%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN726+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 03:17:10 PM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 96 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 103 ( 33 ~; 37 |; 25 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 94 ( 86 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X,Y] : q(X,Y)
| ( ( ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y,Z] :
( ( q(Y,Z)
& q(X,Y) )
=> q(X,Z) )
& ! [X,Y,Z] :
( ( p(Y,Z)
& p(X,Y) )
=> p(X,Z) ) )
=> ! [X,Y] : p(X,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X,Y] : q(X,Y)
| ( ( ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(X,Y)
=> q(Y,X) )
& ! [X,Y,Z] :
( ( q(Y,Z)
& q(X,Y) )
=> q(X,Z) )
& ! [X,Y,Z] :
( ( p(Y,Z)
& p(X,Y) )
=> p(X,Z) ) )
=> ! [X,Y] : p(X,Y) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X,Y] : ~ q(X,Y)
& ? [X,Y] : ~ p(X,Y)
& ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(Y,X)
| ~ q(X,Y) )
& ! [X,Y,Z] :
( q(X,Z)
| ~ q(Y,Z)
| ~ q(X,Y) )
& ! [X,Y,Z] :
( p(X,Z)
| ~ p(Y,Z)
| ~ p(X,Y) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ? [X,Y] : ~ q(X,Y)
& ? [X,Y] : ~ p(X,Y)
& ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(Y,X)
| ~ q(X,Y) )
& ! [X,Z] :
( q(X,Z)
| ! [Y] :
( ~ q(Y,Z)
| ~ q(X,Y) ) )
& ! [X,Z] :
( p(X,Z)
| ! [Y] :
( ~ p(Y,Z)
| ~ p(X,Y) ) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f5,plain,
( ~ q(sK2_skl,sK3_skl)
& ~ p(sK0_skl,sK1_skl)
& ! [X,Y] :
( q(X,Y)
| p(X,Y) )
& ! [X,Y] :
( q(Y,X)
| ~ q(X,Y) )
& ! [X,Z] :
( q(X,Z)
| ! [Y] :
( ~ q(Y,Z)
| ~ q(X,Y) ) )
& ! [X,Z] :
( p(X,Z)
| ! [Y] :
( ~ p(Y,Z)
| ~ p(X,Y) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl,sK3_skl]),skolemize(X,sK0_skl),skolemize(Y,sK1_skl),skolemize(X,sK2_skl),skolemize(Y,sK3_skl)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2] :
( p(X0,X2)
| ~ p(X1,X2)
| ~ p(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( q(X0,X2)
| ~ q(X1,X2)
| ~ q(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f8,plain,
! [X0,X1] :
( q(X1,X0)
| ~ q(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f9,plain,
! [X0,X1] :
( q(X0,X1)
| p(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f10,plain,
~ p(sK0_skl,sK1_skl),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f11,plain,
~ q(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
q(sK0_skl,sK1_skl),
inference(resolution,[status(thm)],[f9,f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( p(X2,X1)
| ~ p(X2,X0)
| q(X0,X1) ),
inference(resolution,[status(thm)],[f9,f6]) ).
fof(f14,plain,
! [X0] :
( q(X0,sK1_skl)
| ~ q(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f12,f7]) ).
fof(f15,plain,
q(sK1_skl,sK0_skl),
inference(resolution,[status(thm)],[f12,f8]) ).
fof(f16,plain,
! [X0] :
( q(X0,sK0_skl)
| ~ q(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f15,f7]) ).
fof(f26,plain,
! [X0,X1,X2] :
( q(X2,X0)
| p(X2,X1)
| q(X0,X1) ),
inference(resolution,[status(thm)],[f13,f9]) ).
fof(f27,plain,
! [X0] :
( q(sK0_skl,X0)
| q(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f26,f10]) ).
fof(f30,plain,
! [X0] :
( q(X0,sK0_skl)
| q(sK0_skl,X0) ),
inference(resolution,[status(thm)],[f27,f16]) ).
fof(f33,plain,
! [X0] : q(sK0_skl,X0),
inference(forward_subsumption_resolution,[status(thm)],[f30,f8]) ).
fof(f37,plain,
! [X0] : q(X0,sK0_skl),
inference(resolution,[status(thm)],[f33,f8]) ).
fof(f38,plain,
! [X0] : q(X0,sK1_skl),
inference(backward_subsumption_resolution,[status(thm)],[f14,f37]) ).
fof(f42,plain,
! [X0] : q(sK1_skl,X0),
inference(resolution,[status(thm)],[f38,f8]) ).
fof(f43,plain,
! [X0,X1] :
( q(X0,X1)
| ~ q(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f42,f7]) ).
fof(f45,plain,
! [X0,X1] : q(X0,X1),
inference(forward_subsumption_resolution,[status(thm)],[f43,f38]) ).
fof(f47,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f11,f45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN726+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n003.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 11:15:18 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.38 % Refutation found
% 0.12/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.40 % Elapsed time: 0.041120 seconds
% 0.12/0.40 % CPU time: 0.116023 seconds
% 0.12/0.40 % Total memory used: 16.688 MB
% 0.12/0.40 % Net memory used: 16.155 MB
%------------------------------------------------------------------------------