%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN350+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 : 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 03:15:50 PM UTC 2026
% Result : Theorem 0.21s 0.50s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 3 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 66 ( 23 ~; 19 |; 14 &)
% ( 5 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-2 aty)
% Number of variables : 31 ( 23 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( ( big_f(Y1,Z)
=> big_f(Y1,Y2) )
& big_f(Y2,Z) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [X] :
? [Y1,Y2] :
! [Z] :
( ( big_f(X,Z)
<=> big_f(Z,X) )
=> ( big_f(X,Z)
<=> ( ( big_f(Y1,Z)
=> big_f(Y1,Y2) )
& big_f(Y2,Z) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
? [X] :
! [Y1,Y2] :
? [Z] :
( ( big_f(X,Z)
<~> ( ( big_f(Y1,Y2)
| ~ big_f(Y1,Z) )
& big_f(Y2,Z) ) )
& ( big_f(X,Z)
<=> big_f(Z,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
? [X] :
! [Y1,Y2] :
? [Z] :
( ( ( ~ big_f(Y1,Y2)
& big_f(Y1,Z) )
| ~ big_f(Y2,Z)
| ~ big_f(X,Z) )
& ( ( ( big_f(Y1,Y2)
| ~ big_f(Y1,Z) )
& big_f(Y2,Z) )
| big_f(X,Z) )
& ( ~ big_f(Z,X)
| big_f(X,Z) )
& ( big_f(Z,X)
| ~ big_f(X,Z) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
! [Y1,Y2] :
( ( ( ~ big_f(Y1,Y2)
& big_f(Y1,sK1_skl(Y2,Y1)) )
| ~ big_f(Y2,sK1_skl(Y2,Y1))
| ~ big_f(sK0_skl,sK1_skl(Y2,Y1)) )
& ( ( ( big_f(Y1,Y2)
| ~ big_f(Y1,sK1_skl(Y2,Y1)) )
& big_f(Y2,sK1_skl(Y2,Y1)) )
| big_f(sK0_skl,sK1_skl(Y2,Y1)) )
& ( ~ big_f(sK1_skl(Y2,Y1),sK0_skl)
| big_f(sK0_skl,sK1_skl(Y2,Y1)) )
& ( big_f(sK1_skl(Y2,Y1),sK0_skl)
| ~ big_f(sK0_skl,sK1_skl(Y2,Y1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(X,sK0_skl),skolemize(Z,sK1_skl(Y2,Y1))],[f4]) ).
fof(f6,plain,
! [X0,X1] :
( big_f(sK1_skl(X0,X1),sK0_skl)
| ~ big_f(sK0_skl,sK1_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0,X1] :
( big_f(X0,sK1_skl(X0,X1))
| big_f(sK0_skl,sK1_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
! [X0,X1] :
( ~ big_f(X1,X0)
| ~ big_f(X0,sK1_skl(X0,X1))
| ~ big_f(sK0_skl,sK1_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
! [X0] :
( ~ big_f(X0,sK0_skl)
| ~ big_f(sK0_skl,sK1_skl(sK0_skl,X0)) ),
inference(resolution,[status(thm)],[f11,f8]) ).
fof(f18,plain,
! [X0,X1] :
( ~ big_f(sK0_skl,sK1_skl(X0,X1))
| ~ big_f(sK0_skl,sK1_skl(sK0_skl,sK1_skl(X0,X1))) ),
inference(resolution,[status(thm)],[f14,f6]) ).
fof(f20,plain,
! [X0,X1] : ~ big_f(sK0_skl,sK1_skl(X0,X1)),
inference(resolution,[status(thm)],[f18,f8]) ).
fof(f28,plain,
! [X0,X1] : big_f(X0,sK1_skl(X0,X1)),
inference(backward_subsumption_resolution,[status(thm)],[f8,f20]) ).
fof(f29,plain,
$false,
inference(resolution,[status(thm)],[f28,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN350+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n002.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.46 % CPULimit : 300
% 0.21/0.46 % WCLimit : 300
% 0.21/0.46 % DateTime : Mon Sep 21 10:53:33 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.48 % Drodi V4.1.1
% 0.21/0.50 % Refutation found
% 0.21/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.24/0.57 % Elapsed time: 0.082646 seconds
% 0.24/0.57 % CPU time: 0.094818 seconds
% 0.24/0.57 % Total memory used: 3.120 MB
% 0.24/0.57 % Net memory used: 3.025 MB
%------------------------------------------------------------------------------