%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT381+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 : n010.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 01:57:04 PM UTC 2026
% Result : Theorem 6.29s 1.57s
% Output : Proof 6.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 52 ( 23 unt; 1 def)
% Number of atoms : 137 ( 13 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 151 ( 66 ~; 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(f12,definition,
! [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('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSup) ).
fof(f12_nnf,plain,
! [W0] :
( ! [W1] :
( ! [W2] :
( ( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aUpperBoundOfIn0(W3,W1,W0) )
| ~ aUpperBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aSupremumOfIn0(W2,W1,W0) )
& ( ( ! [W3] :
( sdtlseqdt0(W2,W3)
| ~ aUpperBoundOfIn0(W3,W1,W0) )
& aUpperBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aSupremumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [W0,W1,W2,W3] :
( ( ( ( ~ sdtlseqdt0(W2,sk5(W0,W1,W2))
& aUpperBoundOfIn0(sk5(W0,W1,W2),W1,W0) )
| ~ aUpperBoundOfIn0(W2,W1,W0)
| ~ aElementOf0(W2,W0)
| aSupremumOfIn0(W2,W1,W0) )
& ( ( ( sdtlseqdt0(W2,W3)
| ~ aUpperBoundOfIn0(W3,W1,W0) )
& aUpperBoundOfIn0(W2,W1,W0)
& aElementOf0(W2,W0) )
| ~ aSupremumOfIn0(W2,W1,W0) ) )
| ~ aSubsetOf0(W1,W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f12_nnf]) ).
cnf(c28,plain,
( sdtlseqdt0(X2,X3)
| ~ aUpperBoundOfIn0(X3,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
fof(f13,hypothesis,
aSet0(xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725) ).
fof(f13_nnf,plain,
aSet0(xT),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c31,plain,
aSet0(xT),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(p150,plain,
( sdtlseqdt0(X1,X2)
| ~ aUpperBoundOfIn0(X2,X0,xT)
| ~ aSupremumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(resolution,[status(thm)],[c28,c31]) ).
fof(f14,hypothesis,
aSubsetOf0(xS,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__725_01) ).
fof(f14_nnf,plain,
aSubsetOf0(xS,xT),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c32,plain,
aSubsetOf0(xS,xT),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(p212,plain,
( sdtlseqdt0(X0,X1)
| ~ aUpperBoundOfIn0(X1,xS,xT)
| ~ aSupremumOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p150,c32]) ).
fof(f15,hypothesis,
( aSupremumOfIn0(xv,xS,xT)
& aSupremumOfIn0(xu,xS,xT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__744) ).
fof(f15_nnf,plain,
( aSupremumOfIn0(xv,xS,xT)
& aSupremumOfIn0(xu,xS,xT) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
( aSupremumOfIn0(xv,xS,xT)
& aSupremumOfIn0(xu,xS,xT) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c34,plain,
aSupremumOfIn0(xv,xS,xT),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p215,plain,
( sdtlseqdt0(xv,X0)
| ~ aUpperBoundOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p212,c34]) ).
cnf(c27,plain,
( aUpperBoundOfIn0(X2,X1,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p144,plain,
( aUpperBoundOfIn0(X1,X0,xT)
| ~ aSupremumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(resolution,[status(thm)],[c27,c31]) ).
cnf(p146,plain,
( aUpperBoundOfIn0(X0,xS,xT)
| ~ aSupremumOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p144,c32]) ).
cnf(c33,plain,
aSupremumOfIn0(xu,xS,xT),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p148,plain,
aUpperBoundOfIn0(xu,xS,xT),
inference(resolution,[status(thm)],[p146,c33]) ).
cnf(p222,plain,
sdtlseqdt0(xv,xu),
inference(resolution,[status(thm)],[p215,p148]) ).
cnf(p214,plain,
( sdtlseqdt0(xu,X0)
| ~ aUpperBoundOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p212,c33]) ).
cnf(p149,plain,
aUpperBoundOfIn0(xv,xS,xT),
inference(resolution,[status(thm)],[p146,c34]) ).
cnf(p218,plain,
sdtlseqdt0(xu,xv),
inference(resolution,[status(thm)],[p214,p149]) ).
cnf(c26,plain,
( aElementOf0(X2,X0)
| ~ aSupremumOfIn0(X2,X1,X0)
| ~ aSubsetOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p114,plain,
( aElementOf0(X1,xT)
| ~ aSupremumOfIn0(X1,X0,xT)
| ~ aSubsetOf0(X0,xT) ),
inference(resolution,[status(thm)],[c26,c31]) ).
cnf(p116,plain,
( aElementOf0(X0,xT)
| ~ aSupremumOfIn0(X0,xS,xT) ),
inference(resolution,[status(thm)],[p114,c32]) ).
cnf(p118,plain,
aElementOf0(xu,xT),
inference(resolution,[status(thm)],[p116,c33]) ).
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(p37,plain,
( aElement0(X0)
| ~ aElementOf0(X0,xT) ),
inference(resolution,[status(thm)],[c2,c31]) ).
cnf(p122,plain,
aElement0(xu),
inference(resolution,[status(thm)],[p118,p37]) ).
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(p124,plain,
( xu = X0
| ~ sdtlseqdt0(X0,xu)
| ~ sdtlseqdt0(xu,X0)
| ~ aElement0(X0) ),
inference(resolution,[status(thm)],[p122,c11]) ).
cnf(p119,plain,
aElementOf0(xv,xT),
inference(resolution,[status(thm)],[p116,c34]) ).
cnf(p126,plain,
aElement0(xv),
inference(resolution,[status(thm)],[p119,p37]) ).
cnf(p143,plain,
( xu = xv
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv) ),
inference(resolution,[status(thm)],[p124,p126]) ).
cnf(p219,plain,
( xu = xv
| ~ sdtlseqdt0(xv,xu) ),
inference(resolution,[status(thm)],[p218,p143]) ).
cnf(p227,plain,
xu = xv,
inference(resolution,[status(thm)],[p222,p219]) ).
fof(f16,conjecture,
xu = xv,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f16_neg,negated_conjecture,
xu != xv,
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f16_nnf,plain,
xu != xv,
inference(nnf_transformation,[status(thm)],[f16_neg]) ).
fof(f16_sk,plain,
xu != xv,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c35,plain,
xu != xv,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p228,plain,
$false,
inference(resolution,[status(thm)],[p227,c35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LAT381+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.42 % Computer : n010.cluster.edu
% 0.15/0.42 % Model : x86_64 x86_64
% 0.15/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.42 % Memory : 8046.5625MB
% 0.15/0.42 % OS : Linux 6.8.0-71-generic
% 0.15/0.42 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Wed Sep 23 21:30:28 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.29/1.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.29/1.57 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------