%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT154-1 : 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 : n014.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 07:49:44 AM UTC 2026
% Result : Unsatisfiable 6.69s 1.34s
% Output : CNFRefutation 6.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 38 ( 38 unt; 0 def)
% Number of atoms : 38 ( 37 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 8 ( 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 : 80 ( 11 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(equation_H42,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,meet(VAR_2,join(VAR_1,join(VAR_3,meet(VAR_0,VAR_2)))))),
file('theBenchmark.p',equation_H42) ).
cnf(c_9,plain,
meet(A,join(B,meet(C,join(A,D)))) = meet(A,join(B,meet(C,join(B,join(D,meet(A,C)))))),
inference(clausify,[status(thm)],[equation_H42]) ).
cnf(c_10,plain,
meet(A,join(B,meet(C,join(B,join(D,meet(A,C)))))) = 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_18,plain,
meet(A,meet(B,join(meet(A,B),C))) = meet(A,B),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_2262,plain,
meet(A,join(B,meet(C,join(B,meet(A,C))))) = meet(A,join(B,meet(C,join(A,meet(A,C))))),
inference(paramod,[status(thm)],[c_2,c_10]) ).
cnf(c_33,plain,
meet(A,join(B,meet(C,join(B,meet(A,C))))) = meet(A,join(B,meet(C,A))),
inference(paramod,[status(thm)],[c_4,c_2262]) ).
cnf(c_39,plain,
meet(A,join(B,meet(C,join(B,join(D,meet(C,A)))))) = meet(A,join(B,meet(C,join(A,D)))),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_2263,plain,
meet(A,B) = meet(A,meet(B,join(C,meet(A,B)))),
inference(paramod,[status(thm)],[c_14,c_7]) ).
cnf(c_55,plain,
meet(A,meet(B,join(C,meet(A,B)))) = meet(A,B),
inference(copy,[status(thm)],[c_2263]) ).
cnf(c_2264,plain,
join(meet(A,join(meet(B,A),C)),meet(B,A)) = meet(A,join(meet(B,A),C)),
inference(paramod,[status(thm)],[c_18,c_13]) ).
cnf(c_66,plain,
join(meet(A,B),meet(B,join(meet(A,B),C))) = meet(B,join(meet(A,B),C)),
inference(paramod,[status(thm)],[c_6,c_2264]) ).
cnf(c_2265,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(meet(a,join(b,meet(a,c))),join(b,meet(c,a)))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_39,c_12]) ).
cnf(c_2266,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(meet(a,join(b,meet(a,c))),join(b,meet(a,c)))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_5,c_2265]) ).
cnf(c_2267,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(c,join(join(b,meet(a,c)),meet(a,join(b,meet(a,c))))))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_6,c_2266]) ).
cnf(c_496,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_13,c_2267]) ).
cnf(c_2268,plain,
meet(A,meet(B,join(meet(C,B),meet(A,B)))) = meet(A,join(meet(C,B),meet(B,A))),
inference(paramod,[status(thm)],[c_66,c_33]) ).
cnf(c_2269,plain,
meet(A,B) = meet(A,join(meet(C,B),meet(B,A))),
inference(paramod,[status(thm)],[c_55,c_2268]) ).
cnf(c_2065,plain,
meet(A,join(meet(B,C),meet(C,A))) = meet(A,C),
inference(copy,[status(thm)],[c_2269]) ).
cnf(c_2102,plain,
meet(A,join(meet(B,C),meet(A,C))) = meet(A,C),
inference(paramod,[status(thm)],[c_5,c_2065]) ).
cnf(c_2260,plain,
meet(A,join(meet(A,B),meet(C,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_6,c_2102]) ).
cnf(c_2261,plain,
$false,
inference(resolve,[status(thm)],[c_2260,c_496]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT154-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Fri Sep 25 20:09:02 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 989796 was started by sandbox on n014,
% 0.11/0.37 % Fri Sep 25 20:09:02 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 6.69/1.34
% 6.69/1.34 % SZS status Unsatisfiable for theBenchmark
% 6.69/1.34
% 6.69/1.34 % Proof 1 at 0.56 (+ 0.14) seconds.
% 6.69/1.34 % Length of proof is 22.
% 6.69/1.34 % Level of proof is 6.
% 6.69/1.34 % Maximum clause weight is 25.000.
% 6.69/1.34 % Given clauses 100.
% 6.69/1.34
% 6.69/1.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------