%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT140-1 : 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 : n005.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 07:49:43 AM UTC 2026
% Result : Unsatisfiable 162.32s 43.82s
% Output : CNFRefutation 162.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 88 ( 88 unt; 0 def)
% Number of atoms : 88 ( 87 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 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 : 220 ( 27 sgn 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(equation_H21,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(VAR_0,VAR_1),meet(VAR_0,VAR_2)) = meet(VAR_0,join(meet(VAR_1,join(VAR_0,meet(VAR_1,VAR_2))),meet(VAR_2,join(VAR_0,VAR_1)))),
file('theBenchmark.p',equation_H21) ).
cnf(c_9,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(meet(B,join(A,meet(B,C))),meet(C,join(A,B)))),
inference(clausify,[status(thm)],[equation_H21]) ).
cnf(c_10,plain,
meet(A,join(meet(B,join(A,meet(B,C))),meet(C,join(A,B)))) = join(meet(A,B),meet(A,C)),
inference(copy,[status(thm)],[c_9]) ).
fof(prove_H2,axiom,
meet(a,join(b,meet(a,c))) != meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))),
file('theBenchmark.p',prove_H2) ).
cnf(c_11,plain,
meet(a,join(b,meet(a,c))) != meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))),
inference(clausify,[status(thm)],[prove_H2]) ).
cnf(c_12,plain,
meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(b,c))))) != 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_4652,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_19,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_4652]) ).
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_22,plain,
join(A,meet(meet(A,B),C)) = A,
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_26,plain,
meet(meet(A,B),C) = meet(A,meet(C,B)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_32,plain,
meet(meet(A,B),join(A,C)) = meet(A,B),
inference(paramod,[status(thm)],[c_26,c_19]) ).
cnf(c_35,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_4653,plain,
join(meet(A,B),meet(A,C)) = meet(join(meet(B,join(A,meet(B,C))),meet(C,join(A,B))),A),
inference(paramod,[status(thm)],[c_10,c_5]) ).
cnf(c_53,plain,
meet(join(meet(A,join(B,meet(A,C))),meet(C,join(B,A))),B) = join(meet(B,A),meet(B,C)),
inference(copy,[status(thm)],[c_4653]) ).
cnf(c_58,plain,
meet(A,join(meet(B,join(A,meet(B,C))),meet(C,join(B,A)))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_6,c_10]) ).
cnf(c_76,plain,
meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(c,b))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_86,plain,
meet(join(A,B),B) = B,
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_105,plain,
meet(a,join(b,meet(c,join(meet(a,join(b,c)),meet(c,b))))) != meet(a,join(b,meet(c,a))),
inference(paramod,[status(thm)],[c_5,c_76]) ).
cnf(c_4654,plain,
A = join(meet(B,A),A),
inference(paramod,[status(thm)],[c_14,c_6]) ).
cnf(c_124,plain,
join(meet(A,B),B) = B,
inference(copy,[status(thm)],[c_4654]) ).
cnf(c_4655,plain,
meet(A,join(meet(B,join(A,meet(B,meet(A,B)))),meet(meet(A,B),join(A,B)))) = meet(A,B),
inference(paramod,[status(thm)],[c_14,c_10]) ).
cnf(c_130,plain,
meet(A,join(meet(B,join(A,meet(B,meet(A,B)))),meet(A,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_32,c_4655]) ).
cnf(c_153,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_14,c_86]) ).
cnf(c_4656,plain,
meet(A,join(meet(B,join(A,meet(A,B))),meet(A,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_153,c_130]) ).
cnf(c_155,plain,
meet(A,join(meet(B,A),meet(A,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_4,c_4656]) ).
cnf(c_4657,plain,
meet(A,B) = meet(join(meet(B,A),meet(A,B)),A),
inference(paramod,[status(thm)],[c_155,c_5]) ).
cnf(c_164,plain,
meet(join(meet(A,B),meet(B,A)),B) = meet(B,A),
inference(copy,[status(thm)],[c_4657]) ).
cnf(c_4658,plain,
meet(meet(A,B),C) = meet(A,meet(join(meet(B,A),meet(A,B)),C)),
inference(paramod,[status(thm)],[c_155,c_7]) ).
cnf(c_4659,plain,
meet(meet(A,B),C) = meet(meet(A,C),join(meet(B,A),meet(A,B))),
inference(paramod,[status(thm)],[c_26,c_4658]) ).
cnf(c_165,plain,
meet(meet(A,B),join(meet(C,A),meet(A,C))) = meet(meet(A,C),B),
inference(copy,[status(thm)],[c_4659]) ).
cnf(c_4660,plain,
meet(join(meet(A,B),meet(B,A)),join(meet(B,join(join(meet(A,B),meet(B,A)),meet(B,C))),meet(C,join(join(meet(A,B),meet(B,A)),B)))) = join(meet(B,A),meet(join(meet(A,B),meet(B,A)),C)),
inference(paramod,[status(thm)],[c_164,c_10]) ).
cnf(c_4661,plain,
meet(join(meet(A,B),meet(B,A)),join(meet(B,join(join(meet(A,B),meet(B,A)),meet(B,C))),meet(C,join(meet(A,B),join(meet(B,A),B))))) = join(meet(B,A),meet(join(meet(A,B),meet(B,A)),C)),
inference(paramod,[status(thm)],[c_8,c_4660]) ).
cnf(c_4662,plain,
meet(join(meet(A,B),meet(B,A)),join(meet(B,join(join(meet(A,B),meet(B,A)),meet(B,C))),meet(C,join(meet(A,B),B)))) = join(meet(B,A),meet(join(meet(A,B),meet(B,A)),C)),
inference(paramod,[status(thm)],[c_16,c_4661]) ).
cnf(c_211,plain,
meet(join(meet(A,B),meet(B,A)),join(meet(B,join(join(meet(A,B),meet(B,A)),meet(B,C))),meet(C,B))) = join(meet(B,A),meet(join(meet(A,B),meet(B,A)),C)),
inference(paramod,[status(thm)],[c_124,c_4662]) ).
cnf(c_234,plain,
join(A,meet(join(meet(A,B),meet(A,C)),D)) = A,
inference(paramod,[status(thm)],[c_10,c_22]) ).
cnf(c_237,plain,
join(A,meet(join(meet(B,A),meet(A,C)),D)) = A,
inference(paramod,[status(thm)],[c_5,c_234]) ).
cnf(c_238,plain,
join(A,meet(join(meet(A,B),meet(C,A)),D)) = A,
inference(paramod,[status(thm)],[c_5,c_234]) ).
cnf(c_4663,plain,
meet(A,meet(join(meet(B,A),meet(A,C)),D)) = meet(join(meet(B,A),meet(A,C)),D),
inference(paramod,[status(thm)],[c_237,c_86]) ).
cnf(c_303,plain,
meet(meet(A,B),join(meet(C,A),meet(A,D))) = meet(join(meet(C,A),meet(A,D)),B),
inference(paramod,[status(thm)],[c_26,c_4663]) ).
cnf(c_307,plain,
meet(join(meet(A,B),meet(B,A)),C) = meet(meet(B,A),C),
inference(paramod,[status(thm)],[c_303,c_165]) ).
cnf(c_4664,plain,
meet(meet(B,A),join(meet(B,join(join(meet(A,B),meet(B,A)),meet(B,C))),meet(C,B))) = join(meet(B,A),meet(join(meet(A,B),meet(B,A)),C)),
inference(paramod,[status(thm)],[c_307,c_211]) ).
cnf(c_4665,plain,
meet(meet(B,A),join(meet(B,join(join(meet(A,B),meet(B,A)),meet(B,C))),meet(C,B))) = join(meet(B,A),meet(meet(B,A),C)),
inference(paramod,[status(thm)],[c_307,c_4664]) ).
cnf(c_310,plain,
meet(meet(A,B),join(meet(A,join(join(meet(B,A),meet(A,B)),meet(A,C))),meet(C,A))) = meet(A,B),
inference(paramod,[status(thm)],[c_4,c_4665]) ).
cnf(c_4666,plain,
meet(A,meet(join(meet(A,B),meet(C,A)),D)) = meet(join(meet(A,B),meet(C,A)),D),
inference(paramod,[status(thm)],[c_238,c_86]) ).
cnf(c_330,plain,
meet(meet(A,B),join(meet(A,C),meet(D,A))) = meet(join(meet(A,C),meet(D,A)),B),
inference(paramod,[status(thm)],[c_26,c_4666]) ).
cnf(c_335,plain,
meet(join(meet(A,join(join(meet(B,A),meet(A,B)),meet(A,C))),meet(C,A)),B) = meet(A,B),
inference(paramod,[status(thm)],[c_330,c_310]) ).
cnf(c_414,plain,
join(meet(A,join(B,C)),meet(A,C)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_86,c_21]) ).
cnf(c_727,plain,
meet(a,join(b,meet(c,join(meet(c,b),meet(a,join(b,c)))))) != meet(a,join(b,meet(c,a))),
inference(paramod,[status(thm)],[c_6,c_105]) ).
cnf(c_831,plain,
meet(join(A,meet(B,C)),join(A,B)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_16,c_35]) ).
cnf(c_906,plain,
join(meet(A,B),meet(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_153,c_21]) ).
cnf(c_914,plain,
meet(join(meet(A,join(meet(B,A),meet(A,C))),meet(C,A)),B) = meet(A,B),
inference(paramod,[status(thm)],[c_906,c_335]) ).
cnf(c_925,plain,
join(join(A,meet(B,C)),meet(C,B)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_906,c_8]) ).
cnf(c_1180,plain,
join(meet(A,join(B,C)),meet(C,A)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_5,c_414]) ).
cnf(c_4667,plain,
join(A,meet(B,C)) = meet(join(A,B),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_831,c_5]) ).
cnf(c_1213,plain,
meet(join(A,B),join(A,meet(B,C))) = join(A,meet(B,C)),
inference(copy,[status(thm)],[c_4667]) ).
cnf(c_1334,plain,
meet(join(meet(A,join(B,meet(A,C))),meet(C,join(A,B))),B) = join(meet(B,A),meet(B,C)),
inference(paramod,[status(thm)],[c_6,c_53]) ).
cnf(c_4668,plain,
meet(A,join(B,C)) = join(meet(C,A),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_1180,c_6]) ).
cnf(c_1585,plain,
join(meet(A,B),meet(B,join(C,A))) = meet(B,join(C,A)),
inference(copy,[status(thm)],[c_4668]) ).
cnf(c_1757,plain,
meet(A,join(meet(B,A),meet(A,C))) = join(meet(B,A),meet(A,C)),
inference(paramod,[status(thm)],[c_124,c_1213]) ).
cnf(c_4669,plain,
meet(join(join(meet(B,A),meet(A,C)),meet(C,A)),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1757,c_914]) ).
cnf(c_1793,plain,
meet(join(meet(A,B),meet(B,C)),A) = meet(B,A),
inference(paramod,[status(thm)],[c_925,c_4669]) ).
cnf(c_4670,plain,
meet(A,B) = meet(B,join(meet(B,A),meet(A,C))),
inference(paramod,[status(thm)],[c_1793,c_5]) ).
cnf(c_1796,plain,
meet(A,join(meet(A,B),meet(B,C))) = meet(B,A),
inference(copy,[status(thm)],[c_4670]) ).
cnf(c_1891,plain,
meet(A,join(meet(A,join(B,C)),C)) = meet(join(B,C),A),
inference(paramod,[status(thm)],[c_86,c_1796]) ).
cnf(c_3942,plain,
join(join(A,meet(B,C)),meet(C,join(D,B))) = join(A,meet(C,join(D,B))),
inference(paramod,[status(thm)],[c_1585,c_8]) ).
cnf(c_4671,plain,
meet(A,join(join(meet(A,B),meet(A,C)),meet(C,join(B,A)))) = meet(join(meet(B,join(A,meet(B,C))),meet(C,join(B,A))),A),
inference(paramod,[status(thm)],[c_58,c_1891]) ).
cnf(c_4672,plain,
meet(A,join(meet(A,B),meet(C,join(B,A)))) = meet(join(meet(B,join(A,meet(B,C))),meet(C,join(B,A))),A),
inference(paramod,[status(thm)],[c_3942,c_4671]) ).
cnf(c_4642,plain,
meet(A,join(meet(A,B),meet(C,join(B,A)))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_1334,c_4672]) ).
cnf(c_4673,plain,
meet(a,join(b,join(meet(c,b),meet(c,a)))) != meet(a,join(b,meet(c,a))),
inference(paramod,[status(thm)],[c_4642,c_727]) ).
cnf(c_4674,plain,
meet(a,join(join(b,meet(c,b)),meet(c,a))) != meet(a,join(b,meet(c,a))),
inference(paramod,[status(thm)],[c_8,c_4673]) ).
cnf(c_4675,plain,
meet(a,join(b,meet(c,a))) != meet(a,join(b,meet(c,a))),
inference(paramod,[status(thm)],[c_14,c_4674]) ).
cnf(c_4651,plain,
$false,
inference(copy,[status(thm)],[c_4675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT140-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.40 % Computer : n005.cluster.edu
% 0.09/0.40 % Model : x86_64 x86_64
% 0.09/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.40 % Memory : 8046.5625MB
% 0.09/0.40 % OS : Linux 6.8.0-71-generic
% 0.09/0.40 % CPULimit : 300
% 0.09/0.40 % WCLimit : 300
% 0.09/0.40 % DateTime : Fri Sep 25 20:07:01 UTC 2026
% 0.09/0.40 % CPUTime :
% 0.09/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.41 % Process 71094 was started by sandbox on n005,
% 0.09/0.41 % Fri Sep 25 20:07:01 2026
% 0.09/0.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.41
% 0.09/0.41 % From the command line: assign(max_seconds, 300).
% 162.32/43.82
% 162.32/43.82 % SZS status Unsatisfiable for theBenchmark
% 162.32/43.82
% 162.32/43.82 % Proof 1 at 1.76 (+ 0.31) seconds.
% 162.32/43.82 % Length of proof is 56.
% 162.32/43.82 % Level of proof is 14.
% 162.32/43.82 % Maximum clause weight is 44.000.
% 162.32/43.82 % Given clauses 184.
% 162.32/43.82
% 162.32/43.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------