%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM429+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 : n003.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 02:20:00 PM UTC 2026
% Result : Theorem 14.26s 2.25s
% Output : Proof 14.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 11 unt; 1 def)
% Number of atoms : 91 ( 34 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 94 ( 29 ~; 17 |; 46 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-4 aty)
% Number of variables : 22 ( 0 sgn 10 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f23,conjecture,
? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f23_neg,negated_conjecture,
~ ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f23_nnf,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f23_neg]) ).
fof(f23_sk,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c45,plain,
( sdtasdt0(xq,X0) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(hi44,negated_conjecture,
ifeq(aInteger0(X0),true,ifeq(sdtasdt0(xq,X0),sdtpldt0(xa,smndt0(xb)),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
fof(f22,hypothesis,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(W0) )
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__853) ).
fof(f22_nnf,plain,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(W0) )
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( sdteqdtlpzmzozddtrp0(xb,xc,xq)
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdtasdt0(xq,sk2) = sdtpldt0(xb,smndt0(xc))
& aInteger0(sk2)
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdtasdt0(xq,sk1) = sdtpldt0(xa,smndt0(xb))
& aInteger0(sk1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk1,sk2])],[f22_nnf]) ).
cnf(c37,plain,
aInteger0(sk1),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi34,axiom,
aInteger0(sk1) = true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(c38,plain,
sdtasdt0(xq,sk1) = sdtpldt0(xa,smndt0(xb)),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi35,axiom,
sdtasdt0(xq,sk1) = sdtpldt0(xa,smndt0(xb)),
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi44,hi34,hi35]) ).
cnf(t1987,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
fof(f17,definition,
! [W0] :
( aInteger0(W0)
=> ! [W1] :
( aDivisorOf0(W1,W0)
<=> ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(f17_nnf,plain,
! [W0] :
( ! [W1] :
( ( ! [W2] :
( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2) )
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( ? [W2] :
( sdtasdt0(W1,W2) = W0
& aInteger0(W2) )
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [W0,W1,W2] :
( ( ( sdtasdt0(W1,W2) != W0
| ~ aInteger0(W2)
| W1 = sz00
| ~ aInteger0(W1)
| aDivisorOf0(W1,W0) )
& ( ( sdtasdt0(W1,sk0(W0,W1)) = W0
& aInteger0(sk0(W0,W1))
& W1 != sz00
& aInteger0(W1) )
| ~ aDivisorOf0(W1,W0) ) )
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f17_nnf]) ).
cnf(c24,plain,
( X1 != sz00
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
fof(f21,hypothesis,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__818) ).
fof(f21_nnf,plain,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
( aInteger0(xc)
& xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c35,plain,
xq != sz00,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c24,c35,c45]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1987]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM429+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n003.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 03:58:05 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.26/2.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.26/2.25 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------