%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC357+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 02:40:55 PM UTC 2026
% Result : Theorem 0.14s 0.50s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 85 ( 16 unt; 10 def)
% Number of atoms : 301 ( 56 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 358 ( 142 ~; 133 |; 52 &)
% ( 16 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 10 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 85 ( 68 !; 17 ?)
% 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(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/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(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| segmentP(V,U)
| ~ 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)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| segmentP(V,U)
| ~ 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(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(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(f219,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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ~ segmentP(V,U)
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X] :
( sP0_prd(X,W)
<=> ( nil = W
& nil = X ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| sP0_prd(X,W) )
& ~ segmentP(V,U)
& neq(V,nil)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( frontsegP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl) )
& ~ segmentP(sK48_skl,sK47_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f421,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f422,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
neq(sK48_skl,nil),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
~ segmentP(sK48_skl,sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( frontsegP(sK50_skl,sK49_skl)
| sP0_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [W,X] :
( ( nil != W
| nil != X
| sP0_prd(X,W) )
& ( ( nil = W
& nil = X )
| ~ sP0_prd(X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ! [W,X] :
( nil != W
| nil != X
| sP0_prd(X,W) )
& ! [W,X] :
( ( nil = W
& nil = X )
| ~ sP0_prd(X,W) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f434,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f441,definition,
( sQ2_spl
<=> frontsegP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ2_spl
| frontsegP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f428,f434,f441]) ).
fof(f451,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(f460,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f461,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f460]) ).
fof(f482,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f423,f425]) ).
fof(f483,plain,
~ segmentP(sK50_skl,sK47_skl),
inference(forward_demodulation,[status(thm)],[f423,f426]) ).
fof(f484,plain,
~ segmentP(sK50_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f424,f483]) ).
fof(f486,plain,
( ~ sQ0_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f435,f431]) ).
fof(f498,plain,
( ~ sQ0_spl
| neq(sK50_skl,sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f486,f482]) ).
fof(f558,definition,
( sQ6_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ6_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f578,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f421]) ).
fof(f579,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f584,plain,
( ~ sQ2_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f442,f123]) ).
fof(f588,definition,
( sQ12_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ12_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f607,definition,
( sQ17_spl
<=> app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f608,plain,
( ~ sQ17_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl ),
inference(component_clause,[status(thm)],[f607]) ).
fof(f610,plain,
( ~ sQ2_spl
| sQ17_spl
| ~ sQ6_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f584,f588,f558,f607,f441]) ).
fof(f611,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f422]) ).
fof(f612,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f611]) ).
fof(f622,definition,
( sQ20_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f624,plain,
( sQ20_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f622]) ).
fof(f629,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f624,f223]) ).
fof(f630,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f629]) ).
fof(f739,definition,
( sQ36_spl
<=> ssList(sK5_skl(sK49_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( sQ36_spl
| ~ ssList(sK5_skl(sK49_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f756,plain,
( sQ36_spl
| ~ frontsegP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f741,f122]) ).
fof(f757,plain,
( sQ36_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f756,f588,f558,f441,f739]) ).
fof(f840,plain,
app(nil,sK49_skl) = sK49_skl,
inference(resolution,[status(thm)],[f249,f421]) ).
fof(f907,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f840,f451]) ).
fof(f916,definition,
! [X0] :
( sQ57_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f917,plain,
! [X0] :
( ~ sQ57_spl
| ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(component_clause,[status(thm)],[f916]) ).
fof(f919,plain,
( ~ sQ20_spl
| ~ sQ6_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f907,f916,f558,f622]) ).
fof(f921,plain,
! [X0] :
( ~ sQ57_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f840,f917]) ).
fof(f1174,plain,
( ~ sQ0_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f498,f461]) ).
fof(f1175,plain,
( ~ sQ0_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1174,f588,f434]) ).
fof(f1489,plain,
( ~ sQ17_spl
| ~ sQ57_spl
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f608,f921]) ).
fof(f1495,definition,
( sQ126_spl
<=> segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1496,plain,
( ~ sQ126_spl
| segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl) ),
inference(component_clause,[status(thm)],[f1495]) ).
fof(f1498,plain,
( ~ sQ17_spl
| ~ sQ57_spl
| ~ sQ36_spl
| sQ126_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1489,f588,f1495,f739,f916,f607]) ).
fof(f1505,plain,
( ~ sQ126_spl
| ~ sQ17_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f608,f1496]) ).
fof(f1506,plain,
( ~ sQ126_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1505,f484]) ).
fof(f1507,plain,
( ~ sQ126_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f1506]) ).
fof(f1508,plain,
$false,
inference(sat_refutation,[status(thm)],[f444,f579,f610,f612,f630,f757,f919,f1175,f1498,f1507]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC357+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 08:13:27 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 0.14/0.50 % Refutation found
% 0.14/0.50 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.52 % Elapsed time: 0.143442 seconds
% 0.14/0.52 % CPU time: 0.770404 seconds
% 0.14/0.52 % Total memory used: 120.027 MB
% 0.14/0.52 % Net memory used: 119.132 MB
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