%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN931+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 03:18:21 PM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 1 unt; 6 def)
% Number of atoms : 103 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 41 ~; 40 |; 18 &)
% ( 8 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 8 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 20 ( 9 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] :
( c
& p(X) )
<=> ( c
& ? [X] : p(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] :
( c
& p(X) )
<=> ( c
& ? [X] : p(X) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] :
( c
& p(X) )
<~> ( c
& ? [X] : p(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( c
& ? [X] : p(X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ? [X] :
( c
& p(X) )
<~> sP0_prd ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ~ sP0_prd
| ! [X] :
( ~ c
| ~ p(X) ) )
& ( sP0_prd
| ? [X] :
( c
& p(X) ) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ~ sP0_prd
| ~ c
| ! [X] : ~ p(X) )
& ( sP0_prd
| ( c
& ? [X] : p(X) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
( ( ~ sP0_prd
| ~ c
| ! [X] : ~ p(X) )
& ( sP0_prd
| ( c
& p(sK0_skl) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f7]) ).
fof(f9,plain,
( sP0_prd
| p(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f10,plain,
( sP0_prd
| c ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f11,plain,
! [X0] :
( ~ sP0_prd
| ~ c
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f12,plain,
( ( ~ c
| ! [X] : ~ p(X)
| sP0_prd )
& ( ( c
& ? [X] : p(X) )
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ( ~ c
| ! [X] : ~ p(X)
| sP0_prd )
& ( ( c
& p(sK1_skl) )
| ~ sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X,sK1_skl)],[f12]) ).
fof(f14,plain,
( p(sK1_skl)
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( c
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0] :
( ~ c
| ~ p(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,definition,
( sQ0_spl
<=> p(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f18,plain,
( ~ sQ0_spl
| p(sK0_skl) ),
inference(component_clause,[status(thm)],[f17]) ).
fof(f20,definition,
( sQ1_spl
<=> sP0_prd ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f23,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f9,f17,f20]) ).
fof(f24,definition,
( sQ2_spl
<=> c ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f10,f24,f20]) ).
fof(f28,definition,
! [X0] :
( sQ3_spl
<=> ~ p(X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f29,plain,
! [X0] :
( ~ sQ3_spl
| ~ p(X0) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f11,f28,f24,f20]) ).
fof(f32,definition,
( sQ4_spl
<=> p(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f33,plain,
( ~ sQ4_spl
| p(sK1_skl) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( sQ4_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f14,f20,f32]) ).
fof(f36,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f15,f20,f24]) ).
fof(f37,plain,
( ~ sQ2_spl
| sQ3_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f16,f20,f28,f24]) ).
fof(f38,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f18,f29]) ).
fof(f39,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f40,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f33,f29]) ).
fof(f41,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f40]) ).
fof(f42,plain,
$false,
inference(sat_refutation,[status(thm)],[f23,f27,f31,f35,f36,f37,f39,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN931+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n006.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 11:30:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.025217 seconds
% 0.14/0.40 % CPU time: 0.039899 seconds
% 0.14/0.40 % Total memory used: 1.547 MB
% 0.14/0.40 % Net memory used: 1.500 MB
%------------------------------------------------------------------------------