%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT142-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 10.75s 11.89s
% Output : CNFRefutation 10.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 80 ( 80 unt; 0 def)
% Number of atoms : 80 ( 79 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 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 : 203 ( 22 sgn 18 !; 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(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_H22,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_2,meet(VAR_0,VAR_1))),meet(VAR_2,join(VAR_0,VAR_1)))),
file('theBenchmark.p',equation_H22) ).
cnf(c_9,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(meet(B,join(C,meet(A,B))),meet(C,join(A,B)))),
inference(clausify,[status(thm)],[equation_H22]) ).
cnf(c_2558,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(meet(C,join(A,B)),meet(B,join(C,meet(A,B))))),
inference(paramod,[status(thm)],[c_6,c_9]) ).
cnf(c_10,plain,
meet(A,join(meet(B,join(A,C)),meet(C,join(B,meet(A,C))))) = join(meet(A,C),meet(A,B)),
inference(copy,[status(thm)],[c_2558]) ).
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_2559,plain,
meet(a,join(b,meet(a,c))) != meet(a,join(meet(c,join(a,b)),meet(a,join(b,meet(a,c))))),
inference(paramod,[status(thm)],[c_6,c_11]) ).
cnf(c_12,plain,
meet(a,join(meet(c,join(a,b)),meet(a,join(b,meet(a,c))))) != meet(a,join(b,meet(a,c))),
inference(copy,[status(thm)],[c_2559]) ).
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_2560,plain,
meet(A,B) = meet(A,meet(A,B)),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_16,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(copy,[status(thm)],[c_2560]) ).
cnf(c_2561,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_2561]) ).
cnf(c_2562,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_2562]) ).
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_2563,plain,
meet(meet(A,B),C) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_5,c_7]) ).
cnf(c_22,plain,
meet(A,meet(B,C)) = meet(B,meet(A,C)),
inference(paramod,[status(thm)],[c_7,c_2563]) ).
cnf(c_26,plain,
meet(join(A,B),join(A,join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_40,plain,
meet(A,join(meet(B,meet(C,join(A,D))),meet(D,join(meet(B,C),meet(A,D))))) = join(meet(A,D),meet(A,meet(B,C))),
inference(paramod,[status(thm)],[c_7,c_10]) ).
cnf(c_2564,plain,
meet(A,meet(B,meet(C,A))) = meet(meet(B,C),A),
inference(paramod,[status(thm)],[c_7,c_17]) ).
cnf(c_58,plain,
meet(A,meet(B,meet(C,A))) = meet(B,meet(C,A)),
inference(paramod,[status(thm)],[c_7,c_2564]) ).
cnf(c_2565,plain,
meet(A,B) = meet(B,meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_3,c_22]) ).
cnf(c_65,plain,
meet(A,meet(B,join(A,C))) = meet(B,A),
inference(copy,[status(thm)],[c_2565]) ).
cnf(c_2566,plain,
meet(A,join(meet(B,C),meet(B,D))) = meet(B,meet(A,join(meet(D,join(B,C)),meet(C,join(D,meet(B,C)))))),
inference(paramod,[status(thm)],[c_10,c_22]) ).
cnf(c_68,plain,
meet(A,meet(B,join(meet(C,join(A,D)),meet(D,join(C,meet(A,D)))))) = meet(B,join(meet(A,D),meet(A,C))),
inference(copy,[status(thm)],[c_2566]) ).
cnf(c_2567,plain,
meet(A,B) = meet(B,meet(A,join(C,B))),
inference(paramod,[status(thm)],[c_14,c_22]) ).
cnf(c_70,plain,
meet(A,meet(B,join(C,A))) = meet(B,A),
inference(copy,[status(thm)],[c_2567]) ).
cnf(c_2568,plain,
meet(A,meet(join(A,B),join(meet(C,join(A,D)),meet(D,join(C,meet(A,D)))))) = join(meet(A,D),meet(A,C)),
inference(paramod,[status(thm)],[c_10,c_19]) ).
cnf(c_119,plain,
meet(join(A,B),join(meet(A,C),meet(A,D))) = join(meet(A,C),meet(A,D)),
inference(paramod,[status(thm)],[c_68,c_2568]) ).
cnf(c_2569,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_120,plain,
join(meet(A,B),meet(join(A,C),B)) = meet(join(A,C),B),
inference(paramod,[status(thm)],[c_6,c_2569]) ).
cnf(c_2570,plain,
meet(A,meet(join(A,B),meet(C,A))) = meet(C,A),
inference(paramod,[status(thm)],[c_17,c_19]) ).
cnf(c_121,plain,
meet(join(A,B),meet(C,A)) = meet(C,A),
inference(paramod,[status(thm)],[c_58,c_2570]) ).
cnf(c_144,plain,
meet(join(A,B),meet(C,B)) = meet(C,B),
inference(paramod,[status(thm)],[c_6,c_121]) ).
cnf(c_2571,plain,
join(meet(join(A,B),C),meet(C,B)) = meet(join(A,B),C),
inference(paramod,[status(thm)],[c_144,c_20]) ).
cnf(c_169,plain,
join(meet(A,B),meet(join(C,B),A)) = meet(join(C,B),A),
inference(paramod,[status(thm)],[c_6,c_2571]) ).
cnf(c_200,plain,
meet(join(A,B),join(B,join(A,C))) = join(B,A),
inference(paramod,[status(thm)],[c_6,c_26]) ).
cnf(c_2572,plain,
meet(meet(A,join(B,C)),join(meet(B,C),meet(B,A))) = meet(B,meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_10,c_65]) ).
cnf(c_2573,plain,
meet(A,meet(join(B,C),join(meet(B,C),meet(B,A)))) = meet(B,meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_7,c_2572]) ).
cnf(c_2574,plain,
meet(A,join(meet(B,C),meet(B,A))) = meet(B,meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_119,c_2573]) ).
cnf(c_249,plain,
meet(A,join(meet(B,C),meet(B,A))) = meet(A,B),
inference(paramod,[status(thm)],[c_65,c_2574]) ).
cnf(c_2575,plain,
join(meet(A,join(B,C)),meet(A,C)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_70,c_13]) ).
cnf(c_260,plain,
join(meet(A,B),meet(A,join(C,B))) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_6,c_2575]) ).
cnf(c_309,plain,
meet(A,join(meet(B,C),meet(C,A))) = meet(A,C),
inference(paramod,[status(thm)],[c_5,c_249]) ).
cnf(c_597,plain,
join(A,meet(join(A,B),join(A,C))) = meet(join(A,B),join(A,C)),
inference(paramod,[status(thm)],[c_3,c_120]) ).
cnf(c_2576,plain,
join(meet(A,B),meet(join(C,meet(A,B)),A)) = meet(join(C,meet(A,B)),A),
inference(paramod,[status(thm)],[c_16,c_169]) ).
cnf(c_2577,plain,
join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(join(C,meet(A,B)),A),
inference(paramod,[status(thm)],[c_5,c_2576]) ).
cnf(c_793,plain,
join(meet(A,B),meet(A,join(C,meet(A,B)))) = meet(A,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_5,c_2577]) ).
cnf(c_2578,plain,
join(meet(join(A,B),join(A,C)),join(B,A)) = meet(join(A,B),join(B,join(A,C))),
inference(paramod,[status(thm)],[c_200,c_260]) ).
cnf(c_2579,plain,
join(join(B,A),meet(join(A,B),join(A,C))) = meet(join(A,B),join(B,join(A,C))),
inference(paramod,[status(thm)],[c_6,c_2578]) ).
cnf(c_2580,plain,
join(B,join(A,meet(join(A,B),join(A,C)))) = meet(join(A,B),join(B,join(A,C))),
inference(paramod,[status(thm)],[c_8,c_2579]) ).
cnf(c_2581,plain,
join(B,meet(join(A,B),join(A,C))) = meet(join(A,B),join(B,join(A,C))),
inference(paramod,[status(thm)],[c_597,c_2580]) ).
cnf(c_1237,plain,
join(A,meet(join(B,A),join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_200,c_2581]) ).
cnf(c_1241,plain,
join(A,meet(join(A,B),join(B,C))) = join(A,B),
inference(paramod,[status(thm)],[c_6,c_1237]) ).
cnf(c_2582,plain,
join(A,meet(join(A,meet(B,C)),C)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_309,c_1241]) ).
cnf(c_1342,plain,
join(A,meet(B,join(A,meet(C,B)))) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_5,c_2582]) ).
cnf(c_2583,plain,
meet(A,join(meet(B,join(A,C)),meet(join(C,D),join(meet(B,join(A,C)),meet(A,join(C,D)))))) = join(meet(A,join(C,D)),meet(A,meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_26,c_40]) ).
cnf(c_2584,plain,
meet(A,join(meet(B,join(A,C)),meet(A,join(C,D)))) = join(meet(A,join(C,D)),meet(A,meet(B,join(A,C)))),
inference(paramod,[status(thm)],[c_1342,c_2583]) ).
cnf(c_2463,plain,
meet(A,join(meet(B,join(A,C)),meet(A,join(C,D)))) = join(meet(A,join(C,D)),meet(B,A)),
inference(paramod,[status(thm)],[c_65,c_2584]) ).
cnf(c_2585,plain,
join(meet(a,join(b,meet(a,c))),meet(c,a)) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_2463,c_12]) ).
cnf(c_2586,plain,
join(meet(a,join(b,meet(a,c))),meet(a,c)) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_5,c_2585]) ).
cnf(c_2587,plain,
join(meet(a,c),meet(a,join(b,meet(a,c)))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_6,c_2586]) ).
cnf(c_2588,plain,
meet(a,join(b,meet(a,c))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_793,c_2587]) ).
cnf(c_2557,plain,
$false,
inference(copy,[status(thm)],[c_2588]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT142-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/10.39 % Computer : n019.cluster.edu
% 0.09/10.39 % Model : x86_64 x86_64
% 0.09/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.39 % Memory : 8046.5625MB
% 0.09/10.39 % OS : Linux 6.8.0-71-generic
% 0.09/10.39 % CPULimit : 300
% 0.09/10.39 % WCLimit : 300
% 0.09/10.39 % DateTime : Fri Sep 25 20:08:44 UTC 2026
% 0.09/10.39 % CPUTime :
% 0.15/10.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/10.40 % Process 3549375 was started by sandbox2 on n019,
% 0.15/10.40 % Fri Sep 25 20:08:44 2026
% 0.15/10.40 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/10.40
% 0.15/10.40 % From the command line: assign(max_seconds, 300).
% 10.75/11.89
% 10.75/11.89 % SZS status Unsatisfiable for theBenchmark
% 10.75/11.89
% 10.75/11.89 % Proof 1 at 1.02 (+ 0.24) seconds.
% 10.75/11.89 % Length of proof is 40.
% 10.75/11.89 % Level of proof is 8.
% 10.75/11.89 % Maximum clause weight is 64.000.
% 10.75/11.89 % Given clauses 95.
% 10.75/11.89
% 10.75/11.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------