%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : NUM531+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 01:40:52 PM UTC 2026
% Result : Theorem 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 24 ( 9 unt; 2 def)
% Number of atoms : 50 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 46 ( 20 ~; 10 |; 11 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 10 ( 7 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
isFinite0(slcrc0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ isFinite0(W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ ( W0 = slcrc0
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [W0] :
( ( isCountable0(W0)
& aSet0(W0) )
=> ~ ( W0 = slcrc0
& ~ ? [W1] : aElementOf0(W1,W0) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f28,plain,
isFinite0(slcrc0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f31,plain,
! [W0] :
( ~ isFinite0(W0)
| ~ isCountable0(W0)
| ~ aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f32,plain,
! [X0] :
( ~ isFinite0(X0)
| ~ isCountable0(X0)
| ~ aSet0(X0) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
? [W0] :
( W0 = slcrc0
& ! [W1] : ~ aElementOf0(W1,W0)
& isCountable0(W0)
& aSet0(W0) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f34,plain,
( sK1_skl = slcrc0
& ! [W1] : ~ aElementOf0(W1,sK1_skl)
& isCountable0(sK1_skl)
& aSet0(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W0,sK1_skl)],[f33]) ).
fof(f35,plain,
aSet0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
isCountable0(sK1_skl),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
sK1_skl = slcrc0,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f43,plain,
( ~ isFinite0(sK1_skl)
| ~ isCountable0(sK1_skl) ),
inference(resolution,[status(thm)],[f32,f35]) ).
fof(f44,definition,
( sQ0_spl
<=> isCountable0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ0_spl
| ~ isCountable0(sK1_skl) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ1_spl
<=> isFinite0(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ1_spl
| ~ isFinite0(sK1_skl) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f44,f47]) ).
fof(f51,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f46,f36]) ).
fof(f52,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f51]) ).
fof(f53,plain,
isFinite0(sK1_skl),
inference(forward_demodulation,[status(thm)],[f38,f28]) ).
fof(f54,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f49]) ).
fof(f55,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f54]) ).
fof(f56,plain,
$false,
inference(sat_refutation,[status(thm)],[f50,f52,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM531+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n001.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.33 % CPULimit : 300
% 0.07/0.33 % WCLimit : 300
% 0.07/0.33 % DateTime : Mon Sep 21 02:43:14 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 0.07/0.36 % Refutation found
% 0.07/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.44 % Elapsed time: 0.097758 seconds
% 0.07/0.44 % CPU time: 0.097742 seconds
% 0.07/0.44 % Total memory used: 6.331 MB
% 0.07/0.44 % Net memory used: 6.306 MB
%------------------------------------------------------------------------------