%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM489+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 02:20:10 PM UTC 2026
% Result : Theorem 12.72s 2.29s
% Output : Proof 12.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 27 unt; 2 def)
% Number of atoms : 121 ( 61 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 130 ( 54 ~; 37 |; 33 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn 15 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f18,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2] :
( W2 = sdtmndt0(W1,W0)
<=> ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
fof(f18_nnf,plain,
! [W0,W1] :
( ! [W2] :
( ( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [W0,W1,W2] :
( ( ( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| W2 = sdtmndt0(W1,W0) )
& ( ( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| W2 != sdtmndt0(W1,W0) ) )
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c29,plain,
( sdtpldt0(X0,X2) = X1
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi27,axiom,
ifeq(aNaturalNumber0(X0),true,ifeq(aNaturalNumber0(X1),true,ifeq(sdtlseqdt0(X0,X1),true,ifeq(X2,sdtmndt0(X1,X0),sdtpldt0(X0,X2),X1),X1),X1),X1) = X1,
inference(equality_encoding,[status(esa)],[c29]) ).
fof(f38,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).
fof(f38_nnf,plain,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c72,plain,
aNaturalNumber0(xp),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi67,axiom,
aNaturalNumber0(xp) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(c70,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi65,axiom,
aNaturalNumber0(xn) = true,
inference(equality_encoding,[status(esa)],[c70]) ).
fof(f41,hypothesis,
sdtlseqdt0(xp,xn),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).
fof(f41_nnf,plain,
sdtlseqdt0(xp,xn),
inference(nnf_transformation,[status(thm)],[f41]) ).
cnf(c76,plain,
sdtlseqdt0(xp,xn),
inference(cnf_transformation,[status(esa)],[f41_nnf]) ).
cnf(hi71,axiom,
sdtlseqdt0(xp,xn) = true,
inference(equality_encoding,[status(esa)],[c76]) ).
fof(f42,hypothesis,
xr = sdtmndt0(xn,xp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1883) ).
fof(f42_nnf,plain,
xr = sdtmndt0(xn,xp),
inference(nnf_transformation,[status(thm)],[f42]) ).
cnf(c77,plain,
xr = sdtmndt0(xn,xp),
inference(cnf_transformation,[status(esa)],[f42_nnf]) ).
cnf(hi72,axiom,
xr = sdtmndt0(xn,xp),
inference(equality_encoding,[status(esa)],[c77]) ).
cnf(h688,plain,
sdtpldt0(xp,xr) = xn,
inference(hyper_resolution,[status(thm)],[hi27,hi67,hi65,hi71,hi72]) ).
fof(f44,conjecture,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f44_neg,negated_conjecture,
xn != sdtpldt0(xp,xr),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f44_nnf,plain,
xn != sdtpldt0(xp,xr),
inference(nnf_transformation,[status(thm)],[f44_neg]) ).
fof(f44_sk,plain,
xn != sdtpldt0(xp,xr),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c80,plain,
xn != sdtpldt0(xp,xr),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi78,negated_conjecture,
ifeq(xn,sdtpldt0(xp,xr),false,true) = true,
inference(equality_encoding,[status(esa)],[c80]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi78,h688]) ).
cnf(t3819,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f2,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f2_nnf,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
sz10 != sz00,
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
fof(f36,definition,
! [W0] :
( aNaturalNumber0(W0)
=> ( isPrime0(W0)
<=> ( ! [W1] :
( ( doDivides0(W1,W0)
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefPrime) ).
fof(f36_nnf,plain,
! [W0] :
( ( ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ! [W1] :
( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [W0,W1] :
( ( ( ( sk2(W0) != W0
& sk2(W0) != sz10
& doDivides0(sk2(W0),W0)
& aNaturalNumber0(sk2(W0)) )
| W0 = sz10
| W0 = sz00
| isPrime0(W0) )
& ( ( ( W1 = W0
| W1 = sz10
| ~ doDivides0(W1,W0)
| ~ aNaturalNumber0(W1) )
& W0 != sz10
& W0 != sz00 )
| ~ isPrime0(W0) ) )
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk2])],[f36_nnf]) ).
cnf(c60,plain,
( X0 != sz00
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(c61,plain,
( X0 != sz10
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
fof(f43,hypothesis,
( sdtlseqdt0(xr,xn)
& xr != xn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1894) ).
fof(f43_nnf,plain,
( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c78,plain,
xr != xn,
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c60,c61,c78,c80]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t3819]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM489+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 04:15:33 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 12.72/2.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.72/2.29 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------