cnf(c_57,plain,
meet(A,meet(join(B,A),C)) = meet(A,C),
inference(copy,[status(thm)],[c_700]) ).
cnf(c_701,plain,
meet(A,B) = meet(A,meet(B,join(C,meet(A,B)))),
inference(paramod,[status(thm)],[c_14,c_7]) ).
cnf(c_58,plain,
meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B),
inference(copy,[status(thm)],[c_701]) ).
cnf(c_59,plain,
meet(A,join(B,join(C,A))) = A,
inference(paramod,[status(thm)],[c_8,c_14]) ).
cnf(c_702,plain,
meet(A,meet(B,meet(C,A))) = meet(meet(B,C),A),
inference(paramod,[status(thm)],[c_7,c_17]) ).
cnf(c_69,plain,
meet(A,meet(B,meet(C,A))) = meet(B,meet(C,A)),
inference(paramod,[status(thm)],[c_7,c_702]) ).
cnf(c_703,plain,
join(join(A,B),meet(C,A)) = join(A,B),
inference(paramod,[status(thm)],[c_3,c_50]) ).
cnf(c_85,plain,
join(A,join(B,meet(C,A))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_703]) ).
cnf(c_86,plain,
join(A,meet(B,meet(A,C))) = A,
inference(paramod,[status(thm)],[c_5,c_50]) ).
cnf(c_99,plain,
meet(A,join(B,join(A,C))) = A,
inference(paramod,[status(thm)],[c_6,c_59]) ).
cnf(c_119,plain,
meet(A,meet(B,join(A,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_5,c_19]) ).
cnf(c_704,plain,
join(join(A,B),meet(A,C)) = join(A,B),
inference(paramod,[status(thm)],[c_19,c_86]) ).
cnf(c_129,plain,
join(A,join(B,meet(A,C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_704]) ).
cnf(c_705,plain,
meet(A,meet(join(B,A),meet(C,A))) = meet(C,A),
inference(paramod,[status(thm)],[c_17,c_57]) ).
cnf(c_197,plain,
meet(join(A,B),meet(C,B)) = meet(C,B),
inference(paramod,[status(thm)],[c_69,c_705]) ).
cnf(c_241,plain,
meet(join(A,B),join(B,A)) = join(A,B),
inference(paramod,[status(thm)],[c_25,c_26]) ).
cnf(c_293,plain,
join(meet(A,join(B,C)),meet(B,A)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_119,c_13]) ).
cnf(c_363,plain,
join(meet(join(A,B),join(A,C)),meet(C,A)) = meet(join(A,B),join(C,A)),
inference(paramod,[status(thm)],[c_33,c_5]) ).
cnf(c_706,plain,
join(join(A,B),meet(C,join(B,A))) = join(A,B),
inference(paramod,[status(thm)],[c_241,c_50]) ).
cnf(c_517,plain,
join(A,join(B,meet(C,join(B,A)))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_706]) ).
cnf(c_527,plain,
join(A,meet(B,join(A,meet(join(C,A),B)))) = meet(join(A,C),join(B,A)),
inference(paramod,[status(thm)],[c_6,c_34]) ).
cnf(c_707,plain,
meet(join(A,B),join(join(A,C),meet(join(B,join(A,C)),A))) = join(join(A,meet(meet(B,join(A,C)),join(A,meet(join(A,C),meet(B,join(A,C)))))),meet(A,B)),
inference(paramod,[status(thm)],[c_34,c_10]) ).
cnf(c_708,plain,
meet(join(A,B),join(join(A,C),meet(A,join(B,join(A,C))))) = join(join(A,meet(meet(B,join(A,C)),join(A,meet(join(A,C),meet(B,join(A,C)))))),meet(A,B)),
inference(paramod,[status(thm)],[c_5,c_707]) ).
cnf(c_709,plain,
meet(join(A,B),join(join(A,C),A)) = join(join(A,meet(meet(B,join(A,C)),join(A,meet(join(A,C),meet(B,join(A,C)))))),meet(A,B)),
inference(paramod,[status(thm)],[c_99,c_708]) ).
cnf(c_710,plain,
meet(join(A,B),join(A,join(A,C))) = join(join(A,meet(meet(B,join(A,C)),join(A,meet(join(A,C),meet(B,join(A,C)))))),meet(A,B)),
inference(paramod,[status(thm)],[c_6,c_709]) ).
cnf(c_711,plain,
meet(join(A,B),join(A,C)) = join(join(A,meet(meet(B,join(A,C)),join(A,meet(join(A,C),meet(B,join(A,C)))))),meet(A,B)),
inference(paramod,[status(thm)],[c_24,c_710]) ).
cnf(c_712,plain,
meet(join(A,B),join(A,C)) = join(join(A,meet(meet(B,join(A,C)),join(A,meet(B,join(A,C))))),meet(A,B)),
inference(paramod,[status(thm)],[c_17,c_711]) ).
cnf(c_713,plain,
meet(join(A,B),join(A,C)) = join(join(A,meet(B,join(A,C))),meet(A,B)),
inference(paramod,[status(thm)],[c_14,c_712]) ).
cnf(c_714,plain,
meet(join(A,B),join(A,C)) = join(A,join(meet(B,join(A,C)),meet(A,B))),
inference(paramod,[status(thm)],[c_8,c_713]) ).
cnf(c_542,plain,
meet(join(A,B),join(A,C)) = join(A,meet(B,join(A,C))),
inference(paramod,[status(thm)],[c_293,c_714]) ).
cnf(c_715,plain,
join(A,meet(join(B,meet(join(C,B),A)),join(A,join(meet(B,join(meet(C,B),A)),meet(A,C))))) = meet(join(A,C),join(join(B,meet(join(C,B),A)),A)),
inference(paramod,[status(thm)],[c_10,c_34]) ).
cnf(c_716,plain,
join(A,meet(join(B,meet(join(C,B),A)),join(A,meet(B,join(meet(C,B),A))))) = meet(join(A,C),join(join(B,meet(join(C,B),A)),A)),
inference(paramod,[status(thm)],[c_129,c_715]) ).
cnf(c_717,plain,
join(A,meet(join(A,meet(B,join(meet(C,B),A))),join(B,meet(join(C,B),A)))) = meet(join(A,C),join(join(B,meet(join(C,B),A)),A)),
inference(paramod,[status(thm)],[c_5,c_716]) ).
cnf(c_718,plain,
join(A,meet(join(A,meet(B,join(meet(C,B),A))),join(B,meet(join(C,B),A)))) = meet(join(A,C),join(A,join(B,meet(join(C,B),A)))),
inference(paramod,[status(thm)],[c_6,c_717]) ).
cnf(c_719,plain,
join(A,meet(join(A,meet(B,join(meet(C,B),A))),join(B,meet(join(C,B),A)))) = meet(join(A,C),join(A,B)),
inference(paramod,[status(thm)],[c_85,c_718]) ).
cnf(c_544,plain,
join(A,meet(join(A,meet(B,join(meet(C,B),A))),join(B,meet(join(C,B),A)))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_542,c_719]) ).
cnf(c_720,plain,
meet(meet(A,join(B,meet(join(B,C),A))),meet(join(B,C),join(A,B))) = meet(A,join(B,meet(join(B,C),A))),
inference(paramod,[status(thm)],[c_34,c_14]) ).
cnf(c_721,plain,
meet(join(B,C),meet(meet(A,join(B,meet(join(B,C),A))),join(A,B))) = meet(A,join(B,meet(join(B,C),A))),
inference(paramod,[status(thm)],[c_22,c_720]) ).
cnf(c_722,plain,
meet(join(B,C),meet(join(A,B),meet(A,join(B,meet(join(B,C),A))))) = meet(A,join(B,meet(join(B,C),A))),
inference(paramod,[status(thm)],[c_5,c_721]) ).
cnf(c_723,plain,
meet(join(B,C),meet(A,meet(join(A,B),join(B,meet(join(B,C),A))))) = meet(A,join(B,meet(join(B,C),A))),
inference(paramod,[status(thm)],[c_22,c_722]) ).
cnf(c_724,plain,
meet(join(B,C),meet(A,join(B,meet(join(B,C),A)))) = meet(A,join(B,meet(join(B,C),A))),
inference(paramod,[status(thm)],[c_19,c_723]) ).
cnf(c_725,plain,
meet(join(B,C),A) = meet(A,join(B,meet(join(B,C),A))),
inference(paramod,[status(thm)],[c_58,c_724]) ).
cnf(c_545,plain,
meet(A,join(B,meet(join(B,C),A))) = meet(join(B,C),A),
inference(copy,[status(thm)],[c_725]) ).
cnf(c_726,plain,
meet(join(A,B),join(A,meet(C,join(A,meet(join(A,B),C))))) = meet(join(A,B),join(C,A)),
inference(paramod,[status(thm)],[c_34,c_16]) ).
cnf(c_727,plain,
meet(join(A,B),join(A,meet(join(A,B),C))) = meet(join(A,B),join(C,A)),
inference(paramod,[status(thm)],[c_545,c_726]) ).
cnf(c_728,plain,
join(A,meet(B,join(A,meet(join(A,B),C)))) = meet(join(A,B),join(C,A)),
inference(paramod,[status(thm)],[c_542,c_727]) ).
cnf(c_546,plain,
meet(join(A,B),join(C,A)) = join(A,meet(B,join(A,meet(join(A,B),C)))),
inference(copy,[status(thm)],[c_728]) ).
cnf(c_729,plain,
meet(A,join(B,meet(C,join(B,meet(join(B,A),C))))) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_34,c_57]) ).
cnf(c_566,plain,
meet(A,join(B,meet(join(B,A),C))) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_545,c_729]) ).
cnf(c_730,plain,
meet(join(A,B),meet(join(C,join(A,B)),join(D,A))) = join(A,meet(D,join(A,meet(join(A,B),D)))),
inference(paramod,[status(thm)],[c_34,c_57]) ).
cnf(c_731,plain,
meet(join(A,B),join(D,A)) = join(A,meet(D,join(A,meet(join(A,B),D)))),
inference(paramod,[status(thm)],[c_57,c_730]) ).
cnf(c_732,plain,
join(A,meet(B,join(A,meet(join(A,B),D)))) = join(A,meet(D,join(A,meet(join(A,B),D)))),
inference(paramod,[status(thm)],[c_546,c_731]) ).
cnf(c_733,plain,
join(A,meet(B,join(D,A))) = join(A,meet(D,join(A,meet(join(A,B),D)))),
inference(paramod,[status(thm)],[c_566,c_732]) ).
cnf(c_734,plain,
join(A,meet(B,join(D,A))) = join(A,meet(join(A,B),D)),
inference(paramod,[status(thm)],[c_545,c_733]) ).
cnf(c_567,plain,
join(A,meet(join(A,B),C)) = join(A,meet(B,join(C,A))),
inference(copy,[status(thm)],[c_734]) ).
cnf(c_735,plain,
join(A,meet(meet(B,C),join(A,meet(B,C)))) = meet(join(A,C),join(meet(B,C),A)),
inference(paramod,[status(thm)],[c_197,c_34]) ).
cnf(c_736,plain,
join(A,meet(B,C)) = meet(join(A,C),join(meet(B,C),A)),
inference(paramod,[status(thm)],[c_14,c_735]) ).
cnf(c_737,plain,
join(A,meet(B,C)) = join(A,meet(C,join(A,meet(join(A,C),meet(B,C))))),
inference(paramod,[status(thm)],[c_546,c_736]) ).
cnf(c_738,plain,
join(A,meet(B,C)) = join(A,meet(C,join(A,meet(B,C)))),
inference(paramod,[status(thm)],[c_197,c_737]) ).
cnf(c_603,plain,
join(A,meet(B,join(A,meet(C,B)))) = join(A,meet(C,B)),
inference(copy,[status(thm)],[c_738]) ).
cnf(c_739,plain,
join(join(A,meet(B,join(A,C))),meet(C,A)) = meet(join(A,B),join(C,A)),
inference(paramod,[status(thm)],[c_542,c_363]) ).
cnf(c_740,plain,
join(A,join(meet(B,join(A,C)),meet(C,A))) = meet(join(A,B),join(C,A)),
inference(paramod,[status(thm)],[c_8,c_739]) ).
cnf(c_741,plain,
join(A,meet(B,join(A,C))) = meet(join(A,B),join(C,A)),
inference(paramod,[status(thm)],[c_85,c_740]) ).
cnf(c_742,plain,
join(A,meet(B,join(A,C))) = join(A,meet(B,join(A,meet(join(A,B),C)))),
inference(paramod,[status(thm)],[c_546,c_741]) ).
cnf(c_743,plain,
join(A,meet(B,join(A,C))) = join(A,meet(B,join(A,meet(B,join(C,A))))),
inference(paramod,[status(thm)],[c_567,c_742]) ).
cnf(c_647,plain,
join(A,meet(B,join(A,meet(B,join(C,A))))) = join(A,meet(B,join(A,C))),
inference(copy,[status(thm)],[c_743]) ).
cnf(c_651,plain,
join(a,meet(b,join(a,c))) != join(a,meet(b,c)),
inference(paramod,[status(thm)],[c_542,c_12]) ).
cnf(c_744,plain,
join(A,meet(join(C,A),B)) = meet(join(A,C),join(B,A)),
inference(paramod,[status(thm)],[c_603,c_527]) ).
cnf(c_745,plain,
join(A,meet(join(C,A),B)) = join(A,meet(C,join(A,meet(join(A,C),B)))),
inference(paramod,[status(thm)],[c_546,c_744]) ).
cnf(c_746,plain,
join(A,meet(join(C,A),B)) = join(A,meet(C,join(A,meet(C,join(B,A))))),
inference(paramod,[status(thm)],[c_567,c_745]) ).
cnf(c_660,plain,
join(A,meet(join(B,A),C)) = join(A,meet(B,join(A,C))),
inference(paramod,[status(thm)],[c_647,c_746]) ).
cnf(c_747,plain,
meet(join(A,B),join(C,A)) = join(A,meet(B,join(A,meet(B,join(C,A))))),
inference(paramod,[status(thm)],[c_567,c_546]) ).
cnf(c_664,plain,
meet(join(A,B),join(C,A)) = join(A,meet(B,join(A,C))),
inference(paramod,[status(thm)],[c_647,c_747]) ).
cnf(c_748,plain,
join(A,meet(join(A,meet(B,join(meet(C,B),A))),join(B,meet(C,join(B,A))))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_660,c_544]) ).
cnf(c_749,plain,
join(A,meet(meet(B,join(meet(C,B),A)),join(join(B,meet(C,join(B,A))),A))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_567,c_748]) ).
cnf(c_750,plain,
join(A,meet(meet(B,join(meet(C,B),A)),join(A,join(B,meet(C,join(B,A)))))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_6,c_749]) ).
cnf(c_751,plain,
join(A,meet(meet(B,join(meet(C,B),A)),join(A,B))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_517,c_750]) ).
cnf(c_752,plain,
join(A,meet(join(A,B),meet(B,join(meet(C,B),A)))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_5,c_751]) ).
cnf(c_753,plain,
join(A,meet(B,meet(join(A,B),join(meet(C,B),A)))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_22,c_752]) ).
cnf(c_754,plain,
join(A,meet(B,join(A,meet(B,join(A,meet(C,B)))))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_664,c_753]) ).
cnf(c_755,plain,
join(A,meet(B,join(A,meet(C,B)))) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_603,c_754]) ).
cnf(c_756,plain,
join(A,meet(C,B)) = join(A,meet(C,join(A,B))),
inference(paramod,[status(thm)],[c_603,c_755]) ).
cnf(c_679,plain,
join(A,meet(B,join(A,C))) = join(A,meet(B,C)),
inference(copy,[status(thm)],[c_756]) ).
cnf(c_680,plain,
$false,
inference(resolve,[status(thm)],[c_679,c_651]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT009-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n017.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 19:52:02 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3014377 was started by sandbox2 on n017,
% 0.10/0.37 % Fri Sep 25 19:52:02 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).
% 0.90/0.54
% 0.90/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.90/0.54
% 0.90/0.54 % Proof 1 at 0.12 (+ 0.04) seconds.
% 0.90/0.54 % Length of proof is 52.
% 0.90/0.54 % Level of proof is 10.
% 0.90/0.54 % Maximum clause weight is 27.000.
% 0.90/0.54 % Given clauses 46.
% 0.90/0.54
% 0.90/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------