%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN070+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 03:15:08 PM UTC 2026
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 4 unt; 4 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 168 ( 72 ~; 67 |; 18 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 50 ( 46 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( ( ( ( big_h(Y,X)
& big_f(Y) )
=> big_g(Y) )
& big_f(X) )
=> big_g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
( ? [X] :
( ~ big_g(X)
& big_f(X) )
=> ? [X1] :
( ! [Y] :
( ( ~ big_g(Y)
& big_f(Y) )
=> big_j(X1,Y) )
& ~ big_g(X1)
& big_f(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( ( big_h(X,Y)
& big_f(Y)
& big_f(X) )
=> ~ big_j(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,conjecture,
! [X] :
( big_f(X)
=> big_g(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
~ ! [X] :
( big_f(X)
=> big_g(X) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X,Y] :
( big_g(X)
| ( ~ big_g(Y)
& big_h(Y,X)
& big_f(Y) )
| ~ big_f(X) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f7,plain,
! [X] :
( big_g(X)
| ( ! [Y] : ~ big_g(Y)
& ! [Y] : big_h(Y,X)
& ! [Y] : big_f(Y) )
| ~ big_f(X) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1] :
( big_g(X0)
| big_f(X1)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( big_g(X0)
| big_h(X1,X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0,X1] :
( big_g(X0)
| ~ big_g(X1)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
( ? [X1] :
( ! [Y] :
( big_j(X1,Y)
| big_g(Y)
| ~ big_f(Y) )
& ~ big_g(X1)
& big_f(X1) )
| ! [X] :
( big_g(X)
| ~ big_f(X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
( ( ! [Y] :
( big_j(sK0_skl,Y)
| big_g(Y)
| ~ big_f(Y) )
& ~ big_g(sK0_skl)
& big_f(sK0_skl) )
| ! [X] :
( big_g(X)
| ~ big_f(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X1,sK0_skl)],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( big_j(sK0_skl,X1)
| big_g(X1)
| ~ big_f(X1)
| big_g(X0)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f16,plain,
! [X,Y] :
( ~ big_j(Y,X)
| ~ big_h(X,Y)
| ~ big_f(Y)
| ~ big_f(X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0,X1] :
( ~ big_j(X1,X0)
| ~ big_h(X0,X1)
| ~ big_f(X1)
| ~ big_f(X0) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
? [X] :
( ~ big_g(X)
& big_f(X) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f19,plain,
( ~ big_g(sK1_skl)
& big_f(sK1_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(X,sK1_skl)],[f18]) ).
fof(f20,plain,
big_f(sK1_skl),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
~ big_g(sK1_skl),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,definition,
! [X0] :
( sQ0_spl
<=> ( big_g(X0)
| ~ big_f(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f23,plain,
! [X0] :
( ~ sQ0_spl
| big_g(X0)
| ~ big_f(X0) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,definition,
! [X1] :
( sQ1_spl
<=> big_f(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f26,plain,
! [X0] :
( ~ sQ1_spl
| big_f(X0) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f8,f22,f25]) ).
fof(f29,definition,
! [X1] :
( sQ2_spl
<=> ~ big_g(X1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f30,plain,
! [X0] :
( ~ sQ2_spl
| ~ big_g(X0) ),
inference(component_clause,[status(thm)],[f29]) ).
fof(f32,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f10,f22,f29]) ).
fof(f41,definition,
! [X1] :
( sQ5_spl
<=> ( big_j(sK0_skl,X1)
| big_g(X1)
| ~ big_f(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f42,plain,
! [X0] :
( ~ sQ5_spl
| big_j(sK0_skl,X0)
| big_g(X0)
| ~ big_f(X0) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f22,f41]) ).
fof(f45,plain,
( ~ sQ0_spl
| ~ big_f(sK1_skl) ),
inference(resolution,[status(thm)],[f23,f21]) ).
fof(f46,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f20]) ).
fof(f47,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ sQ1_spl
| big_g(X1)
| big_h(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f9,f26]) ).
fof(f49,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| big_j(sK0_skl,X0)
| big_g(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f42,f26]) ).
fof(f50,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ big_j(X0,X1)
| ~ big_h(X1,X0)
| ~ big_f(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f26]) ).
fof(f51,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ big_j(X1,X0)
| ~ big_h(X0,X1) ),
inference(resolution,[status(thm)],[f50,f26]) ).
fof(f52,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| big_g(X0)
| ~ big_h(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f51,f49]) ).
fof(f53,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ big_h(X0,sK0_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f52,f30]) ).
fof(f54,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| big_g(sK0_skl) ),
inference(resolution,[status(thm)],[f53,f48]) ).
fof(f55,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f30]) ).
fof(f56,plain,
( ~ sQ1_spl
| ~ sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f55]) ).
fof(f57,plain,
$false,
inference(sat_refutation,[status(thm)],[f28,f32,f44,f47,f56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN070+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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 10:42:28 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.11/0.36 % Drodi V4.1.1
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.037207 seconds
% 0.11/0.40 % CPU time: 0.100806 seconds
% 0.11/0.40 % Total memory used: 14.501 MB
% 0.11/0.40 % Net memory used: 14.074 MB
%------------------------------------------------------------------------------