%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN354+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 : n019.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 03:15:51 PM UTC 2026
% Result : Theorem 0.10s 5.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 3 unt; 4 def)
% Number of atoms : 129 ( 0 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 154 ( 53 ~; 53 |; 26 &)
% ( 9 <=>; 12 =>; 0 <=; 1 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 36 ( 23 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(Y1,Y2)
& big_f(X2,Y1)
& big_f(X1,Y1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [X1,X2] :
? [Y1,Y2] :
! [Z] :
( big_f(X1,X2)
=> ( big_g(X1,X2)
=> ( ( ( big_g(X2,Z)
<=> big_g(Y2,Z) )
=> ( big_f(Y1,Y2)
=> big_f(X2,Y2) ) )
=> ( ( big_g(X2,Z)
<=> big_g(Y1,Z) )
=> ( big_f(Y1,Y2)
& big_f(X2,Y1)
& big_f(X1,Y1) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ~ big_f(Y1,Y2)
| ~ big_f(X2,Y1)
| ~ big_f(X1,Y1) )
& ( big_g(X2,Z)
<=> big_g(Y1,Z) )
& ( big_f(X2,Y2)
| ~ big_f(Y1,Y2)
| ( big_g(X2,Z)
<~> big_g(Y2,Z) ) )
& big_g(X1,X2)
& big_f(X1,X2) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [X1,X2] :
! [Y1,Y2] :
? [Z] :
( ( ~ big_f(Y1,Y2)
| ~ big_f(X2,Y1)
| ~ big_f(X1,Y1) )
& ( ~ big_g(Y1,Z)
| big_g(X2,Z) )
& ( big_g(Y1,Z)
| ~ big_g(X2,Z) )
& ( big_f(X2,Y2)
| ~ big_f(Y1,Y2)
| ( ( ~ big_g(Y2,Z)
| ~ big_g(X2,Z) )
& ( big_g(Y2,Z)
| big_g(X2,Z) ) ) )
& big_g(X1,X2)
& big_f(X1,X2) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
? [X1,X2] :
( ! [Y1,Y2] :
? [Z] :
( ( ~ big_f(Y1,Y2)
| ~ big_f(X2,Y1)
| ~ big_f(X1,Y1) )
& ( ~ big_g(Y1,Z)
| big_g(X2,Z) )
& ( big_g(Y1,Z)
| ~ big_g(X2,Z) )
& ( big_f(X2,Y2)
| ~ big_f(Y1,Y2)
| ( ( ~ big_g(Y2,Z)
| ~ big_g(X2,Z) )
& ( big_g(Y2,Z)
| big_g(X2,Z) ) ) ) )
& big_g(X1,X2)
& big_f(X1,X2) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ! [Y1,Y2] :
( ( ~ big_f(Y1,Y2)
| ~ big_f(sK1_skl,Y1)
| ~ big_f(sK0_skl,Y1) )
& ( ~ big_g(Y1,sK2_skl(Y2,Y1))
| big_g(sK1_skl,sK2_skl(Y2,Y1)) )
& ( big_g(Y1,sK2_skl(Y2,Y1))
| ~ big_g(sK1_skl,sK2_skl(Y2,Y1)) )
& ( big_f(sK1_skl,Y2)
| ~ big_f(Y1,Y2)
| ( ( ~ big_g(Y2,sK2_skl(Y2,Y1))
| ~ big_g(sK1_skl,sK2_skl(Y2,Y1)) )
& ( big_g(Y2,sK2_skl(Y2,Y1))
| big_g(sK1_skl,sK2_skl(Y2,Y1)) ) ) ) )
& big_g(sK0_skl,sK1_skl)
& big_f(sK0_skl,sK1_skl) ),
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))],[f5]) ).
fof(f7,plain,
big_f(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( big_f(sK1_skl,X0)
| ~ big_f(X1,X0)
| big_g(X0,sK2_skl(X0,X1))
| big_g(sK1_skl,sK2_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( big_f(sK1_skl,X0)
| ~ big_f(X1,X0)
| ~ big_g(X0,sK2_skl(X0,X1))
| ~ big_g(sK1_skl,sK2_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,plain,
! [X0,X1] :
( ~ big_f(X0,X1)
| ~ big_f(sK1_skl,X0)
| ~ big_f(sK0_skl,X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
( big_f(sK1_skl,sK1_skl)
| big_g(sK1_skl,sK2_skl(sK1_skl,sK0_skl))
| big_g(sK1_skl,sK2_skl(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f15,definition,
( sQ0_spl
<=> big_g(sK1_skl,sK2_skl(sK1_skl,sK0_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f18,definition,
( sQ1_spl
<=> big_f(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f19,plain,
( ~ sQ1_spl
| big_f(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f15,f18]) ).
fof(f22,plain,
( big_f(sK1_skl,sK1_skl)
| ~ big_g(sK1_skl,sK2_skl(sK1_skl,sK0_skl))
| ~ big_g(sK1_skl,sK2_skl(sK1_skl,sK0_skl)) ),
inference(resolution,[status(thm)],[f10,f7]) ).
fof(f23,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f22,f15,f18]) ).
fof(f24,plain,
! [X0] :
( ~ sQ1_spl
| ~ big_f(sK1_skl,X0)
| ~ big_f(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f19,f13]) ).
fof(f27,definition,
( sQ2_spl
<=> big_f(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f29,plain,
( sQ2_spl
| ~ big_f(sK0_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,definition,
! [X0] :
( sQ3_spl
<=> ~ big_f(sK1_skl,X0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f31,plain,
! [X0] :
( ~ sQ3_spl
| ~ big_f(sK1_skl,X0) ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( ~ sQ1_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f24,f27,f30,f18]) ).
fof(f39,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f7]) ).
fof(f40,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f39]) ).
fof(f43,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f19,f31]) ).
fof(f44,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f43]) ).
fof(f45,plain,
$false,
inference(sat_refutation,[status(thm)],[f21,f23,f33,f40,f44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN354+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n019.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Mon Sep 21 10:51:27 UTC 2026
% 0.10/5.36 % CPUTime :
% 0.10/5.37 % Drodi V4.1.1
% 0.10/5.39 % Refutation found
% 0.10/5.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/5.41 % Elapsed time: 0.040613 seconds
% 0.13/5.41 % CPU time: 0.103261 seconds
% 0.13/5.41 % Total memory used: 14.611 MB
% 0.13/5.41 % Net memory used: 14.151 MB
%------------------------------------------------------------------------------