%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT007-1 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 6.48s 1.24s
% Output : CNFRefutation 6.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 44
% Number of leaves : 3
% Syntax : Number of formulae : 92 ( 92 unt; 0 def)
% Number of atoms : 92 ( 91 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 : 234 ( 22 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_join,axiom,
join(join(a,b),c) != join(a,join(b,c)),
file('theBenchmark.p',prove_associativity_of_join) ).
cnf(c_4,plain,
join(join(a,b),c) != join(a,join(b,c)),
inference(clausify,[status(thm)],[prove_associativity_of_join]) ).
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_7,plain,
join(meet(A,join(B,C)),B) = meet(join(B,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_1788,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_1789,plain,
meet(B,join(C,A)) = meet(B,join(C,meet(A,B))),
inference(paramod,[status(thm)],[c_3,c_1788]) ).
cnf(c_14,plain,
meet(A,join(B,meet(C,A))) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_1789]) ).
cnf(c_1790,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_1791,plain,
meet(B,join(C,A)) = meet(B,join(meet(C,B),A)),
inference(paramod,[status(thm)],[c_3,c_1790]) ).
cnf(c_15,plain,
meet(A,join(meet(B,A),C)) = meet(A,join(B,C)),
inference(copy,[status(thm)],[c_1791]) ).
cnf(c_1792,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_1792]) ).
cnf(c_26,plain,
join(meet(A,join(B,C)),meet(D,join(meet(B,A),C))) = meet(join(meet(B,A),C),join(D,A)),
inference(paramod,[status(thm)],[c_15,c_3]) ).
cnf(c_1793,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_1793]) ).
cnf(c_1794,plain,
meet(join(meet(A,B),C),meet(B,join(A,A))) = join(meet(A,B),meet(A,B)),
inference(paramod,[status(thm)],[c_3,c_33]) ).
cnf(c_40,plain,
meet(join(meet(A,B),C),meet(B,join(A,A))) = meet(B,join(A,A)),
inference(paramod,[status(thm)],[c_3,c_1794]) ).
cnf(c_1795,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_1795]) ).
cnf(c_70,plain,
meet(A,A) = A,
inference(paramod,[status(thm)],[c_56,c_1]) ).
cnf(c_1796,plain,
join(meet(A,A),meet(B,join(C,A))) = meet(join(C,A),join(B,A)),
inference(paramod,[status(thm)],[c_56,c_3]) ).
cnf(c_71,plain,
join(A,meet(B,join(C,A))) = meet(join(C,A),join(B,A)),
inference(paramod,[status(thm)],[c_70,c_1796]) ).
cnf(c_1797,plain,
join(meet(A,A),meet(B,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_56,c_3]) ).
cnf(c_1798,plain,
join(A,meet(B,A)) = meet(A,A),
inference(paramod,[status(thm)],[c_70,c_1797]) ).
cnf(c_73,plain,
join(A,meet(B,A)) = A,
inference(paramod,[status(thm)],[c_70,c_1798]) ).
cnf(c_1799,plain,
join(meet(A,A),B) = meet(join(B,A),join(B,A)),
inference(paramod,[status(thm)],[c_56,c_7]) ).
cnf(c_1800,plain,
join(A,B) = meet(join(B,A),join(B,A)),
inference(paramod,[status(thm)],[c_70,c_1799]) ).
cnf(c_77,plain,
join(A,B) = join(B,A),
inference(paramod,[status(thm)],[c_70,c_1800]) ).
cnf(c_81,plain,
meet(A,join(B,A)) = A,
inference(paramod,[status(thm)],[c_70,c_56]) ).
cnf(c_84,plain,
join(c,join(a,b)) != join(a,join(b,c)),
inference(paramod,[status(thm)],[c_77,c_4]) ).
cnf(c_1801,plain,
meet(A,join(A,A)) = join(A,A),
inference(paramod,[status(thm)],[c_73,c_33]) ).
cnf(c_1802,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_1,c_1801]) ).
cnf(c_94,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1802]) ).
cnf(c_1803,plain,
meet(join(meet(A,B),C),meet(B,A)) = meet(B,join(A,A)),
inference(paramod,[status(thm)],[c_94,c_40]) ).
cnf(c_104,plain,
meet(join(meet(A,B),C),meet(B,A)) = meet(B,A),
inference(paramod,[status(thm)],[c_94,c_1803]) ).
cnf(c_1804,plain,
meet(A,B) = meet(B,join(A,A)),
inference(paramod,[status(thm)],[c_94,c_3]) ).
cnf(c_118,plain,
meet(A,B) = meet(B,A),
inference(paramod,[status(thm)],[c_94,c_1804]) ).
cnf(c_1805,plain,
meet(A,meet(B,A)) = meet(A,join(meet(B,A),B)),
inference(paramod,[status(thm)],[c_94,c_14]) ).
cnf(c_1806,plain,
meet(A,meet(B,A)) = meet(A,join(B,meet(B,A))),
inference(paramod,[status(thm)],[c_77,c_1805]) ).
cnf(c_1807,plain,
meet(A,meet(B,A)) = meet(A,join(B,B)),
inference(paramod,[status(thm)],[c_14,c_1806]) ).
cnf(c_119,plain,
meet(A,meet(B,A)) = meet(A,B),
inference(paramod,[status(thm)],[c_94,c_1807]) ).
cnf(c_122,plain,
meet(meet(A,B),join(meet(B,A),C)) = meet(A,B),
inference(paramod,[status(thm)],[c_118,c_104]) ).
cnf(c_129,plain,
join(meet(A,B),meet(C,A)) = meet(A,join(C,B)),
inference(paramod,[status(thm)],[c_118,c_3]) ).
cnf(c_130,plain,
join(meet(A,B),meet(B,C)) = meet(B,join(C,A)),
inference(paramod,[status(thm)],[c_118,c_3]) ).
cnf(c_133,plain,
meet(A,join(B,meet(A,C))) = meet(A,join(B,C)),
inference(paramod,[status(thm)],[c_118,c_14]) ).
cnf(c_1808,plain,
meet(meet(A,B),join(meet(B,A),C)) = meet(meet(A,B),join(B,C)),
inference(paramod,[status(thm)],[c_119,c_15]) ).
cnf(c_1809,plain,
meet(A,B) = meet(meet(A,B),join(B,C)),
inference(paramod,[status(thm)],[c_122,c_1808]) ).
cnf(c_185,plain,
meet(meet(A,B),join(B,C)) = meet(A,B),
inference(copy,[status(thm)],[c_1809]) ).
cnf(c_1810,plain,
join(meet(meet(A,B),C),meet(B,A)) = meet(meet(A,B),join(B,C)),
inference(paramod,[status(thm)],[c_119,c_129]) ).
cnf(c_1811,plain,
join(meet(B,A),meet(meet(A,B),C)) = meet(meet(A,B),join(B,C)),
inference(paramod,[status(thm)],[c_77,c_1810]) ).
cnf(c_208,plain,
join(meet(A,B),meet(meet(B,A),C)) = meet(B,A),
inference(paramod,[status(thm)],[c_185,c_1811]) ).
cnf(c_1812,plain,
join(meet(A,B),meet(meet(B,A),C)) = meet(meet(B,A),join(C,A)),
inference(paramod,[status(thm)],[c_119,c_130]) ).
cnf(c_1813,plain,
meet(B,A) = meet(meet(B,A),join(C,A)),
inference(paramod,[status(thm)],[c_208,c_1812]) ).
cnf(c_218,plain,
meet(meet(A,B),join(C,B)) = meet(A,B),
inference(copy,[status(thm)],[c_1813]) ).
cnf(c_1814,plain,
join(A,meet(B,C)) = meet(join(A,C),join(meet(B,C),A)),
inference(paramod,[status(thm)],[c_218,c_6]) ).
cnf(c_294,plain,
meet(join(A,B),join(meet(C,B),A)) = join(A,meet(C,B)),
inference(copy,[status(thm)],[c_1814]) ).
cnf(c_1815,plain,
join(A,meet(B,join(A,C))) = meet(join(A,meet(B,C)),join(B,A)),
inference(paramod,[status(thm)],[c_133,c_6]) ).
cnf(c_1816,plain,
meet(join(A,C),join(B,A)) = meet(join(A,meet(B,C)),join(B,A)),
inference(paramod,[status(thm)],[c_6,c_1815]) ).
cnf(c_1817,plain,
meet(join(A,C),join(B,A)) = meet(join(B,A),join(A,meet(B,C))),
inference(paramod,[status(thm)],[c_118,c_1816]) ).
cnf(c_692,plain,
meet(join(A,B),join(B,meet(A,C))) = meet(join(B,C),join(A,B)),
inference(copy,[status(thm)],[c_1817]) ).
cnf(c_1818,plain,
join(meet(A,join(B,C)),C) = meet(join(meet(B,A),C),join(C,A)),
inference(paramod,[status(thm)],[c_81,c_26]) ).
cnf(c_1819,plain,
join(C,meet(A,join(B,C))) = meet(join(meet(B,A),C),join(C,A)),
inference(paramod,[status(thm)],[c_77,c_1818]) ).
cnf(c_1820,plain,
meet(join(B,C),join(A,C)) = meet(join(meet(B,A),C),join(C,A)),
inference(paramod,[status(thm)],[c_71,c_1819]) ).
cnf(c_1821,plain,
meet(join(B,C),join(A,C)) = meet(join(C,A),join(meet(B,A),C)),
inference(paramod,[status(thm)],[c_118,c_1820]) ).
cnf(c_990,plain,
meet(join(A,B),join(C,B)) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_294,c_1821]) ).
cnf(c_1054,plain,
join(A,meet(B,join(C,A))) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_990,c_71]) ).
cnf(c_1822,plain,
meet(join(A,B),join(meet(C,join(A,B)),B)) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_990,c_15]) ).
cnf(c_1823,plain,
meet(join(A,B),join(B,meet(C,join(A,B)))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_77,c_1822]) ).
cnf(c_1824,plain,
meet(join(A,B),join(B,meet(A,C))) = join(B,meet(A,C)),
inference(paramod,[status(thm)],[c_1054,c_1823]) ).
cnf(c_1072,plain,
meet(join(A,B),join(C,A)) = join(A,meet(C,B)),
inference(paramod,[status(thm)],[c_692,c_1824]) ).
cnf(c_1825,plain,
join(A,join(B,meet(C,A))) = meet(join(A,B),join(join(C,B),A)),
inference(paramod,[status(thm)],[c_990,c_6]) ).
cnf(c_1826,plain,
join(A,join(B,meet(C,A))) = join(A,meet(join(C,B),B)),
inference(paramod,[status(thm)],[c_1072,c_1825]) ).
cnf(c_1827,plain,
join(A,join(B,meet(C,A))) = join(A,meet(B,join(C,B))),
inference(paramod,[status(thm)],[c_118,c_1826]) ).
cnf(c_1073,plain,
join(A,join(B,meet(C,A))) = join(A,B),
inference(paramod,[status(thm)],[c_81,c_1827]) ).
cnf(c_1499,plain,
join(join(A,B),join(C,A)) = join(join(A,B),C),
inference(paramod,[status(thm)],[c_1,c_1073]) ).
cnf(c_1503,plain,
join(A,join(meet(B,A),C)) = join(A,C),
inference(paramod,[status(thm)],[c_77,c_1073]) ).
cnf(c_1604,plain,
join(join(A,B),join(B,C)) = join(join(A,B),C),
inference(paramod,[status(thm)],[c_81,c_1503]) ).
cnf(c_1828,plain,
join(join(A,B),C) = join(join(C,A),join(A,B)),
inference(paramod,[status(thm)],[c_1499,c_77]) ).
cnf(c_1741,plain,
join(join(A,B),C) = join(join(C,A),B),
inference(paramod,[status(thm)],[c_1604,c_1828]) ).
cnf(c_1785,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(paramod,[status(thm)],[c_1741,c_77]) ).
cnf(c_1829,plain,
join(join(A,B),C) = join(B,join(C,A)),
inference(paramod,[status(thm)],[c_1741,c_77]) ).
cnf(c_1830,plain,
join(A,join(B,C)) = join(B,join(C,A)),
inference(paramod,[status(thm)],[c_1785,c_1829]) ).
cnf(c_1786,plain,
join(A,join(B,C)) = join(C,join(A,B)),
inference(copy,[status(thm)],[c_1830]) ).
cnf(c_1831,plain,
join(a,join(b,c)) != join(c,join(a,b)),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_1787,plain,
$false,
inference(resolve,[status(thm)],[c_1786,c_1831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT007-1 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 19:57:50 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 2711367 was started by sandbox2 on n018,
% 0.09/0.37 % Fri Sep 25 19:57:50 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 6.48/1.24
% 6.48/1.24 % SZS status Unsatisfiable for theBenchmark
% 6.48/1.24
% 6.48/1.24 % Proof 1 at 0.59 (+ 0.14) seconds.
% 6.48/1.24 % Length of proof is 45.
% 6.48/1.24 % Level of proof is 25.
% 6.48/1.24 % Maximum clause weight is 48.000.
% 6.48/1.24 % Given clauses 92.
% 6.48/1.24
% 6.48/1.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------