%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT171-1 : 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 : n002.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 131.23s 17.30s
% Output : CNFRefutation 131.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 9 ( 9 ~; 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 : 53 ( 4 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_H61_dual,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(VAR_0,VAR_1),meet(VAR_0,VAR_2)) = meet(VAR_0,join(meet(VAR_0,VAR_1),meet(join(VAR_0,VAR_1),VAR_2))),
file('theBenchmark.p',equation_H61_dual) ).
cnf(c_9,plain,
join(meet(A,B),meet(A,C)) = meet(A,join(meet(A,B),meet(join(A,B),C))),
inference(clausify,[status(thm)],[equation_H61_dual]) ).
cnf(c_10,plain,
meet(A,join(meet(A,B),meet(join(A,B),C))) = join(meet(A,B),meet(A,C)),
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,
meet(join(A,B),A) = A,
inference(paramod,[status(thm)],[c_5,c_3]) ).
cnf(c_21,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_7,c_4]) ).
cnf(c_66,plain,
meet(A,join(meet(A,join(B,C)),meet(join(join(A,B),C),D))) = join(meet(A,join(B,C)),meet(A,D)),
inference(paramod,[status(thm)],[c_8,c_10]) ).
cnf(c_71,plain,
meet(a,join(meet(a,join(b,meet(a,c))),meet(join(a,b),c))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_5,c_12]) ).
cnf(c_118,plain,
meet(a,join(meet(a,join(meet(a,c),b)),meet(join(a,b),c))) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_6,c_71]) ).
cnf(c_172,plain,
join(meet(join(meet(A,B),C),A),meet(A,B)) = meet(join(meet(A,B),C),A),
inference(paramod,[status(thm)],[c_13,c_21]) ).
cnf(c_1579,plain,
meet(A,join(meet(A,join(meet(A,B),C)),meet(join(A,C),D))) = join(meet(A,join(meet(A,B),C)),meet(A,D)),
inference(paramod,[status(thm)],[c_4,c_66]) ).
cnf(c_1653,plain,
join(meet(a,join(meet(a,c),b)),meet(a,c)) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_1579,c_118]) ).
cnf(c_1819,plain,
join(meet(join(meet(a,c),b),a),meet(a,c)) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_5,c_1653]) ).
cnf(c_1808,plain,
meet(join(meet(a,c),b),a) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_172,c_1819]) ).
cnf(c_1820,plain,
meet(join(b,meet(a,c)),a) != meet(a,join(b,meet(a,c))),
inference(paramod,[status(thm)],[c_6,c_1808]) ).
cnf(c_1818,plain,
$false,
inference(resolve,[status(thm)],[c_5,c_1820]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT171-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Fri Sep 25 20:13:51 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 4051793 was started by sandbox2 on n002,
% 0.12/0.36 % Fri Sep 25 20:13:51 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 131.23/17.30
% 131.23/17.30 % SZS status Unsatisfiable for theBenchmark
% 131.23/17.30
% 131.23/17.30 % Proof 1 at 0.74 (+ 0.13) seconds.
% 131.23/17.30 % Length of proof is 20.
% 131.23/17.30 % Level of proof is 6.
% 131.23/17.30 % Maximum clause weight is 57.000.
% 131.23/17.30 % Given clauses 106.
% 131.23/17.30
% 131.23/17.30 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------