%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT006-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 07:49:31 AM UTC 2026
% Result : Unsatisfiable 1.87s 0.68s
% Output : CNFRefutation 1.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 50 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 4 ( 4 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 5 ( 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 : 115 ( 12 sgn 5 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(absorption,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,join(VAR_0,VAR_1)) = VAR_0,
file('theBenchmark.p',absorption) ).
cnf(c_1,plain,
meet(A,join(A,B)) = A,
inference(clausify,[status(thm)],[absorption]) ).
fof(distribution,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,VAR_2)) = join(meet(VAR_2,VAR_0),meet(VAR_1,VAR_0)),
file('theBenchmark.p',distribution) ).
cnf(c_2,plain,
meet(A,join(B,C)) = join(meet(C,A),meet(B,A)),
inference(clausify,[status(thm)],[distribution]) ).
cnf(c_3,plain,
join(meet(A,B),meet(C,B)) = meet(B,join(C,A)),
inference(copy,[status(thm)],[c_2]) ).
fof(prove_associativity_of_meet,axiom,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('theBenchmark.p',prove_associativity_of_meet) ).
cnf(c_4,plain,
meet(meet(a,b),c) != meet(a,meet(b,c)),
inference(clausify,[status(thm)],[prove_associativity_of_meet]) ).
cnf(c_5,plain,
meet(meet(A,B),meet(B,join(C,A))) = meet(A,B),
inference(paramod,[status(thm)],[c_3,c_1]) ).
cnf(c_6,plain,
join(A,meet(B,join(A,C))) = meet(join(A,C),join(B,A)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_9,plain,
meet(meet(A,B),B) = meet(A,B),
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_12,plain,
meet(meet(meet(A,B),C),meet(C,meet(B,join(A,D)))) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_3,c_5]) ).
cnf(c_824,plain,
join(meet(A,B),meet(C,B)) = meet(B,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_825,plain,
meet(B,join(C,A)) = meet(B,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_3,c_824]) ).
cnf(c_14,plain,
meet(A,join(B,meet(C,A))) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_825]) ).
cnf(c_826,plain,
join(meet(A,B),meet(C,B)) = meet(B,join(meet(C,B),A)),
inference(paramod,[status(thm)],[c_9,c_3]) ).
cnf(c_827,plain,
meet(B,join(C,A)) = meet(B,join(meet(C,B),A)),
inference(paramod,[status(thm)],[c_3,c_826]) ).
cnf(c_15,plain,
meet(A,join(meet(B,A),C)) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_827]) ).
cnf(c_828,plain,
meet(A,meet(A,join(B,C))) = meet(A,join(meet(C,A),B)),
inference(paramod,[status(thm)],[c_3,c_14]) ).
cnf(c_22,plain,
meet(A,meet(A,join(B,C))) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_15,c_828]) ).
cnf(c_829,plain,
join(A,A) = meet(join(A,B),join(A,A)),
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_33,plain,
meet(join(A,B),join(A,A)) = join(A,A),
inference(copy,[status(thm)],[c_829]) ).
cnf(c_830,plain,
meet(A,A) = meet(A,join(B,A)),
inference(paramod,[status(thm)],[c_1,c_22]) ).
cnf(c_56,plain,
meet(A,join(B,A)) = meet(A,A),
inference(copy,[status(thm)],[c_830]) ).
cnf(c_70,plain,
meet(A,A) = A,
inference(paramod,[status(thm)],[c_56,c_1]) ).
cnf(c_831,plain,
join(meet(A,A),meet(B,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_56,c_3]) ).
cnf(c_832,plain,
join(A,meet(B,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_70,c_831]) ).
cnf(c_73,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_70,c_832]) ).
cnf(c_833,plain,
meet(A,join(A,A)) = join(A,A),
inference(paramod,[status(thm)],[c_73,c_33]) ).
cnf(c_834,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_1,c_833]) ).
cnf(c_93,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_834]) ).
cnf(c_835,plain,
meet(A,B) = meet(B,join(A,A)),
inference(paramod,[status(thm)],[c_93,c_3]) ).
cnf(c_117,plain,
meet(A,B) = meet(B,A),
inference(paramod,[status(thm)],[c_93,c_835]) ).
cnf(c_127,plain,
meet(c,meet(a,b)) != meet(a,meet(b,c)),
inference(paramod,[status(thm)],[c_117,c_4]) ).
cnf(c_129,plain,
join(meet(A,B),meet(C,A)) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_117,c_3]) ).
cnf(c_136,plain,
join(A,meet(A,B)) = A,
inference(paramod,[status(thm)],[c_117,c_73]) ).
cnf(c_836,plain,
meet(A,meet(B,join(C,A))) = meet(A,join(B,meet(C,B))),
inference(paramod,[status(thm)],[c_129,c_15]) ).
cnf(c_197,plain,
meet(A,meet(B,join(C,A))) = meet(A,B),
inference(paramod,[status(thm)],[c_73,c_836]) ).
cnf(c_740,plain,
meet(meet(A,B),meet(C,B)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_73,c_197]) ).
cnf(c_742,plain,
meet(meet(A,B),meet(C,A)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_136,c_197]) ).
cnf(c_837,plain,
meet(meet(meet(A,B),C),meet(C,B)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_197,c_12]) ).
cnf(c_838,plain,
meet(meet(C,B),meet(meet(A,B),C)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_117,c_837]) ).
cnf(c_839,plain,
meet(meet(C,B),meet(A,B)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_742,c_838]) ).
cnf(c_745,plain,
meet(meet(A,B),C) = meet(meet(C,B),A),
inference(paramod,[status(thm)],[c_740,c_839]) ).
cnf(c_821,plain,
meet(meet(A,B),C) = meet(A,meet(C,B)),
inference(paramod,[status(thm)],[c_745,c_117]) ).
cnf(c_840,plain,
meet(meet(A,B),C) = meet(meet(C,A),B),
inference(paramod,[status(thm)],[c_117,c_745]) ).
cnf(c_841,plain,
meet(A,meet(C,B)) = meet(meet(C,A),B),
inference(paramod,[status(thm)],[c_821,c_840]) ).
cnf(c_842,plain,
meet(A,meet(C,B)) = meet(C,meet(B,A)),
inference(paramod,[status(thm)],[c_821,c_841]) ).
cnf(c_822,plain,
meet(A,meet(B,C)) = meet(C,meet(A,B)),
inference(copy,[status(thm)],[c_842]) ).
cnf(c_843,plain,
meet(a,meet(b,c)) != meet(c,meet(a,b)),
inference(copy,[status(thm)],[c_127]) ).
cnf(c_823,plain,
$false,
inference(resolve,[status(thm)],[c_822,c_843]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT006-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 19:59:13 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2105320 was started by sandbox on n015,
% 0.09/0.37 % Fri Sep 25 19:59:13 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 1.87/0.68
% 1.87/0.68 % SZS status Unsatisfiable for theBenchmark
% 1.87/0.68
% 1.87/0.68 % Proof 1 at 0.23 (+ 0.07) seconds.
% 1.87/0.68 % Length of proof is 27.
% 1.87/0.68 % Level of proof is 17.
% 1.87/0.68 % Maximum clause weight is 54.000.
% 1.87/0.68 % Given clauses 67.
% 1.87/0.68
% 1.87/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------