%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : RNG108+4 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.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 02:05:00 PM UTC 2026
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 10 unt; 2 def)
% Number of atoms : 181 ( 48 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 241 ( 101 ~; 85 |; 50 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 41 ( 30 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
aElement0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
aElement0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [W0] :
( aElement0(W0)
=> ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [W0] :
( aElement0(W0)
=> ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
( aElement0(xb)
& aElement0(xa) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,conjecture,
( ( aElementOf0(xb,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) ) )
& ( aElementOf0(xa,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,negated_conjecture,
~ ( ( aElementOf0(xb,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = xb
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) ) )
& ( aElementOf0(xa,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
fof(f48,plain,
aElement0(sz00),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f49,plain,
aElement0(sz10),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f70,plain,
! [W0] :
( ( W0 = sdtasdt0(sz10,W0)
& sdtasdt0(W0,sz10) = W0 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f71,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f79,plain,
! [W0] :
( ( sz00 = sdtasdt0(sz00,W0)
& sdtasdt0(W0,sz00) = sz00 )
| ~ aElement0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f80,plain,
! [X0] :
( sdtasdt0(X0,sz00) = sz00
| ~ aElement0(X0) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f197,plain,
aElement0(xa),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f198,plain,
aElement0(xb),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f237,plain,
( ( ~ aElementOf0(xb,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != xb
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != sz00
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != xa
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != sz00
| ~ aElement0(W0) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f238,definition,
( sP4_prd
<=> ( ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != sz00
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != xa
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != sz00
| ~ aElement0(W0) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f239,plain,
( ( ~ aElementOf0(xb,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != xb
| ~ aElement0(W0) ) )
| sP4_prd ),
inference(formula_renaming,[status(thm)],[f237,f238]) ).
fof(f240,plain,
! [X0] :
( sdtasdt0(xb,X0) != xb
| ~ aElement0(X0)
| sP4_prd ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f270,definition,
( sP6_prd
<=> ( ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != xa
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != sz00
| ~ aElement0(W0) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f271,plain,
( sP4_prd
<=> ( ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != sz00
| ~ aElement0(W0) ) )
| sP6_prd ) ),
inference(formula_renaming,[status(thm)],[f238,f270]) ).
fof(f272,plain,
( ( ( ( aElementOf0(sz00,slsdtgt0(xb))
| ? [W0] :
( sdtasdt0(xb,W0) = sz00
& aElement0(W0) ) )
& ~ sP6_prd )
| sP4_prd )
& ( ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != sz00
| ~ aElement0(W0) ) )
| sP6_prd
| ~ sP4_prd ) ),
inference(NNF_transformation,[status(thm)],[f271]) ).
fof(f273,plain,
( ( ( ( aElementOf0(sz00,slsdtgt0(xb))
| ( sdtasdt0(xb,sK28_skl) = sz00
& aElement0(sK28_skl) ) )
& ~ sP6_prd )
| sP4_prd )
& ( ( ~ aElementOf0(sz00,slsdtgt0(xb))
& ! [W0] :
( sdtasdt0(xb,W0) != sz00
| ~ aElement0(W0) ) )
| sP6_prd
| ~ sP4_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28_skl]),skolemize(W0,sK28_skl)],[f272]) ).
fof(f274,plain,
! [X0] :
( sdtasdt0(xb,X0) != sz00
| ~ aElement0(X0)
| sP6_prd
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f273]) ).
fof(f288,plain,
( ( ( ( aElementOf0(xa,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = xa
& aElement0(W0) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ? [W0] :
( sdtasdt0(xa,W0) = sz00
& aElement0(W0) ) ) )
| sP6_prd )
& ( ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != xa
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != sz00
| ~ aElement0(W0) ) )
| ~ sP6_prd ) ),
inference(NNF_transformation,[status(thm)],[f270]) ).
fof(f289,plain,
( ( ( ( aElementOf0(xa,slsdtgt0(xa))
| ( sdtasdt0(xa,sK31_skl) = xa
& aElement0(sK31_skl) ) )
& ( aElementOf0(sz00,slsdtgt0(xa))
| ( sdtasdt0(xa,sK30_skl) = sz00
& aElement0(sK30_skl) ) ) )
| sP6_prd )
& ( ( ~ aElementOf0(xa,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != xa
| ~ aElement0(W0) ) )
| ( ~ aElementOf0(sz00,slsdtgt0(xa))
& ! [W0] :
( sdtasdt0(xa,W0) != sz00
| ~ aElement0(W0) ) )
| ~ sP6_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(W0,sK30_skl),skolemize(W0,sK31_skl)],[f288]) ).
fof(f290,plain,
! [X0,X1] :
( sdtasdt0(xa,X1) != xa
| ~ aElement0(X1)
| sdtasdt0(xa,X0) != sz00
| ~ aElement0(X0)
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f289]) ).
fof(f314,plain,
( ~ aElement0(sz00)
| sP6_prd
| ~ sP4_prd
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f80,f274]) ).
fof(f315,plain,
( ~ aElement0(sz00)
| sP6_prd
| ~ sP4_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f314,f198]) ).
fof(f317,plain,
( sP6_prd
| ~ sP4_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f315,f48]) ).
fof(f338,plain,
! [X0] :
( ~ aElement0(xa)
| sdtasdt0(xa,X0) != xa
| ~ aElement0(X0)
| ~ aElement0(sz00)
| ~ sP6_prd ),
inference(resolution,[status(thm)],[f290,f80]) ).
fof(f339,plain,
! [X0] :
( ~ aElement0(xa)
| sdtasdt0(xa,X0) != xa
| ~ aElement0(X0)
| ~ sP6_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f48]) ).
fof(f344,plain,
! [X0] :
( sdtasdt0(xa,X0) != xa
| ~ aElement0(X0)
| ~ sP6_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f339,f197]) ).
fof(f349,plain,
( ~ aElement0(sz10)
| ~ sP6_prd
| ~ aElement0(xa) ),
inference(resolution,[status(thm)],[f71,f344]) ).
fof(f350,plain,
( ~ aElement0(sz10)
| sP4_prd
| ~ aElement0(xb) ),
inference(resolution,[status(thm)],[f71,f240]) ).
fof(f352,plain,
( ~ aElement0(sz10)
| ~ sP6_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f349,f197]) ).
fof(f353,plain,
( ~ aElement0(sz10)
| sP4_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f350,f198]) ).
fof(f358,plain,
~ sP4_prd,
inference(backward_subsumption_resolution,[status(thm)],[f317,f359]) ).
fof(f359,plain,
~ sP6_prd,
inference(forward_subsumption_resolution,[status(thm)],[f352,f49]) ).
fof(f365,plain,
~ aElement0(sz10),
inference(forward_subsumption_resolution,[status(thm)],[f353,f358]) ).
fof(f366,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f49,f365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : RNG108+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n015.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 04:23:20 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.51 % Elapsed time: 0.065589 seconds
% 0.17/0.51 % CPU time: 0.170051 seconds
% 0.17/0.51 % Total memory used: 41.055 MB
% 0.17/0.51 % Net memory used: 40.950 MB
%------------------------------------------------------------------------------