%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG105+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n014.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 02:04:59 PM UTC 2026
% Result : Theorem 0.23s 0.54s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 59 ( 14 unt; 1 def)
% Number of atoms : 191 ( 48 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 227 ( 95 ~; 87 |; 36 &)
% ( 4 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 75 ( 67 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [W0,W1] :
( ( aElement0(W1)
& aElement0(W0) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [W0,W1,W2] :
( ( aElement0(W2)
& aElement0(W1)
& aElement0(W0) )
=> ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,definition,
! [W0] :
( aElement0(W0)
=> ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
aElement0(xc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xz)
& aElementOf0(xy,slsdtgt0(xc))
& aElementOf0(xx,slsdtgt0(xc)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
( sdtasdt0(xc,xu) = xx
& aElement0(xu) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
( sdtasdt0(xc,xv) = xy
& aElement0(xv) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,conjecture,
( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
& aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ ( aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
& aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(negated_conjecture,[status(cth)],[f44]) ).
fof(f53,plain,
! [W0,W1] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f54,plain,
! [X0,X1] :
( aElement0(sdtpldt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f55,plain,
! [W0,W1] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f56,plain,
! [X0,X1] :
( aElement0(sdtasdt0(X0,X1))
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f69,plain,
! [W0,W1,W2] :
( sdtasdt0(sdtasdt0(W0,W1),W2) = sdtasdt0(W0,sdtasdt0(W1,W2))
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f70,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f74,plain,
! [W0,W1,W2] :
( ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0))
& sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ~ aElement0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f75,plain,
! [X0,X1,X2] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aElement0(X2)
| ~ aElement0(X1)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f185,plain,
! [W0] :
( ! [W1] :
( W1 = slsdtgt0(W0)
<=> ( ! [W2] :
( aElementOf0(W2,W1)
<=> ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) ) )
& aSet0(W1) ) )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f186,plain,
! [W0] :
( ! [W1] :
( ( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ( ( ! [W2] :
( ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(NNF_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [W0] :
( ( ! [W1] :
( ? [W2] :
( ( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| aElementOf0(W2,W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| ~ aElementOf0(W2,W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ? [W3] :
( sdtasdt0(W0,W3) = W2
& aElement0(W3) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(miniscoping,[status(thm)],[f186]) ).
fof(f188,plain,
! [W0] :
( ( ! [W1] :
( ( ( ( sdtasdt0(W0,sK19_skl(W1,W0)) = sK18_skl(W1,W0)
& aElement0(sK19_skl(W1,W0)) )
| aElementOf0(sK18_skl(W1,W0),W1) )
& ( ! [W3] :
( sdtasdt0(W0,W3) != sK18_skl(W1,W0)
| ~ aElement0(W3) )
| ~ aElementOf0(sK18_skl(W1,W0),W1) ) )
| ~ aSet0(W1)
| W1 = slsdtgt0(W0) )
& ! [W1] :
( ( ! [W2] :
( ! [W3] :
( sdtasdt0(W0,W3) != W2
| ~ aElement0(W3) )
| aElementOf0(W2,W1) )
& ! [W2] :
( ( sdtasdt0(W0,sK17_skl(W2,W1,W0)) = W2
& aElement0(sK17_skl(W2,W1,W0)) )
| ~ aElementOf0(W2,W1) )
& aSet0(W1) )
| W1 != slsdtgt0(W0) ) )
| ~ aElement0(W0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17_skl,sK18_skl,sK19_skl]),skolemize(W3,sK17_skl(W2,W1,W0)),skolemize(W2,sK18_skl(W1,W0)),skolemize(W3,sK19_skl(W1,W0))],[f187]) ).
fof(f192,plain,
! [X0,X1,X2,X3] :
( sdtasdt0(X0,X3) != X2
| ~ aElement0(X3)
| aElementOf0(X2,X1)
| X1 != slsdtgt0(X0)
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f196,plain,
aElement0(xc),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f199,plain,
aElement0(xz),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f200,plain,
aElement0(xu),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f201,plain,
sdtasdt0(xc,xu) = xx,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f202,plain,
aElement0(xv),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f203,plain,
sdtasdt0(xc,xv) = xy,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f205,plain,
sdtasdt0(xz,xx) = sdtasdt0(xc,sdtasdt0(xu,xz)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f206,plain,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f207,plain,
( ~ aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(cnf_transformation,[status(thm)],[f206]) ).
fof(f236,plain,
! [X0,X1] :
( ~ aElement0(X1)
| aElementOf0(sdtasdt0(X0,X1),slsdtgt0(X0))
| ~ aElement0(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f192]) ).
fof(f238,plain,
! [X0] :
( sdtasdt0(xx,X0) = sdtasdt0(xc,sdtasdt0(xu,X0))
| ~ aElement0(X0)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f201,f70]) ).
fof(f240,plain,
! [X0] :
( sdtasdt0(xx,X0) = sdtasdt0(xc,sdtasdt0(xu,X0))
| ~ aElement0(X0)
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f196]) ).
fof(f251,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(xu,X0)) = sdtpldt0(xx,sdtasdt0(xc,X0))
| ~ aElement0(X0)
| ~ aElement0(xu)
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f201,f75]) ).
fof(f255,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(xu,X0)) = sdtpldt0(xx,sdtasdt0(xc,X0))
| ~ aElement0(X0)
| ~ aElement0(xu) ),
inference(forward_subsumption_resolution,[status(thm)],[f251,f196]) ).
fof(f260,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f205,f236]) ).
fof(f265,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| aElementOf0(sdtasdt0(xz,xx),slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[status(thm)],[f260,f196]) ).
fof(f271,plain,
! [X0] :
( sdtasdt0(xx,X0) = sdtasdt0(xc,sdtasdt0(xu,X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f200]) ).
fof(f272,plain,
( sdtasdt0(xx,xz) = sdtasdt0(xz,xx)
| ~ aElement0(xz) ),
inference(paramodulation,[status(thm)],[f205,f271]) ).
fof(f273,plain,
sdtasdt0(xx,xz) = sdtasdt0(xz,xx),
inference(forward_subsumption_resolution,[status(thm)],[f272,f199]) ).
fof(f274,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc)) ),
inference(backward_demodulation,[status(thm)],[f273,f265]) ).
fof(f277,plain,
( ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| ~ aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(backward_demodulation,[status(thm)],[f273,f207]) ).
fof(f362,plain,
! [X0] :
( sdtasdt0(xc,sdtpldt0(xu,X0)) = sdtpldt0(xx,sdtasdt0(xc,X0))
| ~ aElement0(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f255,f200]) ).
fof(f366,plain,
( sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy)
| ~ aElement0(xv) ),
inference(paramodulation,[status(thm)],[f203,f362]) ).
fof(f368,plain,
sdtasdt0(xc,sdtpldt0(xu,xv)) = sdtpldt0(xx,xy),
inference(forward_subsumption_resolution,[status(thm)],[f366,f202]) ).
fof(f409,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc))
| ~ aElement0(xc) ),
inference(paramodulation,[status(thm)],[f368,f236]) ).
fof(f417,plain,
( ~ aElement0(sdtpldt0(xu,xv))
| aElementOf0(sdtpldt0(xx,xy),slsdtgt0(xc)) ),
inference(forward_subsumption_resolution,[status(thm)],[f409,f196]) ).
fof(f491,plain,
( ~ aElementOf0(sdtasdt0(xx,xz),slsdtgt0(xc))
| ~ aElement0(sdtpldt0(xu,xv)) ),
inference(resolution,[status(thm)],[f417,f277]) ).
fof(f494,plain,
( ~ aElement0(sdtasdt0(xu,xz))
| ~ aElement0(sdtpldt0(xu,xv)) ),
inference(resolution,[status(thm)],[f491,f274]) ).
fof(f495,plain,
( ~ aElement0(xv)
| ~ aElement0(xu)
| ~ aElement0(sdtasdt0(xu,xz)) ),
inference(resolution,[status(thm)],[f494,f54]) ).
fof(f496,plain,
( ~ aElement0(xv)
| ~ aElement0(sdtasdt0(xu,xz)) ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f200]) ).
fof(f503,plain,
~ aElement0(sdtasdt0(xu,xz)),
inference(forward_subsumption_resolution,[status(thm)],[f496,f202]) ).
fof(f504,plain,
( ~ aElement0(xz)
| ~ aElement0(xu) ),
inference(resolution,[status(thm)],[f503,f56]) ).
fof(f505,plain,
~ aElement0(xz),
inference(forward_subsumption_resolution,[status(thm)],[f504,f200]) ).
fof(f506,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f505,f199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG105+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.48 % Computer : n014.cluster.edu
% 0.19/0.48 % Model : x86_64 x86_64
% 0.19/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.48 % Memory : 8046.5625MB
% 0.19/0.48 % OS : Linux 6.8.0-71-generic
% 0.19/0.48 % CPULimit : 300
% 0.19/0.48 % WCLimit : 300
% 0.19/0.48 % DateTime : Mon Sep 21 04:20:04 UTC 2026
% 0.19/0.49 % CPUTime :
% 0.19/0.51 % Drodi V4.1.1
% 0.23/0.54 % Refutation found
% 0.23/0.54 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.23/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.60 % Elapsed time: 0.104985 seconds
% 0.23/0.60 % CPU time: 0.274792 seconds
% 0.23/0.60 % Total memory used: 48.648 MB
% 0.23/0.60 % Net memory used: 48.446 MB
%------------------------------------------------------------------------------