%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT005-6 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 07:49:31 AM UTC 2026
% Result : Unsatisfiable 12.35s 2.17s
% Output : CNFRefutation 12.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 76 ( 45 unt; 0 def)
% Number of atoms : 135 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 123 ( 64 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 11 con; 0-0 aty)
% Number of variables : 109 ( 3 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(join_0_and_x,axiom,
! [VAR_0] : join(n0,VAR_0,VAR_0),
file('theBenchmark.p',join_0_and_x) ).
cnf(c_3,plain,
join(n0,A,A),
inference(clausify,[status(thm)],[join_0_and_x]) ).
fof(meet_0_and_x,axiom,
! [VAR_0] : meet(n0,VAR_0,n0),
file('theBenchmark.p',meet_0_and_x) ).
cnf(c_4,plain,
meet(n0,A,n0),
inference(clausify,[status(thm)],[meet_0_and_x]) ).
fof(meet_x_and_x,axiom,
! [VAR_0] : meet(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',meet_x_and_x) ).
cnf(c_5,plain,
meet(A,A,A),
inference(clausify,[status(thm)],[meet_x_and_x]) ).
fof(commutativity_of_meet,axiom,
! [VAR_0,VAR_1,VAR_2] :
( meet(VAR_1,VAR_0,VAR_2)
| ~ meet(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_of_meet) ).
cnf(c_7,plain,
( meet(B,A,C)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_meet]) ).
fof(commutativity_of_join,axiom,
! [VAR_0,VAR_1,VAR_2] :
( join(VAR_1,VAR_0,VAR_2)
| ~ join(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',commutativity_of_join) ).
cnf(c_8,plain,
( join(B,A,C)
| ~ join(A,B,C) ),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(absorbtion2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( meet(VAR_0,VAR_2,VAR_0)
| ~ join(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',absorbtion2) ).
cnf(c_10,plain,
( meet(A,C,A)
| ~ join(A,B,C) ),
inference(clausify,[status(thm)],[absorbtion2]) ).
fof(associativity_of_meet1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( meet(VAR_2,VAR_3,VAR_5)
| ~ meet(VAR_0,VAR_4,VAR_5)
| ~ meet(VAR_1,VAR_3,VAR_4)
| ~ meet(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_meet1) ).
cnf(c_11,plain,
( meet(C,D,F)
| ~ meet(A,E,F)
| ~ meet(B,D,E)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_meet1]) ).
fof(associativity_of_meet2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( meet(VAR_0,VAR_4,VAR_5)
| ~ meet(VAR_2,VAR_3,VAR_5)
| ~ meet(VAR_1,VAR_3,VAR_4)
| ~ meet(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associativity_of_meet2) ).
cnf(c_12,plain,
( meet(A,E,F)
| ~ meet(C,D,F)
| ~ meet(B,D,E)
| ~ meet(A,B,C) ),
inference(clausify,[status(thm)],[associativity_of_meet2]) ).
fof(modularity2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( meet(VAR_1,VAR_3,VAR_5)
| ~ join(VAR_0,VAR_4,VAR_5)
| ~ meet(VAR_2,VAR_1,VAR_4)
| ~ join(VAR_0,VAR_2,VAR_3)
| ~ meet(VAR_0,VAR_1,VAR_0) ),
file('theBenchmark.p',modularity2) ).
cnf(c_16,plain,
( meet(B,D,F)
| ~ join(A,E,F)
| ~ meet(C,B,E)
| ~ join(A,C,D)
| ~ meet(A,B,A) ),
inference(clausify,[status(thm)],[modularity2]) ).
fof(join_x_and_0,axiom,
! [VAR_0] : join(VAR_0,n0,VAR_0),
file('theBenchmark.p',join_x_and_0) ).
cnf(c_22,plain,
join(A,n0,A),
inference(clausify,[status(thm)],[join_x_and_0]) ).
fof(meet_x_and_0,axiom,
! [VAR_0] : meet(VAR_0,n0,n0),
file('theBenchmark.p',meet_x_and_0) ).
cnf(c_23,plain,
meet(A,n0,n0),
inference(clausify,[status(thm)],[meet_x_and_0]) ).
fof(meet_a_and_b,axiom,
meet(a,b,c),
file('theBenchmark.p',meet_a_and_b) ).
cnf(c_27,plain,
meet(a,b,c),
inference(clausify,[status(thm)],[meet_a_and_b]) ).
fof(meet_c_and_r2,axiom,
meet(c,r2,n0),
file('theBenchmark.p',meet_c_and_r2) ).
cnf(c_29,plain,
meet(c,r2,n0),
inference(clausify,[status(thm)],[meet_c_and_r2]) ).
fof(meet_r2_and_b,axiom,
meet(r2,b,e),
file('theBenchmark.p',meet_r2_and_b) ).
cnf(c_30,plain,
meet(r2,b,e),
inference(clausify,[status(thm)],[meet_r2_and_b]) ).
fof(join_a_and_b,axiom,
join(a,b,c2),
file('theBenchmark.p',join_a_and_b) ).
cnf(c_31,plain,
join(a,b,c2),
inference(clausify,[status(thm)],[join_a_and_b]) ).
fof(meet_c2_and_r1,axiom,
meet(c2,r1,n0),
file('theBenchmark.p',meet_c2_and_r1) ).
cnf(c_33,plain,
meet(c2,r1,n0),
inference(clausify,[status(thm)],[meet_c2_and_r1]) ).
fof(meet_r2_and_a,axiom,
meet(r2,a,d),
file('theBenchmark.p',meet_r2_and_a) ).
cnf(c_34,plain,
meet(r2,a,d),
inference(clausify,[status(thm)],[meet_r2_and_a]) ).
fof(join_r1_and_e,axiom,
join(r1,e,a2),
file('theBenchmark.p',join_r1_and_e) ).
cnf(c_35,plain,
join(r1,e,a2),
inference(clausify,[status(thm)],[join_r1_and_e]) ).
fof(join_r1_and_d,axiom,
join(r1,d,b2),
file('theBenchmark.p',join_r1_and_d) ).
cnf(c_36,plain,
join(r1,d,b2),
inference(clausify,[status(thm)],[join_r1_and_d]) ).
fof(meet_a2_and_b2,axiom,
~ meet(a2,b2,r1),
file('theBenchmark.p',meet_a2_and_b2) ).
cnf(c_37,plain,
~ meet(a2,b2,r1),
inference(clausify,[status(thm)],[meet_a2_and_b2]) ).
cnf(c_306,plain,
meet(b,a,c),
inference(resolve,[status(thm)],[c_27,c_7]) ).
cnf(c_5082,plain,
( meet(e,A,C)
| ~ meet(r2,B,C)
| ~ meet(b,A,B) ),
inference(resolve,[status(thm)],[c_11,c_30]) ).
cnf(c_5083,plain,
( meet(e,b,A)
| ~ meet(r2,b,A) ),
inference(resolve,[status(thm)],[c_5082,c_5]) ).
cnf(c_395,plain,
meet(e,b,e),
inference(resolve,[status(thm)],[c_5083,c_30]) ).
cnf(c_414,plain,
meet(a,c2,a),
inference(resolve,[status(thm)],[c_31,c_10]) ).
cnf(c_415,plain,
join(b,a,c2),
inference(resolve,[status(thm)],[c_31,c_8]) ).
cnf(c_465,plain,
meet(r1,c2,n0),
inference(resolve,[status(thm)],[c_33,c_7]) ).
cnf(c_486,plain,
meet(a,r2,d),
inference(resolve,[status(thm)],[c_34,c_7]) ).
cnf(c_557,plain,
meet(r1,b2,r1),
inference(resolve,[status(thm)],[c_36,c_10]) ).
cnf(c_558,plain,
join(d,r1,b2),
inference(resolve,[status(thm)],[c_36,c_8]) ).
cnf(c_5084,plain,
( meet(C,B,E)
| ~ join(n0,D,E)
| ~ meet(A,C,D)
| ~ join(n0,A,B) ),
inference(resolve,[status(thm)],[c_16,c_4]) ).
cnf(c_5085,plain,
( meet(B,A,D)
| ~ join(n0,C,D)
| ~ meet(A,B,C) ),
inference(resolve,[status(thm)],[c_5084,c_3]) ).
cnf(c_5086,plain,
( meet(B,A,C)
| ~ meet(A,B,C) ),
inference(resolve,[status(thm)],[c_5085,c_3]) ).
cnf(c_579,plain,
~ meet(b2,a2,r1),
inference(resolve,[status(thm)],[c_5086,c_37]) ).
cnf(c_5087,plain,
( meet(d,A,C)
| ~ meet(r2,B,C)
| ~ meet(a,A,B) ),
inference(resolve,[status(thm)],[c_11,c_34]) ).
cnf(c_5088,plain,
( meet(d,c2,A)
| ~ meet(r2,a,A) ),
inference(resolve,[status(thm)],[c_5087,c_414]) ).
cnf(c_1024,plain,
meet(d,c2,d),
inference(resolve,[status(thm)],[c_5088,c_34]) ).
cnf(c_1063,plain,
meet(b,c2,b),
inference(resolve,[status(thm)],[c_415,c_10]) ).
cnf(c_5089,plain,
( meet(b,B,C)
| ~ meet(c,A,C)
| ~ meet(a,A,B) ),
inference(resolve,[status(thm)],[c_12,c_306]) ).
cnf(c_5090,plain,
( meet(b,d,A)
| ~ meet(c,r2,A) ),
inference(resolve,[status(thm)],[c_5089,c_486]) ).
cnf(c_1241,plain,
meet(b,d,n0),
inference(resolve,[status(thm)],[c_5090,c_29]) ).
cnf(c_5091,plain,
( meet(b2,B,D)
| ~ join(r1,C,D)
| ~ meet(A,b2,C)
| ~ join(r1,A,B) ),
inference(resolve,[status(thm)],[c_16,c_557]) ).
cnf(c_5092,plain,
( meet(b2,a2,B)
| ~ join(r1,A,B)
| ~ meet(e,b2,A) ),
inference(resolve,[status(thm)],[c_5091,c_35]) ).
cnf(c_5093,plain,
( meet(b2,a2,r1)
| ~ meet(e,b2,n0) ),
inference(resolve,[status(thm)],[c_5092,c_22]) ).
cnf(c_1670,plain,
~ meet(e,b2,n0),
inference(resolve,[status(thm)],[c_5093,c_579]) ).
cnf(c_5094,plain,
( meet(c2,B,D)
| ~ join(d,C,D)
| ~ meet(A,c2,C)
| ~ join(d,A,B) ),
inference(resolve,[status(thm)],[c_16,c_1024]) ).
cnf(c_5095,plain,
( meet(c2,b2,B)
| ~ join(d,A,B)
| ~ meet(r1,c2,A) ),
inference(resolve,[status(thm)],[c_5094,c_558]) ).
cnf(c_5096,plain,
( meet(c2,b2,A)
| ~ join(d,n0,A) ),
inference(resolve,[status(thm)],[c_5095,c_465]) ).
cnf(c_2668,plain,
meet(c2,b2,d),
inference(resolve,[status(thm)],[c_5096,c_22]) ).
cnf(c_5097,plain,
( meet(e,A,C)
| ~ meet(e,B,C)
| ~ meet(b,A,B) ),
inference(resolve,[status(thm)],[c_11,c_395]) ).
cnf(c_5098,plain,
( meet(e,A,n0)
| ~ meet(b,A,n0) ),
inference(resolve,[status(thm)],[c_5097,c_23]) ).
cnf(c_4094,plain,
~ meet(b,b2,n0),
inference(resolve,[status(thm)],[c_5098,c_1670]) ).
cnf(c_5099,plain,
( meet(b,A,C)
| ~ meet(b,B,C)
| ~ meet(c2,A,B) ),
inference(resolve,[status(thm)],[c_11,c_1063]) ).
cnf(c_5100,plain,
( meet(b,b2,A)
| ~ meet(b,d,A) ),
inference(resolve,[status(thm)],[c_5099,c_2668]) ).
cnf(c_5101,plain,
meet(b,b2,n0),
inference(resolve,[status(thm)],[c_5100,c_1241]) ).
cnf(c_5081,plain,
$false,
inference(resolve,[status(thm)],[c_4094,c_5101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT005-6 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.38 % DateTime : Fri Sep 25 19:55:02 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.38 % Process 952957 was started by sandbox2 on n014,
% 0.09/0.38 % Fri Sep 25 19:55:02 2026
% 0.09/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 12.35/2.17
% 12.35/2.17 % SZS status Unsatisfiable for theBenchmark
% 12.35/2.17
% 12.35/2.17 % Proof 1 at 1.34 (+ 0.43) seconds.
% 12.35/2.17 % Length of proof is 36.
% 12.35/2.17 % Level of proof is 4.
% 12.35/2.17 % Maximum clause weight is 25.000.
% 12.35/2.17 % Given clauses 222.
% 12.35/2.17
% 12.35/2.17 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------