%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM595+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 : Thu Sep 24 01:41:07 PM UTC 2026
% Result : Theorem 13.97s 2.21s
% Output : CNFRefutation 13.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 182 ( 49 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 220 ( 79 ~; 69 |; 62 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-2 aty)
% Number of variables : 46 ( 37 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f90,hypothesis,
! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ? [W1] :
( ! [W2] :
( ( ( aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( sbrdtbr0(W2) = xk
& ( aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W3] :
( aElementOf0(W3,W2)
=> aElementOf0(W3,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) )
& aSet0(W2) )
=> sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = W1 )
& aElementOf0(W1,xT) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f92,hypothesis,
( ! [W0] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1] :
( ( ( aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
| ( sbrdtbr0(W1) = xk
& ( aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
| ! [W2] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0))) ) ) ) )
& aSet0(W1) )
=> sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f95,hypothesis,
( sdtlpdtrp0(xd,xi) = xx
& aElementOf0(xi,szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,hypothesis,
( ~ ~ ? [W0] : aElementOf0(W0,xX)
& xX = slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xk)
& ! [W0] :
( ( ( sbrdtbr0(W0) = xk
& ( aSubsetOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
| ( ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xi))) )
& aSet0(W0) ) ) )
=> aElementOf0(W0,xX) )
& ( aElementOf0(W0,xX)
=> ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& ! [W1] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xi))) )
& aSet0(W0) ) ) )
& aSet0(xX) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,conjecture,
aElementOf0(xx,xT),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,negated_conjecture,
~ aElementOf0(xx,xT),
inference(negated_conjecture,[status(cth)],[f97]) ).
fof(f523,plain,
! [W0] :
( ? [W1] :
( ! [W2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = W1
| ( ~ aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W2) != xk
| ( ~ aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ? [W3] :
( ~ aElementOf0(W3,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(W3,W2) ) ) ) )
| ~ aSet0(W2) )
& aElementOf0(W1,xT) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(pre_NNF_transformation,[status(thm)],[f90]) ).
fof(f524,plain,
! [W0] :
( ( ! [W2] :
( sdtlpdtrp0(sdtlpdtrp0(xC,W0),W2) = sK30_skl(W0)
| ( ~ aElementOf0(W2,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W2) != xk
| ( ~ aSubsetOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ aElementOf0(sK31_skl(W2,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(sK31_skl(W2,W0),W2) ) ) )
| ~ aSet0(W2) )
& aElementOf0(sK30_skl(W0),xT) )
| ~ aElementOf0(W0,szNzAzT0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(W1,sK30_skl(W0)),skolemize(W3,sK31_skl(W2,W0))],[f523]) ).
fof(f525,plain,
! [X0] :
( aElementOf0(sK30_skl(X0),xT)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f524]) ).
fof(f528,plain,
! [X0,X1] :
( sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1) = sK30_skl(X0)
| sbrdtbr0(X1) != xk
| ~ aSubsetOf0(X1,sdtlpdtrp0(xN,szszuzczcdt0(X0)))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f524]) ).
fof(f536,plain,
( ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ? [W2] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(W2,W1) ) ) ) )
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(pre_NNF_transformation,[status(thm)],[f92]) ).
fof(f537,plain,
( ! [W0] :
( ! [W1] :
( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1)
| ( ~ aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk))
& ( sbrdtbr0(W1) != xk
| ( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& ~ aElementOf0(sK32_skl(W1,W0),sdtlpdtrp0(xN,szszuzczcdt0(W0)))
& aElementOf0(sK32_skl(W1,W0),W1) ) ) )
| ~ aSet0(W1) )
| ~ aElementOf0(W0,szNzAzT0) )
& szDzozmdt0(xd) = szNzAzT0
& aFunction0(xd) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl]),skolemize(W2,sK32_skl(W1,W0))],[f536]) ).
fof(f543,plain,
! [X0,X1] :
( sdtlpdtrp0(xd,X0) = sdtlpdtrp0(sdtlpdtrp0(xC,X0),X1)
| ~ aElementOf0(X1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(X0)),xk))
| ~ aSet0(X1)
| ~ aElementOf0(X0,szNzAzT0) ),
inference(cnf_transformation,[status(thm)],[f537]) ).
fof(f555,plain,
aElementOf0(xi,szNzAzT0),
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f556,plain,
sdtlpdtrp0(xd,xi) = xx,
inference(cnf_transformation,[status(thm)],[f95]) ).
fof(f557,plain,
( ? [W0] : aElementOf0(W0,xX)
& xX = slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xk)
& ! [W0] :
( ( aElementOf0(W0,xX)
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& ( ? [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,xX) ) )
& aSet0(xX) ),
inference(pre_NNF_transformation,[status(thm)],[f96]) ).
fof(f558,plain,
( ? [W0] : aElementOf0(W0,xX)
& xX = slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xk)
& ! [W0] :
( aElementOf0(W0,xX)
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& ( ? [W1] :
( ~ aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& aElementOf0(W1,W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,xX) )
& aSet0(xX) ),
inference(miniscoping,[status(thm)],[f557]) ).
fof(f559,plain,
( aElementOf0(sK36_skl,xX)
& xX = slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xk)
& ! [W0] :
( aElementOf0(W0,xX)
| sbrdtbr0(W0) != xk
| ( ~ aSubsetOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& ( ( ~ aElementOf0(sK35_skl(W0),sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& aElementOf0(sK35_skl(W0),W0) )
| ~ aSet0(W0) ) ) )
& ! [W0] :
( ( sbrdtbr0(W0) = xk
& aSubsetOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
& ! [W1] :
( aElementOf0(W1,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
| ~ aElementOf0(W1,W0) )
& aSet0(W0) )
| ~ aElementOf0(W0,xX) )
& aSet0(xX) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl]),skolemize(W1,sK35_skl(W0)),skolemize(W0,sK36_skl)],[f558]) ).
fof(f561,plain,
! [X0] :
( aSet0(X0)
| ~ aElementOf0(X0,xX) ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f563,plain,
! [X0] :
( aSubsetOf0(X0,sdtlpdtrp0(xN,szszuzczcdt0(xi)))
| ~ aElementOf0(X0,xX) ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f564,plain,
! [X0] :
( sbrdtbr0(X0) = xk
| ~ aElementOf0(X0,xX) ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f568,plain,
xX = slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(xi)),xk),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f569,plain,
aElementOf0(sK36_skl,xX),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f570,plain,
~ aElementOf0(xx,xT),
inference(cnf_transformation,[status(thm)],[f98]) ).
fof(f897,plain,
aSet0(sK36_skl),
inference(resolution,[status(thm)],[f561,f569]) ).
fof(f1214,plain,
sbrdtbr0(sK36_skl) = xk,
inference(resolution,[status(thm)],[f564,f569]) ).
fof(f8664,plain,
! [X0] :
( sdtlpdtrp0(xd,xi) = sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0)
| ~ aElementOf0(X0,xX)
| ~ aSet0(X0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f568,f543]) ).
fof(f8676,plain,
! [X0] :
( xx = sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0)
| ~ aElementOf0(X0,xX)
| ~ aSet0(X0)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f556,f8664]) ).
fof(f8677,plain,
! [X0] :
( xx = sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0)
| ~ aElementOf0(X0,xX)
| ~ aSet0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8676,f555]) ).
fof(f8825,plain,
! [X0] :
( xx = sdtlpdtrp0(sdtlpdtrp0(xC,xi),X0)
| ~ aElementOf0(X0,xX) ),
inference(forward_subsumption_resolution,[status(thm)],[f8677,f561]) ).
fof(f8826,plain,
xx = sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK36_skl),
inference(resolution,[status(thm)],[f8825,f569]) ).
fof(f9160,plain,
aSubsetOf0(sK36_skl,sdtlpdtrp0(xN,szszuzczcdt0(xi))),
inference(resolution,[status(thm)],[f563,f569]) ).
fof(f9448,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK36_skl) = sK30_skl(xi)
| sbrdtbr0(sK36_skl) != xk
| ~ aSet0(sK36_skl)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(resolution,[status(thm)],[f9160,f528]) ).
fof(f9457,plain,
( sdtlpdtrp0(sdtlpdtrp0(xC,xi),sK36_skl) = sK30_skl(xi)
| xk != xk
| ~ aSet0(sK36_skl)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f1214,f9448]) ).
fof(f9458,plain,
( xx = sK30_skl(xi)
| xk != xk
| ~ aSet0(sK36_skl)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(forward_demodulation,[status(thm)],[f8826,f9457]) ).
fof(f9459,plain,
( xx = sK30_skl(xi)
| ~ aSet0(sK36_skl)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(trivial_equality_resolution,[status(thm)],[f9458]) ).
fof(f9460,plain,
( xx = sK30_skl(xi)
| ~ aSet0(sK36_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f9459,f555]) ).
fof(f9478,plain,
xx = sK30_skl(xi),
inference(forward_subsumption_resolution,[status(thm)],[f9460,f897]) ).
fof(f9479,plain,
( aElementOf0(xx,xT)
| ~ aElementOf0(xi,szNzAzT0) ),
inference(paramodulation,[status(thm)],[f9478,f525]) ).
fof(f9484,plain,
aElementOf0(xx,xT),
inference(forward_subsumption_resolution,[status(thm)],[f9479,f555]) ).
fof(f9485,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f9484,f570]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM595+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.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 : Mon Sep 21 02:47:54 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 13.97/2.21 % Refutation found
% 13.97/2.21 % SZS status Theorem for theBenchmark: Theorem is valid
% 13.97/2.21 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 13.66/2.24 % Elapsed time: 1.863745 seconds
% 13.66/2.24 % CPU time: 14.320998 seconds
% 13.66/2.24 % Total memory used: 242.771 MB
% 13.66/2.24 % Net memory used: 232.515 MB
%------------------------------------------------------------------------------