%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN377+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 : n005.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 03:15:55 PM UTC 2026
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 1 unt; 9 def)
% Number of atoms : 183 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 211 ( 83 ~; 92 |; 15 &)
% ( 19 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 9 prp; 0-1 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 71 ( 58 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ! [X] :
( big_p(X)
<=> ! [Y] : big_p(Y) )
<~> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X] :
( sP0_prd(X)
<=> ( big_p(X)
<=> ! [Y] : big_p(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ! [X] : sP0_prd(X)
<~> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ( ( ! [Y] : big_p(Y)
| ? [X] : big_p(X) )
& ( ? [Y] : ~ big_p(Y)
| ! [X] : ~ big_p(X) ) )
| ? [X] : ~ sP0_prd(X) )
& ( ( ( ? [Y] : ~ big_p(Y)
| ? [X] : big_p(X) )
& ( ! [Y] : big_p(Y)
| ! [X] : ~ big_p(X) ) )
| ! [X] : sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ( ( ! [Y] : big_p(Y)
| big_p(sK4_skl) )
& ( ~ big_p(sK3_skl)
| ! [X] : ~ big_p(X) ) )
| ~ sP0_prd(sK2_skl) )
& ( ( ( ~ big_p(sK1_skl)
| big_p(sK0_skl) )
& ( ! [Y] : big_p(Y)
| ! [X] : ~ big_p(X) ) )
| ! [X] : sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(X,sK2_skl),skolemize(Y,sK3_skl),skolemize(X,sK4_skl)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( big_p(X2)
| ~ big_p(X1)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0] :
( ~ big_p(sK3_skl)
| ~ big_p(X0)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0] :
( big_p(X0)
| big_p(sK4_skl)
| ~ sP0_prd(sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,plain,
! [X] :
( ( ( ( ! [Y] : big_p(Y)
| big_p(X) )
& ( ? [Y] : ~ big_p(Y)
| ~ big_p(X) ) )
| sP0_prd(X) )
& ( ( ( ? [Y] : ~ big_p(Y)
| big_p(X) )
& ( ! [Y] : big_p(Y)
| ~ big_p(X) ) )
| ~ sP0_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ! [X] :
( ( ( ! [Y] : big_p(Y)
| big_p(X) )
& ( ? [Y] : ~ big_p(Y)
| ~ big_p(X) ) )
| sP0_prd(X) )
& ! [X] :
( ( ( ? [Y] : ~ big_p(Y)
| big_p(X) )
& ( ! [Y] : big_p(Y)
| ~ big_p(X) ) )
| ~ sP0_prd(X) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
( ! [X] :
( ( ( ! [Y] : big_p(Y)
| big_p(X) )
& ( ~ big_p(sK6_skl(X))
| ~ big_p(X) ) )
| sP0_prd(X) )
& ! [X] :
( ( ( ~ big_p(sK5_skl(X))
| big_p(X) )
& ( ! [Y] : big_p(Y)
| ~ big_p(X) ) )
| ~ sP0_prd(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl,sK6_skl]),skolemize(Y,sK5_skl(X)),skolemize(Y,sK6_skl(X))],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( big_p(X1)
| ~ big_p(X0)
| ~ sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f17,plain,
! [X0] :
( ~ big_p(sK6_skl(X0))
| ~ big_p(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( big_p(X1)
| big_p(X0)
| sP0_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f19,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f20,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,definition,
! [X1] :
( sQ1_spl
<=> ~ big_p(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f23,plain,
! [X0] :
( ~ sQ1_spl
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,definition,
! [X2] :
( sQ2_spl
<=> big_p(X2) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f26,plain,
! [X0] :
( ~ sQ2_spl
| big_p(X0) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f19,f22,f25]) ).
fof(f36,definition,
( sQ5_spl
<=> sP0_prd(sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( sQ5_spl
| ~ sP0_prd(sK2_skl) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,definition,
( sQ6_spl
<=> big_p(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f41,plain,
( sQ6_spl
| ~ big_p(sK3_skl) ),
inference(component_clause,[status(thm)],[f39]) ).
fof(f42,plain,
( ~ sQ6_spl
| sQ1_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f10,f36,f22,f39]) ).
fof(f43,definition,
( sQ7_spl
<=> big_p(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f44,plain,
( ~ sQ7_spl
| big_p(sK4_skl) ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( sQ2_spl
| sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f11,f36,f43,f25]) ).
fof(f47,definition,
! [X0] :
( sQ8_spl
<=> ( ~ big_p(X0)
| ~ sP0_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f48,plain,
! [X0] :
( ~ sQ8_spl
| ~ big_p(X0)
| ~ sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( sQ2_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f15,f47,f25]) ).
fof(f51,definition,
! [X0] :
( sQ9_spl
<=> ( big_p(X0)
| sP0_prd(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f52,plain,
! [X0] :
( ~ sQ9_spl
| big_p(X0)
| sP0_prd(X0) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( sQ2_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f18,f51,f25]) ).
fof(f55,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f23,f26]) ).
fof(f56,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( sQ5_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f20]) ).
fof(f59,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f60,plain,
! [X0] :
( ~ sQ2_spl
| ~ big_p(sK6_skl(X0))
| sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f26]) ).
fof(f61,plain,
! [X0] :
( ~ sQ2_spl
| sP0_prd(X0) ),
inference(resolution,[status(thm)],[f60,f26]) ).
fof(f62,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f19,f25]) ).
fof(f64,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f44,f23]) ).
fof(f65,plain,
( ~ sQ7_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f64]) ).
fof(f66,plain,
( sQ6_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f41,f26]) ).
fof(f67,plain,
( sQ6_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f66]) ).
fof(f68,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ0_spl
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f20]) ).
fof(f69,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f68]) ).
fof(f70,plain,
( ~ sQ7_spl
| ~ sQ8_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f69]) ).
fof(f73,plain,
! [X0] :
( ~ sQ9_spl
| ~ sQ1_spl
| sP0_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f23]) ).
fof(f74,plain,
( sQ5_spl
| ~ sQ9_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f38,f73]) ).
fof(f75,plain,
( sQ5_spl
| ~ sQ9_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f74]) ).
fof(f76,plain,
$false,
inference(sat_refutation,[status(thm)],[f28,f42,f46,f50,f54,f56,f59,f62,f65,f67,f70,f75]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN377+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n005.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 10:51:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % 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
% 0.12/0.40 % Elapsed time: 0.042583 seconds
% 0.12/0.40 % CPU time: 0.116298 seconds
% 0.12/0.40 % Total memory used: 16.673 MB
% 0.12/0.40 % Net memory used: 16.129 MB
%------------------------------------------------------------------------------