%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT156-1 : 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 : n013.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 07:49:45 AM UTC 2026
% Result : Unsatisfiable 22.36s 3.33s
% Output : CNFRefutation 22.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 71 ( 71 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 9 ( 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 : 161 ( 16 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_of_meet,axiom,
! [VAR_0] : meet(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_meet) ).
cnf(c_1,plain,
meet(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_meet]) ).
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(equation_H49,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] : meet(VAR_0,join(VAR_1,meet(VAR_2,join(VAR_0,VAR_3)))) = meet(VAR_0,join(VAR_1,join(meet(VAR_0,VAR_2),meet(VAR_2,join(VAR_1,VAR_3))))),
file('theBenchmark.p',equation_H49) ).
cnf(c_9,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))),
inference(clausify,[status(thm)],[equation_H49]) ).
cnf(c_10,plain,
meet(A,join(B,join(meet(A,C),meet(C,join(B,D))))) = meet(A,join(B,meet(C,join(A,D)))),
inference(copy,[status(thm)],[c_9]) ).
fof(prove_H6,axiom,
meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
file('theBenchmark.p',prove_H6) ).
cnf(c_11,plain,
meet(a,join(b,meet(a,c))) != meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))),
inference(clausify,[status(thm)],[prove_H6]) ).
cnf(c_12,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(a,b)))) != meet(a,join(b,meet(a,c))),
inference(copy,[status(thm)],[c_11]) ).
cnf(c_13,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_14,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_4308,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_17,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_5,c_4308]) ).
cnf(c_4309,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_4309]) ).
cnf(c_20,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_4310,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_25,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_6,c_4310]) ).
cnf(c_27,plain,
join(A,join(B,meet(join(A,B),C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_4311,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_30,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_8,c_4311]) ).
cnf(c_4312,plain,
meet(a,join(meet(a,join(b,meet(a,c))),join(meet(a,c),meet(c,join(meet(a,join(b,meet(a,c))),b))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_10,c_12]) ).
cnf(c_4313,plain,
meet(a,join(meet(a,join(b,meet(a,c))),join(meet(a,c),meet(c,join(b,meet(a,join(b,meet(a,c)))))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_6,c_4312]) ).
cnf(c_57,plain,
meet(a,join(meet(a,c),join(meet(a,join(b,meet(a,c))),meet(c,join(b,meet(a,join(b,meet(a,c)))))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_30,c_4313]) ).
cnf(c_4314,plain,
meet(A,meet(B,meet(C,A))) = meet(meet(B,C),A),
inference(paramod,[status(thm)],[c_7,c_17]) ).
cnf(c_73,plain,
meet(A,meet(B,meet(C,A))) = meet(B,meet(C,A)),
inference(paramod,[status(thm)],[c_7,c_4314]) ).
cnf(c_121,plain,
meet(A,meet(B,join(A,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_5,c_19]) ).
cnf(c_4315,plain,
join(meet(join(A,B),C),meet(A,C)) = meet(join(A,B),C),
inference(paramod,[status(thm)],[c_19,c_13]) ).
cnf(c_125,plain,
join(meet(A,B),meet(join(A,C),B)) = meet(join(A,C),B),
inference(paramod,[status(thm)],[c_6,c_4315]) ).
cnf(c_4316,plain,
meet(A,meet(join(A,B),meet(C,A))) = meet(C,A),
inference(paramod,[status(thm)],[c_17,c_19]) ).
cnf(c_126,plain,
meet(join(A,B),meet(C,A)) = meet(C,A),
inference(paramod,[status(thm)],[c_73,c_4316]) ).
cnf(c_151,plain,
meet(join(A,B),meet(C,B)) = meet(C,B),
inference(paramod,[status(thm)],[c_6,c_126]) ).
cnf(c_173,plain,
join(meet(join(A,B),C),meet(C,B)) = meet(join(A,B),C),
inference(paramod,[status(thm)],[c_151,c_20]) ).
cnf(c_4317,plain,
join(meet(A,meet(B,join(A,C))),meet(B,join(A,C))) = meet(join(A,C),meet(B,join(A,C))),
inference(paramod,[status(thm)],[c_17,c_125]) ).
cnf(c_4318,plain,
join(meet(A,B),meet(B,join(A,C))) = meet(join(A,C),meet(B,join(A,C))),
inference(paramod,[status(thm)],[c_121,c_4317]) ).
cnf(c_192,plain,
join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)),
inference(paramod,[status(thm)],[c_17,c_4318]) ).
cnf(c_4319,plain,
join(meet(A,join(B,C)),meet(A,C)) = meet(join(B,C),A),
inference(paramod,[status(thm)],[c_5,c_173]) ).
cnf(c_262,plain,
join(meet(A,B),meet(A,join(C,B))) = meet(join(C,B),A),
inference(paramod,[status(thm)],[c_6,c_4319]) ).
cnf(c_4320,plain,
join(meet(join(A,meet(B,C)),C),meet(B,C)) = meet(join(A,meet(B,C)),C),
inference(paramod,[status(thm)],[c_17,c_173]) ).
cnf(c_4321,plain,
join(meet(C,join(A,meet(B,C))),meet(B,C)) = meet(join(A,meet(B,C)),C),
inference(paramod,[status(thm)],[c_5,c_4320]) ).
cnf(c_4322,plain,
join(meet(B,C),meet(C,join(A,meet(B,C)))) = meet(join(A,meet(B,C)),C),
inference(paramod,[status(thm)],[c_6,c_4321]) ).
cnf(c_274,plain,
join(meet(A,B),meet(B,join(C,meet(A,B)))) = meet(B,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_5,c_4322]) ).
cnf(c_311,plain,
join(A,meet(join(B,A),join(A,C))) = meet(join(B,A),join(A,C)),
inference(paramod,[status(thm)],[c_14,c_192]) ).
cnf(c_4323,plain,
meet(A,join(meet(B,C),join(meet(A,B),meet(B,join(meet(B,C),C))))) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_262,c_10]) ).
cnf(c_4324,plain,
meet(A,join(meet(B,C),join(meet(A,B),meet(B,join(C,meet(B,C)))))) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_6,c_4323]) ).
cnf(c_4325,plain,
meet(A,join(meet(B,C),join(meet(A,B),meet(B,C)))) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_13,c_4324]) ).
cnf(c_4326,plain,
meet(A,join(meet(A,B),meet(B,C))) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_25,c_4325]) ).
cnf(c_484,plain,
meet(A,join(meet(A,B),meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_19,c_4326]) ).
cnf(c_514,plain,
meet(A,join(meet(A,B),meet(C,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_5,c_484]) ).
cnf(c_515,plain,
meet(A,join(meet(B,C),meet(A,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_6,c_484]) ).
cnf(c_3786,plain,
join(A,meet(join(A,B),join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_311,c_27]) ).
cnf(c_4327,plain,
join(A,meet(join(A,meet(B,C)),B)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_515,c_3786]) ).
cnf(c_3850,plain,
join(A,meet(B,join(A,meet(B,C)))) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_5,c_4327]) ).
cnf(c_3889,plain,
meet(a,join(meet(a,c),join(meet(a,join(b,meet(a,c))),meet(c,join(b,meet(a,c)))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_3850,c_57]) ).
cnf(c_4328,plain,
meet(a,join(meet(a,join(b,meet(a,c))),join(meet(a,c),meet(c,join(b,meet(a,c)))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_30,c_3889]) ).
cnf(c_4329,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(b,meet(a,c))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_274,c_4328]) ).
cnf(c_4330,plain,
meet(a,join(b,meet(a,c))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_514,c_4329]) ).
cnf(c_4307,plain,
$false,
inference(copy,[status(thm)],[c_4330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT156-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n013.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 20:09:22 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1088918 was started by sandbox on n013,
% 0.09/0.36 % Fri Sep 25 20:09:22 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 22.36/3.33
% 22.36/3.33 % SZS status Unsatisfiable for theBenchmark
% 22.36/3.33
% 22.36/3.33 % Proof 1 at 2.51 (+ 0.42) seconds.
% 22.36/3.33 % Length of proof is 38.
% 22.36/3.33 % Level of proof is 11.
% 22.36/3.33 % Maximum clause weight is 83.000.
% 22.36/3.33 % Given clauses 105.
% 22.36/3.33
% 22.36/3.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------