%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT026-1 : 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 : n019.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 07:49:34 AM UTC 2026
% Result : Unsatisfiable 10.06s 1.76s
% Output : CNFRefutation 10.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 55 unt; 0 def)
% Number of atoms : 55 ( 54 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 6 ( 6 ~; 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 : 129 ( 26 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(idempotence_of_meet,axiom,
! [VAR_0] : meet(VAR_0,VAR_0) = VAR_0,
file('theBenchmark.p',idempotence_of_meet) ).
cnf(c_1,plain,
meet(A,A) = A,
inference(clausify,[status(thm)],[idempotence_of_meet]) ).
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(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_3,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_4,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[commutativity_of_join]) ).
fof(wal_1,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(meet(join(VAR_0,VAR_1),join(VAR_2,VAR_1)),VAR_1) = VAR_1,
file('theBenchmark.p',wal_1) ).
cnf(c_5,plain,
meet(meet(join(A,B),join(C,B)),B) = B,
inference(clausify,[status(thm)],[wal_1]) ).
cnf(c_6,plain,
meet(A,meet(join(B,A),join(C,A))) = A,
inference(paramod,[status(thm)],[c_3,c_5]) ).
fof(wal_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(join(meet(VAR_0,VAR_1),meet(VAR_2,VAR_1)),VAR_1) = VAR_1,
file('theBenchmark.p',wal_2) ).
cnf(c_7,plain,
join(join(meet(A,B),meet(C,B)),B) = B,
inference(clausify,[status(thm)],[wal_2]) ).
cnf(c_8,plain,
join(A,join(meet(B,A),meet(C,A))) = A,
inference(paramod,[status(thm)],[c_4,c_7]) ).
fof(absorbtion,axiom,
! [VAR_0,VAR_1,VAR_2] : meet(VAR_0,join(VAR_1,join(VAR_0,VAR_2))) = VAR_0,
file('theBenchmark.p',absorbtion) ).
cnf(c_9,plain,
meet(A,join(B,join(A,C))) = A,
inference(clausify,[status(thm)],[absorbtion]) ).
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_10,plain,
meet(meet(a,b),c) != meet(a,meet(b,c)),
inference(clausify,[status(thm)],[prove_associativity_of_meet]) ).
cnf(c_11,plain,
meet(c,meet(a,b)) != meet(a,meet(b,c)),
inference(paramod,[status(thm)],[c_3,c_10]) ).
cnf(c_12,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_1,c_6]) ).
cnf(c_16,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_2,c_8]) ).
cnf(c_20,plain,
meet(A,join(B,join(C,A))) = A,
inference(paramod,[status(thm)],[c_4,c_9]) ).
cnf(c_26,plain,
join(A,meet(A,B)) = A,
inference(paramod,[status(thm)],[c_3,c_16]) ).
cnf(c_27,plain,
meet(meet(A,B),meet(B,join(C,meet(A,B)))) = meet(A,B),
inference(paramod,[status(thm)],[c_16,c_6]) ).
cnf(c_47,plain,
meet(meet(A,B),join(C,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_26,c_20]) ).
cnf(c_78,plain,
join(join(A,B),meet(B,C)) = join(A,B),
inference(paramod,[status(thm)],[c_47,c_16]) ).
cnf(c_167,plain,
meet(meet(A,B),meet(B,join(C,A))) = meet(A,B),
inference(paramod,[status(thm)],[c_78,c_27]) ).
cnf(c_803,plain,
join(meet(A,join(B,C)),meet(C,A)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_167,c_16]) ).
cnf(c_1036,plain,
join(meet(A,join(B,C)),meet(A,C)) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_3,c_803]) ).
cnf(c_819,plain,
join(meet(A,B),meet(A,join(C,B))) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_4,c_1036]) ).
cnf(c_1037,plain,
join(meet(A,B),meet(meet(B,C),A)) = meet(A,join(B,meet(B,C))),
inference(paramod,[status(thm)],[c_26,c_803]) ).
cnf(c_823,plain,
join(meet(A,B),meet(meet(B,C),A)) = meet(A,B),
inference(paramod,[status(thm)],[c_26,c_1037]) ).
cnf(c_1038,plain,
join(meet(A,meet(B,C)),meet(A,C)) = meet(A,join(C,meet(B,C))),
inference(paramod,[status(thm)],[c_16,c_819]) ).
cnf(c_1039,plain,
join(meet(A,C),meet(A,meet(B,C))) = meet(A,join(C,meet(B,C))),
inference(paramod,[status(thm)],[c_4,c_1038]) ).
cnf(c_854,plain,
join(meet(A,B),meet(A,meet(C,B))) = meet(A,B),
inference(paramod,[status(thm)],[c_16,c_1039]) ).
cnf(c_1040,plain,
join(meet(A,meet(B,C)),meet(A,B)) = meet(A,join(B,meet(B,C))),
inference(paramod,[status(thm)],[c_26,c_819]) ).
cnf(c_1041,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,join(B,meet(B,C))),
inference(paramod,[status(thm)],[c_4,c_1040]) ).
cnf(c_855,plain,
join(meet(A,B),meet(A,meet(B,C))) = meet(A,B),
inference(paramod,[status(thm)],[c_26,c_1041]) ).
cnf(c_1042,plain,
join(meet(meet(A,join(B,C)),C),meet(C,A)) = meet(meet(A,join(B,C)),C),
inference(paramod,[status(thm)],[c_167,c_823]) ).
cnf(c_1043,plain,
join(meet(C,meet(A,join(B,C))),meet(C,A)) = meet(meet(A,join(B,C)),C),
inference(paramod,[status(thm)],[c_3,c_1042]) ).
cnf(c_1044,plain,
join(meet(C,A),meet(C,meet(A,join(B,C)))) = meet(meet(A,join(B,C)),C),
inference(paramod,[status(thm)],[c_4,c_1043]) ).
cnf(c_1045,plain,
meet(C,A) = meet(meet(A,join(B,C)),C),
inference(paramod,[status(thm)],[c_855,c_1044]) ).
cnf(c_1046,plain,
meet(C,A) = meet(C,meet(A,join(B,C))),
inference(paramod,[status(thm)],[c_3,c_1045]) ).
cnf(c_925,plain,
meet(A,meet(B,join(C,A))) = meet(A,B),
inference(copy,[status(thm)],[c_1046]) ).
cnf(c_928,plain,
meet(A,meet(join(B,A),C)) = meet(A,C),
inference(paramod,[status(thm)],[c_3,c_925]) ).
cnf(c_930,plain,
meet(meet(A,B),meet(C,B)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_16,c_925]) ).
cnf(c_939,plain,
meet(meet(A,B),meet(A,C)) = meet(meet(A,B),C),
inference(paramod,[status(thm)],[c_26,c_928]) ).
cnf(c_1047,plain,
meet(meet(A,meet(B,C)),meet(A,C)) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_854,c_12]) ).
cnf(c_1048,plain,
meet(meet(A,C),meet(A,meet(B,C))) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_3,c_1047]) ).
cnf(c_1049,plain,
meet(meet(A,C),meet(B,C)) = meet(A,meet(B,C)),
inference(paramod,[status(thm)],[c_939,c_1048]) ).
cnf(c_1020,plain,
meet(meet(A,B),C) = meet(A,meet(C,B)),
inference(paramod,[status(thm)],[c_930,c_1049]) ).
cnf(c_1050,plain,
meet(meet(c,b),a) != meet(a,meet(b,c)),
inference(paramod,[status(thm)],[c_1020,c_11]) ).
cnf(c_1051,plain,
meet(meet(b,c),a) != meet(a,meet(b,c)),
inference(paramod,[status(thm)],[c_3,c_1050]) ).
cnf(c_1052,plain,
meet(a,meet(b,c)) != meet(a,meet(b,c)),
inference(paramod,[status(thm)],[c_3,c_1051]) ).
cnf(c_1035,plain,
$false,
inference(copy,[status(thm)],[c_1052]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT026-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n019.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 19:58:03 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.35 % Process 3530741 was started by sandbox on n019,
% 0.07/0.35 % Fri Sep 25 19:58:03 2026
% 0.07/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.35
% 0.07/0.35 % From the command line: assign(max_seconds, 300).
% 10.06/1.76
% 10.06/1.76 % SZS status Unsatisfiable for theBenchmark
% 10.06/1.76
% 10.06/1.76 % Proof 1 at 0.77 (+ 0.26) seconds.
% 10.06/1.76 % Length of proof is 30.
% 10.06/1.76 % Level of proof is 14.
% 10.06/1.76 % Maximum clause weight is 29.000.
% 10.06/1.76 % Given clauses 181.
% 10.06/1.76
% 10.06/1.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------