%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN980+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 03:18:38 PM UTC 2026
% Result : Theorem 0.19s 0.53s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 1 unt; 4 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 87 ( 38 ~; 29 |; 8 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 28 ( 23 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [B] :
( ! [Y] :
( ( r(B)
=> r(Y) )
=> p(f(Y),Y) )
=> ? [X,Y] :
( ( q(f(B),B)
=> q(X,Y) )
& p(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [B] :
( ! [Y] :
( ( r(B)
=> r(Y) )
=> p(f(Y),Y) )
=> ? [X,Y] :
( ( q(f(B),B)
=> q(X,Y) )
& p(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [B] :
( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(B),B) )
| ~ p(X,Y) )
& ! [Y] :
( p(f(Y),Y)
| ( ~ r(Y)
& r(B) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(sK0_skl),sK0_skl) )
| ~ p(X,Y) )
& ! [Y] :
( p(f(Y),Y)
| ( ~ r(Y)
& r(sK0_skl) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(B,sK0_skl)],[f3]) ).
fof(f5,plain,
! [X0] :
( p(f(X0),X0)
| r(sK0_skl) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f6,plain,
! [X0] :
( p(f(X0),X0)
| ~ r(X0) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f7,plain,
! [X0,X1] :
( q(f(sK0_skl),sK0_skl)
| ~ p(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f8,plain,
! [X0,X1] :
( ~ q(X0,X1)
| ~ p(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f9,definition,
( sQ0_spl
<=> r(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f10,plain,
( ~ sQ0_spl
| r(sK0_skl) ),
inference(component_clause,[status(thm)],[f9]) ).
fof(f12,definition,
! [X0] :
( sQ1_spl
<=> p(f(X0),X0) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f13,plain,
! [X0] :
( ~ sQ1_spl
| p(f(X0),X0) ),
inference(component_clause,[status(thm)],[f12]) ).
fof(f15,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f5,f9,f12]) ).
fof(f16,definition,
! [X0,X1] :
( sQ2_spl
<=> ~ p(X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f17,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ p(X0,X1) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,definition,
( sQ3_spl
<=> q(f(sK0_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f20,plain,
( ~ sQ3_spl
| q(f(sK0_skl),sK0_skl) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f7,f16,f19]) ).
fof(f23,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f10,f24]) ).
fof(f24,plain,
! [X0] :
( ~ sQ2_spl
| ~ r(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6,f17]) ).
fof(f25,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( ~ sQ3_spl
| ~ p(f(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f8,f20]) ).
fof(f27,plain,
( ~ sQ3_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f26,f13]) ).
fof(f28,plain,
( ~ sQ3_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f27]) ).
fof(f29,plain,
( ~ sQ0_spl
| p(f(sK0_skl),sK0_skl) ),
inference(resolution,[status(thm)],[f6,f10]) ).
fof(f30,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f26]) ).
fof(f31,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f30]) ).
fof(f32,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f13,f17]) ).
fof(f33,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f32]) ).
fof(f34,plain,
$false,
inference(sat_refutation,[status(thm)],[f15,f22,f25,f28,f31,f33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN980+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.49 % Computer : n002.cluster.edu
% 0.19/0.49 % Model : x86_64 x86_64
% 0.19/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.49 % Memory : 8046.5625MB
% 0.19/0.49 % OS : Linux 6.8.0-71-generic
% 0.19/0.49 % CPULimit : 300
% 0.19/0.49 % WCLimit : 300
% 0.19/0.49 % DateTime : Mon Sep 21 11:34:48 UTC 2026
% 0.19/0.49 % CPUTime :
% 0.19/0.51 % Drodi V4.1.1
% 0.19/0.53 % Refutation found
% 0.19/0.53 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.53 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.57 % Elapsed time: 0.066170 seconds
% 0.24/0.57 % CPU time: 0.123199 seconds
% 0.24/0.57 % Total memory used: 9.250 MB
% 0.24/0.57 % Net memory used: 8.931 MB
%------------------------------------------------------------------------------