%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 02:20:20 PM UTC 2026
% Result : Theorem 11.27s 2.06s
% Output : Proof 11.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 12 unt; 1 def)
% Number of atoms : 97 ( 28 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 90 ( 33 ~; 27 |; 25 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 19 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,definition,
! [W0] :
( W0 = slcrc0
<=> ( ~ ? [W1] : aElementOf0(W1,W0)
& aSet0(W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefEmp) ).
fof(f4_nnf,plain,
! [W0] :
( ( ? [W1] : aElementOf0(W1,W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ! [W1] : ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [W0,W1] :
( ( aElementOf0(sk0(W0),W0)
| ~ aSet0(W0)
| W0 = slcrc0 )
& ( ( ~ aElementOf0(W1,W0)
& aSet0(W0) )
| W0 != slcrc0 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0])],[f4_nnf]) ).
cnf(c6,plain,
( aElementOf0(sk0(X0),X0)
| ~ aSet0(X0)
| X0 = slcrc0 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
fof(f64,hypothesis,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSet0(xQ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2270) ).
fof(f64_nnf,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ! [W0] :
( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [W0] :
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
& sbrdtbr0(xQ) = xk
& aSubsetOf0(xQ,xS)
& ( aElementOf0(W0,xS)
| ~ aElementOf0(W0,xQ) )
& aSet0(xQ) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c157,plain,
aSet0(xQ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(p439,plain,
( aElementOf0(sk0(xQ),xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[c6,c157]) ).
fof(f2,axiom,
! [W0] :
( aSet0(W0)
=> ! [W1] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
fof(f2_nnf,plain,
! [W0] :
( ! [W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) )
| ~ aSet0(W0) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [W0,W1] :
( aElement0(W1)
| ~ aElementOf0(W1,W0)
| ~ aSet0(W0) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( aElement0(X1)
| ~ aElementOf0(X1,X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p311,plain,
( aElement0(X0)
| ~ aElementOf0(X0,xQ) ),
inference(resolution,[status(thm)],[c2,c157]) ).
cnf(p460,plain,
( aElement0(sk0(xQ))
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[p439,p311]) ).
fof(f66,conjecture,
? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f66_neg,negated_conjecture,
~ ? [W0] :
( aElementOf0(W0,xQ)
& aElement0(W0) ),
inference(negated_conjecture,[status(cth)],[f66]) ).
fof(f66_nnf,plain,
! [W0] :
( ~ aElementOf0(W0,xQ)
| ~ aElement0(W0) ),
inference(nnf_transformation,[status(thm)],[f66_neg]) ).
fof(f66_sk,plain,
! [W0] :
( ~ aElementOf0(W0,xQ)
| ~ aElement0(W0) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c165,plain,
( ~ aElementOf0(X0,xQ)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(p461,plain,
( ~ aElementOf0(sk0(xQ),xQ)
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[p460,c165]) ).
cnf(p462,plain,
( xQ = slcrc0
| xQ = slcrc0 ),
inference(resolution,[status(thm)],[p461,p439]) ).
cnf(p463,plain,
xQ = slcrc0,
inference(factoring,[status(thm)],[p462]) ).
cnf(c160,plain,
sbrdtbr0(xQ) = xk,
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(p465,plain,
sbrdtbr0(slcrc0) = xk,
inference(demodulation,[status(thm)],[p463,c160]) ).
fof(f55,axiom,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> sbrdtbr0(slbdtrb0(W0)) = W0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardSeg) ).
fof(f55_nnf,plain,
! [W0] :
( sbrdtbr0(slbdtrb0(W0)) = W0
| ~ aElementOf0(W0,szNzAzT0) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [W0] :
( sbrdtbr0(slbdtrb0(W0)) = W0
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c111,plain,
( sbrdtbr0(slbdtrb0(X0)) = X0
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
fof(f23,axiom,
aElementOf0(sz00,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroNum) ).
fof(f23_nnf,plain,
aElementOf0(sz00,szNzAzT0),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c54,plain,
aElementOf0(sz00,szNzAzT0),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(p361,plain,
sbrdtbr0(slcrc0) = sz00,
inference(resolution,[status(thm)],[c111,c54]) ).
cnf(p468,plain,
xk = sz00,
inference(superposition,[status(thm)],[p465,p361]) ).
fof(f61,hypothesis,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2202_02) ).
fof(f61_nnf,plain,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(nnf_transformation,[status(thm)],[f61]) ).
fof(f61_sk,plain,
( xk != sz00
& aSet0(xT)
& aSet0(xS) ),
inference(skolemisation,[status(esa)],[f61_nnf]) ).
cnf(c128,plain,
xk != sz00,
inference(cnf_transformation,[status(esa)],[f61_sk]) ).
cnf(p469,plain,
sz00 != sz00,
inference(demodulation,[status(thm)],[p468,c128]) ).
cnf(p513,plain,
$false,
inference(equality_resolution,[status(thm)],[p469]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM549+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 04:34:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 11.27/2.06 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.27/2.06 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------