%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 3.07s 0.84s
% Output : CNFRefutation 3.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 20
% Syntax : Number of formulae : 82 ( 45 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 147 ( 76 ~; 71 |; 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 : 127 ( 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_4,plain,
join(n0,A,A),
inference(clausify,[status(thm)],[join_0_and_x]) ).
fof(join_x_and_0,axiom,
! [VAR_0] : join(VAR_0,n0,VAR_0),
file('theBenchmark.p',join_x_and_0) ).
cnf(c_5,plain,
join(A,n0,A),
inference(clausify,[status(thm)],[join_x_and_0]) ).
fof(meet_0_and_x,axiom,
! [VAR_0] : meet(n0,VAR_0,n0),
file('theBenchmark.p',meet_0_and_x) ).
cnf(c_6,plain,
meet(n0,A,n0),
inference(clausify,[status(thm)],[meet_0_and_x]) ).
fof(meet_x_and_0,axiom,
! [VAR_0] : meet(VAR_0,n0,n0),
file('theBenchmark.p',meet_x_and_0) ).
cnf(c_7,plain,
meet(A,n0,n0),
inference(clausify,[status(thm)],[meet_x_and_0]) ).
fof(meet_x_and_x,axiom,
! [VAR_0] : meet(VAR_0,VAR_0,VAR_0),
file('theBenchmark.p',meet_x_and_x) ).
cnf(c_8,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_11,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_12,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_14,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_15,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_16,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_20,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(meet_a2_and_b2,axiom,
~ meet(a2,b2,r1),
file('theBenchmark.p',meet_a2_and_b2) ).
cnf(c_21,plain,
~ meet(a2,b2,r1),
inference(clausify,[status(thm)],[meet_a2_and_b2]) ).
fof(meet_a_and_b,axiom,
meet(a,b,c),
file('theBenchmark.p',meet_a_and_b) ).
cnf(c_22,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_24,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_25,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_26,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_28,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_29,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_30,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_31,plain,
join(r1,d,b2),
inference(clausify,[status(thm)],[join_r1_and_d]) ).
cnf(c_35,plain,
~ meet(b2,a2,r1),
inference(resolve,[status(thm)],[c_21,c_11]) ).
cnf(c_2670,plain,
( meet(C,B,E)
| ~ join(n0,D,E)
| ~ meet(A,C,D)
| ~ join(n0,A,B) ),
inference(resolve,[status(thm)],[c_20,c_6]) ).
cnf(c_2671,plain,
( meet(B,A,D)
| ~ join(n0,C,D)
| ~ meet(A,B,C) ),
inference(resolve,[status(thm)],[c_2670,c_4]) ).
cnf(c_2672,plain,
( meet(b,a,A)
| ~ join(n0,c,A) ),
inference(resolve,[status(thm)],[c_2671,c_22]) ).
cnf(c_36,plain,
meet(b,a,c),
inference(resolve,[status(thm)],[c_2672,c_4]) ).
cnf(c_2673,plain,
( meet(e,A,C)
| ~ meet(r2,B,C)
| ~ meet(b,A,B) ),
inference(resolve,[status(thm)],[c_15,c_25]) ).
cnf(c_2674,plain,
( meet(e,b,A)
| ~ meet(r2,b,A) ),
inference(resolve,[status(thm)],[c_2673,c_8]) ).
cnf(c_45,plain,
meet(e,b,e),
inference(resolve,[status(thm)],[c_2674,c_25]) ).
cnf(c_49,plain,
meet(a,c2,a),
inference(resolve,[status(thm)],[c_14,c_26]) ).
cnf(c_50,plain,
join(b,a,c2),
inference(resolve,[status(thm)],[c_12,c_26]) ).
cnf(c_2675,plain,
( meet(C,B,E)
| ~ join(n0,D,E)
| ~ meet(A,C,D)
| ~ join(n0,A,B) ),
inference(resolve,[status(thm)],[c_20,c_6]) ).
cnf(c_2676,plain,
( meet(B,A,D)
| ~ join(n0,C,D)
| ~ meet(A,B,C) ),
inference(resolve,[status(thm)],[c_2675,c_4]) ).
cnf(c_2677,plain,
( meet(r1,c2,A)
| ~ join(n0,n0,A) ),
inference(resolve,[status(thm)],[c_2676,c_28]) ).
cnf(c_52,plain,
meet(r1,c2,n0),
inference(resolve,[status(thm)],[c_2677,c_5]) ).
cnf(c_2678,plain,
( meet(C,B,E)
| ~ join(n0,D,E)
| ~ meet(A,C,D)
| ~ join(n0,A,B) ),
inference(resolve,[status(thm)],[c_20,c_6]) ).
cnf(c_2679,plain,
( meet(B,A,D)
| ~ join(n0,C,D)
| ~ meet(A,B,C) ),
inference(resolve,[status(thm)],[c_2678,c_4]) ).
cnf(c_2680,plain,
( meet(a,r2,A)
| ~ join(n0,d,A) ),
inference(resolve,[status(thm)],[c_2679,c_29]) ).
cnf(c_53,plain,
meet(a,r2,d),
inference(resolve,[status(thm)],[c_2680,c_4]) ).
cnf(c_66,plain,
meet(r1,b2,r1),
inference(resolve,[status(thm)],[c_14,c_31]) ).
cnf(c_67,plain,
join(d,r1,b2),
inference(resolve,[status(thm)],[c_12,c_31]) ).
cnf(c_2681,plain,
( meet(d,A,C)
| ~ meet(r2,B,C)
| ~ meet(a,A,B) ),
inference(resolve,[status(thm)],[c_15,c_29]) ).
cnf(c_2682,plain,
( meet(d,c2,A)
| ~ meet(r2,a,A) ),
inference(resolve,[status(thm)],[c_2681,c_49]) ).
cnf(c_258,plain,
meet(d,c2,d),
inference(resolve,[status(thm)],[c_2682,c_29]) ).
cnf(c_261,plain,
meet(b,c2,b),
inference(resolve,[status(thm)],[c_14,c_50]) ).
cnf(c_2683,plain,
( meet(b,B,C)
| ~ meet(c,A,C)
| ~ meet(a,A,B) ),
inference(resolve,[status(thm)],[c_16,c_36]) ).
cnf(c_2684,plain,
( meet(b,d,A)
| ~ meet(c,r2,A) ),
inference(resolve,[status(thm)],[c_2683,c_53]) ).
cnf(c_263,plain,
meet(b,d,n0),
inference(resolve,[status(thm)],[c_2684,c_24]) ).
cnf(c_2685,plain,
( meet(b2,B,D)
| ~ join(r1,C,D)
| ~ meet(A,b2,C)
| ~ join(r1,A,B) ),
inference(resolve,[status(thm)],[c_20,c_66]) ).
cnf(c_2686,plain,
( meet(b2,a2,B)
| ~ join(r1,A,B)
| ~ meet(e,b2,A) ),
inference(resolve,[status(thm)],[c_2685,c_30]) ).
cnf(c_2687,plain,
( meet(b2,a2,r1)
| ~ meet(e,b2,n0) ),
inference(resolve,[status(thm)],[c_2686,c_5]) ).
cnf(c_370,plain,
~ meet(e,b2,n0),
inference(resolve,[status(thm)],[c_2687,c_35]) ).
cnf(c_2688,plain,
( meet(c2,B,D)
| ~ join(d,C,D)
| ~ meet(A,c2,C)
| ~ join(d,A,B) ),
inference(resolve,[status(thm)],[c_20,c_258]) ).
cnf(c_2689,plain,
( meet(c2,b2,B)
| ~ join(d,A,B)
| ~ meet(r1,c2,A) ),
inference(resolve,[status(thm)],[c_2688,c_67]) ).
cnf(c_2690,plain,
( meet(c2,b2,A)
| ~ join(d,n0,A) ),
inference(resolve,[status(thm)],[c_2689,c_52]) ).
cnf(c_1134,plain,
meet(c2,b2,d),
inference(resolve,[status(thm)],[c_2690,c_5]) ).
cnf(c_2691,plain,
( meet(e,A,C)
| ~ meet(e,B,C)
| ~ meet(b,A,B) ),
inference(resolve,[status(thm)],[c_15,c_45]) ).
cnf(c_2692,plain,
( meet(e,A,n0)
| ~ meet(b,A,n0) ),
inference(resolve,[status(thm)],[c_2691,c_7]) ).
cnf(c_2020,plain,
~ meet(b,b2,n0),
inference(resolve,[status(thm)],[c_2692,c_370]) ).
cnf(c_2693,plain,
( meet(b,A,C)
| ~ meet(b,B,C)
| ~ meet(c2,A,B) ),
inference(resolve,[status(thm)],[c_15,c_261]) ).
cnf(c_2694,plain,
( meet(b,b2,A)
| ~ meet(b,d,A) ),
inference(resolve,[status(thm)],[c_2693,c_1134]) ).
cnf(c_2668,plain,
meet(b,b2,n0),
inference(resolve,[status(thm)],[c_2694,c_263]) ).
cnf(c_2669,plain,
$false,
inference(resolve,[status(thm)],[c_2668,c_2020]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Fri Sep 25 19:54:43 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 2738881 was started by sandbox2 on n011,
% 0.08/0.35 % Fri Sep 25 19:54:43 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 3.07/0.84
% 3.07/0.84 % SZS status Unsatisfiable for theBenchmark
% 3.07/0.84
% 3.07/0.84 % Proof 1 at 0.40 (+ 0.06) seconds.
% 3.07/0.84 % Length of proof is 37.
% 3.07/0.84 % Level of proof is 5.
% 3.07/0.84 % Maximum clause weight is 22.000.
% 3.07/0.84 % Given clauses 226.
% 3.07/0.84
% 3.07/0.84 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------