%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC068+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 : 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 02:39:50 PM UTC 2026
% Result : Theorem 0.19s 0.46s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 90 ( 15 unt; 10 def)
% Number of atoms : 293 ( 68 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 346 ( 143 ~; 135 |; 39 &)
% ( 14 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 11 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 71 ( 57 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/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/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)
=> ( ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X
| app(X,X) != W ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X
| app(X,X) != W ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
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] :
( ( nil != U
| nil != V )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& app(X,X) = W
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( nil != sK47_skl
| nil != sK48_skl )
& ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& app(sK50_skl,sK50_skl) = sK49_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(f419,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
app(sK50_skl,sK50_skl) = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
sK47_skl = sK49_skl,
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,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,definition,
( sQ0_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( ~ sQ0_spl
| nil = sK48_skl ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f428,plain,
( sQ0_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,definition,
( sQ1_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f431,plain,
( sQ1_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f432,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f426,f429]) ).
fof(f439,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,
( sQ0_spl
| nil != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f422,f428]) ).
fof(f466,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK50_skl)
| segmentP(app(app(sK50_skl,sK50_skl),X0),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f421,f439]) ).
fof(f467,definition,
! [X0] :
( sQ2_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK50_skl,sK50_skl),X0),sK50_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f468,plain,
! [X0] :
( ~ sQ2_spl
| ~ ssList(X0)
| segmentP(app(app(sK50_skl,sK50_skl),X0),sK50_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,definition,
( sQ3_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( sQ3_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f466,f467,f470]) ).
fof(f474,plain,
! [X0] :
( ~ sQ2_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK50_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f421,f468]) ).
fof(f479,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f424]) ).
fof(f480,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f479]) ).
fof(f483,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f490,definition,
( sQ5_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( sQ5_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f494,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f472,f420]) ).
fof(f495,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f494]) ).
fof(f502,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f492,f223]) ).
fof(f503,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f518,plain,
app(sK49_skl,nil) = sK49_skl,
inference(resolution,[status(thm)],[f389,f419]) ).
fof(f545,definition,
( sQ13_spl
<=> sK1_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ13_spl
| sK1_skl = sK0_skl ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f560,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f220,f480]) ).
fof(f573,definition,
! [X0] :
( sQ19_spl
<=> ( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f574,plain,
! [X0] :
( ~ sQ19_spl
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0)
| X0 = nil
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f573]) ).
fof(f576,plain,
( ~ sQ5_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f560,f573,f490]) ).
fof(f577,plain,
! [X0] :
( ~ sQ19_spl
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| X0 = nil
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f574]) ).
fof(f615,plain,
( ~ sQ2_spl
| ~ ssList(nil)
| segmentP(sK49_skl,sK50_skl)
| ~ ssList(app(sK49_skl,nil)) ),
inference(paramodulation,[status(thm)],[f518,f474]) ).
fof(f616,definition,
( sQ22_spl
<=> ssList(app(sK49_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( sQ22_spl
| ~ ssList(app(sK49_skl,nil)) ),
inference(component_clause,[status(thm)],[f616]) ).
fof(f619,definition,
( sQ23_spl
<=> segmentP(sK49_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( ~ sQ2_spl
| ~ sQ5_spl
| sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f615,f616,f619,f490,f467]) ).
fof(f623,plain,
( sQ22_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f518,f618]) ).
fof(f624,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f623,f419]) ).
fof(f625,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f624]) ).
fof(f653,plain,
( ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f546,f105]) ).
fof(f654,plain,
~ sQ13_spl,
inference(contradiction_clause,[status(thm)],[f653]) ).
fof(f730,plain,
( ~ sQ19_spl
| ~ ssList(sK50_skl)
| ~ segmentP(sK49_skl,sK50_skl)
| sK50_skl = nil
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f577,f319]) ).
fof(f739,definition,
( sQ38_spl
<=> sK50_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f740,plain,
( ~ sQ38_spl
| sK50_skl = nil ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f742,plain,
( ~ sQ19_spl
| ~ sQ23_spl
| sQ38_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f730,f470,f739,f619,f573]) ).
fof(f744,plain,
( ~ sQ38_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f740,f465]) ).
fof(f745,plain,
( ~ sQ38_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f744]) ).
fof(f746,plain,
( sQ1_spl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f423,f431]) ).
fof(f747,plain,
( ~ sQ0_spl
| nil = sK50_skl ),
inference(forward_demodulation,[status(thm)],[f422,f427]) ).
fof(f762,plain,
( ~ sQ0_spl
| app(sK50_skl,nil) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f747,f421]) ).
fof(f775,plain,
( ~ sQ0_spl
| app(nil,nil) = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f747,f762]) ).
fof(f776,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f483,f775]) ).
fof(f777,plain,
( ~ sQ0_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f776,f746]) ).
fof(f778,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f777]) ).
fof(f779,plain,
$false,
inference(sat_refutation,[status(thm)],[f432,f473,f495,f503,f576,f622,f625,f654,f742,f745,f778]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC068+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.43 % Computer : n017.cluster.edu
% 0.19/0.43 % Model : x86_64 x86_64
% 0.19/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.43 % Memory : 8046.5625MB
% 0.19/0.43 % OS : Linux 6.8.0-71-generic
% 0.19/0.43 % CPULimit : 300
% 0.19/0.43 % WCLimit : 300
% 0.19/0.43 % DateTime : Mon Sep 21 07:48:26 UTC 2026
% 0.19/0.43 % CPUTime :
% 0.19/0.44 % Drodi V4.1.1
% 0.19/0.46 % Refutation found
% 0.19/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.50 % Elapsed time: 0.065091 seconds
% 0.19/0.50 % CPU time: 0.180249 seconds
% 0.19/0.50 % Total memory used: 42.254 MB
% 0.19/0.50 % Net memory used: 42.117 MB
%------------------------------------------------------------------------------