%------------------------------------------------------------------------------
% 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/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Theorem 1.01s 0.64s
% Output : CNFRefutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 50 unt; 0 def)
% Number of atoms : 66 ( 65 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 4 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 69 ( 0 sgn 17 !; 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(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(X0,meet(X1,X2)) = meet(X1,X2)
=> ( join(X0,X2) = X2
& join(X0,X1) = X1 ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,meet(X1,X2)) = meet(X1,X2)
=> ( join(X0,X2) = X2
& join(X0,X1) = X1 ) ),
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_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_551,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_551]) ).
fof(nnf_14,plain,
? [X0,X1,X2] :
( ( join(X0,X2) != X2
| join(X0,X1) != X1 )
& meet(X1,X2) = join(X0,meet(X1,X2)) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( join(sK2,sK1) != sK1
| join(sK2,sK0) != sK0 )
& meet(sK0,sK1) = join(sK2,meet(sK0,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK2),skolemize(X1,sK0),skolemize(X2,sK1)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
meet(sK0,sK1) = join(sK2,meet(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_552,negated_conjecture,
complement(join(complement(sK0),complement(sK1))) = join(sK2,meet(sK0,sK1)),
inference(paramod,[status(thm)],[c_19,c_31]) ).
cnf(c_553,negated_conjecture,
complement(join(complement(sK0),complement(sK1))) = join(sK2,complement(join(complement(sK0),complement(sK1)))),
inference(paramod,[status(thm)],[c_19,c_552]) ).
cnf(c_32,negated_conjecture,
join(sK2,complement(join(complement(sK0),complement(sK1)))) = complement(join(complement(sK0),complement(sK1))),
inference(copy,[status(thm)],[c_553]) ).
cnf(c_33,negated_conjecture,
( join(sK2,sK1) != sK1
| join(sK2,sK0) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_554,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_35,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_554]) ).
cnf(c_36,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
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_555,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_555]) ).
cnf(c_556,plain,
join(A,B) = join(complement(join(complement(B),C)),join(A,complement(join(complement(B),complement(C))))),
inference(paramod,[status(thm)],[c_18,c_35]) ).
cnf(c_68,plain,
join(complement(join(complement(A),B)),join(C,complement(join(complement(A),complement(B))))) = join(C,A),
inference(copy,[status(thm)],[c_556]) ).
cnf(c_557,plain,
join(A,complement(join(complement(sK0),complement(sK1)))) = join(sK2,join(A,complement(join(complement(sK0),complement(sK1))))),
inference(paramod,[status(thm)],[c_32,c_35]) ).
cnf(c_71,plain,
join(sK2,join(A,complement(join(complement(sK0),complement(sK1))))) = join(A,complement(join(complement(sK0),complement(sK1)))),
inference(copy,[status(thm)],[c_557]) ).
cnf(c_558,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_36,c_15]) ).
cnf(c_72,plain,
join(complement(join(complement(A),complement(B))),complement(join(B,complement(A)))) = A,
inference(copy,[status(thm)],[c_558]) ).
cnf(c_73,plain,
join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B,
inference(paramod,[status(thm)],[c_15,c_36]) ).
cnf(c_559,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_28,c_37]) ).
cnf(c_560,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_559]) ).
cnf(c_561,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_30,c_560]) ).
cnf(c_92,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_561]) ).
cnf(c_98,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_92,c_56]) ).
cnf(c_562,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_98,c_36]) ).
cnf(c_271,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_98,c_562]) ).
cnf(c_563,plain,
join(complement(join(complement(sK0),sK1)),complement(join(complement(sK0),complement(sK1)))) = join(sK2,sK0),
inference(paramod,[status(thm)],[c_32,c_68]) ).
cnf(c_564,plain,
join(complement(join(sK1,complement(sK0))),complement(join(complement(sK0),complement(sK1)))) = join(sK2,sK0),
inference(paramod,[status(thm)],[c_15,c_563]) ).
cnf(c_565,plain,
complement(complement(sK0)) = join(sK2,sK0),
inference(paramod,[status(thm)],[c_271,c_564]) ).
cnf(c_566,plain,
sK0 = join(sK2,sK0),
inference(paramod,[status(thm)],[c_98,c_565]) ).
cnf(c_497,plain,
join(sK2,sK0) = sK0,
inference(copy,[status(thm)],[c_566]) ).
cnf(c_567,negated_conjecture,
( join(sK2,sK1) != sK1
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_497,c_33]) ).
cnf(c_513,negated_conjecture,
join(sK2,sK1) != sK1,
inference(copy,[status(thm)],[c_567]) ).
cnf(c_568,plain,
join(sK2,sK1) = join(complement(join(complement(sK1),complement(complement(sK0)))),complement(join(complement(sK0),complement(sK1)))),
inference(paramod,[status(thm)],[c_72,c_71]) ).
cnf(c_569,plain,
join(sK2,sK1) = join(complement(join(complement(sK1),sK0)),complement(join(complement(sK0),complement(sK1)))),
inference(paramod,[status(thm)],[c_98,c_568]) ).
cnf(c_570,plain,
join(sK2,sK1) = join(complement(join(sK0,complement(sK1))),complement(join(complement(sK0),complement(sK1)))),
inference(paramod,[status(thm)],[c_15,c_569]) ).
cnf(c_571,plain,
join(sK2,sK1) = sK1,
inference(paramod,[status(thm)],[c_73,c_570]) ).
cnf(c_550,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_513,c_571]) ).
%------------------------------------------------------------------------------
%----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/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n016.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 05:46:14 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 129309 was started by sandbox on n016,
% 0.15/0.42 % Sat Sep 26 05:46:14 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 1.01/0.64
% 1.01/0.64 % SZS status Theorem for theBenchmark
% 1.01/0.64
% 1.01/0.64 % Proof 1 at 0.14 (+ 0.06) seconds.
% 1.01/0.64 % Length of proof is 32.
% 1.01/0.64 % Level of proof is 9.
% 1.01/0.64 % Maximum clause weight is 57.000.
% 1.01/0.64 % Given clauses 89.
% 1.01/0.64
% 1.01/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------