%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM491+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 : n001.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 70.55s 14.57s
% Output : Proof 70.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 9
% Syntax : Number of formulae : 71 ( 45 unt; 2 def)
% Number of atoms : 160 ( 75 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 153 ( 64 ~; 47 |; 35 &)
% ( 2 <=>; 5 =>; 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 : 60 ( 2 sgn 26 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f29,definition,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> ( doDivides0(W0,W1)
<=> ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
fof(f29_nnf,plain,
! [W0,W1] :
( ( ( ! [W2] :
( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2) )
| doDivides0(W0,W1) )
& ( ? [W2] :
( W1 = sdtasdt0(W0,W2)
& aNaturalNumber0(W2) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [W0,W1,W2] :
( ( ( W1 != sdtasdt0(W0,W2)
| ~ aNaturalNumber0(W2)
| doDivides0(W0,W1) )
& ( ( W1 = sdtasdt0(W0,sk1(W0,W1))
& aNaturalNumber0(sk1(W0,W1)) )
| ~ doDivides0(W0,W1) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1])],[f29_nnf]) ).
cnf(c51,plain,
( X1 != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| doDivides0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(t224,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(aNaturalNumber0(X3),true,ifeq(X2,sdtasdt0(X1,X3),doDivides0(X1,X2),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(t276,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,ifeq(aNaturalNumber0(X3),true,ifeq(X2,sdtasdt0(X1,X3),doDivides0(X1,X2),true),true),true),true) = true,
inference(orient,[status(thm)],[t224]) ).
cnf(t87,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t87]) ).
cnf(t277,plain,
true = ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(sdtasdt0(X1,X2)),true,ifeq(aNaturalNumber0(X2),true,doDivides0(X1,sdtasdt0(X1,X2)),true),true),true),
inference(cp,[status(thm)],[t276,t256]) ).
cnf(t14715,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(sdtasdt0(X1,X2)),true,ifeq(aNaturalNumber0(X2),true,doDivides0(X1,sdtasdt0(X1,X2)),true),true),true) = true,
inference(orient,[status(thm)],[t277]) ).
fof(f4,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f4_nnf,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [W0,W1] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t197,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,aNaturalNumber0(sdtasdt0(X1,X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t311,plain,
ifeq(aNaturalNumber0(X1),true,ifeq(aNaturalNumber0(X2),true,aNaturalNumber0(sdtasdt0(X1,X2)),true),true) = true,
inference(orient,[status(thm)],[t197]) ).
fof(f8,axiom,
! [W0,W1] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W0) )
=> sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulComm) ).
fof(f8_nnf,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [W0,W1] :
( sdtasdt0(W0,W1) = sdtasdt0(W1,W0)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c10,plain,
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(aNaturalNumber0(X0),true,ifeq(aNaturalNumber0(X1),true,sdtasdt0(X0,X1),sdtasdt0(X1,X0)),sdtasdt0(X1,X0)) = sdtasdt0(X1,X0),
inference(equality_encoding,[status(esa)],[c10]) ).
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(c71,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi66,axiom,
aNaturalNumber0(xm) = true,
inference(equality_encoding,[status(esa)],[c71]) ).
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(t109,plain,
sdtasdt0(xp,xm) = sdtasdt0(xm,xp),
inference(hyper_resolution,[status(thm)],[hi8,hi66,hi67]) ).
cnf(t4942,plain,
sdtasdt0(xm,xp) = sdtasdt0(xp,xm),
inference(orient,[status(thm)],[t109]) ).
cnf(t4943,plain,
true = ifeq(aNaturalNumber0(xm),true,ifeq(aNaturalNumber0(xp),true,aNaturalNumber0(sdtasdt0(xp,xm)),true),true),
inference(cp,[status(thm)],[t311,t4942]) ).
cnf(t2,plain,
aNaturalNumber0(xm) = true,
inference(equality_encoding,[status(esa)],[c71]) ).
cnf(t1817,plain,
aNaturalNumber0(xm) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t15096,plain,
true = ifeq(true,true,ifeq(aNaturalNumber0(xp),true,aNaturalNumber0(sdtasdt0(xp,xm)),true),true),
inference(step,[status(thm)],[t4943,t1817]) ).
cnf(t15097,plain,
true = ifeq(aNaturalNumber0(xp),true,aNaturalNumber0(sdtasdt0(xp,xm)),true),
inference(step,[status(thm)],[t15096,t256]) ).
cnf(t4,plain,
aNaturalNumber0(xp) = true,
inference(equality_encoding,[status(esa)],[c72]) ).
cnf(t1931,plain,
aNaturalNumber0(xp) = true,
inference(orient,[status(thm)],[t4]) ).
cnf(t15098,plain,
true = ifeq(true,true,aNaturalNumber0(sdtasdt0(xp,xm)),true),
inference(step,[status(thm)],[t15097,t1931]) ).
cnf(t15099,plain,
true = aNaturalNumber0(sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t15098,t256]) ).
cnf(t9311,plain,
aNaturalNumber0(sdtasdt0(xp,xm)) = true,
inference(orient,[status(thm)],[t15099]) ).
cnf(t14743,plain,
true = ifeq(aNaturalNumber0(xp),true,ifeq(true,true,ifeq(aNaturalNumber0(xm),true,doDivides0(xp,sdtasdt0(xp,xm)),true),true),true),
inference(cp,[status(thm)],[t14715,t9311]) ).
cnf(t15496,plain,
true = ifeq(true,true,ifeq(true,true,ifeq(aNaturalNumber0(xm),true,doDivides0(xp,sdtasdt0(xp,xm)),true),true),true),
inference(step,[status(thm)],[t14743,t1931]) ).
cnf(t15497,plain,
true = ifeq(true,true,ifeq(aNaturalNumber0(xm),true,doDivides0(xp,sdtasdt0(xp,xm)),true),true),
inference(step,[status(thm)],[t15496,t256]) ).
cnf(t15498,plain,
true = ifeq(aNaturalNumber0(xm),true,doDivides0(xp,sdtasdt0(xp,xm)),true),
inference(step,[status(thm)],[t15497,t256]) ).
cnf(t15499,plain,
true = ifeq(true,true,doDivides0(xp,sdtasdt0(xp,xm)),true),
inference(step,[status(thm)],[t15498,t1817]) ).
cnf(t15500,plain,
true = doDivides0(xp,sdtasdt0(xp,xm)),
inference(step,[status(thm)],[t15499,t256]) ).
fof(f47,conjecture,
doDivides0(xp,sdtasdt0(xp,xm)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f47_neg,negated_conjecture,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f47_nnf,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(nnf_transformation,[status(thm)],[f47_neg]) ).
fof(f47_sk,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(skolemisation,[status(esa)],[f47_nnf]) ).
cnf(c83,plain,
~ doDivides0(xp,sdtasdt0(xp,xm)),
inference(cnf_transformation,[status(esa)],[f47_sk]) ).
cnf(t86,plain,
doDivides0(xp,sdtasdt0(xp,xm)) = false,
inference(equality_encoding,[status(esa)],[c83]) ).
cnf(t5657,plain,
doDivides0(xp,sdtasdt0(xp,xm)) = false,
inference(orient,[status(thm)],[t86]) ).
cnf(t15501,plain,
true = false,
inference(step,[status(thm)],[t15500,t5657]) ).
cnf(t14898,plain,
false = true,
inference(orient,[status(thm)],[t15501]) ).
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,c83]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t14898]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM491+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/5.35 % Computer : n001.cluster.edu
% 0.08/5.35 % Model : x86_64 x86_64
% 0.08/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.35 % Memory : 8046.5625MB
% 0.08/5.35 % OS : Linux 6.8.0-71-generic
% 0.08/5.35 % CPULimit : 300
% 0.08/5.35 % WCLimit : 300
% 0.08/5.35 % DateTime : Thu Sep 24 04:21:12 UTC 2026
% 0.08/5.35 % CPUTime :
% 0.08/5.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 70.55/14.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.55/14.57 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------