%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT382+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 : Fri Sep 25 01:57:05 PM UTC 2026
% Result : Theorem 5.19s 6.15s
% Output : Proof 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 24 unt; 1 def)
% Number of atoms : 138 ( 14 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 152 ( 67 ~; 62 |; 15 &)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 0 sgn 24 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,definition,
! [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('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefInf) ).
fof(f11_nnf,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( ? [W3] :
( ~ sdtlseqdt0(W3,W2)
& aLowerBoundOfIn0(W3,W1,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aInfimumOfIn0(W2,W1,W0) )
& ( ( ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aLowerBoundOfIn0(W3,W1,W0) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aInfimumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( ~ sdtlseqdt0(sk4(W0,W1,W2),W2)
& aLowerBoundOfIn0(sk4(W0,W1,W2),W1,W0) )
| ~ aLowerBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aInfimumOfIn0(W2,W1,W0) )
& ( ( ( sdtlseqdt0(W3,W2)
| ~ aLowerBoundOfIn0(W3,W1,W0) )
& aLowerBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aInfimumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk4])],[f11_nnf]) ).
cnf(c23,plain,
( sdtlseqdt0(X3,X2)
| ~ aLowerBoundOfIn0(X3,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
fof(f14,hypothesis,
aSet0(xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773) ).
fof(f14_nnf,plain,
aSet0(xT),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c32,plain,
aSet0(xT),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p178,plain,
( sdtlseqdt0(X2,X1)
| ~ aLowerBoundOfIn0(X2,X0,xT)
| ~ aInfimumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(resolution,[status(thm)],[c23,c32]) ).
fof(f15,hypothesis,
aSubsetOf0(xS,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773_01) ).
fof(f15_nnf,plain,
aSubsetOf0(xS,xT),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c33,plain,
aSubsetOf0(xS,xT),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(p180,plain,
( sdtlseqdt0(X1,X0)
| ~ aLowerBoundOfIn0(X1,xS,xT)
| ~ aInfimumOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p178,c33]) ).
fof(f16,hypothesis,
( aInfimumOfIn0(xv,xS,xT)
& aInfimumOfIn0(xu,xS,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__792) ).
fof(f16_nnf,plain,
( aInfimumOfIn0(xv,xS,xT)
& aInfimumOfIn0(xu,xS,xT) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
( aInfimumOfIn0(xv,xS,xT)
& aInfimumOfIn0(xu,xS,xT) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c35,plain,
aInfimumOfIn0(xv,xS,xT),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p183,plain,
( sdtlseqdt0(X0,xv)
| ~ aLowerBoundOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p180,c35]) ).
cnf(c22,plain,
( aLowerBoundOfIn0(X2,X1,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p104,plain,
( aLowerBoundOfIn0(X1,X0,xT)
| ~ aInfimumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(resolution,[status(thm)],[c22,c32]) ).
cnf(p106,plain,
( aLowerBoundOfIn0(X0,xS,xT)
| ~ aInfimumOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p104,c33]) ).
cnf(c34,plain,
aInfimumOfIn0(xu,xS,xT),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p108,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(resolution,[status(thm)],[p106,c34]) ).
cnf(p188,plain,
sdtlseqdt0(xu,xv),
inference(resolution,[status(thm)],[p183,p108]) ).
cnf(p182,plain,
( sdtlseqdt0(X0,xu)
| ~ aLowerBoundOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p180,c34]) ).
cnf(p109,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(resolution,[status(thm)],[p106,c35]) ).
cnf(p184,plain,
sdtlseqdt0(xv,xu),
inference(resolution,[status(thm)],[p182,p109]) ).
fof(f7,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> ( ( sdtlseqdt0(W1,W0)
& sdtlseqdt0(W0,W1) )
=> W0 = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mASymm) ).
fof(f7_nnf,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0,W1] :
( W0 = W1
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c11,plain,
( X0 = X1
| ~ sdtlseqdt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c21,plain,
( aElementOf0(X2,X0)
| ~ aInfimumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p88,plain,
( aElementOf0(X1,xT)
| ~ aInfimumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(resolution,[status(thm)],[c21,c32]) ).
cnf(p90,plain,
( aElementOf0(X0,xT)
| ~ aInfimumOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p88,c33]) ).
cnf(p93,plain,
aElementOf0(xv,xT),
inference(resolution,[status(thm)],[p90,c35]) ).
fof(f2,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f2_nnf,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [W0,W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p38,plain,
( aElement0(X0)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[status(thm)],[c2,c32]) ).
cnf(p96,plain,
aElement0(xv),
inference(resolution,[status(thm)],[p93,p38]) ).
cnf(p120,plain,
( xv = X0
| ~ sdtlseqdt0(X0,xv)
| ~ sdtlseqdt0(xv,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[c11,p96]) ).
cnf(p92,plain,
aElementOf0(xu,xT),
inference(resolution,[status(thm)],[p90,c34]) ).
cnf(p94,plain,
aElement0(xu),
inference(resolution,[status(thm)],[p92,p38]) ).
cnf(p128,plain,
( xv = xu
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu) ),
inference(resolution,[status(thm)],[p120,p94]) ).
cnf(p185,plain,
( xv = xu
| ~ sdtlseqdt0(xu,xv) ),
inference(resolution,[status(thm)],[p184,p128]) ).
cnf(p192,plain,
xv = xu,
inference(resolution,[status(thm)],[p188,p185]) ).
fof(f17,conjecture,
xu = xv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f17_neg,negated_conjecture,
xu != xv,
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f17_nnf,plain,
xu != xv,
inference(nnf_transformation,[status(thm)],[f17_neg]) ).
fof(f17_sk,plain,
xu != xv,
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c36,plain,
xu != xv,
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p193,plain,
xu != xu,
inference(demodulation,[status(thm)],[p192,c36]) ).
cnf(p194,plain,
$false,
inference(equality_resolution,[status(thm)],[p193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT382+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/5.40 % Computer : n006.cluster.edu
% 0.13/5.40 % Model : x86_64 x86_64
% 0.13/5.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/5.40 % Memory : 8046.5625MB
% 0.13/5.40 % OS : Linux 6.8.0-71-generic
% 0.13/5.40 % CPULimit : 300
% 0.13/5.40 % WCLimit : 300
% 0.13/5.40 % DateTime : Wed Sep 23 21:30:31 UTC 2026
% 0.13/5.40 % CPUTime :
% 0.13/5.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.19/6.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.19/6.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------