%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM484+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 : 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 02:20:09 PM UTC 2026
% Result : Theorem 16.07s 2.60s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 17 unt; 1 def)
% Number of atoms : 88 ( 40 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 109 ( 54 ~; 27 |; 25 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 14 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f40,hypothesis,
~ isPrime0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1725) ).
fof(f40_nnf,plain,
~ isPrime0(xk),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
~ isPrime0(xk),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c73,plain,
~ isPrime0(xk),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi72,axiom,
ifeq(isPrime0(xk),true,false,true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
fof(f41,hypothesis,
~ ~ isPrime0(xk),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1737) ).
fof(f41_nnf,plain,
isPrime0(xk),
inference(nnf_transformation,[status(thm)],[f41]) ).
cnf(c74,plain,
isPrime0(xk),
inference(cnf_transformation,[status(esa)],[f41_nnf]) ).
cnf(hi66,axiom,
isPrime0(xk) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi72,hi66]) ).
cnf(t2886,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(f39,hypothesis,
( xk != sz10
& xk != sz00 ),
file('/export/starexec/sandbox/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(c71,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(c72,plain,
xk != sz10,
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
fof(f42,conjecture,
? [W0] :
( isPrime0(W0)
& doDivides0(W0,xk)
& aNaturalNumber0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f42_neg,negated_conjecture,
~ ? [W0] :
( isPrime0(W0)
& doDivides0(W0,xk)
& aNaturalNumber0(W0) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f42_nnf,plain,
! [W0] :
( ~ isPrime0(W0)
| ~ doDivides0(W0,xk)
| ~ aNaturalNumber0(W0) ),
inference(nnf_transformation,[status(thm)],[f42_neg]) ).
fof(f42_sk,plain,
! [W0] :
( ~ isPrime0(W0)
| ~ doDivides0(W0,xk)
| ~ aNaturalNumber0(W0) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c75,plain,
( ~ isPrime0(X0)
| ~ doDivides0(X0,xk)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c60,c61,c71,c72,c73,c75]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t2886]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM484+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.36 % Computer : n013.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 04:12:22 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 16.07/2.60 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.07/2.60 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------