%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 03:17:10 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 2
% Syntax : Number of formulae : 25 ( 5 unt; 1 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 131 ( 49 ~; 48 |; 23 &)
% ( 7 <=>; 2 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 30 ( 26 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( r(X)
=> s(X) )
<=> ! [X] :
( ( s(X)
& r(X) )
<=> r(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( r(X)
=> s(X) )
<=> ! [X] :
( ( s(X)
& r(X) )
<=> r(X) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] :
( s(X)
| ~ r(X) )
<~> ! [X] :
( ( s(X)
& r(X) )
<=> r(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( s(X)
| ~ r(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ! [X] : sP0_prd(X)
<~> ! [X] :
( ( s(X)
& r(X) )
<=> r(X) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ? [X] :
( ( r(X)
| ( s(X)
& r(X) ) )
& ( ~ r(X)
| ~ s(X)
| ~ r(X) ) )
| ? [X] : ~ sP0_prd(X) )
& ( ! [X] :
( ( ~ r(X)
| ( s(X)
& r(X) ) )
& ( r(X)
| ~ s(X)
| ~ r(X) ) )
| ! [X] : sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ? [X] :
( ( r(X)
| ( s(X)
& r(X) ) )
& ( ~ r(X)
| ~ s(X)
| ~ r(X) ) )
| ? [X] : ~ sP0_prd(X) )
& ( ( ! [X] :
( ~ r(X)
| ( s(X)
& r(X) ) )
& ! [X] :
( r(X)
| ~ s(X)
| ~ r(X) ) )
| ! [X] : sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ( ( r(sK1_skl)
| ( s(sK1_skl)
& r(sK1_skl) ) )
& ( ~ r(sK1_skl)
| ~ s(sK1_skl)
| ~ r(sK1_skl) ) )
| ~ sP0_prd(sK0_skl) )
& ( ( ! [X] :
( ~ r(X)
| ( s(X)
& r(X) ) )
& ! [X] :
( r(X)
| ~ s(X)
| ~ r(X) ) )
| ! [X] : sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl)],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( ~ r(X1)
| s(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
( ~ r(sK1_skl)
| ~ s(sK1_skl)
| ~ r(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f13,plain,
( r(sK1_skl)
| r(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f15,plain,
! [X] :
( ( ( ~ s(X)
& r(X) )
| sP0_prd(X) )
& ( s(X)
| ~ r(X)
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
( ! [X] :
( ( ~ s(X)
& r(X) )
| sP0_prd(X) )
& ! [X] :
( s(X)
| ~ r(X)
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] :
( s(X0)
| ~ r(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0] :
( r(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0] :
( ~ s(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f20,plain,
( ~ s(sK1_skl)
| ~ r(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f12]) ).
fof(f21,plain,
( r(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f13]) ).
fof(f25,plain,
( ~ r(sK1_skl)
| ~ sP0_prd(sK0_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f20,f26]) ).
fof(f26,plain,
! [X0] :
( s(X0)
| ~ r(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f11]) ).
fof(f27,plain,
~ sP0_prd(sK0_skl),
inference(forward_subsumption_resolution,[status(thm)],[f25,f21]) ).
fof(f28,plain,
~ s(sK0_skl),
inference(resolution,[status(thm)],[f27,f19]) ).
fof(f29,plain,
r(sK0_skl),
inference(resolution,[status(thm)],[f27,f18]) ).
fof(f30,plain,
~ r(sK0_skl),
inference(resolution,[status(thm)],[f28,f26]) ).
fof(f31,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f30,f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN724+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 11:14:47 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.049019 seconds
% 0.14/0.41 % CPU time: 0.063697 seconds
% 0.14/0.41 % Total memory used: 2.076 MB
% 0.14/0.41 % Net memory used: 2.036 MB
%------------------------------------------------------------------------------