%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC024+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 : n017.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 02:39:38 PM UTC 2026
% Result : Theorem 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 56 ( 18 unt; 0 def)
% Number of atoms : 244 ( 66 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 312 ( 124 ~; 110 |; 59 &)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 74 ( 53 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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 = W
& nil != X )
| ! [Z] :
( ssList(Z)
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( app(X3,cons(X1,nil)) = W
& ssList(X3) )
& app(cons(X1,nil),X2) = Z
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(W,Z) != X ) )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| 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 = W
& nil != X )
| ! [Z] :
( ssList(Z)
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( app(X3,cons(X1,nil)) = W
& ssList(X3) )
& app(cons(X1,nil),X2) = Z
& ssList(X2) )
& ssItem(X1) )
| ~ equalelemsP(W)
| app(W,Z) != X ) )
| ? [Y] :
( frontsegP(U,Y)
& frontsegP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
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 != W
| nil = X )
& ? [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( app(X3,cons(X1,nil)) != W
| ~ ssList(X3) )
| app(cons(X1,nil),X2) != Z
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(W)
& app(W,Z) = X
& ssList(Z) )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(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,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ? [Z] :
( ! [X1] :
( ! [X3] :
( app(X3,cons(X1,nil)) != W
| ~ ssList(X3) )
| ! [X2] :
( app(cons(X1,nil),X2) != Z
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(W)
& app(W,Z) = X
& ssList(Z) )
& ! [Y] :
( ~ frontsegP(U,Y)
| ~ frontsegP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f415]) ).
fof(f417,plain,
( ( nil != sK49_skl
| nil = sK50_skl )
& ! [X1] :
( ! [X3] :
( app(X3,cons(X1,nil)) != sK49_skl
| ~ ssList(X3) )
| ! [X2] :
( app(cons(X1,nil),X2) != sK51_skl
| ~ ssList(X2) )
| ~ ssItem(X1) )
& equalelemsP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_skl
& ssList(sK51_skl)
& ! [Y] :
( ~ frontsegP(sK47_skl,Y)
| ~ frontsegP(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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_skl)],[f416]) ).
fof(f419,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f424,plain,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f425,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f427,plain,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f430,plain,
( nil != sK49_skl
| nil = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f435,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f464,plain,
app(sK49_skl,sK51_skl) = sK48_skl,
inference(forward_demodulation,[status(thm)],[f422,f427]) ).
fof(f465,plain,
( nil != sK49_skl
| nil = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f422,f430]) ).
fof(f466,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f425]) ).
fof(f467,plain,
( ~ frontsegP(sK49_skl,sK48_skl)
| ~ frontsegP(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f466,f424]) ).
fof(f469,plain,
( ~ frontsegP(sK49_skl,sK48_skl)
| ~ frontsegP(sK48_skl,sK48_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f419]) ).
fof(f471,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,sK51_skl)) ),
inference(paramodulation,[status(thm)],[f464,f435]) ).
fof(f472,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f464,f471]) ).
fof(f473,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f419]) ).
fof(f474,plain,
( ~ ssList(sK48_skl)
| ~ frontsegP(sK49_skl,sK48_skl) ),
inference(resolution,[status(thm)],[f469,f286]) ).
fof(f475,plain,
~ frontsegP(sK49_skl,sK48_skl),
inference(forward_subsumption_resolution,[status(thm)],[f474,f419]) ).
fof(f476,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f420]) ).
fof(f481,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f220,f466]) ).
fof(f484,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| X0 = nil
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f481]) ).
fof(f485,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| X0 = nil
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f223]) ).
fof(f500,plain,
( ~ ssList(sK51_skl)
| ~ frontsegP(sK49_skl,sK49_skl)
| sK49_skl = nil
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f485,f476]) ).
fof(f503,plain,
( ~ ssList(sK51_skl)
| ~ frontsegP(sK49_skl,sK49_skl)
| sK49_skl = nil ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f420]) ).
fof(f505,plain,
( ~ frontsegP(sK49_skl,sK49_skl)
| sK49_skl = nil ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f426]) ).
fof(f506,plain,
( ~ ssList(sK49_skl)
| sK49_skl = nil ),
inference(resolution,[status(thm)],[f505,f286]) ).
fof(f507,plain,
sK49_skl = nil,
inference(forward_subsumption_resolution,[status(thm)],[f506,f420]) ).
fof(f511,plain,
( ~ ssList(sK51_skl)
| frontsegP(sK48_skl,nil) ),
inference(backward_demodulation,[status(thm)],[f507,f476]) ).
fof(f512,plain,
~ frontsegP(nil,sK48_skl),
inference(backward_demodulation,[status(thm)],[f507,f475]) ).
fof(f514,plain,
( nil != nil
| nil = sK48_skl ),
inference(backward_demodulation,[status(thm)],[f507,f465]) ).
fof(f519,plain,
frontsegP(sK48_skl,nil),
inference(forward_subsumption_resolution,[status(thm)],[f511,f426]) ).
fof(f520,plain,
nil = sK48_skl,
inference(trivial_equality_resolution,[status(thm)],[f514]) ).
fof(f526,plain,
frontsegP(nil,nil),
inference(forward_demodulation,[status(thm)],[f520,f519]) ).
fof(f528,plain,
~ frontsegP(nil,nil),
inference(forward_demodulation,[status(thm)],[f520,f512]) ).
fof(f529,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f528,f526]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC024+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/5.39 % Computer : n017.cluster.edu
% 0.12/5.39 % Model : x86_64 x86_64
% 0.12/5.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.39 % Memory : 8046.5625MB
% 0.12/5.39 % OS : Linux 6.8.0-71-generic
% 0.12/5.39 % CPULimit : 300
% 0.12/5.39 % WCLimit : 300
% 0.12/5.39 % DateTime : Mon Sep 21 07:45:18 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.15/5.41 % Drodi V4.1.1
% 0.15/5.42 % Refutation found
% 0.15/5.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.45 % Elapsed time: 0.054592 seconds
% 0.15/5.45 % CPU time: 0.163909 seconds
% 0.15/5.45 % Total memory used: 69.460 MB
% 0.15/5.45 % Net memory used: 69.351 MB
%------------------------------------------------------------------------------