%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM489+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 14.79s 2.31s
% Output : Proof 14.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 17 unt; 1 def)
% Number of atoms : 124 ( 71 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 144 ( 54 ~; 31 |; 55 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-4 aty)
% Number of variables : 19 ( 0 sgn 11 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f44,conjecture,
xn = sdtpldt0(xp,xr),
file('/export/starexec/sandbox/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(c217,plain,
xn != sdtpldt0(xp,xr),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi215,negated_conjecture,
ifeq(xn,sdtpldt0(xp,xr),false,true) = true,
inference(equality_encoding,[status(esa)],[c217]) ).
fof(f42,hypothesis,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1883) ).
fof(f42_nnf,plain,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
( xr = sdtmndt0(xn,xp)
& sdtpldt0(xp,xr) = xn
& aNaturalNumber0(xr) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c211,plain,
sdtpldt0(xp,xr) = xn,
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi204,axiom,
sdtpldt0(xp,xr) = xn,
inference(equality_encoding,[status(esa)],[c211]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi215,hi204]) ).
cnf(t6626,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f2,axiom,
( sz10 != sz00
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/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/sandbox/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(f40,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( ( ( doDivides0(W0,xp)
| ? [W1] :
( xp = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xp
| W0 = sz10 ) )
& xp != sz10
& xp != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f40_nnf,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& ? [W0] :
( sdtasdt0(xn,xm) = sdtasdt0(xp,W0)
& aNaturalNumber0(W0) )
& isPrime0(xp)
& ! [W0] :
( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ! [W1] :
( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [W0,W1] :
( doDivides0(xp,sdtasdt0(xn,xm))
& sdtasdt0(xn,xm) = sdtasdt0(xp,sk8)
& aNaturalNumber0(sk8)
& isPrime0(xp)
& ( W0 = xp
| W0 = sz10
| ( ~ doDivides0(W0,xp)
& ( xp != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& xp != sz10
& xp != sz00 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk8])],[f40_nnf]) ).
cnf(c199,plain,
xp != sz00,
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(c200,plain,
xp != sz10,
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
fof(f43,hypothesis,
( sdtlseqdt0(xr,xn)
& ? [W0] :
( sdtpldt0(xr,W0) = xn
& aNaturalNumber0(W0) )
& xr != xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1894) ).
fof(f43_nnf,plain,
( sdtlseqdt0(xr,xn)
& ? [W0] :
( sdtpldt0(xr,W0) = xn
& aNaturalNumber0(W0) )
& xr != xn ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
( sdtlseqdt0(xr,xn)
& sdtpldt0(xr,sk10) = xn
& aNaturalNumber0(sk10)
& xr != xn ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk10])],[f43_nnf]) ).
cnf(c213,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,c199,c200,c213,c217]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t6626]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM489+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Thu Sep 24 04:14:21 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 14.79/2.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.79/2.31 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------