%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN051+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 : n011.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 03:15:02 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 1 unt; 5 def)
% Number of atoms : 80 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 77 ( 34 ~; 31 |; 2 &)
% ( 7 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 7 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 18 ( 10 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
? [X] :
( p
=> big_f(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
? [X] :
( big_f(X)
=> p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,conjecture,
? [X] :
( p
<=> big_f(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ ? [X] :
( p
<=> big_f(X) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
? [X] :
( big_f(X)
| ~ p ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
( ? [X] : big_f(X)
| ~ p ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f7,plain,
( big_f(sK0_skl)
| ~ p ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl)],[f6]) ).
fof(f8,plain,
( big_f(sK0_skl)
| ~ p ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
? [X] :
( p
| ~ big_f(X) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
( p
| ? [X] : ~ big_f(X) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f11,plain,
( p
| ~ big_f(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X,sK1_skl)],[f10]) ).
fof(f12,plain,
( p
| ~ big_f(sK1_skl) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [X] :
( p
<~> big_f(X) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X] :
( ( ~ big_f(X)
| ~ p )
& ( big_f(X)
| p ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ( ! [X] : ~ big_f(X)
| ~ p )
& ( ! [X] : big_f(X)
| p ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0] :
( big_f(X0)
| p ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] :
( ~ big_f(X0)
| ~ p ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,definition,
( sQ0_spl
<=> p ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f21,definition,
( sQ1_spl
<=> big_f(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( ~ sQ1_spl
| big_f(sK0_skl) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f18,f21]) ).
fof(f25,definition,
( sQ2_spl
<=> big_f(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( sQ2_spl
| ~ big_f(sK1_skl) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f12,f25,f18]) ).
fof(f29,definition,
! [X0] :
( sQ3_spl
<=> big_f(X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f30,plain,
! [X0] :
( ~ sQ3_spl
| big_f(X0) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f16,f18,f29]) ).
fof(f33,definition,
! [X0] :
( sQ4_spl
<=> ~ big_f(X0) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f34,plain,
! [X0] :
( ~ sQ4_spl
| ~ big_f(X0) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f17,f18,f33]) ).
fof(f37,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f30,f34]) ).
fof(f38,plain,
( ~ sQ3_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f37]) ).
fof(f39,plain,
( sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f30]) ).
fof(f40,plain,
( sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f39]) ).
fof(f41,plain,
( ~ sQ1_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f34]) ).
fof(f42,plain,
( ~ sQ1_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f41]) ).
fof(f43,plain,
$false,
inference(sat_refutation,[status(thm)],[f24,f28,f32,f36,f38,f40,f42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN051+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 10:40:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.046882 seconds
% 0.08/0.42 % CPU time: 0.108832 seconds
% 0.08/0.42 % Total memory used: 16.459 MB
% 0.08/0.42 % Net memory used: 15.856 MB
%------------------------------------------------------------------------------