%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LAT382+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 : n017.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 10.43s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 91 ( 9 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 89 ( 39 ~; 37 |; 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(mDefInf,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aSubsetOf0(W1,W0)
=> ! [W2] :
( aInfimumOfIn0(W2,W1,W0)
<=> ( ! [W3] :
( aLowerBoundOfIn0(W3,W1,W0)
=> sdtlseqdt0(W3,W2) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) ) ) ) ),
file('theBenchmark.p',mDefInf) ).
fof(m__792,axiom,
( aInfimumOfIn0(xv,xS,xT)
& aInfimumOfIn0(xu,xS,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__]) ).
fof(m__773_01,axiom,
aSubsetOf0(xS,xT),
file('theBenchmark.p',m__773_01) ).
cnf(c_20,plain,
aSubsetOf0(xS,xT),
inference(clausify,[status(thm)],[m__773_01]) ).
cnf(c_28,plain,
( sdtlseqdt0(D,C)
| ~ aLowerBoundOfIn0(D,B,A)
| ~ aInfimumOfIn0(C,B,A)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefInf]) ).
cnf(c_29,plain,
( aLowerBoundOfIn0(C,B,A)
| ~ aInfimumOfIn0(C,B,A)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefInf]) ).
cnf(c_30,plain,
( aElementOf0(C,A)
| ~ aInfimumOfIn0(C,B,A)
| ~ aSubsetOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mDefInf]) ).
cnf(c_133,plain,
( aElementOf0(A,xT)
| ~ aInfimumOfIn0(A,xS,xT)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_30,c_20]) ).
cnf(c_134,plain,
( aLowerBoundOfIn0(A,xS,xT)
| ~ aInfimumOfIn0(A,xS,xT)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_29,c_20]) ).
cnf(c_135,plain,
( sdtlseqdt0(B,A)
| ~ aLowerBoundOfIn0(B,xS,xT)
| ~ aInfimumOfIn0(A,xS,xT)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_144,plain,
( aElement0(B)
| ~ aElementOf0(B,A)
| ~ aSet0(A) ),
inference(clausify,[status(thm)],[mEOfElem]) ).
cnf(c_146,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_148,plain,
aSet0(xT),
inference(clausify,[status(thm)],[m__773]) ).
cnf(c_149,plain,
aInfimumOfIn0(xu,xS,xT),
inference(clausify,[status(thm)],[m__792]) ).
cnf(c_150,plain,
aInfimumOfIn0(xv,xS,xT),
inference(clausify,[status(thm)],[m__792]) ).
cnf(c_151,negated_conjecture,
xv != xu,
inference(clausify,[status(thm)],[m___neg]) ).
cnf(c_214,plain,
( sdtlseqdt0(B,A)
| ~ aLowerBoundOfIn0(B,xS,xT)
| ~ aInfimumOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_148,c_135]) ).
cnf(c_215,plain,
( aLowerBoundOfIn0(A,xS,xT)
| ~ aInfimumOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_148,c_134]) ).
cnf(c_216,plain,
( aElementOf0(A,xT)
| ~ aInfimumOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_148,c_133]) ).
cnf(c_247,plain,
( sdtlseqdt0(A,xv)
| ~ aLowerBoundOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_214,c_150]) ).
cnf(c_248,plain,
( sdtlseqdt0(A,xu)
| ~ aLowerBoundOfIn0(A,xS,xT) ),
inference(resolve,[status(thm)],[c_214,c_149]) ).
cnf(c_249,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(resolve,[status(thm)],[c_215,c_150]) ).
cnf(c_250,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(resolve,[status(thm)],[c_215,c_149]) ).
cnf(c_251,plain,
aElementOf0(xv,xT),
inference(resolve,[status(thm)],[c_216,c_150]) ).
cnf(c_252,plain,
aElementOf0(xu,xT),
inference(resolve,[status(thm)],[c_216,c_149]) ).
cnf(c_287,plain,
( aElement0(xv)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_251,c_144]) ).
cnf(c_259,plain,
aElement0(xv),
inference(resolve,[status(thm)],[c_148,c_287]) ).
cnf(c_288,plain,
( aElement0(xu)
| ~ aSet0(xT) ),
inference(resolve,[status(thm)],[c_252,c_144]) ).
cnf(c_272,plain,
aElement0(xu),
inference(resolve,[status(thm)],[c_148,c_288]) ).
cnf(c_280,plain,
sdtlseqdt0(xv,xu),
inference(resolve,[status(thm)],[c_249,c_248]) ).
cnf(c_282,plain,
sdtlseqdt0(xu,xv),
inference(resolve,[status(thm)],[c_250,c_247]) ).
cnf(c_289,plain,
( xv = xu
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv)
| ~ aElement0(xu) ),
inference(resolve,[status(thm)],[c_280,c_146]) ).
cnf(c_290,plain,
( xv = xu
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ),
inference(resolve,[status(thm)],[c_272,c_289]) ).
cnf(c_291,plain,
( xv = xu
| ~ sdtlseqdt0(xu,xv) ),
inference(resolve,[status(thm)],[c_259,c_290]) ).
cnf(c_292,plain,
xv = xu,
inference(resolve,[status(thm)],[c_282,c_291]) ).
cnf(c_286,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_151,c_292]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT382+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n017.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Fri Sep 25 21:33:13 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/10.37 % Process 3241503 was started by sandbox2 on n017,
% 0.08/10.37 % Fri Sep 25 21:33:13 2026
% 0.08/10.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/10.38
% 0.08/10.38 % From the command line: assign(max_seconds, 300).
% 0.14/10.43
% 0.14/10.43 % SZS status Theorem for theBenchmark
% 0.14/10.43
% 0.14/10.43 % Proof 1 at 0.03 (+ 0.00) seconds.
% 0.14/10.43 % Length of proof is 32.
% 0.14/10.43 % Level of proof is 6.
% 0.14/10.43 % Maximum clause weight is 18.000.
% 0.14/10.43 % Given clauses 141.
% 0.14/10.43
% 0.14/10.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------