%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC351+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 : n001.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 02:40:53 PM UTC 2026
% Result : Theorem 0.09s 0.55s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 14 unt; 4 def)
% Number of atoms : 183 ( 45 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 218 ( 75 ~; 69 |; 56 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 58 ( 37 !; 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(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = W
& nil != X )
| frontsegP(V,U)
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| ~ 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 )
| frontsegP(V,U)
| ! [Y] :
( ssList(Y)
=> ( ? [Z] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( lt(X2,Z)
& app(X3,cons(X2,nil)) = W
& ssList(X3) )
& ssItem(X2) )
& app(cons(Z,nil),X1) = Y
& ssList(X1) )
& ssItem(Z) )
| ~ strictorderedP(W)
| app(W,Y) != X ) )
| ~ 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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( nil != W
| nil = X )
& ~ frontsegP(V,U)
& ? [Y] :
( ! [Z] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ~ lt(X2,Z)
| app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& 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 )
& ~ frontsegP(V,U)
& ? [Y] :
( ! [Z] :
( ! [X2] :
( ~ lt(X2,Z)
| ! [X3] :
( app(X3,cons(X2,nil)) != W
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != Y
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(W)
& app(W,Y) = X
& 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 )
& ~ frontsegP(sK48_skl,sK47_skl)
& ! [Z] :
( ! [X2] :
( ~ lt(X2,Z)
| ! [X3] :
( app(X3,cons(X2,nil)) != sK49_skl
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ! [X1] :
( app(cons(Z,nil),X1) != sK51_skl
| ~ ssList(X1) )
| ~ ssItem(Z) )
& strictorderedP(sK49_skl)
& app(sK49_skl,sK51_skl) = sK50_skl
& ssList(sK51_skl)
& 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(Y,sK51_skl)],[f416]) ).
fof(f420,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f421,plain,
ssList(sK50_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(f425,plain,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f426,plain,
app(sK49_skl,sK51_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f429,plain,
~ frontsegP(sK48_skl,sK47_skl),
inference(cnf_transformation,[status(thm)],[f417]) ).
fof(f442,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f483,plain,
~ frontsegP(sK48_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f423,f429]) ).
fof(f484,plain,
~ frontsegP(sK50_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f422,f483]) ).
fof(f486,plain,
( ~ ssList(sK51_skl)
| frontsegP(app(sK49_skl,sK51_skl),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f426,f442]) ).
fof(f487,definition,
( sQ2_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f489,plain,
( sQ2_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f487]) ).
fof(f490,definition,
( sQ3_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ3_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,definition,
( sQ4_spl
<=> frontsegP(app(sK49_skl,sK51_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f494,plain,
( ~ sQ4_spl
| frontsegP(app(sK49_skl,sK51_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
( sQ5_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( sQ5_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( ~ sQ5_spl
| sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f486,f487,f490,f493,f496]) ).
fof(f500,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f425]) ).
fof(f501,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f500]) ).
fof(f502,plain,
( ~ sQ4_spl
| frontsegP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f426,f494]) ).
fof(f503,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f484]) ).
fof(f504,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f489,f421]) ).
fof(f506,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f508,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f420]) ).
fof(f509,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f510,plain,
$false,
inference(sat_refutation,[status(thm)],[f499,f501,f504,f506,f509]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC351+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.51 % Computer : n001.cluster.edu
% 0.09/0.51 % Model : x86_64 x86_64
% 0.09/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.51 % Memory : 8046.5625MB
% 0.09/0.51 % OS : Linux 6.8.0-71-generic
% 0.09/0.51 % CPULimit : 300
% 0.09/0.51 % WCLimit : 300
% 0.09/0.51 % DateTime : Mon Sep 21 08:23:44 UTC 2026
% 0.09/0.51 % CPUTime :
% 0.09/0.53 % Drodi V4.1.1
% 0.09/0.55 % Refutation found
% 0.09/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.60 % Elapsed time: 0.070601 seconds
% 0.14/0.60 % CPU time: 0.173197 seconds
% 0.14/0.60 % Total memory used: 110.549 MB
% 0.14/0.60 % Net memory used: 110.384 MB
%------------------------------------------------------------------------------