%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT168-1 : 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 : 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 07:49:46 AM UTC 2026
% Result : Unsatisfiable 80.66s 11.71s
% Output : CNFRefutation 80.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 43 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 97 ( 11 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_H18_dual,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(join(VAR_0,VAR_1),join(VAR_0,VAR_2)) = join(VAR_0,meet(join(VAR_0,VAR_1),meet(join(VAR_0,VAR_2),join(VAR_1,meet(VAR_0,VAR_2))))),
file('theBenchmark.p',equation_H18_dual) ).
cnf(c_9,plain,
meet(join(A,B),join(A,C)) = join(A,meet(join(A,B),meet(join(A,C),join(B,meet(A,C))))),
inference(clausify,[status(thm)],[equation_H18_dual]) ).
cnf(c_10,plain,
join(A,meet(join(A,B),meet(join(A,C),join(B,meet(A,C))))) = meet(join(A,B),join(A,C)),
inference(copy,[status(thm)],[c_9]) ).
fof(prove_H58,axiom,
meet(a,join(b,c)) != meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))),
file('theBenchmark.p',prove_H58) ).
cnf(c_11,plain,
meet(a,join(b,c)) != meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))),
inference(clausify,[status(thm)],[prove_H58]) ).
cnf(c_12,plain,
meet(a,join(b,meet(join(a,b),join(c,meet(a,b))))) != meet(a,join(b,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_4890,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_4890]) ).
cnf(c_4891,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_4891]) ).
cnf(c_4892,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_4892]) ).
cnf(c_32,plain,
join(A,meet(join(A,B),meet(join(A,C),join(B,meet(C,A))))) = meet(join(A,B),join(A,C)),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_4893,plain,
join(A,B) = join(A,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_13,c_8]) ).
cnf(c_43,plain,
join(A,join(meet(B,A),C)) = join(A,C),
inference(copy,[status(thm)],[c_4893]) ).
cnf(c_75,plain,
meet(join(A,B),join(A,join(C,B))) = join(A,B),
inference(paramod,[status(thm)],[c_30,c_14]) ).
cnf(c_260,plain,
join(A,meet(join(A,B),meet(join(C,A),join(B,meet(C,A))))) = meet(join(A,B),join(A,C)),
inference(paramod,[status(thm)],[c_6,c_32]) ).
cnf(c_4894,plain,
meet(join(A,B),join(join(C,B),A)) = join(A,B),
inference(paramod,[status(thm)],[c_6,c_75]) ).
cnf(c_672,plain,
meet(join(A,B),join(C,join(B,A))) = join(A,B),
inference(paramod,[status(thm)],[c_8,c_4894]) ).
cnf(c_4895,plain,
meet(join(A,meet(B,C)),join(C,A)) = join(A,meet(B,C)),
inference(paramod,[status(thm)],[c_43,c_672]) ).
cnf(c_1323,plain,
meet(join(A,B),join(B,meet(C,A))) = join(B,meet(C,A)),
inference(paramod,[status(thm)],[c_5,c_4895]) ).
cnf(c_4896,plain,
meet(A,join(B,meet(C,D))) = meet(join(D,B),meet(A,join(B,meet(C,D)))),
inference(paramod,[status(thm)],[c_1323,c_22]) ).
cnf(c_4757,plain,
meet(join(A,B),meet(C,join(B,meet(D,A)))) = meet(C,join(B,meet(D,A))),
inference(copy,[status(thm)],[c_4896]) ).
cnf(c_4875,plain,
join(A,meet(join(B,A),join(C,meet(B,A)))) = meet(join(A,C),join(A,B)),
inference(paramod,[status(thm)],[c_4757,c_260]) ).
cnf(c_4897,plain,
meet(a,meet(join(b,c),join(b,a))) != meet(a,join(b,c)),
inference(paramod,[status(thm)],[c_4875,c_12]) ).
cnf(c_4898,plain,
meet(a,meet(join(b,c),join(a,b))) != meet(a,join(b,c)),
inference(paramod,[status(thm)],[c_6,c_4897]) ).
cnf(c_4899,plain,
meet(a,meet(join(a,b),join(b,c))) != meet(a,join(b,c)),
inference(paramod,[status(thm)],[c_5,c_4898]) ).
cnf(c_4900,plain,
meet(a,join(b,c)) != meet(a,join(b,c)),
inference(paramod,[status(thm)],[c_19,c_4899]) ).
cnf(c_4889,plain,
$false,
inference(copy,[status(thm)],[c_4900]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT168-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.37 % Computer : n026.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Fri Sep 25 20:13:26 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.37 % Process 3341847 was started by sandbox2 on n026,
% 0.13/0.37 % Fri Sep 25 20:13:26 2026
% 0.13/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 80.66/11.71
% 80.66/11.71 % SZS status Unsatisfiable for theBenchmark
% 80.66/11.71
% 80.66/11.71 % Proof 1 at 2.80 (+ 0.46) seconds.
% 80.66/11.71 % Length of proof is 24.
% 80.66/11.71 % Level of proof is 7.
% 80.66/11.71 % Maximum clause weight is 53.000.
% 80.66/11.71 % Given clauses 133.
% 80.66/11.71
% 80.66/11.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------