%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN374+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 : n015.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 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 1 unt; 7 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 202 ( 83 ~; 88 |; 12 &)
% ( 17 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-1 aty)
% Number of variables : 76 ( 62 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<=> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X] :
! [Y] :
( big_p(X)
<=> big_p(Y) )
<~> ( ? [X] : big_p(X)
<=> ! [Y] : big_p(Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( big_p(X)
<=> big_p(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ? [X] :
! [Y] : sP0_prd(Y,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] :
? [Y] : ~ sP0_prd(Y,X) )
& ( ( ( ? [Y] : ~ big_p(Y)
| ? [X] : big_p(X) )
& ( ! [Y] : big_p(Y)
| ! [X] : ~ big_p(X) ) )
| ? [X] :
! [Y] : sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ( ( ! [Y] : big_p(Y)
| big_p(sK5_skl) )
& ( ~ big_p(sK4_skl)
| ! [X] : ~ big_p(X) ) )
| ! [X] : ~ sP0_prd(sK3_skl(X),X) )
& ( ( ( ~ big_p(sK2_skl)
| big_p(sK1_skl) )
& ( ! [Y] : big_p(Y)
| ! [X] : ~ big_p(X) ) )
| ! [Y] : sP0_prd(Y,sK0_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(X,sK0_skl),skolemize(X,sK1_skl),skolemize(Y,sK2_skl),skolemize(Y,sK3_skl(X)),skolemize(Y,sK4_skl),skolemize(X,sK5_skl)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( big_p(X2)
| ~ big_p(X1)
| sP0_prd(X0,sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( ~ big_p(sK4_skl)
| ~ big_p(X1)
| ~ sP0_prd(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0,X1] :
( big_p(X1)
| big_p(sK5_skl)
| ~ sP0_prd(sK3_skl(X0),X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,plain,
! [X,Y] :
( ( ( ( big_p(Y)
| big_p(X) )
& ( ~ big_p(Y)
| ~ big_p(X) ) )
| sP0_prd(Y,X) )
& ( ( ( ~ big_p(Y)
| big_p(X) )
& ( big_p(Y)
| ~ big_p(X) ) )
| ~ sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( ! [X,Y] :
( ( ( big_p(Y)
| big_p(X) )
& ( ~ big_p(Y)
| ~ big_p(X) ) )
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ( ~ big_p(Y)
| big_p(X) )
& ( big_p(Y)
| ~ big_p(X) ) )
| ~ sP0_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( big_p(X0)
| ~ big_p(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ~ big_p(X0)
| big_p(X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( ~ big_p(X0)
| ~ big_p(X1)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( big_p(X0)
| big_p(X1)
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f18,definition,
! [X0] :
( sQ0_spl
<=> sP0_prd(X0,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f19,plain,
! [X0] :
( ~ sQ0_spl
| sP0_prd(X0,sK0_skl) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,definition,
! [X1] :
( sQ1_spl
<=> ~ big_p(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f22,plain,
! [X0] :
( ~ sQ1_spl
| ~ big_p(X0) ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,definition,
! [X2] :
( sQ2_spl
<=> big_p(X2) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f25,plain,
! [X0] :
( ~ sQ2_spl
| big_p(X0) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f18,f21,f24]) ).
fof(f35,definition,
! [X0] :
( sQ5_spl
<=> ~ sP0_prd(sK3_skl(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f36,plain,
! [X0] :
( ~ sQ5_spl
| ~ sP0_prd(sK3_skl(X0),X0) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ6_spl
<=> big_p(sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( sQ6_spl
| ~ big_p(sK4_skl) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( ~ sQ6_spl
| sQ1_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f10,f35,f21,f38]) ).
fof(f42,definition,
( sQ7_spl
<=> big_p(sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( ~ sQ7_spl
| big_p(sK5_skl) ),
inference(component_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( sQ2_spl
| sQ7_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f11,f35,f42,f24]) ).
fof(f46,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f25]) ).
fof(f47,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f46]) ).
fof(f48,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| $false ),
inference(resolution,[status(thm)],[f36,f19]) ).
fof(f49,plain,
( ~ sQ0_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f48]) ).
fof(f50,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f22]) ).
fof(f51,plain,
( ~ sQ7_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f50]) ).
fof(f52,plain,
( sQ6_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f40,f25]) ).
fof(f53,plain,
( sQ6_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f60,plain,
! [X0] :
( sQ6_spl
| ~ big_p(X0)
| ~ sP0_prd(sK4_skl,X0) ),
inference(resolution,[status(thm)],[f14,f40]) ).
fof(f61,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ big_p(sK0_skl) ),
inference(resolution,[status(thm)],[f60,f19]) ).
fof(f65,plain,
! [X0] :
( ~ sQ0_spl
| sQ6_spl
| ~ big_p(X0)
| ~ sP0_prd(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f61,f15]) ).
fof(f66,plain,
! [X0] :
( ~ sQ0_spl
| sQ6_spl
| ~ big_p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f65,f19]) ).
fof(f67,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f43,f66]) ).
fof(f68,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f67]) ).
fof(f73,plain,
! [X0,X1] :
( ~ sQ1_spl
| big_p(X0)
| sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f22]) ).
fof(f74,plain,
! [X0,X1] :
( ~ sQ1_spl
| sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f73,f22]) ).
fof(f75,plain,
( ~ sQ5_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f74]) ).
fof(f76,plain,
( ~ sQ5_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ big_p(X0)
| sP0_prd(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f16,f25]) ).
fof(f78,plain,
! [X0,X1] :
( ~ sQ2_spl
| sP0_prd(X0,X1) ),
inference(resolution,[status(thm)],[f77,f25]) ).
fof(f79,plain,
( ~ sQ5_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f36,f78]) ).
fof(f80,plain,
( ~ sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f81,plain,
$false,
inference(sat_refutation,[status(thm)],[f27,f41,f45,f47,f49,f51,f53,f68,f76,f80]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN374+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n015.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 10:55:24 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.046119 seconds
% 0.13/0.41 % CPU time: 0.113635 seconds
% 0.13/0.41 % Total memory used: 16.682 MB
% 0.13/0.41 % Net memory used: 16.169 MB
%------------------------------------------------------------------------------