%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT381+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 : n015.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 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 19 unt; 0 def)
% Number of atoms : 95 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 96 ( 43 ~; 40 |; 5 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 32 ( 0 sgn 8 !; 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(mDefSup,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2] :
( aSupremumOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( aUpperBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W2,W3) )
& aUpperBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) ) ) ) ),
file('theBenchmark.p',mDefSup) ).
fof(m__744,axiom,
( aSupremumOfIn0(xv,xS,xT)
& aSupremumOfIn0(xu,xS,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__]) ).
fof(m__725_01,axiom,
aSubsetOf0(xS,xT),
file('theBenchmark.p',m__725_01) ).
cnf(c_19,plain,
aSubsetOf0(xS,xT),
inference(clausify,[status(thm)],[m__725_01]) ).
cnf(c_21,plain,
( sdtlseqdt0(C,D)
| ~ aUpperBoundOfIn0(D,B,A)
| ~ aSupremumOfIn0(C,B,A)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSup]) ).
cnf(c_22,plain,
( aUpperBoundOfIn0(C,B,A)
| ~ aSupremumOfIn0(C,B,A)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSup]) ).
cnf(c_23,plain,
( aElementOf0(C,A)
| ~ aSupremumOfIn0(C,B,A)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefSup]) ).
cnf(c_132,plain,
( aElementOf0(A,xT)
| ~ aSupremumOfIn0(A,xS,xT)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_133,plain,
( aUpperBoundOfIn0(A,xS,xT)
| ~ aSupremumOfIn0(A,xS,xT)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_134,plain,
( sdtlseqdt0(A,B)
| ~ aUpperBoundOfIn0(B,xS,xT)
| ~ aSupremumOfIn0(A,xS,xT)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_137,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_139,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_141,plain,
aSet0(xT),
inference(clausify,[status(thm)],[m__725]) ).
cnf(c_142,plain,
aSupremumOfIn0(xu,xS,xT),
inference(clausify,[status(thm)],[m__744]) ).
cnf(c_143,plain,
aSupremumOfIn0(xv,xS,xT),
inference(clausify,[status(thm)],[m__744]) ).
cnf(c_144,negated_conjecture,
xv != xu,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_199,plain,
( sdtlseqdt0(A,B)
| ~ aUpperBoundOfIn0(B,xS,xT)
| ~ aSupremumOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_141,c_134]) ).
cnf(c_200,plain,
( aUpperBoundOfIn0(A,xS,xT)
| ~ aSupremumOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_141,c_133]) ).
cnf(c_201,plain,
( aElementOf0(A,xT)
| ~ aSupremumOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_141,c_132]) ).
cnf(c_237,plain,
( sdtlseqdt0(xv,A)
| ~ aUpperBoundOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_199,c_143]) ).
cnf(c_238,plain,
( sdtlseqdt0(xu,A)
| ~ aUpperBoundOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_199,c_142]) ).
cnf(c_239,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(resolve,[status(thm)],[c_200,c_143]) ).
cnf(c_240,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(resolve,[status(thm)],[c_200,c_142]) ).
cnf(c_241,plain,
aElementOf0(xv,xT),
inference(resolve,[status(thm)],[c_201,c_143]) ).
cnf(c_242,plain,
aElementOf0(xu,xT),
inference(resolve,[status(thm)],[c_201,c_142]) ).
cnf(c_243,plain,
sdtlseqdt0(xu,xv),
inference(resolve,[status(thm)],[c_239,c_238]) ).
cnf(c_276,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_241,c_137]) ).
cnf(c_252,plain,
aElement0(xv),
inference(resolve,[status(thm)],[c_141,c_276]) ).
cnf(c_277,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_242,c_137]) ).
cnf(c_264,plain,
aElement0(xu),
inference(resolve,[status(thm)],[c_141,c_277]) ).
cnf(c_278,plain,
( xu = xv
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(resolve,[status(thm)],[c_243,c_139]) ).
cnf(c_279,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(copy,[status(thm)],[c_278]) ).
cnf(c_280,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) ),
inference(resolve,[status(thm)],[c_252,c_279]) ).
cnf(c_281,plain,
( xv = xu
| ~ sdtlseqdt0(xv,xu) ),
inference(resolve,[status(thm)],[c_264,c_280]) ).
cnf(c_274,negated_conjecture,
~ sdtlseqdt0(xv,xu),
inference(resolve,[status(thm)],[c_144,c_281]) ).
cnf(c_282,plain,
sdtlseqdt0(xv,xu),
inference(resolve,[status(thm)],[c_240,c_237]) ).
cnf(c_275,plain,
$false,
inference(resolve,[status(thm)],[c_274,c_282]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT381+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 : n015.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 : Fri Sep 25 21:40:43 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2327645 was started by sandbox2 on n015,
% 0.09/0.36 % Fri Sep 25 21:40:43 2026
% 0.09/0.36 % 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).
% 0.09/0.41
% 0.09/0.41 % SZS status Theorem for theBenchmark
% 0.09/0.41
% 0.09/0.41 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.09/0.41 % Length of proof is 32.
% 0.09/0.41 % Level of proof is 7.
% 0.09/0.41 % Maximum clause weight is 18.000.
% 0.09/0.41 % Given clauses 135.
% 0.09/0.41
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------