%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT164-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n013.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 07:49:45 AM UTC 2026
% Result : Unsatisfiable 233.36s 44.43s
% Output : CNFRefutation 233.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 8
% Syntax : Number of formulae : 64 ( 64 unt; 0 def)
% Number of atoms : 64 ( 63 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 155 ( 11 sgn 16 !; 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(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(equation_H76,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_1,VAR_3)))) = meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_3,meet(VAR_0,VAR_1))))),
file('theBenchmark.p',equation_H76) ).
cnf(c_9,plain,
meet(A,join(B,meet(C,join(B,D)))) = meet(A,join(B,meet(C,join(D,meet(A,B))))),
inference(clausify,[status(thm)],[equation_H76]) ).
cnf(c_10,plain,
meet(A,join(B,meet(C,join(D,meet(A,B))))) = meet(A,join(B,meet(C,join(B,D)))),
inference(copy,[status(thm)],[c_9]) ).
fof(prove_H6,axiom,
meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
file('theBenchmark.p',prove_H6) ).
cnf(c_11,plain,
meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(clausify,[status(thm)],[prove_H6]) ).
cnf(c_12,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) != meet(a,join(b,meet(a,c))),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,plain,
meet(join(A,B),A) = A,
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_14,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_16,plain,
join(meet(A,B),A) = A,
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_3820,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_17,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_3820]) ).
cnf(c_18,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_21,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_3821,plain,
meet(meet(A,B),C) = meet(meet(B,C),A),
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_24,plain,
meet(meet(A,B),C) = meet(meet(C,A),B),
inference(copy,[status(thm)],[c_3821]) ).
cnf(c_26,plain,
meet(meet(A,B),C) = meet(A,meet(C,B)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_3822,plain,
meet(A,join(B,meet(C,A))) = meet(A,join(B,meet(C,join(B,A)))),
inference(paramod,[status(thm)],[c_4,c_10]) ).
cnf(c_52,plain,
meet(A,join(B,meet(C,join(B,A)))) = meet(A,join(B,meet(C,A))),
inference(copy,[status(thm)],[c_3822]) ).
cnf(c_55,plain,
meet(A,join(B,meet(join(C,meet(A,B)),D))) = meet(A,join(B,meet(D,join(B,C)))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_71,plain,
meet(a,join(meet(a,join(b,meet(c,a))),meet(c,join(a,b)))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_82,plain,
meet(join(A,B),B) = B,
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_91,plain,
meet(a,join(meet(a,join(b,meet(c,a))),meet(c,join(a,b)))) != meet(a,join(b,meet(c,a))),
inference(paramod,[status(thm)],[c_5,c_71]) ).
cnf(c_3823,plain,
meet(A,B) = meet(join(C,A),meet(A,B)),
inference(paramod,[status(thm)],[c_82,c_7]) ).
cnf(c_135,plain,
meet(join(A,B),meet(B,C)) = meet(B,C),
inference(copy,[status(thm)],[c_3823]) ).
cnf(c_139,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_14,c_82]) ).
cnf(c_3824,plain,
meet(meet(A,B),C) = meet(A,meet(meet(A,B),C)),
inference(paramod,[status(thm)],[c_17,c_7]) ).
cnf(c_3825,plain,
meet(meet(A,B),C) = meet(meet(A,C),meet(A,B)),
inference(paramod,[status(thm)],[c_26,c_3824]) ).
cnf(c_145,plain,
meet(meet(A,B),meet(A,C)) = meet(meet(A,C),B),
inference(copy,[status(thm)],[c_3825]) ).
cnf(c_3826,plain,
meet(meet(meet(A,meet(B,C)),B),C) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_18,c_7]) ).
cnf(c_3827,plain,
meet(meet(meet(B,A),meet(B,C)),C) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_24,c_3826]) ).
cnf(c_3828,plain,
meet(meet(meet(B,C),A),C) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_145,c_3827]) ).
cnf(c_148,plain,
meet(meet(A,B),meet(C,B)) = meet(C,meet(A,B)),
inference(paramod,[status(thm)],[c_7,c_3828]) ).
cnf(c_3829,plain,
meet(meet(A,B),meet(C,B)) = meet(A,meet(C,B)),
inference(paramod,[status(thm)],[c_139,c_7]) ).
cnf(c_250,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_148,c_3829]) ).
cnf(c_264,plain,
join(meet(A,join(B,C)),meet(A,B)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_13,c_21]) ).
cnf(c_286,plain,
meet(a,join(meet(a,join(b,meet(c,a))),meet(c,join(b,a)))) != meet(a,join(b,meet(c,a))),
inference(paramod,[status(thm)],[c_6,c_91]) ).
cnf(c_3830,plain,
meet(A,join(B,C)) = join(meet(A,B),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_264,c_6]) ).
cnf(c_407,plain,
join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_3830]) ).
cnf(c_576,plain,
join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)),
inference(paramod,[status(thm)],[c_13,c_407]) ).
cnf(c_3831,plain,
meet(A,join(B,meet(join(B,A),join(B,C)))) = meet(A,join(B,meet(join(C,meet(A,B)),A))),
inference(paramod,[status(thm)],[c_55,c_52]) ).
cnf(c_3832,plain,
meet(A,meet(join(B,A),join(B,C))) = meet(A,join(B,meet(join(C,meet(A,B)),A))),
inference(paramod,[status(thm)],[c_576,c_3831]) ).
cnf(c_3833,plain,
meet(join(B,A),meet(A,join(B,C))) = meet(A,join(B,meet(join(C,meet(A,B)),A))),
inference(paramod,[status(thm)],[c_250,c_3832]) ).
cnf(c_3834,plain,
meet(A,join(B,C)) = meet(A,join(B,meet(join(C,meet(A,B)),A))),
inference(paramod,[status(thm)],[c_135,c_3833]) ).
cnf(c_3835,plain,
meet(A,join(B,C)) = meet(A,join(B,meet(A,join(B,C)))),
inference(paramod,[status(thm)],[c_55,c_3834]) ).
cnf(c_1961,plain,
meet(A,join(B,meet(A,join(B,C)))) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_3835]) ).
cnf(c_3836,plain,
meet(A,join(meet(B,C),meet(A,B))) = meet(A,join(meet(B,C),B)),
inference(paramod,[status(thm)],[c_16,c_1961]) ).
cnf(c_1997,plain,
meet(A,join(meet(B,C),meet(A,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_16,c_3836]) ).
cnf(c_2029,plain,
meet(A,join(meet(A,B),meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_6,c_1997]) ).
cnf(c_2243,plain,
meet(A,join(meet(A,join(B,C)),C)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_82,c_2029]) ).
cnf(c_3837,plain,
meet(A,join(meet(A,join(B,meet(C,A))),meet(C,join(B,A)))) = meet(A,join(B,meet(C,join(B,A)))),
inference(paramod,[status(thm)],[c_52,c_2243]) ).
cnf(c_3818,plain,
meet(A,join(meet(A,join(B,meet(C,A))),meet(C,join(B,A)))) = meet(A,join(B,meet(C,A))),
inference(paramod,[status(thm)],[c_52,c_3837]) ).
cnf(c_3819,plain,
$false,
inference(resolve,[status(thm)],[c_3818,c_286]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT164-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.42 % Computer : n013.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Fri Sep 25 20:09:51 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 1089704 was started by sandbox on n013,
% 0.15/0.42 % Fri Sep 25 20:09:51 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 233.36/44.43
% 233.36/44.43 % SZS status Unsatisfiable for theBenchmark
% 233.36/44.43
% 233.36/44.43 % Proof 1 at 1.49 (+ 0.31) seconds.
% 233.36/44.43 % Length of proof is 38.
% 233.36/44.43 % Level of proof is 10.
% 233.36/44.43 % Maximum clause weight is 28.000.
% 233.36/44.43 % Given clauses 186.
% 233.36/44.43
% 233.36/44.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------