%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL046-1 : TPTP v9.3.1. Released v4.0.0.
% 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 08:25:07 AM UTC 2026
% Result : Unsatisfiable 1.23s 0.66s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 56 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(maddux2_join_associativity_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c_2,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[maddux2_join_associativity_2]) ).
cnf(c_3,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(maddux3_a_kind_of_de_Morgan_3,axiom,
! [VAR_0,VAR_1] : VAR_0 = join(complement(join(complement(VAR_0),complement(VAR_1))),complement(join(complement(VAR_0),VAR_1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c_4,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c_544,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_544]) ).
fof(maddux4_definiton_of_meet_4,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = complement(join(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c_6,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet_4]) ).
fof(def_top_12,axiom,
! [VAR_0] : top = join(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_top_12) ).
cnf(c_16,plain,
top = join(A,complement(A)),
inference(clausify,[status(thm)],[def_top_12]) ).
cnf(c_17,plain,
join(A,complement(A)) = top,
inference(copy,[status(thm)],[c_16]) ).
fof(def_zero_13,axiom,
! [VAR_0] : zero = meet(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_zero_13) ).
cnf(c_18,plain,
zero = meet(A,complement(A)),
inference(clausify,[status(thm)],[def_zero_13]) ).
cnf(c_545,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_546,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_545]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_546]) ).
fof(goals_14,axiom,
join(sk1,meet(sk2,sk3)) = meet(sk2,sk3),
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
join(sk1,meet(sk2,sk3)) = meet(sk2,sk3),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_547,plain,
join(sk1,complement(join(complement(sk2),complement(sk3)))) = meet(sk2,sk3),
inference(paramod,[status(thm)],[c_6,c_20]) ).
cnf(c_21,plain,
join(sk1,complement(join(complement(sk2),complement(sk3)))) = complement(join(complement(sk2),complement(sk3))),
inference(paramod,[status(thm)],[c_6,c_547]) ).
fof(goals_15,axiom,
( join(sk1,sk3) != sk3
| join(sk1,sk2) != sk2 ),
file('theBenchmark.p',goals_15) ).
cnf(c_22,plain,
( join(sk1,sk3) != sk3
| join(sk1,sk2) != sk2 ),
inference(clausify,[status(thm)],[goals_15]) ).
cnf(c_548,plain,
( join(sk1,sk3) != sk3
| join(sk2,sk1) != sk2 ),
inference(paramod,[status(thm)],[c_1,c_22]) ).
cnf(c_23,plain,
( join(sk3,sk1) != sk3
| join(sk2,sk1) != sk2 ),
inference(paramod,[status(thm)],[c_1,c_548]) ).
cnf(c_549,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_25,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_549]) ).
cnf(c_26,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_27,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_550,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_550]) ).
cnf(c_551,plain,
join(A,B) = join(complement(join(complement(B),C)),join(A,complement(join(complement(B),complement(C))))),
inference(paramod,[status(thm)],[c_5,c_25]) ).
cnf(c_58,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_551]) ).
cnf(c_552,plain,
join(A,complement(join(complement(sk2),complement(sk3)))) = join(sk1,join(A,complement(join(complement(sk2),complement(sk3))))),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_61,plain,
join(sk1,join(A,complement(join(complement(sk2),complement(sk3))))) = join(A,complement(join(complement(sk2),complement(sk3)))),
inference(copy,[status(thm)],[c_552]) ).
cnf(c_553,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_26,c_1]) ).
cnf(c_62,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_553]) ).
cnf(c_63,plain,
join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B,
inference(paramod,[status(thm)],[c_1,c_26]) ).
cnf(c_554,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_27]) ).
cnf(c_555,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_554]) ).
cnf(c_556,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_555]) ).
cnf(c_82,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_556]) ).
cnf(c_88,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_82,c_46]) ).
cnf(c_557,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_88,c_26]) ).
cnf(c_261,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_88,c_557]) ).
cnf(c_558,plain,
join(complement(join(complement(sk2),sk3)),complement(join(complement(sk2),complement(sk3)))) = join(sk1,sk2),
inference(paramod,[status(thm)],[c_21,c_58]) ).
cnf(c_559,plain,
join(complement(join(sk3,complement(sk2))),complement(join(complement(sk2),complement(sk3)))) = join(sk1,sk2),
inference(paramod,[status(thm)],[c_1,c_558]) ).
cnf(c_560,plain,
complement(complement(sk2)) = join(sk1,sk2),
inference(paramod,[status(thm)],[c_261,c_559]) ).
cnf(c_561,plain,
sk2 = join(sk1,sk2),
inference(paramod,[status(thm)],[c_88,c_560]) ).
cnf(c_562,plain,
sk2 = join(sk2,sk1),
inference(paramod,[status(thm)],[c_1,c_561]) ).
cnf(c_487,plain,
join(sk2,sk1) = sk2,
inference(copy,[status(thm)],[c_562]) ).
cnf(c_563,plain,
( join(sk3,sk1) != sk3
| sk2 != sk2 ),
inference(paramod,[status(thm)],[c_487,c_23]) ).
cnf(c_503,plain,
join(sk3,sk1) != sk3,
inference(copy,[status(thm)],[c_563]) ).
cnf(c_564,plain,
join(sk1,sk3) = join(complement(join(complement(sk3),complement(complement(sk2)))),complement(join(complement(sk2),complement(sk3)))),
inference(paramod,[status(thm)],[c_62,c_61]) ).
cnf(c_565,plain,
join(sk3,sk1) = join(complement(join(complement(sk3),complement(complement(sk2)))),complement(join(complement(sk2),complement(sk3)))),
inference(paramod,[status(thm)],[c_1,c_564]) ).
cnf(c_566,plain,
join(sk3,sk1) = join(complement(join(complement(sk3),sk2)),complement(join(complement(sk2),complement(sk3)))),
inference(paramod,[status(thm)],[c_88,c_565]) ).
cnf(c_567,plain,
join(sk3,sk1) = join(complement(join(sk2,complement(sk3))),complement(join(complement(sk2),complement(sk3)))),
inference(paramod,[status(thm)],[c_1,c_566]) ).
cnf(c_568,plain,
join(sk3,sk1) = sk3,
inference(paramod,[status(thm)],[c_63,c_567]) ).
cnf(c_543,plain,
$false,
inference(resolve,[status(thm)],[c_503,c_568]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : REL046-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n018.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 05:43:36 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 3849512 was started by sandbox2 on n018,
% 0.15/0.43 % Sat Sep 26 05:43:36 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 1.23/0.66
% 1.23/0.66 % SZS status Unsatisfiable for theBenchmark
% 1.23/0.66
% 1.23/0.66 % Proof 1 at 0.14 (+ 0.07) seconds.
% 1.23/0.66 % Length of proof is 28.
% 1.23/0.66 % Level of proof is 8.
% 1.23/0.66 % Maximum clause weight is 57.000.
% 1.23/0.66 % Given clauses 89.
% 1.23/0.66
% 1.23/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------