%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT143-1 : 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 : n017.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 22.69s 3.60s
% Output : CNFRefutation 22.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% 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 : 8 ( 8 ~; 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 : 92 ( 10 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_H24,axiom,
! [VAR_0,VAR_1,VAR_2] : join(meet(VAR_0,VAR_1),meet(VAR_1,VAR_2)) = join(meet(VAR_0,VAR_1),meet(VAR_1,join(meet(VAR_0,VAR_1),meet(VAR_2,join(VAR_0,VAR_1))))),
file('theBenchmark.p',equation_H24) ).
cnf(c_9,plain,
join(meet(A,B),meet(B,C)) = join(meet(A,B),meet(B,join(meet(A,B),meet(C,join(A,B))))),
inference(clausify,[status(thm)],[equation_H24]) ).
cnf(c_10,plain,
join(meet(A,B),meet(B,join(meet(A,B),meet(C,join(A,B))))) = join(meet(A,B),meet(B,C)),
inference(copy,[status(thm)],[c_9]) ).
fof(prove_H15,axiom,
meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
file('theBenchmark.p',prove_H15) ).
cnf(c_11,plain,
meet(a,join(meet(a,b),meet(a,c))) != meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))),
inference(clausify,[status(thm)],[prove_H15]) ).
cnf(c_12,plain,
meet(a,join(meet(a,b),join(meet(a,c),meet(c,join(a,b))))) != meet(a,join(meet(a,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_2894,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_2894]) ).
cnf(c_2895,plain,
join(A,B) = join(A,join(meet(A,C),B)),
inference(paramod,[status(thm)],[c_4,c_8]) ).
cnf(c_28,plain,
join(A,join(meet(A,B),C)) = join(A,C),
inference(copy,[status(thm)],[c_2895]) ).
cnf(c_33,plain,
join(meet(A,B),meet(B,join(meet(B,A),meet(C,join(A,B))))) = join(meet(A,B),meet(B,C)),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_66,plain,
meet(A,meet(B,join(meet(B,A),C))) = meet(A,B),
inference(paramod,[status(thm)],[c_5,c_18]) ).
cnf(c_2896,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_107,plain,
join(meet(A,B),meet(join(A,C),B)) = meet(join(A,C),B),
inference(paramod,[status(thm)],[c_6,c_2896]) ).
cnf(c_2897,plain,
meet(join(meet(A,B),C),join(A,C)) = join(meet(A,B),C),
inference(paramod,[status(thm)],[c_28,c_14]) ).
cnf(c_148,plain,
meet(join(A,B),join(meet(A,C),B)) = join(meet(A,C),B),
inference(paramod,[status(thm)],[c_5,c_2897]) ).
cnf(c_294,plain,
join(meet(A,B),meet(B,join(A,C))) = meet(join(A,C),B),
inference(paramod,[status(thm)],[c_5,c_107]) ).
cnf(c_2898,plain,
meet(a,join(meet(a,b),meet(join(a,b),c))) != meet(a,join(meet(a,b),meet(a,c))),
inference(paramod,[status(thm)],[c_294,c_12]) ).
cnf(c_315,plain,
meet(a,join(meet(a,b),meet(c,join(a,b)))) != meet(a,join(meet(a,b),meet(a,c))),
inference(paramod,[status(thm)],[c_5,c_2898]) ).
cnf(c_347,plain,
join(meet(A,B),meet(B,join(meet(B,A),meet(C,join(B,A))))) = join(meet(A,B),meet(B,C)),
inference(paramod,[status(thm)],[c_6,c_33]) ).
cnf(c_426,plain,
meet(A,join(meet(A,B),meet(A,C))) = join(meet(A,B),meet(A,C)),
inference(paramod,[status(thm)],[c_4,c_148]) ).
cnf(c_450,plain,
meet(a,join(meet(a,b),meet(c,join(a,b)))) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_426,c_315]) ).
cnf(c_2899,plain,
join(meet(A,join(meet(A,B),C)),meet(B,A)) = meet(A,join(meet(A,B),C)),
inference(paramod,[status(thm)],[c_66,c_13]) ).
cnf(c_2854,plain,
join(meet(A,B),meet(B,join(meet(B,A),C))) = meet(B,join(meet(B,A),C)),
inference(paramod,[status(thm)],[c_6,c_2899]) ).
cnf(c_2891,plain,
meet(A,join(meet(A,B),meet(C,join(A,B)))) = join(meet(B,A),meet(A,C)),
inference(paramod,[status(thm)],[c_2854,c_347]) ).
cnf(c_2900,plain,
join(meet(b,a),meet(a,c)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_2891,c_450]) ).
cnf(c_2901,plain,
join(meet(a,b),meet(a,c)) != join(meet(a,b),meet(a,c)),
inference(paramod,[status(thm)],[c_5,c_2900]) ).
cnf(c_2893,plain,
$false,
inference(copy,[status(thm)],[c_2901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LAT143-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.63 % Computer : n017.cluster.edu
% 0.16/0.63 % Model : x86_64 x86_64
% 0.16/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.63 % Memory : 8046.5625MB
% 0.16/0.63 % OS : Linux 6.8.0-71-generic
% 0.16/0.63 % CPULimit : 300
% 0.16/0.63 % WCLimit : 300
% 0.16/0.63 % DateTime : Fri Sep 25 20:03:32 UTC 2026
% 0.16/0.64 % CPUTime :
% 0.16/0.64 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.64 % Process 3049106 was started by sandbox2 on n017,
% 0.16/0.64 % Fri Sep 25 20:03:32 2026
% 0.16/0.64 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.65
% 0.16/0.65 % From the command line: assign(max_seconds, 300).
% 22.69/3.60
% 22.69/3.60 % SZS status Unsatisfiable for theBenchmark
% 22.69/3.60
% 22.69/3.60 % Proof 1 at 2.42 (+ 0.50) seconds.
% 22.69/3.60 % Length of proof is 27.
% 22.69/3.60 % Level of proof is 6.
% 22.69/3.60 % Maximum clause weight is 57.000.
% 22.69/3.60 % Given clauses 125.
% 22.69/3.60
% 22.69/3.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------