%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT019-1 : 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 : 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 07:49:33 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.48s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 65 ( 65 unt; 0 def)
% Number of atoms : 65 ( 64 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 162 ( 0 sgn 18 !; 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(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_3,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_4,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_5,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_6,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[associativity_of_join]) ).
fof(quasi_lattice2,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(join(VAR_0,meet(VAR_1,VAR_2)),join(VAR_0,VAR_1)) = join(VAR_0,meet(VAR_1,VAR_2)),
file('theBenchmark.p',quasi_lattice2) ).
cnf(c_9,plain,
meet(join(A,meet(B,C)),join(A,B)) = join(A,meet(B,C)),
inference(clausify,[status(thm)],[quasi_lattice2]) ).
cnf(c_10,plain,
meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_3,c_9]) ).
fof(distributivity_law,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_law) ).
cnf(c_11,plain,
meet(A,join(B,C)) = join(meet(A,B),meet(A,C)),
inference(clausify,[status(thm)],[distributivity_law]) ).
cnf(c_12,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_11]) ).
fof(prove_distributivity_law_dual,axiom,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
file('theBenchmark.p',prove_distributivity_law_dual) ).
cnf(c_13,plain,
join(a,meet(b,c)) != meet(join(a,b),join(a,c)),
inference(clausify,[status(thm)],[prove_distributivity_law_dual]) ).
cnf(c_424,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_16,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_424]) ).
cnf(c_425,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_3,c_5]) ).
cnf(c_19,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_425]) ).
cnf(c_426,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_21,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_426]) ).
cnf(c_427,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_22,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_4,c_427]) ).
cnf(c_428,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_4,c_6]) ).
cnf(c_24,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_428]) ).
cnf(c_28,plain,
meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_4,c_10]) ).
cnf(c_33,plain,
join(A,meet(A,B)) = meet(A,join(A,B)),
inference(paramod,[status(thm)],[c_1,c_12]) ).
cnf(c_35,plain,
join(meet(A,B),meet(B,C)) = meet(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_12]) ).
cnf(c_37,plain,
join(meet(A,join(B,C)),D) = join(meet(A,B),join(meet(A,C),D)),
inference(paramod,[status(thm)],[c_12,c_6]) ).
cnf(c_429,plain,
meet(join(meet(A,B),A),meet(A,join(B,C))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_12,c_10]) ).
cnf(c_430,plain,
meet(join(A,meet(A,B)),meet(A,join(B,C))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_4,c_429]) ).
cnf(c_431,plain,
meet(meet(A,join(A,B)),meet(A,join(B,C))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_33,c_430]) ).
cnf(c_432,plain,
meet(A,meet(meet(A,join(A,B)),join(B,C))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_19,c_431]) ).
cnf(c_433,plain,
meet(A,meet(A,meet(join(A,B),join(B,C)))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_432]) ).
cnf(c_434,plain,
meet(A,meet(join(A,B),join(B,C))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_16,c_433]) ).
cnf(c_38,plain,
meet(A,meet(join(A,B),join(B,C))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_12,c_434]) ).
cnf(c_435,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(B,meet(A,C))),
inference(paramod,[status(thm)],[c_16,c_12]) ).
cnf(c_436,plain,
meet(A,join(B,C)) = meet(A,join(B,meet(A,C))),
inference(paramod,[status(thm)],[c_12,c_435]) ).
cnf(c_47,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_436]) ).
cnf(c_437,plain,
meet(join(A,B),join(A,meet(join(A,B),C))) = join(A,meet(join(A,B),C)),
inference(paramod,[status(thm)],[c_21,c_10]) ).
cnf(c_438,plain,
meet(join(A,B),join(A,C)) = join(A,meet(join(A,B),C)),
inference(paramod,[status(thm)],[c_47,c_437]) ).
cnf(c_56,plain,
join(A,meet(join(A,B),C)) = meet(join(A,B),join(A,C)),
inference(copy,[status(thm)],[c_438]) ).
cnf(c_439,plain,
meet(join(A,B),join(B,meet(join(A,B),C))) = join(B,meet(join(A,B),C)),
inference(paramod,[status(thm)],[c_22,c_10]) ).
cnf(c_440,plain,
meet(join(A,B),join(B,C)) = join(B,meet(join(A,B),C)),
inference(paramod,[status(thm)],[c_47,c_439]) ).
cnf(c_60,plain,
join(A,meet(join(B,A),C)) = meet(join(B,A),join(A,C)),
inference(copy,[status(thm)],[c_440]) ).
cnf(c_441,plain,
join(meet(join(A,B),B),meet(join(A,B),meet(A,C))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_28,c_12]) ).
cnf(c_442,plain,
join(meet(B,join(A,B)),meet(join(A,B),meet(A,C))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_3,c_441]) ).
cnf(c_443,plain,
join(meet(B,join(A,B)),meet(A,meet(join(A,B),C))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_19,c_442]) ).
cnf(c_444,plain,
join(meet(B,A),join(meet(B,B),meet(A,meet(join(A,B),C)))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_37,c_443]) ).
cnf(c_445,plain,
join(meet(B,A),join(B,meet(A,meet(join(A,B),C)))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_1,c_444]) ).
cnf(c_446,plain,
join(B,join(meet(B,A),meet(A,meet(join(A,B),C)))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_24,c_445]) ).
cnf(c_447,plain,
join(B,meet(A,join(B,meet(join(A,B),C)))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_35,c_446]) ).
cnf(c_448,plain,
join(B,meet(A,meet(join(A,B),join(B,C)))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_60,c_447]) ).
cnf(c_102,plain,
join(A,meet(B,join(A,C))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_38,c_448]) ).
cnf(c_449,plain,
join(A,meet(join(A,B),C)) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_3,c_102]) ).
cnf(c_450,plain,
meet(join(A,B),join(A,C)) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_56,c_449]) ).
cnf(c_323,plain,
join(A,meet(B,C)) = meet(join(A,C),join(A,B)),
inference(copy,[status(thm)],[c_450]) ).
cnf(c_451,plain,
meet(join(a,c),join(a,b)) != meet(join(a,b),join(a,c)),
inference(paramod,[status(thm)],[c_323,c_13]) ).
cnf(c_452,plain,
meet(join(a,b),join(a,c)) != meet(join(a,b),join(a,c)),
inference(paramod,[status(thm)],[c_3,c_451]) ).
cnf(c_423,plain,
$false,
inference(copy,[status(thm)],[c_452]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT019-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n001.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Fri Sep 25 20:02:55 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 4091550 was started by sandbox2 on n001,
% 0.11/0.37 % Fri Sep 25 20:02:55 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.48
% 0.15/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.48
% 0.15/0.48 % Proof 1 at 0.08 (+ 0.01) seconds.
% 0.15/0.48 % Length of proof is 27.
% 0.15/0.48 % Level of proof is 6.
% 0.15/0.48 % Maximum clause weight is 17.000.
% 0.15/0.48 % Given clauses 37.
% 0.15/0.48
% 0.15/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------