%------------------------------------------------------------------------------
% File : Twee---2.7
% Problem : REL049+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 : Tue Sep 29 12:33:34 PM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 30 unt; 0 def)
% Number of atoms : 57 ( 56 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 7 ~; 0 |; 12 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 32 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(c1,conjecture,
! [X0,X1,X2] :
( ( join(X0,X1) = X1
& join(X2,X1) = X1 )
=> join(join(X0,X2),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c2,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( ( join(X0_2,X1_2) = X1_2
& join(X2_2,X1_2) = X1_2 )
=> join(join(X0_2,X2_2),X1_2) = X1_2 ),
inference(negate_conjecture,[status(cth)],[c1]) ).
fof(c3,plain,
( join(x0,x1) = x1
& join(join(x0,x2),x1) != x1
& join(x2,x1) = x1 ),
inference(clausify,[status(esa)],[c2]) ).
cnf(c4,plain,
join(join(x0,x2),x1) != x1,
inference(clausify,[status(thm)],[c3]) ).
cnf(c5,axiom,
join(X0_2,X1_2) = join(X1_2,X0_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux1_join_commutativity) ).
cnf(c6,plain,
join(join(x0,x2),x1) = join(x1,join(x0,x2)),
inference(substitution,[status(thm)],[c5]) ).
cnf(c7,plain,
join(x0,x2) = join(x2,x0),
inference(substitution,[status(thm)],[c5]) ).
cnf(c8,plain,
join(x1,join(x0,x2)) = join(x1,join(x2,x0)),
inference(congruence,[status(thm)],[c7]) ).
cnf(c9,plain,
join(x0,X) = join(X,x0),
inference(substitution,[status(thm)],[c5]) ).
cnf(c10,plain,
join(X,x0) = join(x0,X),
inference(symmetry,[status(thm)],[c9]) ).
cnf(c11,plain,
join(x1,join(X,x0)) = join(x1,join(x0,X)),
inference(congruence,[status(thm)],[c10]) ).
cnf(c12,axiom,
join(X0_2,join(X1_2,X2_2)) = join(join(X0_2,X1_2),X2_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maddux2_join_associativity) ).
cnf(c13,plain,
join(x1,join(x0,X)) = join(join(x1,x0),X),
inference(substitution,[status(thm)],[c12]) ).
cnf(c14,plain,
join(x0,x1) = join(x1,x0),
inference(substitution,[status(thm)],[c5]) ).
cnf(c15,plain,
join(x1,x0) = join(x0,x1),
inference(symmetry,[status(thm)],[c14]) ).
fof(c16,conjecture,
! [X0_2,X1_2,X2_2] :
( ( join(X0_2,X1_2) = X1_2
& join(X2_2,X1_2) = X1_2 )
=> join(join(X0_2,X2_2),X1_2) = X1_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c17,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( ( join(X0_2,X1_2) = X1_2
& join(X2_2,X1_2) = X1_2 )
=> join(join(X0_2,X2_2),X1_2) = X1_2 ),
inference(negate_conjecture,[status(cth)],[c16]) ).
fof(c18,plain,
( join(x0,x1) = x1
& join(join(x0,x2),x1) != x1
& join(x2,x1) = x1 ),
inference(clausify,[status(esa)],[c17]) ).
cnf(c19,plain,
join(x0,x1) = x1,
inference(clausify,[status(thm)],[c18]) ).
cnf(c20,plain,
join(x1,x0) = x1,
inference(transitivity,[status(thm)],[c15,c19]) ).
cnf(c21,plain,
join(join(x1,x0),X) = join(x1,X),
inference(congruence,[status(thm)],[c20]) ).
cnf(c22,plain,
join(x1,X) = join(X,x1),
inference(substitution,[status(thm)],[c5]) ).
cnf(c23,plain,
join(join(x1,x0),X) = join(X,x1),
inference(transitivity,[status(thm)],[c21,c22]) ).
cnf(c24,plain,
join(x1,join(x0,X)) = join(X,x1),
inference(transitivity,[status(thm)],[c13,c23]) ).
cnf(c25,plain,
join(x1,join(X,x0)) = join(X,x1),
inference(transitivity,[status(thm)],[c11,c24]) ).
cnf(c26,plain,
join(x1,join(x2,x0)) = join(x2,x1),
inference(substitution,[status(thm)],[c25]) ).
cnf(c27,plain,
join(x2,x1) = join(x1,x2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c28,plain,
join(x2,x1) = join(x1,x2),
inference(substitution,[status(thm)],[c5]) ).
cnf(c29,plain,
join(x1,x2) = join(x2,x1),
inference(symmetry,[status(thm)],[c28]) ).
fof(c30,conjecture,
! [X0_2,X1_2,X2_2] :
( ( join(X0_2,X1_2) = X1_2
& join(X2_2,X1_2) = X1_2 )
=> join(join(X0_2,X2_2),X1_2) = X1_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
fof(c31,negated_conjecture,
~ ! [X0_2,X1_2,X2_2] :
( ( join(X0_2,X1_2) = X1_2
& join(X2_2,X1_2) = X1_2 )
=> join(join(X0_2,X2_2),X1_2) = X1_2 ),
inference(negate_conjecture,[status(cth)],[c30]) ).
fof(c32,plain,
( join(x0,x1) = x1
& join(join(x0,x2),x1) != x1
& join(x2,x1) = x1 ),
inference(clausify,[status(esa)],[c31]) ).
cnf(c33,plain,
join(x2,x1) = x1,
inference(clausify,[status(thm)],[c32]) ).
cnf(c34,plain,
join(x1,x2) = x1,
inference(transitivity,[status(thm)],[c29,c33]) ).
cnf(c35,plain,
join(x2,x1) = x1,
inference(transitivity,[status(thm)],[c27,c34]) ).
cnf(c36,plain,
join(x1,join(x2,x0)) = x1,
inference(transitivity,[status(thm)],[c26,c35]) ).
cnf(c37,plain,
join(x1,join(x0,x2)) = x1,
inference(transitivity,[status(thm)],[c8,c36]) ).
cnf(c38,plain,
join(join(x0,x2),x1) = x1,
inference(transitivity,[status(thm)],[c6,c37]) ).
cnf(c39,plain,
$false,
inference(resolution,[status(thm)],[c4,c38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL049+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.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 : Sun Sep 27 22:56:46 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_twee /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.50 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --complete-subsets --ground-joining-incomplete-limit 15 --flatten-every 2
% 0.19/0.50
% 0.19/0.50 % SZS status Theorem
% 0.19/0.50
% 0.19/0.51 % SZS output start CNFRefutation
% See solution above
% 0.19/0.53
% 0.19/0.53 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------