%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT089-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 07:49:40 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.47s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 6
% Syntax : Number of formulae : 77 ( 77 unt; 0 def)
% Number of atoms : 77 ( 76 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 146 ( 28 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(wal_absorbtion_1,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_1),meet(VAR_0,join(VAR_0,VAR_1))) = VAR_0,
file('theBenchmark.p',wal_absorbtion_1) ).
cnf(c_1,plain,
join(meet(A,B),meet(A,join(A,B))) = A,
inference(clausify,[status(thm)],[wal_absorbtion_1]) ).
fof(wal_absorbtion_2,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_0),meet(VAR_1,join(VAR_0,VAR_0))) = VAR_0,
file('theBenchmark.p',wal_absorbtion_2) ).
cnf(c_2,plain,
join(meet(A,A),meet(B,join(A,A))) = A,
inference(clausify,[status(thm)],[wal_absorbtion_2]) ).
fof(wal_absorbtion_3,axiom,
! [VAR_0,VAR_1] : join(meet(VAR_0,VAR_1),meet(VAR_1,join(VAR_0,VAR_1))) = VAR_1,
file('theBenchmark.p',wal_absorbtion_3) ).
cnf(c_3,plain,
join(meet(A,B),meet(B,join(A,B))) = B,
inference(clausify,[status(thm)],[wal_absorbtion_3]) ).
fof(wal_absorbtion_4,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(join(VAR_0,VAR_1),join(VAR_2,VAR_0)),VAR_0) = VAR_0,
file('theBenchmark.p',wal_absorbtion_4) ).
cnf(c_4,plain,
meet(meet(join(A,B),join(C,A)),A) = A,
inference(clausify,[status(thm)],[wal_absorbtion_4]) ).
fof(wal_absorbtion_5,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet(VAR_0,VAR_1),meet(VAR_2,VAR_0)),VAR_0) = VAR_0,
file('theBenchmark.p',wal_absorbtion_5) ).
cnf(c_5,plain,
join(join(meet(A,B),meet(C,A)),A) = A,
inference(clausify,[status(thm)],[wal_absorbtion_5]) ).
fof(prove_normal_axioms_2,axiom,
meet(b,a) != meet(a,b),
file('theBenchmark.p',prove_normal_axioms_2) ).
cnf(c_6,plain,
meet(b,a) != meet(a,b),
inference(clausify,[status(thm)],[prove_normal_axioms_2]) ).
cnf(c_7,plain,
join(meet(meet(A,B),meet(A,join(A,B))),meet(meet(A,B),A)) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_19,plain,
meet(meet(A,join(B,meet(C,A))),meet(C,A)) = meet(C,A),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_22,plain,
join(meet(join(meet(A,B),meet(C,A)),A),meet(A,A)) = A,
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_24,plain,
meet(meet(join(A,B),A),A) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_26,plain,
join(join(meet(A,B),A),A) = A,
inference(paramod,[status(thm)],[c_4,c_5]) ).
cnf(c_36,plain,
join(A,meet(A,join(meet(join(A,B),A),A))) = A,
inference(paramod,[status(thm)],[c_24,c_3]) ).
cnf(c_41,plain,
join(meet(join(meet(A,B),A),A),meet(join(meet(A,B),A),A)) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_26,c_1]) ).
cnf(c_42,plain,
join(meet(join(meet(A,B),A),A),meet(A,A)) = A,
inference(paramod,[status(thm)],[c_26,c_3]) ).
cnf(c_47,plain,
join(join(A,meet(join(A,B),A)),meet(join(A,B),A)) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_24,c_26]) ).
cnf(c_64,plain,
meet(meet(A,join(B,A)),A) = A,
inference(paramod,[status(thm)],[c_36,c_4]) ).
cnf(c_66,plain,
meet(meet(A,A),A) = A,
inference(paramod,[status(thm)],[c_36,c_24]) ).
cnf(c_68,plain,
join(A,meet(A,join(meet(A,A),A))) = A,
inference(paramod,[status(thm)],[c_36,c_36]) ).
cnf(c_82,plain,
join(A,meet(meet(A,join(B,A)),join(meet(A,join(B,A)),A))) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_64,c_1]) ).
cnf(c_306,plain,
meet(meet(meet(A,join(B,A)),A),meet(A,join(B,A))) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_3,c_64]) ).
cnf(c_86,plain,
meet(A,meet(A,join(B,A))) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_64,c_306]) ).
cnf(c_307,plain,
meet(meet(meet(A,A),A),meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_42,c_64]) ).
cnf(c_94,plain,
meet(A,meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_66,c_307]) ).
cnf(c_101,plain,
join(meet(A,A),meet(A,join(A,meet(A,A)))) = A,
inference(paramod,[status(thm)],[c_94,c_1]) ).
cnf(c_308,plain,
join(meet(A,meet(A,join(meet(A,A),A))),meet(A,A)) = A,
inference(paramod,[status(thm)],[c_68,c_1]) ).
cnf(c_104,plain,
join(meet(A,join(meet(A,A),A)),meet(A,A)) = A,
inference(paramod,[status(thm)],[c_86,c_308]) ).
cnf(c_309,plain,
meet(meet(A,meet(A,A)),meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_101,c_24]) ).
cnf(c_139,plain,
meet(meet(A,A),meet(A,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_94,c_309]) ).
cnf(c_144,plain,
join(meet(A,A),meet(B,join(meet(A,A),meet(A,A)))) = meet(A,A),
inference(paramod,[status(thm)],[c_139,c_2]) ).
cnf(c_155,plain,
join(A,A) = A,
inference(paramod,[status(thm)],[c_104,c_5]) ).
cnf(c_310,plain,
join(meet(A,A),meet(A,A)) = A,
inference(paramod,[status(thm)],[c_104,c_22]) ).
cnf(c_157,plain,
meet(A,A) = A,
inference(paramod,[status(thm)],[c_155,c_310]) ).
cnf(c_311,plain,
join(A,meet(B,join(meet(A,A),meet(A,A)))) = meet(A,A),
inference(paramod,[status(thm)],[c_157,c_144]) ).
cnf(c_312,plain,
join(A,meet(B,join(A,meet(A,A)))) = meet(A,A),
inference(paramod,[status(thm)],[c_157,c_311]) ).
cnf(c_313,plain,
join(A,meet(B,join(A,A))) = meet(A,A),
inference(paramod,[status(thm)],[c_157,c_312]) ).
cnf(c_314,plain,
join(A,meet(B,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_155,c_313]) ).
cnf(c_158,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_157,c_314]) ).
cnf(c_162,plain,
meet(join(meet(A,B),A),A) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_155,c_41]) ).
cnf(c_315,plain,
join(A,meet(join(A,B),A)) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_158,c_47]) ).
cnf(c_316,plain,
A = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_158,c_315]) ).
cnf(c_176,plain,
meet(join(A,B),A) = A,
inference(copy,[status(thm)],[c_316]) ).
cnf(c_183,plain,
join(A,meet(join(A,B),join(join(A,B),A))) = join(A,B),
inference(paramod,[status(thm)],[c_176,c_1]) ).
cnf(c_184,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_176]) ).
cnf(c_317,plain,
join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(meet(join(A,B),A),join(A,B))) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_176,c_7]) ).
cnf(c_318,plain,
join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = meet(join(A,B),A),
inference(paramod,[status(thm)],[c_176,c_317]) ).
cnf(c_188,plain,
join(meet(A,meet(join(A,B),join(join(A,B),A))),meet(A,join(A,B))) = A,
inference(paramod,[status(thm)],[c_176,c_318]) ).
cnf(c_190,plain,
meet(A,join(meet(A,B),A)) = join(meet(A,B),A),
inference(paramod,[status(thm)],[c_26,c_176]) ).
cnf(c_319,plain,
join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,meet(A,B)),A)) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_184,c_7]) ).
cnf(c_320,plain,
join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,B),A)) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_184,c_319]) ).
cnf(c_199,plain,
join(meet(meet(A,B),meet(A,join(A,meet(A,B)))),meet(meet(A,B),A)) = meet(A,B),
inference(paramod,[status(thm)],[c_184,c_320]) ).
cnf(c_321,plain,
meet(meet(join(A,B),join(C,A)),join(A,meet(join(A,B),join(C,A)))) = join(meet(meet(join(A,B),join(C,A)),A),meet(join(A,B),join(C,A))),
inference(paramod,[status(thm)],[c_4,c_190]) ).
cnf(c_215,plain,
meet(meet(join(A,B),join(C,A)),join(A,meet(join(A,B),join(C,A)))) = join(A,meet(join(A,B),join(C,A))),
inference(paramod,[status(thm)],[c_4,c_321]) ).
cnf(c_322,plain,
meet(join(meet(A,B),A),A) = A,
inference(paramod,[status(thm)],[c_190,c_64]) ).
cnf(c_217,plain,
join(meet(A,B),A) = A,
inference(paramod,[status(thm)],[c_162,c_322]) ).
cnf(c_323,plain,
join(A,meet(meet(A,join(B,A)),A)) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_217,c_82]) ).
cnf(c_324,plain,
join(A,A) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_64,c_323]) ).
cnf(c_325,plain,
A = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_155,c_324]) ).
cnf(c_221,plain,
meet(A,join(B,A)) = A,
inference(copy,[status(thm)],[c_325]) ).
cnf(c_326,plain,
meet(join(A,B),join(C,A)) = join(A,meet(join(A,B),join(C,A))),
inference(paramod,[status(thm)],[c_221,c_215]) ).
cnf(c_223,plain,
join(A,meet(join(A,B),join(C,A))) = meet(join(A,B),join(C,A)),
inference(copy,[status(thm)],[c_326]) ).
cnf(c_224,plain,
meet(join(A,B),join(join(A,B),A)) = join(A,B),
inference(paramod,[status(thm)],[c_223,c_183]) ).
cnf(c_327,plain,
join(meet(A,join(A,B)),meet(A,join(A,B))) = A,
inference(paramod,[status(thm)],[c_224,c_188]) ).
cnf(c_225,plain,
meet(A,join(A,B)) = A,
inference(paramod,[status(thm)],[c_155,c_327]) ).
cnf(c_328,plain,
join(meet(meet(A,B),A),meet(meet(A,B),A)) = meet(A,B),
inference(paramod,[status(thm)],[c_225,c_199]) ).
cnf(c_230,plain,
meet(meet(A,B),A) = meet(A,B),
inference(paramod,[status(thm)],[c_155,c_328]) ).
cnf(c_243,plain,
join(A,meet(A,B)) = A,
inference(paramod,[status(thm)],[c_230,c_158]) ).
cnf(c_252,plain,
meet(meet(A,B),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_243,c_19]) ).
cnf(c_329,plain,
meet(meet(A,B),meet(B,A)) = meet(meet(B,A),meet(A,B)),
inference(paramod,[status(thm)],[c_252,c_230]) ).
cnf(c_330,plain,
meet(B,A) = meet(meet(B,A),meet(A,B)),
inference(paramod,[status(thm)],[c_252,c_329]) ).
cnf(c_304,plain,
meet(A,B) = meet(B,A),
inference(paramod,[status(thm)],[c_252,c_330]) ).
cnf(c_305,plain,
$false,
inference(resolve,[status(thm)],[c_304,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT089-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n026.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 20:06:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 3332396 was started by sandbox on n026,
% 0.11/0.37 % Fri Sep 25 20:06:10 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 0.11/0.47
% 0.11/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.47
% 0.11/0.47 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.11/0.47 % Length of proof is 46.
% 0.11/0.47 % Level of proof is 20.
% 0.11/0.47 % Maximum clause weight is 66.000.
% 0.11/0.47 % Given clauses 57.
% 0.11/0.47
% 0.11/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------