%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC373+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 : n012.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 02:40:59 PM UTC 2026
% Result : Theorem 0.08s 0.35s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of formulae : 67 ( 17 unt; 8 def)
% Number of atoms : 219 ( 31 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 250 ( 98 ~; 97 |; 30 &)
% ( 12 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 61 ( 48 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = 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(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)
=> ( segmentP(V,U)
| ~ rearsegP(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)
=> ( segmentP(V,U)
| ~ rearsegP(X,W)
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
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(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] :
( ~ segmentP(V,U)
& rearsegP(X,W)
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ~ segmentP(sK48_skl,sK47_skl)
& rearsegP(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,
rearsegP(sK50_skl,sK49_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
~ segmentP(sK48_skl,sK47_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f431,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(f458,plain,
rearsegP(sK48_skl,sK49_skl),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f459,plain,
rearsegP(sK48_skl,sK47_skl),
inference(forward_demodulation,[status(thm)],[f422,f458]) ).
fof(f462,definition,
( sQ0_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ0_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,definition,
( sQ1_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( sQ1_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f488,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f464,f417]) ).
fof(f489,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f488]) ).
fof(f499,definition,
( sQ7_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( sQ7_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f504,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f223]) ).
fof(f505,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f504]) ).
fof(f531,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f467,f418]) ).
fof(f532,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f541,plain,
( app(sK6_skl(sK47_skl,sK48_skl),sK47_skl) = sK48_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f129,f459]) ).
fof(f550,definition,
( sQ13_spl
<=> app(sK6_skl(sK47_skl,sK48_skl),sK47_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( ~ sQ13_spl
| app(sK6_skl(sK47_skl,sK48_skl),sK47_skl) = sK48_skl ),
inference(component_clause,[status(thm)],[f550]) ).
fof(f553,plain,
( sQ13_spl
| ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f541,f465,f462,f550]) ).
fof(f587,plain,
! [X0] :
( ~ sQ13_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK47_skl,sK48_skl))
| segmentP(app(app(sK6_skl(sK47_skl,sK48_skl),sK47_skl),X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f551,f431]) ).
fof(f589,definition,
( sQ20_spl
<=> ssList(sK6_skl(sK47_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( sQ20_spl
| ~ ssList(sK6_skl(sK47_skl,sK48_skl)) ),
inference(component_clause,[status(thm)],[f589]) ).
fof(f600,definition,
! [X0] :
( sQ23_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(sK47_skl,sK48_skl),sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f601,plain,
! [X0] :
( ~ sQ23_spl
| ~ ssList(X0)
| segmentP(app(app(sK6_skl(sK47_skl,sK48_skl),sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,plain,
( ~ sQ13_spl
| ~ sQ20_spl
| ~ sQ0_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f587,f600,f462,f589,f550]) ).
fof(f656,plain,
( sQ20_spl
| ~ rearsegP(sK48_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f591,f128]) ).
fof(f657,definition,
( sQ31_spl
<=> rearsegP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( sQ31_spl
| ~ rearsegP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f657]) ).
fof(f660,plain,
( sQ20_spl
| ~ sQ31_spl
| ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f656,f465,f462,f657,f589]) ).
fof(f661,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f659,f459]) ).
fof(f662,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f661]) ).
fof(f664,plain,
! [X0] :
( ~ sQ23_spl
| ~ sQ13_spl
| ~ ssList(X0)
| segmentP(app(sK48_skl,X0),sK47_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f551,f601]) ).
fof(f1774,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f418]) ).
fof(f1787,plain,
( ~ sQ23_spl
| ~ sQ13_spl
| ~ ssList(nil)
| segmentP(app(sK48_skl,nil),sK47_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f1774,f664]) ).
fof(f1795,definition,
( sQ125_spl
<=> segmentP(app(sK48_skl,nil),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1796,plain,
( ~ sQ125_spl
| segmentP(app(sK48_skl,nil),sK47_skl) ),
inference(component_clause,[status(thm)],[f1795]) ).
fof(f1798,plain,
( ~ sQ23_spl
| ~ sQ13_spl
| ~ sQ7_spl
| sQ125_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f1787,f465,f1795,f499,f550,f600]) ).
fof(f1821,plain,
( ~ sQ125_spl
| segmentP(sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f1774,f1796]) ).
fof(f1822,plain,
( ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1821,f424]) ).
fof(f1823,plain,
~ sQ125_spl,
inference(contradiction_clause,[status(thm)],[f1822]) ).
fof(f1824,plain,
$false,
inference(sat_refutation,[status(thm)],[f489,f505,f532,f553,f603,f660,f662,f1798,f1823]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC373+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Mon Sep 21 08:18:52 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.31 % Drodi V4.1.1
% 0.08/0.35 % Refutation found
% 0.08/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.38 % Elapsed time: 0.067248 seconds
% 0.08/0.38 % CPU time: 0.338605 seconds
% 0.08/0.38 % Total memory used: 117.038 MB
% 0.08/0.38 % Net memory used: 116.268 MB
%------------------------------------------------------------------------------