%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN334+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 : n015.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 03:15:47 PM UTC 2026
% Result : Theorem 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 3 unt; 0 def)
% Number of atoms : 101 ( 0 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 128 ( 53 ~; 44 |; 14 &)
% ( 8 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 48 ( 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [X,Y] :
! [Z] :
( ( big_f(X,Y)
=> ( big_f(X,Z)
<=> big_g(Y,Z) ) )
=> ( ( big_f(X,Y)
<=> ( big_f(Z,Z)
=> big_g(Z,Z) ) )
=> ( big_g(X,Y)
<=> big_g(Z,Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ? [X,Y] :
! [Z] :
( ( big_f(X,Y)
=> ( big_f(X,Z)
<=> big_g(Y,Z) ) )
=> ( ( big_f(X,Y)
<=> ( big_f(Z,Z)
=> big_g(Z,Z) ) )
=> ( big_g(X,Y)
<=> big_g(Z,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [X,Y] :
? [Z] :
( ( big_g(X,Y)
<~> big_g(Z,Z) )
& ( big_f(X,Y)
<=> ( big_g(Z,Z)
| ~ big_f(Z,Z) ) )
& ( ( big_f(X,Z)
<=> big_g(Y,Z) )
| ~ big_f(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
! [X,Y] :
? [Z] :
( ( ~ big_g(Z,Z)
| ~ big_g(X,Y) )
& ( big_g(Z,Z)
| big_g(X,Y) )
& ( ( ~ big_g(Z,Z)
& big_f(Z,Z) )
| big_f(X,Y) )
& ( big_g(Z,Z)
| ~ big_f(Z,Z)
| ~ big_f(X,Y) )
& ( ( ( ~ big_g(Y,Z)
| big_f(X,Z) )
& ( big_g(Y,Z)
| ~ big_f(X,Z) ) )
| ~ big_f(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
! [X,Y] :
( ( ~ big_g(sK0_skl(Y,X),sK0_skl(Y,X))
| ~ big_g(X,Y) )
& ( big_g(sK0_skl(Y,X),sK0_skl(Y,X))
| big_g(X,Y) )
& ( ( ~ big_g(sK0_skl(Y,X),sK0_skl(Y,X))
& big_f(sK0_skl(Y,X),sK0_skl(Y,X)) )
| big_f(X,Y) )
& ( big_g(sK0_skl(Y,X),sK0_skl(Y,X))
| ~ big_f(sK0_skl(Y,X),sK0_skl(Y,X))
| ~ big_f(X,Y) )
& ( ( ( ~ big_g(Y,sK0_skl(Y,X))
| big_f(X,sK0_skl(Y,X)) )
& ( big_g(Y,sK0_skl(Y,X))
| ~ big_f(X,sK0_skl(Y,X)) ) )
| ~ big_f(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Z,sK0_skl(Y,X))],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( big_g(X1,sK0_skl(X1,X0))
| ~ big_f(X0,sK0_skl(X1,X0))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1] :
( ~ big_g(X1,sK0_skl(X1,X0))
| big_f(X0,sK0_skl(X1,X0))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0,X1] :
( big_g(sK0_skl(X1,X0),sK0_skl(X1,X0))
| ~ big_f(sK0_skl(X1,X0),sK0_skl(X1,X0))
| ~ big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0,X1] :
( big_f(sK0_skl(X1,X0),sK0_skl(X1,X0))
| big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( ~ big_g(sK0_skl(X1,X0),sK0_skl(X1,X0))
| big_f(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1] :
( big_g(sK0_skl(X1,X0),sK0_skl(X1,X0))
| big_g(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0,X1] :
( ~ big_g(sK0_skl(X1,X0),sK0_skl(X1,X0))
| ~ big_g(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0,X1] :
( ~ big_g(X0,X1)
| ~ big_f(sK0_skl(X1,X0),sK0_skl(X1,X0))
| ~ big_f(X0,X1) ),
inference(resolution,[status(thm)],[f8,f12]) ).
fof(f16,plain,
! [X0,X1] :
( ~ big_g(sK0_skl(sK0_skl(X1,X0),sK0_skl(X1,X0)),sK0_skl(sK0_skl(X1,X0),sK0_skl(X1,X0)))
| ~ big_g(X0,X1)
| ~ big_f(X0,X1) ),
inference(resolution,[status(thm)],[f14,f10]) ).
fof(f18,plain,
! [X0,X1] :
( big_g(sK0_skl(X1,X0),sK0_skl(X1,X0))
| ~ big_g(X0,X1)
| ~ big_f(X0,X1) ),
inference(resolution,[status(thm)],[f16,f11]) ).
fof(f19,plain,
! [X0,X1] :
( big_g(sK0_skl(X1,X0),sK0_skl(X1,X0))
| ~ big_f(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f18,f11]) ).
fof(f21,plain,
! [X0,X1] :
( ~ big_g(X0,X1)
| ~ big_f(X0,X1) ),
inference(resolution,[status(thm)],[f19,f12]) ).
fof(f23,plain,
! [X0,X1] :
( ~ big_g(X1,sK0_skl(X1,X0))
| ~ big_f(X0,X1)
| ~ big_g(X0,sK0_skl(X1,X0)) ),
inference(resolution,[status(thm)],[f21,f7]) ).
fof(f25,plain,
! [X0] :
( ~ big_f(X0,sK0_skl(X0,X0))
| ~ big_f(X0,X0)
| ~ big_f(X0,X0) ),
inference(resolution,[status(thm)],[f23,f6]) ).
fof(f28,plain,
! [X0] :
( ~ big_f(X0,X0)
| ~ big_g(X0,sK0_skl(X0,X0)) ),
inference(factoring,[status(thm)],[f23]) ).
fof(f29,plain,
! [X0] :
( ~ big_f(X0,sK0_skl(X0,X0))
| ~ big_f(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f25]) ).
fof(f33,plain,
! [X0] :
( ~ big_g(sK0_skl(sK0_skl(X0,X0),X0),sK0_skl(sK0_skl(X0,X0),X0))
| ~ big_f(X0,X0) ),
inference(resolution,[status(thm)],[f29,f10]) ).
fof(f38,plain,
! [X0] :
( big_g(X0,sK0_skl(X0,X0))
| ~ big_f(X0,X0) ),
inference(resolution,[status(thm)],[f33,f11]) ).
fof(f39,plain,
! [X0] : ~ big_f(X0,X0),
inference(forward_subsumption_resolution,[status(thm)],[f38,f28]) ).
fof(f40,plain,
! [X0,X1] : big_f(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f9,f39]) ).
fof(f46,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f39,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN334+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n015.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.45 % CPULimit : 300
% 0.17/0.45 % WCLimit : 300
% 0.17/0.45 % DateTime : Mon Sep 21 10:53:06 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.48 % Drodi V4.1.1
% 0.17/0.50 % Refutation found
% 0.17/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.56 % Elapsed time: 0.086704 seconds
% 0.17/0.56 % CPU time: 0.101325 seconds
% 0.17/0.56 % Total memory used: 2.775 MB
% 0.17/0.56 % Net memory used: 2.743 MB
%------------------------------------------------------------------------------