%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT381+3 : 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 : n002.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 07:50:29 AM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 74 ( 10 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 67 ( 21 ~; 21 |; 15 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 16 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEOfElem,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('theBenchmark.p',mEOfElem) ).
fof(mASymm,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('theBenchmark.p',mASymm) ).
fof(m__744,axiom,
( aSupremumOfIn0(xv,xS,xT)
& ! [W0] :
( ( aUpperBoundOfIn0(W0,xS,xT)
| ( ! [W1] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W1,W0) )
& aElementOf0(W0,xT) ) )
=> sdtlseqdt0(xv,W0) )
& aUpperBoundOfIn0(xv,xS,xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,xv) )
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aSupremumOfIn0(xu,xS,xT)
& ! [W0] :
( ( aUpperBoundOfIn0(W0,xS,xT)
| ( ! [W1] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W1,W0) )
& aElementOf0(W0,xT) ) )
=> sdtlseqdt0(xu,W0) )
& aUpperBoundOfIn0(xu,xS,xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(W0,xu) )
& aElementOf0(xu,xT)
& aElementOf0(xu,xT) ),
file('theBenchmark.p',m__744) ).
fof(m__,conjecture,
xu = xv,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
xu != xv,
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_138,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_140,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mASymm]) ).
fof(m__725,axiom,
aSet0(xT),
file('theBenchmark.p',m__725) ).
cnf(c_142,plain,
aSet0(xT),
inference(clausify,[status(thm)],[m__725]) ).
cnf(c_145,plain,
aElementOf0(xu,xT),
inference(clausify,[status(thm)],[m__744]) ).
cnf(c_147,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(clausify,[status(thm)],[m__744]) ).
cnf(c_150,plain,
( sdtlseqdt0(xu,A)
| ~ aUpperBoundOfIn0(A,xS,xT) ),
inference(clausify,[status(thm)],[m__744]) ).
cnf(c_152,plain,
aElementOf0(xv,xT),
inference(clausify,[status(thm)],[m__744]) ).
cnf(c_154,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(clausify,[status(thm)],[m__744]) ).
cnf(c_157,plain,
( sdtlseqdt0(xv,A)
| ~ aUpperBoundOfIn0(A,xS,xT) ),
inference(clausify,[status(thm)],[m__744]) ).
cnf(c_159,negated_conjecture,
xv != xu,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_274,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_145,c_138]) ).
cnf(c_238,plain,
aElement0(xu),
inference(resolve,[status(thm)],[c_142,c_274]) ).
cnf(c_275,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_152,c_138]) ).
cnf(c_248,plain,
aElement0(xv),
inference(resolve,[status(thm)],[c_142,c_275]) ).
cnf(c_255,plain,
sdtlseqdt0(xu,xv),
inference(resolve,[status(thm)],[c_154,c_150]) ).
cnf(c_259,plain,
sdtlseqdt0(xv,xu),
inference(resolve,[status(thm)],[c_157,c_147]) ).
cnf(c_276,plain,
( xu = xv
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(resolve,[status(thm)],[c_255,c_140]) ).
cnf(c_277,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(copy,[status(thm)],[c_276]) ).
cnf(c_278,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) ),
inference(resolve,[status(thm)],[c_248,c_277]) ).
cnf(c_279,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu) ),
inference(resolve,[status(thm)],[c_238,c_278]) ).
cnf(c_280,plain,
xv = xu,
inference(resolve,[status(thm)],[c_259,c_279]) ).
cnf(c_273,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_159,c_280]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT381+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n002.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 21:40:06 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 47631 was started by sandbox2 on n002,
% 0.17/0.43 % Fri Sep 25 21:40:06 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Theorem for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.17/0.50 % Length of proof is 19.
% 0.17/0.50 % Level of proof is 3.
% 0.17/0.50 % Maximum clause weight is 13.000.
% 0.17/0.50 % Given clauses 141.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------