%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL008+2 : TPTP v9.3.1. Released v4.0.0.
% 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 08:24:46 AM UTC 2026
% Result : Theorem 6.73s 1.40s
% Output : CNFRefutation 6.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 96 ( 78 unt; 0 def)
% Number of atoms : 114 ( 113 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 52 ( 34 ~; 16 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 142 ( 0 sgn 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2))
& join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2))) = composition(X0,join(X1,X2))
& join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) = join(composition(X0,X1),composition(X0,X2)) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_15,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_16,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_17,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_18,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_15,c_17]) ).
cnf(c_19,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_21,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_22,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_23,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_24,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_25,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_26,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_1879,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_15,c_26]) ).
cnf(c_27,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_1879]) ).
cnf(c_28,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_29,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_1880,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_19,c_29]) ).
cnf(c_30,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_28,c_1880]) ).
fof(nnf_14,plain,
? [X0,X1,X2] :
( composition(X0,join(X1,X2)) != join(join(composition(X0,X1),composition(X0,X2)),composition(X0,join(X1,X2)))
| join(composition(X0,X1),composition(X0,X2)) != join(join(composition(X0,join(X1,X2)),composition(X0,X1)),composition(X0,X2)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(join(composition(sK0,join(sK1,sK2)),composition(sK0,sK1)),composition(sK0,sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(join(composition(sK0,join(sK1,sK2)),composition(sK0,sK1)),composition(sK0,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_1881,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(join(composition(sK0,sK1),composition(sK0,join(sK1,sK2))),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_15,c_31]) ).
cnf(c_1882,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(join(composition(sK0,sK1),composition(sK0,sK2)),composition(sK0,join(sK1,sK2)))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) ),
inference(paramod,[status(thm)],[c_15,c_1881]) ).
cnf(c_1883,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2))))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) ),
inference(paramod,[status(thm)],[c_16,c_1882]) ).
cnf(c_1884,negated_conjecture,
( composition(sK0,join(sK1,sK2)) != join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2))))
| join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(copy,[status(thm)],[c_1883]) ).
cnf(c_32,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(copy,[status(thm)],[c_1884]) ).
cnf(c_1885,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_34,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_1885]) ).
cnf(c_35,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_34,c_32]) ).
cnf(c_37,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_1886,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_44,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1886]) ).
cnf(c_1887,plain,
converse(join(composition(A,B),composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_22,c_25]) ).
cnf(c_1888,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_24,c_1887]) ).
cnf(c_1889,plain,
join(composition(converse(B),converse(A)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_25,c_1888]) ).
cnf(c_1890,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_25,c_1889]) ).
cnf(c_1891,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),join(converse(A),converse(C))),
inference(paramod,[status(thm)],[c_24,c_1890]) ).
cnf(c_45,plain,
composition(converse(A),join(converse(B),converse(C))) = join(composition(converse(A),converse(B)),composition(converse(A),converse(C))),
inference(copy,[status(thm)],[c_1891]) ).
cnf(c_1892,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_56,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_30,c_1892]) ).
cnf(c_1893,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_28,c_18]) ).
cnf(c_1894,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_30,c_1893]) ).
cnf(c_57,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_1894]) ).
cnf(c_1895,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_44]) ).
cnf(c_86,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_1895]) ).
cnf(c_1896,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_86,c_21]) ).
cnf(c_88,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1896]) ).
cnf(c_92,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_86,c_27]) ).
cnf(c_93,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_88,c_86]) ).
cnf(c_94,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_93,c_92]) ).
cnf(c_95,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_94,c_57]) ).
cnf(c_1897,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_37]) ).
cnf(c_1898,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_1897]) ).
cnf(c_1899,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_1898]) ).
cnf(c_106,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_1899]) ).
cnf(c_112,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_106,c_56]) ).
cnf(c_113,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_112,c_106]) ).
cnf(c_114,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_112,c_95]) ).
cnf(c_116,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_114,c_113]) ).
cnf(c_1900,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_116,c_18]) ).
cnf(c_1901,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_116,c_1900]) ).
cnf(c_1902,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_18,c_1901]) ).
cnf(c_166,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1902]) ).
cnf(c_1903,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_166,c_16]) ).
cnf(c_167,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1903]) ).
cnf(c_1904,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_166,c_16]) ).
cnf(c_169,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_15,c_1904]) ).
cnf(c_1905,plain,
composition(A,join(converse(B),converse(C))) = join(composition(converse(converse(A)),converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_23,c_45]) ).
cnf(c_1906,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_23,c_1905]) ).
cnf(c_211,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_1906]) ).
cnf(c_1907,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_211]) ).
cnf(c_1669,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_23,c_1907]) ).
cnf(c_1908,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_23,c_1669]) ).
cnf(c_1834,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_23,c_1908]) ).
cnf(c_1909,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,sK2)))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_1834,c_35]) ).
cnf(c_1910,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),join(composition(sK0,sK1),composition(sK0,sK2))) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_169,c_1909]) ).
cnf(c_1911,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),composition(sK0,join(sK1,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_167,c_1910]) ).
cnf(c_1912,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK2),join(composition(sK0,sK1),composition(sK0,sK2)))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_1834,c_1911]) ).
cnf(c_1913,negated_conjecture,
( join(composition(sK0,sK1),join(composition(sK0,sK1),composition(sK0,sK2))) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_169,c_1912]) ).
cnf(c_1914,negated_conjecture,
( join(composition(sK0,sK1),composition(sK0,sK2)) != composition(sK0,join(sK1,sK2))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_167,c_1913]) ).
cnf(c_1915,negated_conjecture,
( join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2))
| join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)) ),
inference(paramod,[status(thm)],[c_1834,c_1914]) ).
cnf(c_1916,negated_conjecture,
join(composition(sK0,sK1),composition(sK0,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)),
inference(copy,[status(thm)],[c_1915]) ).
cnf(c_1878,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_1916]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL008+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n019.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 05:26:03 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 477869 was started by sandbox on n019,
% 0.18/0.44 % Sat Sep 26 05:26:03 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 6.73/1.40
% 6.73/1.40 % SZS status Theorem for theBenchmark
% 6.73/1.40
% 6.73/1.40 % Proof 1 at 0.69 (+ 0.24) seconds.
% 6.73/1.40 % Length of proof is 55.
% 6.73/1.40 % Level of proof is 12.
% 6.73/1.40 % Maximum clause weight is 75.000.
% 6.73/1.40 % Given clauses 171.
% 6.73/1.40
% 6.73/1.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------