%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN367+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.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 03:15:54 PM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 5 unt; 4 def)
% Number of atoms : 78 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 34 ~; 25 |; 19 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 27 ( 23 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( ( big_r(X)
& ~ p )
| ( big_q(X)
& p ) )
=> ( ! [X] : big_r(X)
| ! [X] : big_q(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( ( big_r(X)
& ~ p )
| ( big_q(X)
& p ) )
=> ( ! [X] : big_r(X)
| ! [X] : big_q(X) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] : ~ big_r(X)
& ? [X] : ~ big_q(X)
& ! [X] :
( ( big_r(X)
& ~ p )
| ( big_q(X)
& p ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( big_q(X)
& p ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ? [X] : ~ big_r(X)
& ? [X] : ~ big_q(X)
& ! [X] :
( ( big_r(X)
& ~ p )
| sP0_prd(X) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ~ big_r(sK1_skl)
& ~ big_q(sK0_skl)
& ! [X] :
( ( big_r(X)
& ~ p )
| sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl)],[f5]) ).
fof(f7,plain,
! [X0] :
( ~ p
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0] :
( big_r(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
~ big_q(sK0_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
~ big_r(sK1_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
! [X] :
( ( ~ big_q(X)
| ~ p
| sP0_prd(X) )
& ( ( big_q(X)
& p )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f12,plain,
( ! [X] :
( ~ big_q(X)
| ~ p
| sP0_prd(X) )
& ! [X] :
( ( big_q(X)
& p )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f13,plain,
! [X0] :
( p
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0] :
( big_q(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f17,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,definition,
( sQ1_spl
<=> p ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f16,f19]) ).
fof(f23,definition,
! [X0] :
( sQ2_spl
<=> ~ sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f24,plain,
! [X0] :
( ~ sQ2_spl
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f13,f23,f19]) ).
fof(f33,plain,
( ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f34]) ).
fof(f34,plain,
! [X0] :
( ~ sQ0_spl
| big_q(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f14,f17]) ).
fof(f35,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f10,f37]) ).
fof(f37,plain,
! [X0] :
( ~ sQ2_spl
| big_r(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8,f24]) ).
fof(f38,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f36]) ).
fof(f39,plain,
$false,
inference(sat_refutation,[status(thm)],[f22,f26,f35,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN367+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n007.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 10:49:50 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.036054 seconds
% 0.12/0.39 % CPU time: 0.082791 seconds
% 0.12/0.39 % Total memory used: 10.850 MB
% 0.12/0.39 % Net memory used: 10.469 MB
%------------------------------------------------------------------------------