%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n018.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 14.38s 2.25s
% Output : Proof 14.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 19 unt; 1 def)
% Number of atoms : 173 ( 88 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 208 ( 75 ~; 57 |; 66 &)
% ( 1 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-4 aty)
% Number of variables : 39 ( 0 sgn 19 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f10,axiom,
! [W0] :
( aNaturalNumber0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f10_nnf,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c12,plain,
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(aNaturalNumber0(X0),true,sdtasdt0(X0,sz10),X0) = X0,
inference(equality_encoding,[status(esa)],[c12]) ).
fof(f37,hypothesis,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
fof(f37_nnf,plain,
aNaturalNumber0(xk),
inference(nnf_transformation,[status(thm)],[f37]) ).
cnf(c67,plain,
aNaturalNumber0(xk),
inference(cnf_transformation,[status(esa)],[f37_nnf]) ).
cnf(hi62,axiom,
aNaturalNumber0(xk) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(h120,plain,
sdtasdt0(xk,sz10) = xk,
inference(hyper_resolution,[status(thm)],[hi10,hi62]) ).
fof(f40,conjecture,
( ( isPrime0(xk)
& ! [W0] :
( ( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xk
| W0 = sz10 ) ) )
=> ? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f40_neg,negated_conjecture,
~ ( ( isPrime0(xk)
& ! [W0] :
( ( ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) )
=> ( W0 = xk
| W0 = sz10 ) ) )
=> ? [W0] :
( ( isPrime0(W0)
| ( ! [W1] :
( ( doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
=> ( W1 = W0
| W1 = sz10 ) )
& W0 != sz10
& W0 != sz00 ) )
& ( doDivides0(W0,xk)
| ? [W1] :
( xk = sdtasdt0(W0,W1)
& aNaturalNumber0(W1) ) )
& aNaturalNumber0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f40_nnf,plain,
( ! [W0] :
( ( ~ isPrime0(W0)
& ( ? [W1] :
( W1 != W0
& W1 != sz10
& doDivides0(W1,W0)
& ? [W2] :
( W0 = sdtasdt0(W1,W2)
& aNaturalNumber0(W2) )
& aNaturalNumber0(W1) )
| W0 = sz10
| W0 = sz00 ) )
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& isPrime0(xk)
& ! [W0] :
( W0 = xk
| W0 = sz10
| ( ~ doDivides0(W0,xk)
& ! [W1] :
( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f40_neg]) ).
fof(f40_sk,plain,
! [W0,W1] :
( ( ( ~ isPrime0(W0)
& ( ( sk5(W0) != W0
& sk5(W0) != sz10
& doDivides0(sk5(W0),W0)
& W0 = sdtasdt0(sk5(W0),sk6(W0))
& aNaturalNumber0(sk6(W0))
& aNaturalNumber0(sk5(W0)) )
| W0 = sz10
| W0 = sz00 ) )
| ( ~ doDivides0(W0,xk)
& ( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) )
& isPrime0(xk)
& ( W0 = xk
| W0 = sz10
| ( ~ doDivides0(W0,xk)
& ( xk != sdtasdt0(W0,W1)
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(W0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5,sk6])],[f40_nnf]) ).
cnf(c88,plain,
( ~ isPrime0(X0)
| xk != sdtasdt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi92,negated_conjecture,
ifeq(aNaturalNumber0(X0),true,ifeq(aNaturalNumber0(X1),true,ifeq(xk,sdtasdt0(X0,X1),ifeq(isPrime0(X0),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c88]) ).
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(c2,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
aNaturalNumber0(sz10) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(c81,plain,
isPrime0(xk),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi74,negated_conjecture,
isPrime0(xk) = true,
inference(equality_encoding,[status(esa)],[c81]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi92,hi62,hi1,h120,hi74]) ).
cnf(t4691,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
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(f39,hypothesis,
( xk != sz10
& xk != sz00 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716_04) ).
fof(f39_nnf,plain,
( xk != sz10
& xk != sz00 ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
( xk != sz10
& xk != sz00 ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c77,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(c78,plain,
xk != sz10,
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(c95,plain,
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c60,c61,c77,c78,c88,c95]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4691]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM482+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 04:15:03 UTC 2026
% 0.13/0.36 % CPUTime :
% 0.13/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.38/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.38/2.25 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------