%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN965+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 03:18:35 PM UTC 2026
% Result : Theorem 0.10s 0.38s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 4 unt; 1 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 64 ( 23 ~; 18 |; 18 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 56 ( 46 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
? [Z] :
! [X] :
? [Y] :
( ( ( p(Y,Z)
& p(Z,Y) )
=> p(Y,X) )
& ( p(Y,X)
=> ? [W] : p(W,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ? [Z] :
! [X] :
? [Y] :
( ( ( p(Y,Z)
& p(Z,Y) )
=> p(Y,X) )
& ( p(Y,X)
=> ? [W] : p(W,Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
! [X,Y] :
( sP0_prd(Y,X)
<=> ( ! [W] : ~ p(W,Y)
& p(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| sP0_prd(Y,X) ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
! [Z,Y] :
( ( ~ p(Y,sK0_skl(Z))
& p(Y,Z)
& p(Z,Y) )
| sP0_prd(Y,sK0_skl(Z)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(Z))],[f5]) ).
fof(f8,plain,
! [X0,X1] :
( p(X0,X1)
| sP0_prd(X0,sK0_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( ~ p(X0,sK0_skl(X1))
| sP0_prd(X0,sK0_skl(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X,Y] :
( ( ? [W] : p(W,Y)
| ~ p(Y,X)
| sP0_prd(Y,X) )
& ( ( ! [W] : ~ p(W,Y)
& p(Y,X) )
| ~ sP0_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f11,plain,
( ! [X,Y] :
( ? [W] : p(W,Y)
| ~ p(Y,X)
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ! [W] : ~ p(W,Y)
& p(Y,X) )
| ~ sP0_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f12,plain,
( ! [X,Y] :
( p(sK1_skl(Y,X),Y)
| ~ p(Y,X)
| sP0_prd(Y,X) )
& ! [X,Y] :
( ( ! [W] : ~ p(W,Y)
& p(Y,X) )
| ~ sP0_prd(Y,X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(W,sK1_skl(Y,X))],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( p(X0,X1)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ p(X2,X0)
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ p(X2,X0)
| p(X0,X1) ),
inference(resolution,[status(thm)],[f8,f14]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ p(X2,X0)
| sP0_prd(X0,sK0_skl(X1)) ),
inference(resolution,[status(thm)],[f9,f17]) ).
fof(f21,plain,
! [X0,X1] : ~ p(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f18,f14]) ).
fof(f22,plain,
! [X0,X1] : sP0_prd(X0,sK0_skl(X1)),
inference(backward_subsumption_resolution,[status(thm)],[f8,f21]) ).
fof(f24,plain,
! [X0,X1] : ~ sP0_prd(X0,X1),
inference(backward_subsumption_resolution,[status(thm)],[f13,f21]) ).
fof(f25,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f22,f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN965+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n008.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 11:31:53 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 0.10/0.38 % Refutation found
% 0.10/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.40 % Elapsed time: 0.033818 seconds
% 0.14/0.40 % CPU time: 0.093514 seconds
% 0.14/0.40 % Total memory used: 13.964 MB
% 0.14/0.40 % Net memory used: 13.462 MB
%------------------------------------------------------------------------------