%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN722+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 03:17:10 PM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 5 unt; 6 def)
% Number of atoms : 102 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 120 ( 51 ~; 51 |; 12 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 18 ( 15 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
~ ( ( ~ p(b)
| ~ p(a) )
& ! [X] :
? [Y] :
( ~ q(d)
| ~ q(c)
| ~ q(Y)
| ~ q(X)
| p(X) )
& ! [Z] :
( q(Z)
& ( r(Z)
| p(Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ~ ( ( ~ p(b)
| ~ p(a) )
& ! [X] :
? [Y] :
( ~ q(d)
| ~ q(c)
| ~ q(Y)
| ~ q(X)
| p(X) )
& ! [Z] :
( q(Z)
& ( r(Z)
| p(Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ~ p(b)
| ~ p(a) )
& ( ~ q(d)
| ~ q(c)
| ? [Y] : ~ q(Y)
| ! [X] :
( ~ q(X)
| p(X) ) )
& ! [Z] : q(Z)
& ! [Z] :
( r(Z)
| p(Z) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f4,plain,
( ( ~ p(b)
| ~ p(a) )
& ( ~ q(d)
| ~ q(c)
| ~ q(sK0_skl)
| ! [X] :
( ~ q(X)
| p(X) ) )
& ! [Z] : q(Z)
& ! [Z] :
( r(Z)
| p(Z) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Y,sK0_skl)],[f3]) ).
fof(f6,plain,
! [X0] : q(X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f7,plain,
! [X0] :
( ~ q(d)
| ~ q(c)
| ~ q(sK0_skl)
| ~ q(X0)
| p(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f8,plain,
( ~ p(b)
| ~ p(a) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f9,definition,
! [X0] :
( sQ0_spl
<=> ( ~ q(X0)
| p(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f10,plain,
! [X0] :
( ~ sQ0_spl
| ~ q(X0)
| p(X0) ),
inference(component_clause,[status(thm)],[f9]) ).
fof(f12,definition,
( sQ1_spl
<=> q(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f14,plain,
( sQ1_spl
| ~ q(sK0_skl) ),
inference(component_clause,[status(thm)],[f12]) ).
fof(f15,definition,
( sQ2_spl
<=> q(c) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f17,plain,
( sQ2_spl
| ~ q(c) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,definition,
( sQ3_spl
<=> q(d) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f20,plain,
( sQ3_spl
| ~ q(d) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7,f9,f12,f15,f18]) ).
fof(f22,definition,
( sQ4_spl
<=> p(a) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f24,plain,
( sQ4_spl
| ~ p(a) ),
inference(component_clause,[status(thm)],[f22]) ).
fof(f25,definition,
( sQ5_spl
<=> p(b) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( sQ5_spl
| ~ p(b) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f8,f22,f25]) ).
fof(f29,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f20,f6]) ).
fof(f30,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f31,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f6]) ).
fof(f32,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0] :
( ~ sQ0_spl
| p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f10,f6]) ).
fof(f34,plain,
( sQ4_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f24,f33]) ).
fof(f35,plain,
( sQ4_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f34]) ).
fof(f36,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f14,f6]) ).
fof(f37,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f36]) ).
fof(f38,plain,
( sQ5_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f27,f33]) ).
fof(f39,plain,
( sQ5_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f38]) ).
fof(f40,plain,
$false,
inference(sat_refutation,[status(thm)],[f21,f28,f30,f32,f35,f37,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN722+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n026.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 11:15:53 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.40 % Refutation found
% 0.09/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.050000 seconds
% 0.09/0.44 % CPU time: 0.117082 seconds
% 0.09/0.44 % Total memory used: 16.515 MB
% 0.09/0.44 % Net memory used: 15.953 MB
%------------------------------------------------------------------------------