%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT013-1 : 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 : n001.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 07:49:32 AM UTC 2026
% Result : Unsatisfiable 10.42s 1.75s
% Output : CNFRefutation 10.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 5
% Syntax : Number of formulae : 75 ( 75 unt; 0 def)
% Number of atoms : 75 ( 74 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 : 189 ( 35 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mckenzie1,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,meet(VAR_1,meet(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',mckenzie1) ).
cnf(c_1,plain,
join(A,meet(B,meet(A,C))) = A,
inference(clausify,[status(thm)],[mckenzie1]) ).
fof(mckenzie2,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,join(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',mckenzie2) ).
cnf(c_2,plain,
meet(A,join(B,join(A,C))) = A,
inference(clausify,[status(thm)],[mckenzie2]) ).
fof(mckenzie3,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet(VAR_0,VAR_1),meet(VAR_1,VAR_2)),VAR_1) = VAR_1,
file('theBenchmark.p',mckenzie3) ).
cnf(c_3,plain,
join(join(meet(A,B),meet(B,C)),B) = B,
inference(clausify,[status(thm)],[mckenzie3]) ).
fof(mckenzie4,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(join(VAR_0,VAR_1),join(VAR_1,VAR_2)),VAR_1) = VAR_1,
file('theBenchmark.p',mckenzie4) ).
cnf(c_4,plain,
meet(meet(join(A,B),join(B,C)),B) = B,
inference(clausify,[status(thm)],[mckenzie4]) ).
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_5,plain,
meet(meet(a,b),c) != meet(a,meet(b,c)),
inference(clausify,[status(thm)],[prove_associativity_of_meet]) ).
cnf(c_6,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_2,c_1]) ).
cnf(c_7,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_2]) ).
cnf(c_8,plain,
join(meet(A,B),B) = B,
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_10,plain,
meet(A,join(A,B)) = A,
inference(paramod,[status(thm)],[c_3,c_2]) ).
cnf(c_13,plain,
join(A,meet(A,B)) = A,
inference(paramod,[status(thm)],[c_4,c_1]) ).
cnf(c_15,plain,
meet(join(A,B),B) = B,
inference(paramod,[status(thm)],[c_2,c_4]) ).
cnf(c_18,plain,
meet(meet(A,join(meet(B,A),C)),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_6,c_4]) ).
cnf(c_20,plain,
join(join(A,meet(join(B,A),C)),join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_7,c_3]) ).
cnf(c_23,plain,
meet(meet(A,B),join(C,B)) = meet(A,B),
inference(paramod,[status(thm)],[c_8,c_2]) ).
cnf(c_24,plain,
join(A,join(B,join(A,C))) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_26,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_7,c_8]) ).
cnf(c_29,plain,
join(join(A,B),A) = join(A,B),
inference(paramod,[status(thm)],[c_10,c_6]) ).
cnf(c_40,plain,
meet(A,meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_6,c_15]) ).
cnf(c_41,plain,
meet(A,meet(A,B)) = meet(A,B),
inference(paramod,[status(thm)],[c_13,c_15]) ).
cnf(c_915,plain,
join(meet(A,B),A) = join(A,meet(A,B)),
inference(paramod,[status(thm)],[c_13,c_26]) ).
cnf(c_46,plain,
join(meet(A,B),A) = A,
inference(paramod,[status(thm)],[c_13,c_915]) ).
cnf(c_49,plain,
meet(meet(A,B),join(C,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_46,c_2]) ).
cnf(c_60,plain,
join(meet(A,B),meet(B,join(meet(A,B),C))) = meet(B,join(meet(A,B),C)),
inference(paramod,[status(thm)],[c_18,c_46]) ).
cnf(c_61,plain,
meet(meet(A,B),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_46,c_18]) ).
cnf(c_66,plain,
meet(join(A,B),A) = A,
inference(paramod,[status(thm)],[c_29,c_15]) ).
cnf(c_77,plain,
join(A,meet(B,meet(C,A))) = A,
inference(paramod,[status(thm)],[c_40,c_1]) ).
cnf(c_89,plain,
join(join(A,B),join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_66,c_20]) ).
cnf(c_916,plain,
join(meet(A,B),join(C,A)) = join(C,join(meet(A,B),A)),
inference(paramod,[status(thm)],[c_46,c_24]) ).
cnf(c_115,plain,
join(meet(A,B),join(C,A)) = join(C,A),
inference(paramod,[status(thm)],[c_46,c_916]) ).
cnf(c_172,plain,
meet(A,meet(B,meet(C,A))) = meet(B,meet(C,A)),
inference(paramod,[status(thm)],[c_77,c_15]) ).
cnf(c_318,plain,
join(meet(A,B),meet(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_61,c_13]) ).
cnf(c_917,plain,
join(meet(A,B),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_61,c_46]) ).
cnf(c_319,plain,
meet(A,B) = meet(B,A),
inference(paramod,[status(thm)],[c_318,c_917]) ).
cnf(c_918,plain,
meet(meet(A,B),join(C,meet(B,A))) = meet(meet(B,A),meet(A,B)),
inference(paramod,[status(thm)],[c_61,c_49]) ).
cnf(c_322,plain,
meet(meet(A,B),join(C,meet(B,A))) = meet(A,B),
inference(paramod,[status(thm)],[c_61,c_918]) ).
cnf(c_359,plain,
meet(c,meet(a,b)) != meet(a,meet(b,c)),
inference(paramod,[status(thm)],[c_319,c_5]) ).
cnf(c_919,plain,
join(join(A,B),join(B,A)) = join(join(B,A),join(A,B)),
inference(paramod,[status(thm)],[c_89,c_29]) ).
cnf(c_920,plain,
join(B,A) = join(join(B,A),join(A,B)),
inference(paramod,[status(thm)],[c_89,c_919]) ).
cnf(c_391,plain,
join(A,B) = join(B,A),
inference(paramod,[status(thm)],[c_89,c_920]) ).
cnf(c_921,plain,
join(meet(A,B),meet(B,join(C,A))) = meet(B,join(meet(A,B),join(C,A))),
inference(paramod,[status(thm)],[c_115,c_60]) ).
cnf(c_424,plain,
join(meet(A,B),meet(B,join(C,A))) = meet(B,join(C,A)),
inference(paramod,[status(thm)],[c_115,c_921]) ).
cnf(c_922,plain,
join(meet(meet(A,B),C),meet(C,B)) = meet(C,join(B,meet(A,B))),
inference(paramod,[status(thm)],[c_6,c_424]) ).
cnf(c_542,plain,
join(meet(meet(A,B),C),meet(C,B)) = meet(C,B),
inference(paramod,[status(thm)],[c_6,c_922]) ).
cnf(c_923,plain,
join(meet(meet(A,B),C),meet(C,A)) = meet(C,join(A,meet(A,B))),
inference(paramod,[status(thm)],[c_13,c_424]) ).
cnf(c_543,plain,
join(meet(meet(A,B),C),meet(C,A)) = meet(C,A),
inference(paramod,[status(thm)],[c_13,c_923]) ).
cnf(c_924,plain,
join(meet(A,meet(B,C)),meet(A,C)) = meet(A,C),
inference(paramod,[status(thm)],[c_319,c_542]) ).
cnf(c_629,plain,
join(meet(A,B),meet(A,meet(C,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_391,c_924]) ).
cnf(c_634,plain,
join(meet(A,B),meet(join(C,B),A)) = meet(join(C,B),A),
inference(paramod,[status(thm)],[c_23,c_543]) ).
cnf(c_925,plain,
join(meet(A,meet(B,C)),meet(A,B)) = meet(A,B),
inference(paramod,[status(thm)],[c_319,c_543]) ).
cnf(c_640,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_391,c_925]) ).
cnf(c_817,plain,
join(meet(A,B),meet(B,meet(C,A))) = meet(B,A),
inference(paramod,[status(thm)],[c_319,c_629]) ).
cnf(c_926,plain,
join(meet(A,B),meet(B,meet(join(C,B),A))) = meet(B,join(meet(A,B),meet(join(C,B),A))),
inference(paramod,[status(thm)],[c_634,c_60]) ).
cnf(c_927,plain,
meet(B,A) = meet(B,join(meet(A,B),meet(join(C,B),A))),
inference(paramod,[status(thm)],[c_817,c_926]) ).
cnf(c_928,plain,
meet(B,A) = meet(B,meet(join(C,B),A)),
inference(paramod,[status(thm)],[c_634,c_927]) ).
cnf(c_840,plain,
meet(A,meet(join(B,A),C)) = meet(A,C),
inference(copy,[status(thm)],[c_928]) ).
cnf(c_861,plain,
meet(meet(A,B),meet(B,C)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_6,c_840]) ).
cnf(c_862,plain,
meet(meet(A,B),meet(A,C)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_13,c_840]) ).
cnf(c_929,plain,
meet(meet(A,meet(B,C)),meet(A,B)) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_640,c_7]) ).
cnf(c_930,plain,
meet(meet(A,B),meet(A,meet(B,C))) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_319,c_929]) ).
cnf(c_931,plain,
meet(meet(A,B),meet(B,C)) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_862,c_930]) ).
cnf(c_910,plain,
meet(meet(A,B),C) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_861,c_931]) ).
cnf(c_932,plain,
meet(meet(meet(A,B),C),meet(C,A)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_640,c_322]) ).
cnf(c_933,plain,
meet(meet(A,meet(B,C)),meet(C,A)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_910,c_932]) ).
cnf(c_934,plain,
meet(A,meet(meet(B,C),meet(C,A))) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_910,c_933]) ).
cnf(c_935,plain,
meet(A,meet(B,meet(C,meet(C,A)))) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_910,c_934]) ).
cnf(c_936,plain,
meet(A,meet(B,meet(C,A))) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_41,c_935]) ).
cnf(c_937,plain,
meet(B,meet(C,A)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_172,c_936]) ).
cnf(c_913,plain,
meet(A,meet(B,C)) = meet(C,meet(A,B)),
inference(paramod,[status(thm)],[c_910,c_937]) ).
cnf(c_938,plain,
meet(a,meet(b,c)) != meet(c,meet(a,b)),
inference(copy,[status(thm)],[c_359]) ).
cnf(c_914,plain,
$false,
inference(resolve,[status(thm)],[c_913,c_938]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT013-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n001.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 20:01:41 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 4089883 was started by sandbox on n001,
% 0.09/0.36 % Fri Sep 25 20:01:41 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 10.42/1.75
% 10.42/1.75 % SZS status Unsatisfiable for theBenchmark
% 10.42/1.75
% 10.42/1.75 % Proof 1 at 0.96 (+ 0.35) seconds.
% 10.42/1.75 % Length of proof is 46.
% 10.42/1.75 % Level of proof is 13.
% 10.42/1.75 % Maximum clause weight is 29.000.
% 10.42/1.75 % Given clauses 177.
% 10.42/1.75
% 10.42/1.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------