%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM487+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 02:20:09 PM UTC 2026
% Result : Theorem 116.14s 20.75s
% Output : Proof 116.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 14
% Syntax : Number of formulae : 133 ( 93 unt; 3 def)
% Number of atoms : 274 ( 154 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 234 ( 93 ~; 80 |; 49 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 102 ( 2 sgn 41 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(t199,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(isPrime0(X1),true,ifeq(X1,sz00,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c60]) ).
cnf(t317,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(isPrime0(X1),true,ifeq(X1,sz00,false,true),true),true) = true,
inference(orient,[status(thm)],[t199]) ).
fof(f40,hypothesis,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1860) ).
fof(f40_nnf,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
( doDivides0(xp,sdtasdt0(xn,xm))
& isPrime0(xp) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c74,plain,
isPrime0(xp),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(t6,plain,
isPrime0(xp) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t3160,plain,
isPrime0(xp) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t3161,plain,
true = ifeq(aNaturalNumber0(xp),true,ifeq(true,true,ifeq(xp,sz00,false,true),true),true),
inference(cp,[status(thm)],[t317,t3160]) ).
fof(f38,hypothesis,
( aNaturalNumber0(xp)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/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(t4,plain,
aNaturalNumber0(xp) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(t1929,plain,
aNaturalNumber0(xp) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t46273,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(xp,sz00,false,true),true),true),
inference(step,[status(thm)],[t3161,t1929]) ).
cnf(t86,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t86]) ).
cnf(t46274,plain,
true = ifeq(true,true,ifeq(xp,sz00,false,true),true),
inference(step,[status(thm)],[t46273,t256]) ).
cnf(t46275,plain,
true = ifeq(xp,sz00,false,true),
inference(step,[status(thm)],[t46274,t256]) ).
cnf(t10896,plain,
ifeq(xp,sz00,false,true) = true,
inference(orient,[status(thm)],[t46275]) ).
fof(f13,axiom,
! [W0,W1,W2] :
( ( aNaturalNumber0(W2)
& aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0)
| sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
=> W1 = W2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f13_nnf,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [W0,W1,W2] :
( W1 = W2
| ( sdtpldt0(W1,W0) != sdtpldt0(W2,W0)
& sdtpldt0(W0,W1) != sdtpldt0(W0,W2) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c19,plain,
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t224,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(aNaturalNumber0(X3),true,ifeq(sdtpldt0(X2,X1),sdtpldt0(X3,X1),X2,X3),X3),X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t257,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(aNaturalNumber0(X3),true,ifeq(sdtpldt0(X2,X1),sdtpldt0(X3,X1),X2,X3),X3),X3),X3) = X3,
inference(orient,[status(thm)],[t224]) ).
fof(f1,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f1_nnf,plain,
aNaturalNumber0(sz00),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(t0,plain,
aNaturalNumber0(sz00) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t333,plain,
aNaturalNumber0(sz00) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t347,plain,
X1 = ifeq(aNaturalNumber0(X2),true,ifeq(true,true,ifeq(aNaturalNumber0(X1),true,ifeq(sdtpldt0(sz00,X2),sdtpldt0(X1,X2),sz00,X1),X1),X1),X1),
inference(cp,[status(thm)],[t257,t333]) ).
cnf(t49219,plain,
X1 = ifeq(aNaturalNumber0(X2),true,ifeq(aNaturalNumber0(X1),true,ifeq(sdtpldt0(sz00,X2),sdtpldt0(X1,X2),sz00,X1),X1),X1),
inference(step,[status(thm)],[t347,t256]) ).
cnf(t45285,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(sdtpldt0(sz00,X1),sdtpldt0(X2,X1),sz00,X2),X2),X2) = X2,
inference(orient,[status(thm)],[t49219]) ).
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/sandbox/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]) ).
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/sandbox/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/sandbox/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(t78,plain,
sdtpldt0(xp,xr) = xn,
inference(hyper_resolution,[status(thm)],[hi27,hi67,hi65,hi71,hi72]) ).
cnf(t5215,plain,
sdtpldt0(xp,xr) = xn,
inference(orient,[status(thm)],[t78]) ).
fof(f43,conjecture,
( sdtlseqdt0(xr,xn)
& xr != xn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f43_neg,negated_conjecture,
~ ( sdtlseqdt0(xr,xn)
& xr != xn ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f43_nnf,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn ),
inference(nnf_transformation,[status(thm)],[f43_neg]) ).
fof(f43_sk,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c78,plain,
( ~ sdtlseqdt0(xr,xn)
| xr = xn ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t146,plain,
ifeq(sdtlseqdt0(xr,xn),true,xr,xn) = xn,
inference(equality_encoding,[status(esa)],[c78]) ).
cnf(t4294,plain,
ifeq(sdtlseqdt0(xr,xn),true,xr,xn) = xn,
inference(orient,[status(thm)],[t146]) ).
fof(f17,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
fof(f17_nnf,plain,
! [W0,W1] :
( ( ( ! [W2] :
( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2) )
| sdtlseqdt0(W0,W1) )
& ( ? [W2] :
( sdtpldt0(W0,W2) = W1
& aNaturalNumber0(W2) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [W0,W1,W2] :
( ( ( sdtpldt0(W0,W2) != W1
| ~ aNaturalNumber0(W2)
| sdtlseqdt0(W0,W1) )
& ( ( sdtpldt0(W0,sk0(W0,W1)) = W1
& aNaturalNumber0(sk0(W0,W1)) )
| ~ sdtlseqdt0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f17_nnf]) ).
cnf(c27,plain,
( sdtpldt0(X0,X2) != X1
| ~ aNaturalNumber0(X2)
| sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(t223,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(aNaturalNumber0(X3),true,ifeq(sdtpldt0(X1,X3),X2,sdtlseqdt0(X1,X2),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(t282,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(aNaturalNumber0(X3),true,ifeq(sdtpldt0(X1,X3),X2,sdtlseqdt0(X1,X2),true),true),true),true) = true,
inference(orient,[status(thm)],[t223]) ).
cnf(t283,plain,
true = ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(sdtpldt0(X1,X2)),true,ifeq(aNaturalNumber0(X2),true,sdtlseqdt0(X1,sdtpldt0(X1,X2)),true),true),true),
inference(cp,[status(thm)],[t282,t256]) ).
cnf(t16934,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(sdtpldt0(X1,X2)),true,ifeq(aNaturalNumber0(X2),true,sdtlseqdt0(X1,sdtpldt0(X1,X2)),true),true),true) = true,
inference(orient,[status(thm)],[t283]) ).
fof(f5,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f5_nnf,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [W0,W1] :
( sdtpldt0(W0,W1) = sdtpldt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t209,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,sdtpldt0(X1,X2),sdtpldt0(X2,X1)),sdtpldt0(X2,X1)) = sdtpldt0(X2,X1),
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t4273,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,sdtpldt0(X1,X2),sdtpldt0(X2,X1)),sdtpldt0(X2,X1)) = sdtpldt0(X2,X1),
inference(orient,[status(thm)],[t209]) ).
cnf(t5216,plain,
sdtpldt0(xr,xp) = ifeq(aNaturalNumber0(xp),true,ifeq(aNaturalNumber0(xr),true,xn,sdtpldt0(xr,xp)),sdtpldt0(xr,xp)),
inference(cp,[status(thm)],[t4273,t5215]) ).
cnf(t45999,plain,
sdtpldt0(xr,xp) = ifeq(true,true,ifeq(aNaturalNumber0(xr),true,xn,sdtpldt0(xr,xp)),sdtpldt0(xr,xp)),
inference(step,[status(thm)],[t5216,t1929]) ).
cnf(t46000,plain,
sdtpldt0(xr,xp) = ifeq(aNaturalNumber0(xr),true,xn,sdtpldt0(xr,xp)),
inference(step,[status(thm)],[t45999,t256]) ).
cnf(c28,plain,
( aNaturalNumber0(X2)
| X2 != sdtmndt0(X1,X0)
| ~ sdtlseqdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi26,axiom,
ifeq(aNaturalNumber0(X0),true,ifeq(aNaturalNumber0(X1),true,ifeq(sdtlseqdt0(X0,X1),true,ifeq(X2,sdtmndt0(X1,X0),aNaturalNumber0(X2),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t5,plain,
aNaturalNumber0(xr) = true,
inference(hyper_resolution,[status(thm)],[hi26,hi67,hi65,hi71,hi72]) ).
cnf(t2043,plain,
aNaturalNumber0(xr) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t46001,plain,
sdtpldt0(xr,xp) = ifeq(true,true,xn,sdtpldt0(xr,xp)),
inference(step,[status(thm)],[t46000,t2043]) ).
cnf(t46002,plain,
sdtpldt0(xr,xp) = xn,
inference(step,[status(thm)],[t46001,t256]) ).
cnf(t5600,plain,
sdtpldt0(xr,xp) = xn,
inference(orient,[status(thm)],[t46002]) ).
cnf(t16989,plain,
true = ifeq(aNaturalNumber0(xr),true,ifeq(aNaturalNumber0(xn),true,ifeq(aNaturalNumber0(xp),true,sdtlseqdt0(xr,sdtpldt0(xr,xp)),true),true),true),
inference(cp,[status(thm)],[t16934,t5600]) ).
cnf(t46935,plain,
true = ifeq(true,true,ifeq(aNaturalNumber0(xn),true,ifeq(aNaturalNumber0(xp),true,sdtlseqdt0(xr,sdtpldt0(xr,xp)),true),true),true),
inference(step,[status(thm)],[t16989,t2043]) ).
cnf(t46936,plain,
true = ifeq(aNaturalNumber0(xn),true,ifeq(aNaturalNumber0(xp),true,sdtlseqdt0(xr,sdtpldt0(xr,xp)),true),true),
inference(step,[status(thm)],[t46935,t256]) ).
cnf(t3,plain,
aNaturalNumber0(xn) = true,
inference(equality_encoding,[status(esa)],[c70]) ).
cnf(t1587,plain,
aNaturalNumber0(xn) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t46937,plain,
true = ifeq(true,true,ifeq(aNaturalNumber0(xp),true,sdtlseqdt0(xr,sdtpldt0(xr,xp)),true),true),
inference(step,[status(thm)],[t46936,t1587]) ).
cnf(t46938,plain,
true = ifeq(aNaturalNumber0(xp),true,sdtlseqdt0(xr,sdtpldt0(xr,xp)),true),
inference(step,[status(thm)],[t46937,t256]) ).
cnf(t46939,plain,
true = ifeq(true,true,sdtlseqdt0(xr,sdtpldt0(xr,xp)),true),
inference(step,[status(thm)],[t46938,t1929]) ).
cnf(t46940,plain,
true = sdtlseqdt0(xr,sdtpldt0(xr,xp)),
inference(step,[status(thm)],[t46939,t256]) ).
cnf(t46941,plain,
true = sdtlseqdt0(xr,xn),
inference(step,[status(thm)],[t46940,t5600]) ).
cnf(t17087,plain,
sdtlseqdt0(xr,xn) = true,
inference(orient,[status(thm)],[t46941]) ).
cnf(t46942,plain,
ifeq(true,true,xr,xn) = xn,
inference(step,[status(thm)],[t4294,t17087]) ).
cnf(t46943,plain,
xr = xn,
inference(step,[status(thm)],[t46942,t256]) ).
cnf(t17111,plain,
xr = xn,
inference(rw,[status(thm)],[t46943]) ).
cnf(t17112,plain,
xn = xr,
inference(orient,[status(thm)],[t17111]) ).
cnf(t46944,plain,
sdtpldt0(xp,xr) = xr,
inference(step,[status(thm)],[t5215,t17112]) ).
cnf(t17113,plain,
sdtpldt0(xp,xr) = xr,
inference(orient,[status(thm)],[t46944]) ).
cnf(t45485,plain,
xp = ifeq(aNaturalNumber0(xr),true,ifeq(aNaturalNumber0(xp),true,ifeq(sdtpldt0(sz00,xr),xr,sz00,xp),xp),xp),
inference(cp,[status(thm)],[t45285,t17113]) ).
cnf(t49220,plain,
xp = ifeq(true,true,ifeq(aNaturalNumber0(xp),true,ifeq(sdtpldt0(sz00,xr),xr,sz00,xp),xp),xp),
inference(step,[status(thm)],[t45485,t2043]) ).
cnf(t49221,plain,
xp = ifeq(aNaturalNumber0(xp),true,ifeq(sdtpldt0(sz00,xr),xr,sz00,xp),xp),
inference(step,[status(thm)],[t49220,t256]) ).
cnf(t49222,plain,
xp = ifeq(true,true,ifeq(sdtpldt0(sz00,xr),xr,sz00,xp),xp),
inference(step,[status(thm)],[t49221,t1929]) ).
cnf(t49223,plain,
xp = ifeq(sdtpldt0(sz00,xr),xr,sz00,xp),
inference(step,[status(thm)],[t49222,t256]) ).
cnf(h704,plain,
aNaturalNumber0(xr) = true,
inference(hyper_resolution,[status(thm)],[hi26,hi67,hi65,hi71,hi72]) ).
fof(f7,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f7_nnf,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [W0] :
( ( W0 = sdtpldt0(sz00,W0)
& sdtpldt0(W0,sz00) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c9,plain,
( X0 = sdtpldt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(aNaturalNumber0(X0),true,X0,sdtpldt0(sz00,X0)) = sdtpldt0(sz00,X0),
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t77,plain,
sdtpldt0(sz00,xr) = xr,
inference(hyper_resolution,[status(thm)],[hi7,h704]) ).
cnf(t5506,plain,
sdtpldt0(sz00,xr) = xr,
inference(orient,[status(thm)],[t77]) ).
cnf(t49224,plain,
xp = ifeq(xr,xr,sz00,xp),
inference(step,[status(thm)],[t49223,t5506]) ).
cnf(t49225,plain,
xp = sz00,
inference(step,[status(thm)],[t49224,t256]) ).
cnf(t45486,plain,
sz00 = xp,
inference(orient,[status(thm)],[t49225]) ).
cnf(t49251,plain,
ifeq(xp,xp,false,true) = true,
inference(step,[status(thm)],[t10896,t45486]) ).
cnf(t49252,plain,
false = true,
inference(step,[status(thm)],[t49251,t256]) ).
cnf(t45500,plain,
false = true,
inference(rw,[status(thm)],[t49252]) ).
cnf(t45941,plain,
false = true,
inference(orient,[status(thm)],[t45500]) ).
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]) ).
cnf(c61,plain,
( X0 != sz10
| ~ isPrime0(X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c60,c61]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t45941]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM487+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.59 % Computer : n006.cluster.edu
% 0.09/5.59 % Model : x86_64 x86_64
% 0.09/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.59 % Memory : 8046.5625MB
% 0.09/5.59 % OS : Linux 6.8.0-71-generic
% 0.09/5.59 % CPULimit : 300
% 0.09/5.59 % WCLimit : 300
% 0.09/5.59 % DateTime : Thu Sep 24 04:14:09 UTC 2026
% 0.09/5.60 % CPUTime :
% 0.09/5.60 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 116.14/20.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 116.14/20.75 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------