%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN345+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 : n007.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 03:15:49 PM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 3 unt; 7 def)
% Number of atoms : 139 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 159 ( 57 ~; 55 |; 19 &)
% ( 9 <=>; 18 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 8 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 39 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( ( ( big_f(X1,X2,Y1)
=> big_f(Y2,Y1,Z) )
=> ( big_f(X1,X1,X2)
=> big_f(X1,X2,X2) ) )
=> ( ( ( big_f(X2,Y1,Y2)
=> big_f(Y1,Z,Z) )
=> ( big_f(X1,X2,X2)
=> big_f(X1,X1,X2) ) )
=> ( big_f(Y1,Y2,Z)
=> ( ( big_f(X1,X1,X2)
<=> big_f(X1,X2,X2) )
& big_f(X2,X2,Y1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( ( ( big_f(X1,X2,Y1)
=> big_f(Y2,Y1,Z) )
=> ( big_f(X1,X1,X2)
=> big_f(X1,X2,X2) ) )
=> ( ( ( big_f(X2,Y1,Y2)
=> big_f(Y1,Z,Z) )
=> ( big_f(X1,X2,X2)
=> big_f(X1,X1,X2) ) )
=> ( big_f(Y1,Y2,Z)
=> ( ( big_f(X1,X1,X2)
<=> big_f(X1,X2,X2) )
& big_f(X2,X2,Y1) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( big_f(X1,X1,X2)
<~> big_f(X1,X2,X2) )
| ~ big_f(X2,X2,Y1) )
& big_f(Y1,Y2,Z)
& ( big_f(X1,X1,X2)
| ~ big_f(X1,X2,X2)
| ( ~ big_f(Y1,Z,Z)
& big_f(X2,Y1,Y2) ) )
& ( big_f(X1,X2,X2)
| ~ big_f(X1,X1,X2)
| ( ~ big_f(Y2,Y1,Z)
& big_f(X1,X2,Y1) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ( ( ~ big_f(X1,X2,X2)
| ~ big_f(X1,X1,X2) )
& ( big_f(X1,X2,X2)
| big_f(X1,X1,X2) ) )
| ~ big_f(X2,X2,Y1) )
& big_f(Y1,Y2,Z)
& ( big_f(X1,X1,X2)
| ~ big_f(X1,X2,X2)
| ( ~ big_f(Y1,Z,Z)
& big_f(X2,Y1,Y2) ) )
& ( big_f(X1,X2,X2)
| ~ big_f(X1,X1,X2)
| ( ~ big_f(Y2,Y1,Z)
& big_f(X1,X2,Y1) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
! [Y1,Y2] :
( ( ( ( ~ big_f(sK0_skl,sK1_skl,sK1_skl)
| ~ big_f(sK0_skl,sK0_skl,sK1_skl) )
& ( big_f(sK0_skl,sK1_skl,sK1_skl)
| big_f(sK0_skl,sK0_skl,sK1_skl) ) )
| ~ big_f(sK1_skl,sK1_skl,Y1) )
& big_f(Y1,Y2,sK2_skl(Y2,Y1))
& ( big_f(sK0_skl,sK0_skl,sK1_skl)
| ~ big_f(sK0_skl,sK1_skl,sK1_skl)
| ( ~ big_f(Y1,sK2_skl(Y2,Y1),sK2_skl(Y2,Y1))
& big_f(sK1_skl,Y1,Y2) ) )
& ( big_f(sK0_skl,sK1_skl,sK1_skl)
| ~ big_f(sK0_skl,sK0_skl,sK1_skl)
| ( ~ big_f(Y2,Y1,sK2_skl(Y2,Y1))
& big_f(sK0_skl,sK1_skl,Y1) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(X1,sK0_skl),skolemize(X2,sK1_skl),skolemize(Z,sK2_skl(Y2,Y1))],[f4]) ).
fof(f6,plain,
! [X0] :
( big_f(sK0_skl,sK1_skl,sK1_skl)
| ~ big_f(sK0_skl,sK0_skl,sK1_skl)
| big_f(sK0_skl,sK1_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( big_f(sK0_skl,sK1_skl,sK1_skl)
| ~ big_f(sK0_skl,sK0_skl,sK1_skl)
| ~ big_f(X0,X1,sK2_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0,X1] :
( big_f(sK0_skl,sK0_skl,sK1_skl)
| ~ big_f(sK0_skl,sK1_skl,sK1_skl)
| big_f(sK1_skl,X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0,X1] :
( big_f(sK0_skl,sK0_skl,sK1_skl)
| ~ big_f(sK0_skl,sK1_skl,sK1_skl)
| ~ big_f(X0,sK2_skl(X1,X0),sK2_skl(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,plain,
! [X0,X1] : big_f(X0,X1,sK2_skl(X1,X0)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0] :
( big_f(sK0_skl,sK1_skl,sK1_skl)
| big_f(sK0_skl,sK0_skl,sK1_skl)
| ~ big_f(sK1_skl,sK1_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0] :
( ~ big_f(sK0_skl,sK1_skl,sK1_skl)
| ~ big_f(sK0_skl,sK0_skl,sK1_skl)
| ~ big_f(sK1_skl,sK1_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,definition,
! [X0] :
( sQ0_spl
<=> big_f(sK0_skl,sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f14,plain,
! [X0] :
( ~ sQ0_spl
| big_f(sK0_skl,sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,definition,
( sQ1_spl
<=> big_f(sK0_skl,sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f19,definition,
( sQ2_spl
<=> big_f(sK0_skl,sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f22,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6,f13,f16,f19]) ).
fof(f23,definition,
! [X0,X1] :
( sQ3_spl
<=> ~ big_f(X0,X1,sK2_skl(X0,X1)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ big_f(X0,X1,sK2_skl(X0,X1)) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( sQ2_spl
| ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f7,f23,f16,f19]) ).
fof(f27,definition,
! [X0,X1] :
( sQ4_spl
<=> big_f(sK1_skl,X0,X1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sQ4_spl
| big_f(sK1_skl,X0,X1) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,plain,
( sQ1_spl
| ~ sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f8,f27,f19,f16]) ).
fof(f31,definition,
! [X0,X1] :
( sQ5_spl
<=> ~ big_f(X0,sK2_skl(X1,X0),sK2_skl(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f32,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ big_f(X0,sK2_skl(X1,X0),sK2_skl(X1,X0)) ),
inference(component_clause,[status(thm)],[f31]) ).
fof(f34,plain,
( sQ1_spl
| ~ sQ2_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f9,f31,f19,f16]) ).
fof(f35,definition,
! [X0] :
( sQ6_spl
<=> ~ big_f(sK1_skl,sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f36,plain,
! [X0] :
( ~ sQ6_spl
| ~ big_f(sK1_skl,sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,plain,
( sQ2_spl
| sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f11,f35,f16,f19]) ).
fof(f39,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f12,f35,f16,f19]) ).
fof(f42,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(resolution,[status(thm)],[f24,f14]) ).
fof(f44,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f42]) ).
fof(f45,plain,
( ~ sQ4_spl
| ~ sQ5_spl
| $false ),
inference(resolution,[status(thm)],[f32,f28]) ).
fof(f46,plain,
( ~ sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f45]) ).
fof(f47,plain,
( ~ sQ6_spl
| $false ),
inference(resolution,[status(thm)],[f36,f10]) ).
fof(f48,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f47]) ).
fof(f49,plain,
$false,
inference(sat_refutation,[status(thm)],[f22,f26,f30,f34,f38,f39,f44,f46,f48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN345+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 10:48:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.38 % Refutation found
% 0.09/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.40 % Elapsed time: 0.030865 seconds
% 0.09/0.40 % CPU time: 0.101428 seconds
% 0.09/0.40 % Total memory used: 16.691 MB
% 0.09/0.40 % Net memory used: 16.197 MB
%------------------------------------------------------------------------------