%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC090+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:39:55 PM UTC 2026
% Result : Theorem 192.97s 25.13s
% Output : CNFRefutation 110.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 7
% Syntax : Number of formulae : 80 ( 27 unt; 0 def)
% Number of atoms : 268 ( 48 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 327 ( 139 ~; 126 |; 39 &)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 78 ( 64 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(X1,Z) != W
| app(Z,X1) != X ) ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(X1,Z) != W
| app(Z,X1) != X ) ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
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(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ? [Z] :
( ? [X1] :
( app(X1,Z) = W
& app(Z,X1) = X
& ssList(X1) )
& ssList(Z) )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( app(sK52_skl,sK51_skl) = sK49_skl
& app(sK51_skl,sK52_skl) = sK50_skl
& ssList(sK52_skl)
& ssList(sK51_skl)
& ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK48_skl,nil)
& 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,sK51_skl,sK52_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_skl),skolemize(X1,sK52_skl)],[f415]) ).
fof(f417,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f420,plain,
ssList(sK50_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,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
app(sK51_skl,sK52_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
app(sK52_skl,sK51_skl) = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f465,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f469,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK51_skl)
| segmentP(app(app(sK51_skl,sK52_skl),X0),sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f427,f435]) ).
fof(f470,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK51_skl)
| segmentP(app(sK50_skl,X0),sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f427,f469]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK51_skl)
| segmentP(app(sK50_skl,X0),sK52_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f426]) ).
fof(f472,plain,
app(sK52_skl,sK51_skl) = sK47_skl,
inference(forward_demodulation,[status(thm)],[f422,f428]) ).
fof(f473,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK52_skl)
| segmentP(app(app(sK52_skl,sK51_skl),X0),sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f472,f435]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK52_skl)
| segmentP(app(sK47_skl,X0),sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f472,f473]) ).
fof(f475,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK52_skl)
| segmentP(app(sK47_skl,X0),sK51_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f474,f425]) ).
fof(f476,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f424]) ).
fof(f477,plain,
( ~ ssList(sK50_skl)
| ~ segmentP(sK47_skl,sK50_skl)
| ~ neq(sK50_skl,nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f476,f319]) ).
fof(f478,plain,
( ~ segmentP(sK47_skl,sK50_skl)
| ~ neq(sK50_skl,nil)
| ~ ssList(sK50_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f477]) ).
fof(f479,plain,
( ~ segmentP(sK47_skl,sK50_skl)
| ~ neq(sK50_skl,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f420]) ).
fof(f481,plain,
app(nil,sK52_skl) = sK52_skl,
inference(resolution,[status(thm)],[f249,f426]) ).
fof(f488,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK52_skl),X0),sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK52_skl,X0)) ),
inference(paramodulation,[status(thm)],[f481,f435]) ).
fof(f489,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(sK52_skl,X0),sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK52_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f481,f488]) ).
fof(f490,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(sK52_skl,X0),sK52_skl)
| ~ ssList(app(sK52_skl,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f426]) ).
fof(f517,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(app(sK50_skl,X0),sK52_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f425]) ).
fof(f525,plain,
app(sK51_skl,nil) = sK51_skl,
inference(resolution,[status(thm)],[f389,f425]) ).
fof(f528,plain,
app(sK50_skl,nil) = sK50_skl,
inference(resolution,[status(thm)],[f389,f420]) ).
fof(f530,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f417]) ).
fof(f545,plain,
( ~ ssList(nil)
| segmentP(sK50_skl,sK52_skl)
| ~ ssList(app(sK50_skl,nil)) ),
inference(paramodulation,[status(thm)],[f528,f517]) ).
fof(f548,plain,
( ~ ssList(nil)
| segmentP(sK50_skl,sK52_skl)
| ~ ssList(sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f528,f545]) ).
fof(f549,plain,
( ~ ssList(nil)
| segmentP(sK50_skl,sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f420]) ).
fof(f574,plain,
segmentP(sK50_skl,sK52_skl),
inference(forward_subsumption_resolution,[status(thm)],[f549,f223]) ).
fof(f575,plain,
( ~ segmentP(sK47_skl,sK52_skl)
| ~ neq(sK52_skl,nil)
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f574,f476]) ).
fof(f576,plain,
( ~ segmentP(sK47_skl,sK52_skl)
| ~ neq(sK52_skl,nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f575,f426]) ).
fof(f583,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(app(sK47_skl,X0),sK51_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f475,f426]) ).
fof(f584,plain,
( ~ ssList(nil)
| segmentP(sK47_skl,sK51_skl)
| ~ ssList(app(sK47_skl,nil)) ),
inference(paramodulation,[status(thm)],[f530,f583]) ).
fof(f585,plain,
( ~ ssList(nil)
| segmentP(sK47_skl,sK51_skl)
| ~ ssList(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f530,f584]) ).
fof(f586,plain,
( ~ ssList(nil)
| segmentP(sK47_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f585,f417]) ).
fof(f654,plain,
segmentP(sK47_skl,sK51_skl),
inference(forward_subsumption_resolution,[status(thm)],[f586,f223]) ).
fof(f665,plain,
~ segmentP(sK47_skl,sK50_skl),
inference(forward_subsumption_resolution,[status(thm)],[f479,f465]) ).
fof(f22413,plain,
! [X0] :
( ~ ssList(X0)
| segmentP(app(sK52_skl,X0),sK52_skl)
| ~ ssList(app(sK52_skl,X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f223]) ).
fof(f22417,plain,
( ~ ssList(sK51_skl)
| segmentP(app(sK52_skl,sK51_skl),sK52_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f472,f22413]) ).
fof(f22422,plain,
( ~ ssList(sK51_skl)
| segmentP(sK47_skl,sK52_skl)
| ~ ssList(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f472,f22417]) ).
fof(f22423,plain,
( ~ ssList(sK51_skl)
| segmentP(sK47_skl,sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f22422,f417]) ).
fof(f22424,plain,
~ neq(sK52_skl,nil),
inference(backward_subsumption_resolution,[status(thm)],[f576,f22425]) ).
fof(f22425,plain,
segmentP(sK47_skl,sK52_skl),
inference(forward_subsumption_resolution,[status(thm)],[f22423,f425]) ).
fof(f22500,plain,
( sK52_skl = nil
| ~ ssList(nil)
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f22424,f220]) ).
fof(f22501,plain,
( sK52_skl = nil
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f22500,f426]) ).
fof(f22945,plain,
app(sK51_skl,sK52_skl) = sK51_skl,
inference(backward_demodulation,[status(thm)],[f22970,f525]) ).
fof(f22970,plain,
sK52_skl = nil,
inference(forward_subsumption_resolution,[status(thm)],[f22501,f223]) ).
fof(f23122,plain,
sK50_skl = sK51_skl,
inference(forward_demodulation,[status(thm)],[f427,f22945]) ).
fof(f23213,plain,
segmentP(sK47_skl,sK50_skl),
inference(backward_demodulation,[status(thm)],[f23122,f654]) ).
fof(f23271,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f23213,f665]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC090+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n016.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 21 07:59:37 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.47 % Drodi V4.1.1
% 192.97/25.13 % Refutation found
% 192.97/25.13 % SZS status Theorem for theBenchmark: Theorem is valid
% 192.97/25.13 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 196.10/25.90 % Elapsed time: 25.454497 seconds
% 196.10/25.90 % CPU time: 195.774049 seconds
% 196.10/25.90 % Total memory used: 456.336 MB
% 196.10/25.90 % Net memory used: 413.567 MB
%------------------------------------------------------------------------------