%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM427+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 : n019.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 24.01s 3.79s
% Output : Proof 24.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 17 unt; 1 def)
% Number of atoms : 92 ( 35 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 94 ( 38 ~; 24 |; 29 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 23 ( 0 sgn 13 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(f3_nnf,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [W0] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi2,axiom,
ifeq(aInteger0(X0),true,aInteger0(smndt0(X0)),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
fof(f22,hypothesis,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__747) ).
fof(f22_nnf,plain,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c39,plain,
aInteger0(xn),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(hi36,axiom,
aInteger0(xn) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h1633,plain,
aInteger0(smndt0(xn)) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi36]) ).
fof(f24,conjecture,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa))
& aInteger0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(f24_neg,negated_conjecture,
~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa))
& aInteger0(W0) ) ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f24_nnf,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(W0) ) ),
inference(nnf_transformation,[status(thm)],[f24_neg]) ).
fof(f24_sk,plain,
! [W0] :
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
& ( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(W0) ) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c42,plain,
( sdtasdt0(xq,X0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi41,negated_conjecture,
ifeq(aInteger0(X0),true,ifeq(sdtasdt0(xq,X0),sdtpldt0(xb,smndt0(xa)),false,true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
fof(f23,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__767) ).
fof(f23_nnf,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c41,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi38,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(equality_encoding,[status(esa)],[c41]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi41,h1633,hi38]) ).
cnf(t1641,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(f20,hypothesis,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__704) ).
fof(f20_nnf,plain,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
( xq != sz00
& aInteger0(xq)
& aInteger0(xb)
& aInteger0(xa) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c34,plain,
xq != sz00,
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(c43,plain,
~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(c44,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c24,c34,c42,c43,c44]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1641]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM427+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 03:56:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 24.01/3.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.01/3.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------