%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT382+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 : n011.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 07:50:30 AM UTC 2026
% Result : Theorem 0.14s 0.65s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 15 unt; 0 def)
% Number of atoms : 70 ( 9 equ)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 61 ( 18 ~; 18 |; 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__792,axiom,
( aInfimumOfIn0(xv,xS,xT)
& ! [W0] :
( ( aLowerBoundOfIn0(W0,xS,xT)
| ( ! [W1] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) )
& aElementOf0(W0,xT) ) )
=> sdtlseqdt0(W0,xv) )
& aLowerBoundOfIn0(xv,xS,xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xv,W0) )
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& aInfimumOfIn0(xu,xS,xT)
& ! [W0] :
( ( aLowerBoundOfIn0(W0,xS,xT)
| ( ! [W1] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) )
& aElementOf0(W0,xT) ) )
=> sdtlseqdt0(W0,xu) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aElementOf0(xu,xT)
& aElementOf0(xu,xT) ),
file('theBenchmark.p',m__792) ).
fof(m__,conjecture,
xu = xv,
file('theBenchmark.p',m__) ).
fof(m___neg,negated_conjecture,
xu != xv,
inference(assume_negation,[status(cth)],[m__]) ).
cnf(c_145,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_147,plain,
( B = A
| ~ sdtlseqdt0(B,A)
| ~ sdtlseqdt0(A,B)
| ~ aElement0(B)
| ~ aElement0(A) ),
inference(clausify,[status(thm)],[mASymm]) ).
fof(m__773,axiom,
aSet0(xT),
file('theBenchmark.p',m__773) ).
cnf(c_149,plain,
aSet0(xT),
inference(clausify,[status(thm)],[m__773]) ).
cnf(c_152,plain,
aElementOf0(xu,xT),
inference(clausify,[status(thm)],[m__792]) ).
cnf(c_154,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(clausify,[status(thm)],[m__792]) ).
cnf(c_157,plain,
( sdtlseqdt0(A,xu)
| ~ aLowerBoundOfIn0(A,xS,xT) ),
inference(clausify,[status(thm)],[m__792]) ).
cnf(c_159,plain,
aElementOf0(xv,xT),
inference(clausify,[status(thm)],[m__792]) ).
cnf(c_161,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(clausify,[status(thm)],[m__792]) ).
cnf(c_164,plain,
( sdtlseqdt0(A,xv)
| ~ aLowerBoundOfIn0(A,xS,xT) ),
inference(clausify,[status(thm)],[m__792]) ).
cnf(c_166,negated_conjecture,
xv != xu,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_284,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_152,c_145]) ).
cnf(c_248,plain,
aElement0(xu),
inference(resolve,[status(thm)],[c_149,c_284]) ).
cnf(c_285,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_159,c_145]) ).
cnf(c_258,plain,
aElement0(xv),
inference(resolve,[status(thm)],[c_149,c_285]) ).
cnf(c_265,plain,
sdtlseqdt0(xv,xu),
inference(resolve,[status(thm)],[c_161,c_157]) ).
cnf(c_269,plain,
sdtlseqdt0(xu,xv),
inference(resolve,[status(thm)],[c_164,c_154]) ).
cnf(c_286,plain,
( xv = xu
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv)
| ~ aElement0(xu) ),
inference(resolve,[status(thm)],[c_265,c_147]) ).
cnf(c_287,plain,
( xv = xu
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ),
inference(resolve,[status(thm)],[c_248,c_286]) ).
cnf(c_288,plain,
( xv = xu
| ~ sdtlseqdt0(xu,xv) ),
inference(resolve,[status(thm)],[c_258,c_287]) ).
cnf(c_289,plain,
xv = xu,
inference(resolve,[status(thm)],[c_269,c_288]) ).
cnf(c_283,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_166,c_289]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT382+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.58 % Computer : n011.cluster.edu
% 0.09/0.58 % Model : x86_64 x86_64
% 0.09/0.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.58 % Memory : 8046.5625MB
% 0.09/0.58 % OS : Linux 6.8.0-71-generic
% 0.09/0.58 % CPULimit : 300
% 0.09/0.58 % WCLimit : 300
% 0.09/0.58 % DateTime : Fri Sep 25 21:38:00 UTC 2026
% 0.09/0.58 % CPUTime :
% 0.09/0.59 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.59 % Process 2965816 was started by sandbox2 on n011,
% 0.09/0.59 % Fri Sep 25 21:38:00 2026
% 0.09/0.59 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.59
% 0.09/0.59 % From the command line: assign(max_seconds, 300).
% 0.14/0.65
% 0.14/0.65 % SZS status Theorem for theBenchmark
% 0.14/0.65
% 0.14/0.65 % Proof 1 at 0.04 (+ 0.01) seconds.
% 0.14/0.65 % Length of proof is 19.
% 0.14/0.65 % Level of proof is 3.
% 0.14/0.65 % Maximum clause weight is 18.000.
% 0.14/0.65 % Given clauses 148.
% 0.14/0.65
% 0.14/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------