%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC008+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 : n008.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 02:39:33 PM UTC 2026
% Result : Theorem 0.24s 0.99s
% Output : CNFRefutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 62 ( 17 unt; 8 def)
% Number of atoms : 214 ( 49 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 247 ( 95 ~; 91 |; 40 &)
% ( 10 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 9 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 54 ( 39 !; 15 ?)
% 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(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ? [X2] :
( equalelemsP(X2)
& segmentP(X2,W)
& frontsegP(X,X2)
& neq(W,X2)
& ssList(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| ~ equalelemsP(W)
| ~ frontsegP(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)
=> ( ? [X2] :
( equalelemsP(X2)
& segmentP(X2,W)
& frontsegP(X,X2)
& neq(W,X2)
& ssList(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( app(Y,X1) = U
& app(app(Y,Z),X1) = V
& ssList(X1) )
& ssList(Z) )
& ssList(Y) )
| ~ equalelemsP(W)
| ~ frontsegP(X,W)
| 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(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
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] :
( ! [X2] :
( ~ equalelemsP(X2)
| ~ segmentP(X2,W)
| ~ frontsegP(X,X2)
| ~ neq(W,X2)
| ~ ssList(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != U
| app(app(Y,Z),X1) != V
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& equalelemsP(W)
& frontsegP(X,W)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ! [X2] :
( ~ equalelemsP(X2)
| ~ segmentP(X2,sK49_skl)
| ~ frontsegP(sK50_skl,X2)
| ~ neq(sK49_skl,X2)
| ~ ssList(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( app(Y,X1) != sK47_skl
| app(app(Y,Z),X1) != sK48_skl
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssList(Y) )
& equalelemsP(sK49_skl)
& frontsegP(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(f417,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f418,plain,
ssList(sK48_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,
frontsegP(sK50_skl,sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
! [X0,X1,X2] :
( app(X0,X2) != sK47_skl
| app(app(X0,X1),X2) != sK48_skl
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f461,plain,
frontsegP(sK48_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f462,plain,
frontsegP(sK48_skl,sK47_skl),
inference(forward_demodulation,[status(thm)],[f422,f461]) ).
fof(f489,definition,
( sQ4_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( sQ4_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f495,definition,
( sQ6_spl
<=> frontsegP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ6_spl
| ~ frontsegP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f504,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f462]) ).
fof(f505,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f506,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f417]) ).
fof(f507,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f546,plain,
( app(sK47_skl,sK5_skl(sK47_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f123,f462]) ).
fof(f549,definition,
( sQ12_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( sQ12_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f552,definition,
( sQ13_spl
<=> app(sK47_skl,sK5_skl(sK47_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( ~ sQ13_spl
| app(sK47_skl,sK5_skl(sK47_skl,sK48_skl)) = sK48_skl ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,plain,
( sQ13_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f546,f549,f489,f552]) ).
fof(f562,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f551,f418]) ).
fof(f563,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f562]) ).
fof(f579,plain,
! [X0] :
( ~ sQ13_spl
| app(sK47_skl,X0) != sK47_skl
| app(sK48_skl,X0) != sK48_skl
| ~ ssList(X0)
| ~ ssList(sK5_skl(sK47_skl,sK48_skl))
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f553,f425]) ).
fof(f580,definition,
( sQ17_spl
<=> ssList(sK5_skl(sK47_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f582,plain,
( sQ17_spl
| ~ ssList(sK5_skl(sK47_skl,sK48_skl)) ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f584,definition,
! [X0] :
( sQ18_spl
<=> ( app(sK47_skl,X0) != sK47_skl
| app(sK48_skl,X0) != sK48_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f585,plain,
! [X0] :
( ~ sQ18_spl
| app(sK47_skl,X0) != sK47_skl
| app(sK48_skl,X0) != sK48_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f584]) ).
fof(f587,plain,
( ~ sQ13_spl
| sQ18_spl
| ~ sQ17_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f579,f489,f580,f584,f552]) ).
fof(f588,plain,
( sQ17_spl
| ~ frontsegP(sK48_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f582,f122]) ).
fof(f589,plain,
( sQ17_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f588,f549,f489,f495,f580]) ).
fof(f597,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f418]) ).
fof(f598,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f417]) ).
fof(f865,definition,
( sQ43_spl
<=> app(sK48_skl,nil) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f867,plain,
( sQ43_spl
| app(sK48_skl,nil) != sK48_skl ),
inference(component_clause,[status(thm)],[f865]) ).
fof(f879,plain,
( sQ43_spl
| sK48_skl != sK48_skl ),
inference(forward_demodulation,[status(thm)],[f597,f867]) ).
fof(f880,plain,
( sQ43_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f879]) ).
fof(f881,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f880]) ).
fof(f968,plain,
( ~ sQ18_spl
| app(sK47_skl,nil) != sK47_skl
| app(sK48_skl,nil) != sK48_skl ),
inference(resolution,[status(thm)],[f585,f223]) ).
fof(f978,definition,
( sQ53_spl
<=> app(sK47_skl,nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f980,plain,
( sQ53_spl
| app(sK47_skl,nil) != sK47_skl ),
inference(component_clause,[status(thm)],[f978]) ).
fof(f981,plain,
( ~ sQ18_spl
| ~ sQ53_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f968,f865,f978,f584]) ).
fof(f986,plain,
( sQ53_spl
| sK47_skl != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f598,f980]) ).
fof(f987,plain,
( sQ53_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f986]) ).
fof(f988,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f987]) ).
fof(f989,plain,
$false,
inference(sat_refutation,[status(thm)],[f505,f507,f555,f563,f587,f589,f881,f981,f988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC008+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Mon Sep 21 07:49:40 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.47 % Drodi V4.1.1
% 0.24/0.99 % Refutation found
% 0.24/0.99 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.24/0.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.22/1.04 % Elapsed time: 0.575954 seconds
% 3.22/1.04 % CPU time: 3.823469 seconds
% 3.22/1.04 % Total memory used: 140.163 MB
% 3.22/1.04 % Net memory used: 137.647 MB
%------------------------------------------------------------------------------