%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT005-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12.04s 1.99s
% Output : CNFRefutation 12.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 89 ( 86 unt; 0 def)
% Number of atoms : 92 ( 91 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 5 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 97 ( 9 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(x_join_0,axiom,
! [VAR_0] : join(VAR_0,n0) = VAR_0,
file('theBenchmark.p',x_join_0) ).
cnf(c_10,plain,
join(A,n0) = A,
inference(clausify,[status(thm)],[x_join_0]) ).
fof(modular,axiom,
! [VAR_0,VAR_1,VAR_2] :
( meet(VAR_1,join(VAR_0,VAR_2)) = join(VAR_0,meet(VAR_2,VAR_1))
| meet(VAR_0,VAR_1) != VAR_0 ),
file('theBenchmark.p',modular) ).
cnf(c_13,plain,
( meet(B,join(A,C)) = join(A,meet(C,B))
| meet(A,B) != A ),
inference(clausify,[status(thm)],[modular]) ).
cnf(c_14,plain,
( join(A,meet(C,B)) = meet(B,join(A,C))
| meet(A,B) != A ),
inference(copy,[status(thm)],[c_13]) ).
fof(r2_complement_meet_a_b_2,axiom,
meet(r2,meet(a,b)) = n0,
file('theBenchmark.p',r2_complement_meet_a_b_2) ).
cnf(c_16,plain,
meet(r2,meet(a,b)) = n0,
inference(clausify,[status(thm)],[r2_complement_meet_a_b_2]) ).
fof(r1_complement_join_a_b_2,axiom,
meet(r1,join(a,b)) = n0,
file('theBenchmark.p',r1_complement_join_a_b_2) ).
cnf(c_18,plain,
meet(r1,join(a,b)) = n0,
inference(clausify,[status(thm)],[r1_complement_join_a_b_2]) ).
fof(define_b2,axiom,
join(r1,meet(a,r2)) = b2,
file('theBenchmark.p',define_b2) ).
cnf(c_19,plain,
join(r1,meet(a,r2)) = b2,
inference(clausify,[status(thm)],[define_b2]) ).
fof(define_a2,axiom,
join(r1,meet(b,r2)) = a2,
file('theBenchmark.p',define_a2) ).
cnf(c_20,plain,
join(r1,meet(b,r2)) = a2,
inference(clausify,[status(thm)],[define_a2]) ).
fof(prove_SAMs_lemma,axiom,
meet(a2,b2) != r1,
file('theBenchmark.p',prove_SAMs_lemma) ).
cnf(c_21,plain,
meet(a2,b2) != r1,
inference(clausify,[status(thm)],[prove_SAMs_lemma]) ).
cnf(c_23,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_4701,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_28,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_4701]) ).
cnf(c_30,plain,
meet(A,meet(B,C)) = meet(C,meet(A,B)),
inference(paramod,[status(thm)],[c_7,c_5]) ).
cnf(c_4702,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_31,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_4702]) ).
cnf(c_4703,plain,
meet(b,meet(r2,a)) = n0,
inference(paramod,[status(thm)],[c_30,c_16]) ).
cnf(c_4704,plain,
meet(b,meet(a,r2)) = n0,
inference(paramod,[status(thm)],[c_5,c_4703]) ).
cnf(c_32,plain,
meet(a,meet(b,r2)) = n0,
inference(paramod,[status(thm)],[c_31,c_4704]) ).
cnf(c_4705,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_35,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_6,c_4705]) ).
cnf(c_4706,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_38,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_4706]) ).
cnf(c_4707,plain,
A = join(n0,A),
inference(paramod,[status(thm)],[c_10,c_6]) ).
cnf(c_43,plain,
join(n0,A) = A,
inference(copy,[status(thm)],[c_4707]) ).
cnf(c_51,plain,
meet(r1,a2) = r1,
inference(paramod,[status(thm)],[c_20,c_3]) ).
cnf(c_4708,plain,
join(a2,A) = join(r1,join(meet(b,r2),A)),
inference(paramod,[status(thm)],[c_20,c_8]) ).
cnf(c_52,plain,
join(r1,join(meet(b,r2),A)) = join(a2,A),
inference(copy,[status(thm)],[c_4708]) ).
cnf(c_60,plain,
join(r1,meet(A,a2)) = meet(a2,join(r1,A)),
inference(resolve,[status(thm)],[c_14,c_51]) ).
cnf(c_64,plain,
join(A,meet(B,join(C,A))) = meet(join(C,A),join(A,B)),
inference(resolve,[status(thm)],[c_14,c_23]) ).
cnf(c_4709,plain,
meet(meet(b,r2),a2) = meet(b,r2),
inference(paramod,[status(thm)],[c_20,c_23]) ).
cnf(c_4710,plain,
meet(a2,meet(b,r2)) = meet(b,r2),
inference(paramod,[status(thm)],[c_5,c_4709]) ).
cnf(c_4711,plain,
meet(b,meet(a2,r2)) = meet(b,r2),
inference(paramod,[status(thm)],[c_31,c_4710]) ).
cnf(c_69,plain,
meet(b,meet(r2,a2)) = meet(b,r2),
inference(paramod,[status(thm)],[c_5,c_4711]) ).
cnf(c_4712,plain,
join(A,join(B,join(C,A))) = join(join(B,C),A),
inference(paramod,[status(thm)],[c_8,c_35]) ).
cnf(c_89,plain,
join(A,join(B,join(C,A))) = join(B,join(C,A)),
inference(paramod,[status(thm)],[c_8,c_4712]) ).
cnf(c_124,plain,
join(r1,meet(A,meet(B,a2))) = meet(a2,join(r1,meet(A,B))),
inference(paramod,[status(thm)],[c_7,c_60]) ).
cnf(c_4713,plain,
meet(meet(A,b),meet(r2,a2)) = meet(A,meet(b,r2)),
inference(paramod,[status(thm)],[c_69,c_7]) ).
cnf(c_4714,plain,
meet(r2,meet(meet(A,b),a2)) = meet(A,meet(b,r2)),
inference(paramod,[status(thm)],[c_31,c_4713]) ).
cnf(c_178,plain,
meet(r2,meet(a2,meet(A,b))) = meet(A,meet(b,r2)),
inference(paramod,[status(thm)],[c_5,c_4714]) ).
cnf(c_4715,plain,
join(A,join(meet(A,B),join(C,A))) = join(C,A),
inference(paramod,[status(thm)],[c_35,c_38]) ).
cnf(c_272,plain,
join(meet(A,B),join(C,A)) = join(C,A),
inference(paramod,[status(thm)],[c_89,c_4715]) ).
cnf(c_4716,plain,
join(r1,join(A,b)) = join(a2,join(A,b)),
inference(paramod,[status(thm)],[c_272,c_52]) ).
cnf(c_555,plain,
join(a2,join(A,b)) = join(r1,join(A,b)),
inference(copy,[status(thm)],[c_4716]) ).
cnf(c_4717,plain,
join(b,n0) = meet(join(a,b),join(b,r1)),
inference(paramod,[status(thm)],[c_18,c_64]) ).
cnf(c_4718,plain,
b = meet(join(a,b),join(b,r1)),
inference(paramod,[status(thm)],[c_10,c_4717]) ).
cnf(c_726,plain,
meet(join(a,b),join(b,r1)) = b,
inference(copy,[status(thm)],[c_4718]) ).
cnf(c_4719,plain,
meet(a,b) = meet(a,join(b,r1)),
inference(paramod,[status(thm)],[c_726,c_28]) ).
cnf(c_771,plain,
meet(a,join(b,r1)) = meet(a,b),
inference(copy,[status(thm)],[c_4719]) ).
cnf(c_4720,plain,
join(a2,b) = join(r1,join(b,b)),
inference(paramod,[status(thm)],[c_2,c_555]) ).
cnf(c_4721,plain,
join(b,a2) = join(r1,join(b,b)),
inference(paramod,[status(thm)],[c_6,c_4720]) ).
cnf(c_4722,plain,
join(b,a2) = join(r1,b),
inference(paramod,[status(thm)],[c_2,c_4721]) ).
cnf(c_937,plain,
join(b,a2) = join(b,r1),
inference(paramod,[status(thm)],[c_6,c_4722]) ).
cnf(c_956,plain,
meet(a2,join(b,r1)) = a2,
inference(paramod,[status(thm)],[c_937,c_23]) ).
cnf(c_4723,plain,
meet(A,a2) = meet(a2,meet(A,join(b,r1))),
inference(paramod,[status(thm)],[c_956,c_31]) ).
cnf(c_961,plain,
meet(a2,meet(A,join(b,r1))) = meet(A,a2),
inference(copy,[status(thm)],[c_4723]) ).
cnf(c_4724,plain,
meet(a2,meet(a,b)) = meet(a,a2),
inference(paramod,[status(thm)],[c_771,c_961]) ).
cnf(c_4725,plain,
meet(a,meet(a2,b)) = meet(a,a2),
inference(paramod,[status(thm)],[c_31,c_4724]) ).
cnf(c_3080,plain,
meet(a,meet(b,a2)) = meet(a,a2),
inference(paramod,[status(thm)],[c_5,c_4725]) ).
cnf(c_4726,plain,
meet(r2,meet(a2,meet(a,b))) = n0,
inference(paramod,[status(thm)],[c_32,c_178]) ).
cnf(c_4727,plain,
meet(r2,meet(a,meet(a2,b))) = n0,
inference(paramod,[status(thm)],[c_31,c_4726]) ).
cnf(c_4728,plain,
meet(r2,meet(a,meet(b,a2))) = n0,
inference(paramod,[status(thm)],[c_5,c_4727]) ).
cnf(c_4729,plain,
meet(r2,meet(a,a2)) = n0,
inference(paramod,[status(thm)],[c_3080,c_4728]) ).
cnf(c_4665,plain,
meet(a,meet(r2,a2)) = n0,
inference(paramod,[status(thm)],[c_31,c_4729]) ).
cnf(c_4730,plain,
join(r1,n0) = meet(a2,join(r1,meet(a,r2))),
inference(paramod,[status(thm)],[c_4665,c_124]) ).
cnf(c_4731,plain,
join(n0,r1) = meet(a2,join(r1,meet(a,r2))),
inference(paramod,[status(thm)],[c_6,c_4730]) ).
cnf(c_4732,plain,
r1 = meet(a2,join(r1,meet(a,r2))),
inference(paramod,[status(thm)],[c_43,c_4731]) ).
cnf(c_4733,plain,
r1 = meet(a2,b2),
inference(paramod,[status(thm)],[c_19,c_4732]) ).
cnf(c_4734,plain,
meet(a2,b2) = r1,
inference(copy,[status(thm)],[c_4733]) ).
cnf(c_4700,plain,
$false,
inference(resolve,[status(thm)],[c_21,c_4734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT005-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Fri Sep 25 19:58:04 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.36 % Process 4008366 was started by sandbox on n002,
% 0.13/0.36 % Fri Sep 25 19:58:04 2026
% 0.13/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 12.04/1.99
% 12.04/1.99 % SZS status Unsatisfiable for theBenchmark
% 12.04/1.99
% 12.04/1.99 % Proof 1 at 1.23 (+ 0.35) seconds.
% 12.04/1.99 % Length of proof is 41.
% 12.04/1.99 % Level of proof is 10.
% 12.04/1.99 % Maximum clause weight is 39.000.
% 12.04/1.99 % Given clauses 475.
% 12.04/1.99
% 12.04/1.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------