%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC019+1 : TPTP v9.3.1. Released v2.4.0.
% 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 02:39:36 PM UTC 2026
% Result : Theorem 0.18s 0.52s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 119 ( 40 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 148 ( 63 ~; 47 |; 25 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 31 ( 25 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = U
& nil = V )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| X != W
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = U
& nil = V )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| X != W
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f285,plain,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f286,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != U
| nil != V )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& X = W
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( nil != sK47_skl
| nil != sK48_skl )
& ! [Y] :
( ~ frontsegP(sK47_skl,Y)
| ~ frontsegP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK50_skl = sK49_skl
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f415]) ).
fof(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
sK50_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f462,plain,
sK48_skl = sK49_skl,
inference(backward_demodulation,[status(thm)],[f423,f421]) ).
fof(f464,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f462,f424]) ).
fof(f465,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f464]) ).
fof(f466,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f465]) ).
fof(f467,plain,
( ~ neq(sK49_skl,nil)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f286,f466]) ).
fof(f468,plain,
( ~ neq(sK49_skl,nil)
| ~ ssList(sK49_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f467]) ).
fof(f469,plain,
~ neq(sK49_skl,nil),
inference(forward_subsumption_resolution,[status(thm)],[f468,f419]) ).
fof(f473,plain,
( sK49_skl = nil
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f469,f220]) ).
fof(f474,plain,
( sK49_skl = nil
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f419]) ).
fof(f475,plain,
( nil != sK47_skl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f462,f425]) ).
fof(f476,plain,
( nil != sK49_skl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f422,f475]) ).
fof(f477,plain,
nil != sK49_skl,
inference(duplicate_literals_removal,[status(thm)],[f476]) ).
fof(f478,plain,
sK49_skl != sK49_skl,
inference(backward_demodulation,[status(thm)],[f491,f477]) ).
fof(f491,plain,
sK49_skl = nil,
inference(forward_subsumption_resolution,[status(thm)],[f474,f223]) ).
fof(f492,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f478]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC019+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n003.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 07:51:16 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.50 % Drodi V4.1.1
% 0.18/0.52 % Refutation found
% 0.18/0.52 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.23/0.57 % Elapsed time: 0.100034 seconds
% 0.23/0.57 % CPU time: 0.125401 seconds
% 0.23/0.57 % Total memory used: 20.784 MB
% 0.23/0.57 % Net memory used: 20.751 MB
%------------------------------------------------------------------------------