%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN347+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 : n017.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 03:15:50 PM UTC 2026
% Result : Theorem 0.14s 5.41s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 1 unt; 7 def)
% Number of atoms : 137 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 161 ( 65 ~; 69 |; 11 &)
% ( 14 <=>; 0 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 52 ( 42 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [Z1,Z2] :
? [X1,X2] :
! [Y] :
( ( big_f(Z1,Y)
<=> big_f(Z2,Y) )
| ( ( big_f(X1,Y)
<=> big_f(X2,Y) )
<=> big_f(Z1,Z2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [Z1,Z2] :
? [X1,X2] :
! [Y] :
( ( big_f(Z1,Y)
<=> big_f(Z2,Y) )
| ( ( big_f(X1,Y)
<=> big_f(X2,Y) )
<=> big_f(Z1,Z2) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [Z1,Z2] :
! [X1,X2] :
? [Y] :
( ( big_f(Z1,Y)
<~> big_f(Z2,Y) )
& ( ( big_f(X1,Y)
<=> big_f(X2,Y) )
<~> big_f(Z1,Z2) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [Z1,Z2] :
! [X1,X2] :
? [Y] :
( ( ~ big_f(Z2,Y)
| ~ big_f(Z1,Y) )
& ( big_f(Z2,Y)
| big_f(Z1,Y) )
& ( ~ big_f(Z1,Z2)
| ( ( big_f(X2,Y)
| big_f(X1,Y) )
& ( ~ big_f(X2,Y)
| ~ big_f(X1,Y) ) ) )
& ( big_f(Z1,Z2)
| ( ( ~ big_f(X2,Y)
| big_f(X1,Y) )
& ( big_f(X2,Y)
| ~ big_f(X1,Y) ) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
! [X1,X2] :
( ( ~ big_f(sK1_skl,sK2_skl(X2,X1))
| ~ big_f(sK0_skl,sK2_skl(X2,X1)) )
& ( big_f(sK1_skl,sK2_skl(X2,X1))
| big_f(sK0_skl,sK2_skl(X2,X1)) )
& ( ~ big_f(sK0_skl,sK1_skl)
| ( ( big_f(X2,sK2_skl(X2,X1))
| big_f(X1,sK2_skl(X2,X1)) )
& ( ~ big_f(X2,sK2_skl(X2,X1))
| ~ big_f(X1,sK2_skl(X2,X1)) ) ) )
& ( big_f(sK0_skl,sK1_skl)
| ( ( ~ big_f(X2,sK2_skl(X2,X1))
| big_f(X1,sK2_skl(X2,X1)) )
& ( big_f(X2,sK2_skl(X2,X1))
| ~ big_f(X1,sK2_skl(X2,X1)) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Z1,sK0_skl),skolemize(Z2,sK1_skl),skolemize(Y,sK2_skl(X2,X1))],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( big_f(sK0_skl,sK1_skl)
| big_f(X1,sK2_skl(X1,X0))
| ~ big_f(X0,sK2_skl(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( big_f(sK0_skl,sK1_skl)
| ~ big_f(X1,sK2_skl(X1,X0))
| big_f(X0,sK2_skl(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0,X1] :
( ~ big_f(sK0_skl,sK1_skl)
| ~ big_f(X1,sK2_skl(X1,X0))
| ~ big_f(X0,sK2_skl(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0,X1] :
( ~ big_f(sK0_skl,sK1_skl)
| big_f(X1,sK2_skl(X1,X0))
| big_f(X0,sK2_skl(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( big_f(sK1_skl,sK2_skl(X0,X1))
| big_f(sK0_skl,sK2_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_f(sK1_skl,sK2_skl(X0,X1))
| ~ big_f(sK0_skl,sK2_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,definition,
! [X0,X1] :
( sQ0_spl
<=> ( big_f(X1,sK2_skl(X1,X0))
| ~ big_f(X0,sK2_skl(X1,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f13,plain,
! [X0,X1] :
( ~ sQ0_spl
| big_f(X1,sK2_skl(X1,X0))
| ~ big_f(X0,sK2_skl(X1,X0)) ),
inference(component_clause,[status(thm)],[f12]) ).
fof(f15,definition,
( sQ1_spl
<=> big_f(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f18,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6,f12,f15]) ).
fof(f19,definition,
! [X0,X1] :
( sQ2_spl
<=> ( ~ big_f(X1,sK2_skl(X1,X0))
| big_f(X0,sK2_skl(X1,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f20,plain,
! [X0,X1] :
( ~ sQ2_spl
| ~ big_f(X1,sK2_skl(X1,X0))
| big_f(X0,sK2_skl(X1,X0)) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f7,f19,f15]) ).
fof(f23,definition,
! [X0,X1] :
( sQ3_spl
<=> ( ~ big_f(X1,sK2_skl(X1,X0))
| ~ big_f(X0,sK2_skl(X1,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f24,plain,
! [X0,X1] :
( ~ sQ3_spl
| ~ big_f(X1,sK2_skl(X1,X0))
| ~ big_f(X0,sK2_skl(X1,X0)) ),
inference(component_clause,[status(thm)],[f23]) ).
fof(f26,plain,
( ~ sQ1_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f8,f23,f15]) ).
fof(f27,definition,
! [X0,X1] :
( sQ4_spl
<=> ( big_f(X1,sK2_skl(X1,X0))
| big_f(X0,sK2_skl(X1,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f28,plain,
! [X0,X1] :
( ~ sQ4_spl
| big_f(X1,sK2_skl(X1,X0))
| big_f(X0,sK2_skl(X1,X0)) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,plain,
( ~ sQ1_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f9,f27,f15]) ).
fof(f31,plain,
! [X0] :
( ~ sQ4_spl
| ~ sQ3_spl
| ~ big_f(X0,sK2_skl(X0,X0)) ),
inference(resolution,[status(thm)],[f24,f28]) ).
fof(f35,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| $false ),
inference(resolution,[status(thm)],[f31,f28]) ).
fof(f39,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f35]) ).
fof(f40,plain,
! [X0] :
( ~ sQ0_spl
| ~ big_f(X0,sK2_skl(sK0_skl,X0))
| ~ big_f(sK1_skl,sK2_skl(sK0_skl,X0)) ),
inference(resolution,[status(thm)],[f11,f13]) ).
fof(f43,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ big_f(sK0_skl,sK2_skl(sK0_skl,sK1_skl))
| ~ big_f(sK1_skl,sK2_skl(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f40,f20]) ).
fof(f44,definition,
( sQ5_spl
<=> big_f(sK1_skl,sK2_skl(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f46,plain,
( sQ5_spl
| ~ big_f(sK1_skl,sK2_skl(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,definition,
( sQ6_spl
<=> big_f(sK0_skl,sK2_skl(sK0_skl,sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f49,plain,
( sQ6_spl
| ~ big_f(sK0_skl,sK2_skl(sK0_skl,sK1_skl)) ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f43,f44,f47,f12,f19]) ).
fof(f58,plain,
( sQ5_spl
| big_f(sK0_skl,sK2_skl(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f46,f10]) ).
fof(f61,plain,
( sQ5_spl
| ~ sQ2_spl
| ~ big_f(sK0_skl,sK2_skl(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f20,f46]) ).
fof(f63,plain,
( sQ5_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f58]) ).
fof(f64,plain,
( sQ5_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ big_f(sK1_skl,sK2_skl(sK0_skl,sK1_skl)) ),
inference(resolution,[status(thm)],[f49,f13]) ).
fof(f66,plain,
( ~ sQ0_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f65,f44,f47,f12]) ).
fof(f67,plain,
$false,
inference(sat_refutation,[status(thm)],[f18,f22,f26,f30,f39,f50,f64,f66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN347+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.39 % Computer : n017.cluster.edu
% 0.09/5.39 % Model : x86_64 x86_64
% 0.09/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.39 % Memory : 8046.5625MB
% 0.09/5.39 % OS : Linux 6.8.0-71-generic
% 0.09/5.39 % CPULimit : 300
% 0.09/5.39 % WCLimit : 300
% 0.09/5.39 % DateTime : Mon Sep 21 10:46:18 UTC 2026
% 0.09/5.39 % CPUTime :
% 0.09/5.40 % Drodi V4.1.1
% 0.14/5.41 % Refutation found
% 0.14/5.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/5.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/5.43 % Elapsed time: 0.035241 seconds
% 0.14/5.43 % CPU time: 0.094123 seconds
% 0.14/5.43 % Total memory used: 11.956 MB
% 0.14/5.43 % Net memory used: 11.585 MB
%------------------------------------------------------------------------------