%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL048+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 : n013.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 0.09s 0.44s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 7
% Syntax : Number of formulae : 81 ( 75 unt; 0 def)
% Number of atoms : 91 ( 90 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 4 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 75 ( 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(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = X2 ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(join(X0,X1),X2) = X2
=> ( join(X1,X2) = X2
& join(X0,X2) = 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_31,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_32,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_225,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_19,c_32]) ).
cnf(c_33,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_225]) ).
fof(nnf_14,plain,
? [X0,X1,X2] :
( ( join(X1,X2) != X2
| join(X0,X2) != X2 )
& join(join(X0,X1),X2) = X2 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( join(sK1,sK2) != sK2
| join(sK0,sK2) != sK2 )
& join(join(sK0,sK1),sK2) = sK2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_14]) ).
cnf(c_34,negated_conjecture,
join(join(sK0,sK1),sK2) = sK2,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_35,negated_conjecture,
join(sK2,join(sK0,sK1)) = sK2,
inference(paramod,[status(thm)],[c_15,c_34]) ).
cnf(c_36,negated_conjecture,
( join(sK1,sK2) != sK2
| join(sK0,sK2) != sK2 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_37,plain,
join(A,join(B,C)) = join(C,join(A,B)),
inference(paramod,[status(thm)],[c_16,c_15]) ).
cnf(c_226,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_15,c_16]) ).
cnf(c_38,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_16,c_226]) ).
cnf(c_227,negated_conjecture,
join(sK1,join(sK2,sK0)) = sK2,
inference(paramod,[status(thm)],[c_37,c_35]) ).
cnf(c_228,negated_conjecture,
join(sK1,join(sK0,sK2)) = sK2,
inference(paramod,[status(thm)],[c_15,c_227]) ).
cnf(c_39,negated_conjecture,
join(sK0,join(sK1,sK2)) = sK2,
inference(paramod,[status(thm)],[c_38,c_228]) ).
cnf(c_40,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_41,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_15,c_18]) ).
cnf(c_229,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_18]) ).
cnf(c_68,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_229]) ).
cnf(c_73,plain,
join(top,zero) = top,
inference(paramod,[status(thm)],[c_33,c_31]) ).
cnf(c_230,plain,
join(top,A) = join(top,join(zero,A)),
inference(paramod,[status(thm)],[c_73,c_16]) ).
cnf(c_80,plain,
join(top,join(zero,A)) = join(top,A),
inference(copy,[status(thm)],[c_230]) ).
cnf(c_231,plain,
join(top,top) = join(top,complement(zero)),
inference(paramod,[status(thm)],[c_31,c_80]) ).
cnf(c_88,plain,
join(top,complement(zero)) = join(top,top),
inference(copy,[status(thm)],[c_231]) ).
cnf(c_232,plain,
join(complement(join(top,top)),complement(join(complement(zero),complement(top)))) = zero,
inference(paramod,[status(thm)],[c_88,c_40]) ).
cnf(c_233,plain,
join(complement(join(top,top)),complement(join(complement(zero),zero))) = zero,
inference(paramod,[status(thm)],[c_33,c_232]) ).
cnf(c_234,plain,
join(complement(join(top,top)),complement(join(zero,complement(zero)))) = zero,
inference(paramod,[status(thm)],[c_15,c_233]) ).
cnf(c_235,plain,
join(complement(join(top,top)),complement(top)) = zero,
inference(paramod,[status(thm)],[c_31,c_234]) ).
cnf(c_236,plain,
join(complement(join(top,top)),zero) = zero,
inference(paramod,[status(thm)],[c_33,c_235]) ).
cnf(c_103,plain,
join(zero,complement(join(top,top))) = zero,
inference(paramod,[status(thm)],[c_15,c_236]) ).
cnf(c_237,plain,
join(zero,A) = join(zero,join(complement(join(top,top)),A)),
inference(paramod,[status(thm)],[c_103,c_16]) ).
cnf(c_105,plain,
join(zero,join(complement(join(top,top)),A)) = join(zero,A),
inference(copy,[status(thm)],[c_237]) ).
cnf(c_238,plain,
join(top,zero) = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_103,c_80]) ).
cnf(c_239,plain,
top = join(top,complement(join(top,top))),
inference(paramod,[status(thm)],[c_73,c_238]) ).
cnf(c_107,plain,
join(top,complement(join(top,top))) = top,
inference(copy,[status(thm)],[c_239]) ).
cnf(c_240,plain,
join(complement(top),complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_107,c_40]) ).
cnf(c_241,plain,
join(zero,complement(join(complement(join(top,top)),complement(top)))) = join(top,top),
inference(paramod,[status(thm)],[c_33,c_240]) ).
cnf(c_242,plain,
join(zero,complement(join(complement(join(top,top)),zero))) = join(top,top),
inference(paramod,[status(thm)],[c_33,c_241]) ).
cnf(c_243,plain,
join(zero,complement(join(zero,complement(join(top,top))))) = join(top,top),
inference(paramod,[status(thm)],[c_15,c_242]) ).
cnf(c_244,plain,
join(zero,complement(zero)) = join(top,top),
inference(paramod,[status(thm)],[c_103,c_243]) ).
cnf(c_245,plain,
top = join(top,top),
inference(paramod,[status(thm)],[c_31,c_244]) ).
cnf(c_111,plain,
join(top,top) = top,
inference(copy,[status(thm)],[c_245]) ).
cnf(c_246,plain,
join(zero,join(complement(top),A)) = join(zero,A),
inference(paramod,[status(thm)],[c_111,c_105]) ).
cnf(c_113,plain,
join(zero,join(zero,A)) = join(zero,A),
inference(paramod,[status(thm)],[c_33,c_246]) ).
cnf(c_247,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_41]) ).
cnf(c_248,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_15,c_247]) ).
cnf(c_249,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_248]) ).
cnf(c_127,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_15,c_249]) ).
cnf(c_133,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_127,c_68]) ).
cnf(c_134,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_127]) ).
cnf(c_250,plain,
join(zero,complement(A)) = join(zero,complement(join(A,A))),
inference(paramod,[status(thm)],[c_134,c_113]) ).
cnf(c_166,plain,
join(zero,complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_134,c_250]) ).
cnf(c_251,plain,
join(zero,join(zero,complement(join(A,A)))) = complement(A),
inference(paramod,[status(thm)],[c_134,c_113]) ).
cnf(c_252,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_166,c_251]) ).
cnf(c_167,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_166,c_252]) ).
cnf(c_253,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_167,c_133]) ).
cnf(c_254,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_133,c_253]) ).
cnf(c_180,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_254]) ).
cnf(c_255,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_180,c_16]) ).
cnf(c_192,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_255]) ).
cnf(c_256,plain,
join(sK0,sK2) = join(sK0,join(sK1,sK2)),
inference(paramod,[status(thm)],[c_39,c_192]) ).
cnf(c_212,plain,
join(sK0,sK2) = sK2,
inference(paramod,[status(thm)],[c_39,c_256]) ).
cnf(c_257,negated_conjecture,
( join(sK1,sK2) != sK2
| sK2 != sK2 ),
inference(paramod,[status(thm)],[c_212,c_36]) ).
cnf(c_213,negated_conjecture,
join(sK1,sK2) != sK2,
inference(copy,[status(thm)],[c_257]) ).
cnf(c_258,plain,
join(A,sK2) = join(sK0,join(A,sK2)),
inference(paramod,[status(thm)],[c_212,c_38]) ).
cnf(c_222,plain,
join(sK0,join(A,sK2)) = join(A,sK2),
inference(copy,[status(thm)],[c_258]) ).
cnf(c_259,negated_conjecture,
join(sK1,sK2) = sK2,
inference(paramod,[status(thm)],[c_222,c_39]) ).
cnf(c_224,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_213,c_259]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL048+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 : Sat Sep 26 05:41:21 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 2052133 was started by sandbox2 on n013,
% 0.09/0.37 % Sat Sep 26 05:41:21 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).
% 0.09/0.44
% 0.09/0.44 % SZS status Theorem for theBenchmark
% 0.09/0.44
% 0.09/0.44 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.09/0.44 % Length of proof is 43.
% 0.09/0.44 % Level of proof is 16.
% 0.09/0.44 % Maximum clause weight is 57.000.
% 0.09/0.44 % Given clauses 52.
% 0.09/0.44
% 0.09/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------