%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT160-1 : 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 13.34s 2.15s
% Output : CNFRefutation 13.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 58 ( 58 unt; 0 def)
% Number of atoms : 58 ( 57 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 143 ( 15 sgn 19 !; 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_H52,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_2,VAR_3),meet(VAR_2,join(VAR_0,VAR_1))))),
file('theBenchmark.p',equation_H52) ).
cnf(c_9,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,join(meet(C,D),meet(C,join(A,B))))),
inference(clausify,[status(thm)],[equation_H52]) ).
cnf(c_10,plain,
meet(A,join(B,join(meet(C,D),meet(C,join(A,B))))) = meet(A,join(B,meet(C,join(A,D)))),
inference(copy,[status(thm)],[c_9]) ).
fof(prove_H51,axiom,
meet(a,join(b,meet(c,join(a,d)))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
file('theBenchmark.p',prove_H51) ).
cnf(c_11,plain,
meet(a,join(b,meet(c,join(a,d)))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(clausify,[status(thm)],[prove_H51]) ).
cnf(c_12,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_5,c_4]) ).
cnf(c_13,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_6,c_3]) ).
cnf(c_3250,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_7]) ).
cnf(c_16,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_5,c_3250]) ).
cnf(c_3251,plain,
meet(A,B) = meet(A,meet(join(A,C),B)),
inference(paramod,[status(thm)],[c_3,c_7]) ).
cnf(c_18,plain,
meet(A,meet(join(A,B),C)) = meet(A,C),
inference(copy,[status(thm)],[c_3251]) ).
cnf(c_3252,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_27,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_3252]) ).
cnf(c_3253,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_6,c_8]) ).
cnf(c_29,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_8,c_3253]) ).
cnf(c_36,plain,
meet(A,join(B,join(meet(C,meet(A,D)),meet(C,join(A,B))))) = meet(A,join(B,meet(C,A))),
inference(paramod,[status(thm)],[c_4,c_10]) ).
cnf(c_3254,plain,
meet(A,join(B,join(C,join(meet(D,E),meet(D,join(A,join(B,C))))))) = meet(A,join(join(B,C),meet(D,join(A,E)))),
inference(paramod,[status(thm)],[c_8,c_10]) ).
cnf(c_49,plain,
meet(A,join(B,join(C,join(meet(D,E),meet(D,join(A,join(B,C))))))) = meet(A,join(B,join(C,meet(D,join(A,E))))),
inference(paramod,[status(thm)],[c_8,c_3254]) ).
cnf(c_55,plain,
meet(a,join(b,join(meet(c,d),meet(c,join(a,b))))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(paramod,[status(thm)],[c_10,c_11]) ).
cnf(c_111,plain,
meet(A,meet(B,join(A,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_5,c_18]) ).
cnf(c_3255,plain,
join(meet(join(A,B),C),meet(A,C)) = meet(join(A,B),C),
inference(paramod,[status(thm)],[c_18,c_12]) ).
cnf(c_115,plain,
join(meet(A,B),meet(join(A,C),B)) = meet(join(A,C),B),
inference(paramod,[status(thm)],[c_6,c_3255]) ).
cnf(c_3256,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_16,c_115]) ).
cnf(c_3257,plain,
join(meet(A,B),meet(B,join(A,C))) = meet(join(A,C),meet(B,join(A,C))),
inference(paramod,[status(thm)],[c_111,c_3256]) ).
cnf(c_180,plain,
join(meet(A,B),meet(B,join(A,C))) = meet(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_3257]) ).
cnf(c_288,plain,
join(meet(A,B),meet(A,join(B,C))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_5,c_180]) ).
cnf(c_3258,plain,
meet(join(meet(A,B),C),join(A,C)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_27,c_13]) ).
cnf(c_349,plain,
meet(join(A,B),join(meet(A,C),B)) = join(meet(A,C),B),
inference(paramod,[status(thm)],[c_5,c_3258]) ).
cnf(c_3259,plain,
meet(A,join(B,join(C,join(meet(D,meet(A,E)),meet(D,join(A,join(B,C))))))) = meet(A,join(join(B,C),meet(D,A))),
inference(paramod,[status(thm)],[c_8,c_36]) ).
cnf(c_586,plain,
meet(A,join(B,join(C,join(meet(D,meet(A,E)),meet(D,join(A,join(B,C))))))) = meet(A,join(B,join(C,meet(D,A)))),
inference(paramod,[status(thm)],[c_8,c_3259]) ).
cnf(c_3260,plain,
meet(meet(A,join(B,C)),join(meet(meet(A,B),D),meet(A,join(B,C)))) = join(meet(meet(A,B),D),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_288,c_349]) ).
cnf(c_3261,plain,
meet(meet(A,join(B,C)),join(meet(A,meet(B,D)),meet(A,join(B,C)))) = join(meet(meet(A,B),D),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_7,c_3260]) ).
cnf(c_3262,plain,
meet(A,join(B,C)) = join(meet(meet(A,B),D),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_13,c_3261]) ).
cnf(c_3263,plain,
meet(A,join(B,C)) = join(meet(A,meet(B,D)),meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_7,c_3262]) ).
cnf(c_2425,plain,
join(meet(A,meet(B,C)),meet(A,join(B,D))) = meet(A,join(B,D)),
inference(copy,[status(thm)],[c_3263]) ).
cnf(c_2450,plain,
meet(A,join(B,join(C,meet(D,join(A,join(B,C)))))) = meet(A,join(B,join(C,meet(D,A)))),
inference(paramod,[status(thm)],[c_2425,c_586]) ).
cnf(c_3264,plain,
meet(a,join(b,join(meet(c,d),join(meet(c,b),meet(c,join(a,join(b,meet(c,d)))))))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(paramod,[status(thm)],[c_49,c_55]) ).
cnf(c_3265,plain,
meet(a,join(b,join(meet(c,d),join(meet(b,c),meet(c,join(a,join(b,meet(c,d)))))))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(paramod,[status(thm)],[c_5,c_3264]) ).
cnf(c_3266,plain,
meet(a,join(b,join(meet(b,c),join(meet(c,d),meet(c,join(a,join(b,meet(c,d)))))))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(paramod,[status(thm)],[c_29,c_3265]) ).
cnf(c_3267,plain,
meet(a,join(b,join(meet(c,d),meet(c,join(a,join(b,meet(c,d))))))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(paramod,[status(thm)],[c_27,c_3266]) ).
cnf(c_3268,plain,
meet(a,join(b,join(meet(c,d),meet(c,a)))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(paramod,[status(thm)],[c_2450,c_3267]) ).
cnf(c_3269,plain,
meet(a,join(b,join(meet(c,d),meet(a,c)))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(paramod,[status(thm)],[c_5,c_3268]) ).
cnf(c_3270,plain,
meet(a,join(b,join(meet(a,c),meet(c,d)))) != meet(a,join(b,join(meet(a,c),meet(c,d)))),
inference(paramod,[status(thm)],[c_6,c_3269]) ).
cnf(c_3249,plain,
$false,
inference(copy,[status(thm)],[c_3270]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT160-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.41 % Computer : n013.cluster.edu
% 0.17/0.41 % Model : x86_64 x86_64
% 0.17/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.41 % Memory : 8046.5625MB
% 0.17/0.41 % OS : Linux 6.8.0-71-generic
% 0.17/0.41 % CPULimit : 300
% 0.17/0.41 % WCLimit : 300
% 0.17/0.41 % DateTime : Fri Sep 25 20:09:36 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 1089322 was started by sandbox on n013,
% 0.17/0.42 % Fri Sep 25 20:09:36 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.42
% 0.17/0.42 % From the command line: assign(max_seconds, 300).
% 13.34/2.15
% 13.34/2.15 % SZS status Unsatisfiable for theBenchmark
% 13.34/2.15
% 13.34/2.15 % Proof 1 at 1.43 (+ 0.27) seconds.
% 13.34/2.15 % Length of proof is 28.
% 13.34/2.15 % Level of proof is 7.
% 13.34/2.15 % Maximum clause weight is 94.000.
% 13.34/2.15 % Given clauses 86.
% 13.34/2.15
% 13.34/2.15 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------