%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LAT385+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 5.60s 6.22s
% Output : Proof 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 6 unt; 0 def)
% Number of atoms : 215 ( 9 equ)
% Maximal formula atoms : 37 ( 10 avg)
% Number of connectives : 255 ( 61 ~; 55 |; 119 &)
% ( 0 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 1 sgn 38 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,hypothesis,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [W0,W1] :
( ( aElementOf0(W1,szDzozmdt0(xf))
& aElementOf0(W0,szDzozmdt0(xf)) )
=> ( sdtlseqdt0(W0,W1)
=> sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1)) ) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [W0] :
( ( aSubsetOf0(W0,xU)
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xU) )
& aSet0(W0) ) )
=> ? [W1] :
( ? [W2] :
( aSupremumOfIn0(W2,W0,xU)
& ! [W3] :
( ( aUpperBoundOfIn0(W3,W0,xU)
| ( ! [W4] :
( aElementOf0(W4,W0)
=> sdtlseqdt0(W4,W3) )
& aElementOf0(W3,xU) ) )
=> sdtlseqdt0(W2,W3) )
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( aElementOf0(W3,W0)
=> sdtlseqdt0(W3,W2) )
& aElementOf0(W2,xU)
& aElementOf0(W2,xU) )
& aInfimumOfIn0(W1,W0,xU)
& ! [W2] :
( ( aLowerBoundOfIn0(W2,W0,xU)
| ( ! [W3] :
( aElementOf0(W3,W0)
=> sdtlseqdt0(W2,W3) )
& aElementOf0(W2,xU) ) )
=> sdtlseqdt0(W2,W1) )
& aLowerBoundOfIn0(W1,W0,xU)
& ! [W2] :
( aElementOf0(W2,W0)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,xU)
& aElementOf0(W1,xU) ) )
& aSet0(xU) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1123) ).
fof(f23_nnf,plain,
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ! [W0,W1] :
( sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1))
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ aElementOf0(W0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ! [W0] :
( ? [W1] :
( ? [W2] :
( aSupremumOfIn0(W2,W0,xU)
& ! [W3] :
( sdtlseqdt0(W2,W3)
| ( ~ aUpperBoundOfIn0(W3,W0,xU)
& ( ? [W4] :
( ~ sdtlseqdt0(W4,W3)
& aElementOf0(W4,W0) )
| ~ aElementOf0(W3,xU) ) ) )
& aUpperBoundOfIn0(W2,W0,xU)
& ! [W3] :
( sdtlseqdt0(W3,W2)
| ~ aElementOf0(W3,W0) )
& aElementOf0(W2,xU)
& aElementOf0(W2,xU) )
& aInfimumOfIn0(W1,W0,xU)
& ! [W2] :
( sdtlseqdt0(W2,W1)
| ( ~ aLowerBoundOfIn0(W2,W0,xU)
& ( ? [W3] :
( ~ sdtlseqdt0(W2,W3)
& aElementOf0(W3,W0) )
| ~ aElementOf0(W2,xU) ) ) )
& aLowerBoundOfIn0(W1,W0,xU)
& ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(W1,xU)
& aElementOf0(W1,xU) )
| ( ~ aSubsetOf0(W0,xU)
& ( ? [W1] :
( ~ aElementOf0(W1,xU)
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& aSet0(xU) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [W0,W2,W3,W1] :
( isOn0(xf,xU)
& szRzazndt0(xf) = xU
& szDzozmdt0(xf) = szRzazndt0(xf)
& isMonotone0(xf)
& ( sdtlseqdt0(sdtlpdtrp0(xf,W0),sdtlpdtrp0(xf,W1))
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szDzozmdt0(xf))
| ~ aElementOf0(W0,szDzozmdt0(xf)) )
& aFunction0(xf)
& aCompleteLattice0(xU)
& ( ( aSupremumOfIn0(sk14(W0),W0,xU)
& ( sdtlseqdt0(sk14(W0),W3)
| ( ~ aUpperBoundOfIn0(W3,W0,xU)
& ( ( ~ sdtlseqdt0(sk15(W0,W3),W3)
& aElementOf0(sk15(W0,W3),W0) )
| ~ aElementOf0(W3,xU) ) ) )
& aUpperBoundOfIn0(sk14(W0),W0,xU)
& ( sdtlseqdt0(W3,sk14(W0))
| ~ aElementOf0(W3,W0) )
& aElementOf0(sk14(W0),xU)
& aElementOf0(sk14(W0),xU)
& aInfimumOfIn0(sk12(W0),W0,xU)
& ( sdtlseqdt0(W2,sk12(W0))
| ( ~ aLowerBoundOfIn0(W2,W0,xU)
& ( ( ~ sdtlseqdt0(W2,sk13(W0,W2))
& aElementOf0(sk13(W0,W2),W0) )
| ~ aElementOf0(W2,xU) ) ) )
& aLowerBoundOfIn0(sk12(W0),W0,xU)
& ( sdtlseqdt0(sk12(W0),W2)
| ~ aElementOf0(W2,W0) )
& aElementOf0(sk12(W0),xU)
& aElementOf0(sk12(W0),xU) )
| ( ~ aSubsetOf0(W0,xU)
& ( ( ~ aElementOf0(sk11(W0),xU)
& aElementOf0(sk11(W0),W0) )
| ~ aSet0(W0) ) ) )
& aSet0(xU) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11,sk12,sk13,sk14,sk15])],[f23_nnf]) ).
cnf(c77,plain,
( aInfimumOfIn0(sk12(X0),X0,xU)
| ~ aElementOf0(sk11(X0),xU)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
fof(f26,hypothesis,
( xP = cS1241(xU,xf,xT)
& ! [W0] :
( ( ( ( aUpperBoundOfIn0(W0,xT,xU)
| ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) ) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) )
=> aElementOf0(W0,xP) )
& ( aElementOf0(W0,xP)
=> ( aUpperBoundOfIn0(W0,xT,xU)
& ! [W1] :
( aElementOf0(W1,xT)
=> sdtlseqdt0(W1,W0) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) ) ) )
& aSet0(xP) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1244) ).
fof(f26_nnf,plain,
( xP = cS1241(xU,xf,xT)
& ! [W0] :
( ( aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aElementOf0(W1,xT) ) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ aElementOf0(W0,xU) )
& ( ( aUpperBoundOfIn0(W0,xT,xU)
& ! [W1] :
( sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,xT) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) )
| ~ aElementOf0(W0,xP) ) )
& aSet0(xP) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [W0,W1] :
( xP = cS1241(xU,xf,xT)
& ( aElementOf0(W0,xP)
| ( ~ aUpperBoundOfIn0(W0,xT,xU)
& ~ sdtlseqdt0(sk16(W0),W0)
& aElementOf0(sk16(W0),xT) )
| ~ sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
| ~ aElementOf0(W0,xU) )
& ( ( aUpperBoundOfIn0(W0,xT,xU)
& ( sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,xT) )
& sdtlseqdt0(sdtlpdtrp0(xf,W0),W0)
& aElementOf0(W0,xU) )
| ~ aElementOf0(W0,xP) )
& aSet0(xP) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk16])],[f26_nnf]) ).
cnf(c119,plain,
aSet0(xP),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p756,plain,
( aInfimumOfIn0(sk12(xP),xP,xU)
| ~ aElementOf0(sk11(xP),xU) ),
inference(resolution,[status(thm)],[c77,c119]) ).
cnf(c61,plain,
( aInfimumOfIn0(sk12(X0),X0,xU)
| aElementOf0(sk11(X0),X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p588,plain,
( aInfimumOfIn0(sk12(xP),xP,xU)
| aElementOf0(sk11(xP),xP) ),
inference(resolution,[status(thm)],[c61,c119]) ).
fof(f27,conjecture,
? [W0] :
( aInfimumOfIn0(W0,xP,xU)
| ( ! [W1] :
( ( aLowerBoundOfIn0(W1,xP,xU)
& ! [W2] :
( aElementOf0(W2,xP)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,xU) )
=> sdtlseqdt0(W1,W0) )
& ( aLowerBoundOfIn0(W0,xP,xU)
| ( ! [W1] :
( aElementOf0(W1,xP)
=> sdtlseqdt0(W0,W1) )
& aElementOf0(W0,xU) ) )
& aElementOf0(W0,xU) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f27_neg,negated_conjecture,
~ ? [W0] :
( aInfimumOfIn0(W0,xP,xU)
| ( ! [W1] :
( ( aLowerBoundOfIn0(W1,xP,xU)
& ! [W2] :
( aElementOf0(W2,xP)
=> sdtlseqdt0(W1,W2) )
& aElementOf0(W1,xU) )
=> sdtlseqdt0(W1,W0) )
& ( aLowerBoundOfIn0(W0,xP,xU)
| ( ! [W1] :
( aElementOf0(W1,xP)
=> sdtlseqdt0(W0,W1) )
& aElementOf0(W0,xU) ) )
& aElementOf0(W0,xU) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
fof(f27_nnf,plain,
! [W0] :
( ~ aInfimumOfIn0(W0,xP,xU)
& ( ? [W1] :
( ~ sdtlseqdt0(W1,W0)
& aLowerBoundOfIn0(W1,xP,xU)
& ! [W2] :
( sdtlseqdt0(W1,W2)
| ~ aElementOf0(W2,xP) )
& aElementOf0(W1,xU) )
| ( ~ aLowerBoundOfIn0(W0,xP,xU)
& ( ? [W1] :
( ~ sdtlseqdt0(W0,W1)
& aElementOf0(W1,xP) )
| ~ aElementOf0(W0,xU) ) )
| ~ aElementOf0(W0,xU) ) ),
inference(nnf_transformation,[status(thm)],[f27_neg]) ).
fof(f27_sk,plain,
! [W0,W2] :
( ~ aInfimumOfIn0(W0,xP,xU)
& ( ( ~ sdtlseqdt0(sk18(W0),W0)
& aLowerBoundOfIn0(sk18(W0),xP,xU)
& ( sdtlseqdt0(sk18(W0),W2)
| ~ aElementOf0(W2,xP) )
& aElementOf0(sk18(W0),xU) )
| ( ~ aLowerBoundOfIn0(W0,xP,xU)
& ( ( ~ sdtlseqdt0(W0,sk17(W0))
& aElementOf0(sk17(W0),xP) )
| ~ aElementOf0(W0,xU) ) )
| ~ aElementOf0(W0,xU) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk17,sk18])],[f27_nnf]) ).
cnf(c140,plain,
~ aInfimumOfIn0(X0,xP,xU),
inference(cnf_transformation,[status(esa)],[f27_sk]) ).
cnf(p607,plain,
aElementOf0(sk11(xP),xP),
inference(resolution,[status(thm)],[p588,c140]) ).
cnf(c120,plain,
( aElementOf0(X0,xU)
| ~ aElementOf0(X0,xP) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(p609,plain,
aElementOf0(sk11(xP),xU),
inference(resolution,[status(thm)],[p607,c120]) ).
cnf(p865,plain,
aInfimumOfIn0(sk12(xP),xP,xU),
inference(resolution,[status(thm)],[p756,p609]) ).
cnf(p866,plain,
$false,
inference(resolution,[status(thm)],[p865,c140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT385+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n004.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Wed Sep 23 21:31:12 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.60/6.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.60/6.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------