%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC083+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 : n018.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 02:39:53 PM UTC 2026
% Result : Theorem 11.87s 1.96s
% Output : CNFRefutation 11.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 37
% Syntax : Number of formulae : 185 ( 34 unt; 25 def)
% Number of atoms : 561 ( 77 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 656 ( 280 ~; 266 |; 51 &)
% ( 31 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 32 ( 30 usr; 26 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 10 con; 0-2 aty)
% Number of variables : 141 ( 121 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(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(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
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(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
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] :
( ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( app(Z,X2) != X
| app(app(Z,X1),X2) != W
| ~ ssList(X2) ) ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( app(Z,X2) != X
| app(app(Z,X1),X2) != W
| ~ ssList(X2) ) ) )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil)
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
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(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
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(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| 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(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(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
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(f320,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( segmentP(app(app(W,U),X),V)
| ~ segmentP(U,V)
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
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] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( app(Z,X2) = X
& app(app(Z,X1),X2) = W
& ssList(X2) )
& ssList(X1) )
& ssList(Z) )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ 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,
( app(sK51_skl,sK53_skl) = sK50_skl
& app(app(sK51_skl,sK52_skl),sK53_skl) = sK49_skl
& ssList(sK53_skl)
& ssList(sK52_skl)
& ssList(sK51_skl)
& ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& 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,sK52_skl,sK53_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_skl),skolemize(X1,sK52_skl),skolemize(X2,sK53_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,
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,
neq(sK48_skl,nil),
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,
ssList(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
app(app(sK51_skl,sK52_skl),sK53_skl) = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
app(sK51_skl,sK53_skl) = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f435,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f436,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(f462,plain,
neq(sK50_skl,nil),
inference(forward_demodulation,[status(thm)],[f421,f423]) ).
fof(f467,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK51_skl)
| segmentP(app(app(sK51_skl,sK53_skl),X0),sK53_skl)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f429,f436]) ).
fof(f468,definition,
! [X0] :
( sQ0_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK51_skl,sK53_skl),X0),sK53_skl)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f469,plain,
! [X0] :
( ~ sQ0_spl
| ~ ssList(X0)
| segmentP(app(app(sK51_skl,sK53_skl),X0),sK53_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(component_clause,[status(thm)],[f468]) ).
fof(f471,definition,
( sQ1_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( sQ1_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,definition,
( sQ2_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f476,plain,
( sQ2_spl
| ~ ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f474]) ).
fof(f477,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f467,f468,f471,f474]) ).
fof(f478,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f476,f425]) ).
fof(f479,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f478]) ).
fof(f480,plain,
! [X0] :
( ~ sQ0_spl
| ~ ssList(X0)
| segmentP(app(sK50_skl,X0),sK53_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f429,f469]) ).
fof(f482,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(app(sK51_skl,sK52_skl))
| segmentP(app(app(app(sK51_skl,sK52_skl),sK53_skl),X0),sK53_skl)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f428,f436]) ).
fof(f483,definition,
( sQ3_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f485,plain,
( sQ3_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f483]) ).
fof(f486,definition,
( sQ4_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( sQ4_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f493,definition,
! [X0] :
( sQ6_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(app(sK51_skl,sK52_skl),sK53_skl),X0),sK53_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f494,plain,
! [X0] :
( ~ sQ6_spl
| ~ ssList(X0)
| segmentP(app(app(app(sK51_skl,sK52_skl),sK53_skl),X0),sK53_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
( sQ7_spl
<=> ssList(app(sK51_skl,sK52_skl)) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( ~ sQ7_spl
| ssList(app(sK51_skl,sK52_skl)) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f498,plain,
( sQ7_spl
| ~ ssList(app(sK51_skl,sK52_skl)) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,plain,
( ~ sQ7_spl
| ~ sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f482,f493,f471,f496]) ).
fof(f500,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f427]) ).
fof(f501,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f500]) ).
fof(f502,plain,
! [X0] :
( ~ sQ6_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK53_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f428,f494]) ).
fof(f504,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f421,f424]) ).
fof(f505,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f422,f504]) ).
fof(f507,definition,
( sQ8_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ8_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f519,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f420]) ).
fof(f520,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f519]) ).
fof(f522,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f532,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f524,f223]) ).
fof(f533,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f541,plain,
app(nil,sK51_skl) = sK51_skl,
inference(resolution,[status(thm)],[f249,f425]) ).
fof(f567,plain,
! [X0] :
( nil != cons(sK1_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f235,f104]) ).
fof(f568,plain,
! [X0] :
( nil != cons(sK0_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f235,f103]) ).
fof(f580,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f426]) ).
fof(f581,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f580]) ).
fof(f583,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f419]) ).
fof(f584,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f583]) ).
fof(f613,plain,
app(sK51_skl,nil) = sK51_skl,
inference(resolution,[status(thm)],[f389,f425]) ).
fof(f615,plain,
app(sK50_skl,nil) = sK50_skl,
inference(resolution,[status(thm)],[f389,f420]) ).
fof(f616,plain,
app(sK49_skl,nil) = sK49_skl,
inference(resolution,[status(thm)],[f389,f419]) ).
fof(f635,plain,
( ~ sQ0_spl
| ~ ssList(nil)
| segmentP(app(sK50_skl,nil),sK53_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f615,f480]) ).
fof(f637,definition,
( sQ28_spl
<=> segmentP(app(sK50_skl,nil),sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( ~ sQ28_spl
| segmentP(app(sK50_skl,nil),sK53_skl) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,plain,
( ~ sQ0_spl
| ~ sQ11_spl
| sQ28_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f635,f507,f637,f522,f468]) ).
fof(f645,plain,
( ~ sQ28_spl
| segmentP(sK50_skl,sK53_skl) ),
inference(forward_demodulation,[status(thm)],[f615,f638]) ).
fof(f647,plain,
( ~ sQ28_spl
| ~ segmentP(sK49_skl,sK53_skl)
| ~ neq(sK53_skl,nil)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f645,f505]) ).
fof(f648,definition,
( sQ30_spl
<=> neq(sK53_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f650,plain,
( sQ30_spl
| ~ neq(sK53_skl,nil) ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f651,definition,
( sQ31_spl
<=> segmentP(sK49_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f653,plain,
( sQ31_spl
| ~ segmentP(sK49_skl,sK53_skl) ),
inference(component_clause,[status(thm)],[f651]) ).
fof(f654,plain,
( ~ sQ28_spl
| ~ sQ31_spl
| ~ sQ30_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f647,f471,f648,f651,f637]) ).
fof(f658,plain,
! [X0] :
( ssList(app(X0,sK52_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f245,f426]) ).
fof(f665,plain,
( sQ30_spl
| sK53_skl = nil
| ~ ssList(nil)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f650,f220]) ).
fof(f666,definition,
( sQ32_spl
<=> sK53_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( ~ sQ32_spl
| sK53_skl = nil ),
inference(component_clause,[status(thm)],[f666]) ).
fof(f669,plain,
( sQ30_spl
| sQ32_spl
| ~ sQ11_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f665,f471,f522,f666,f648]) ).
fof(f674,plain,
( ~ sQ32_spl
| app(app(sK51_skl,sK52_skl),nil) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f667,f428]) ).
fof(f675,plain,
( ~ sQ32_spl
| app(sK51_skl,nil) = sK50_skl ),
inference(backward_demodulation,[status(thm)],[f667,f429]) ).
fof(f679,plain,
( ~ sQ32_spl
| sK51_skl = sK50_skl ),
inference(forward_demodulation,[status(thm)],[f613,f675]) ).
fof(f683,plain,
! [X0] :
( ~ sQ32_spl
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK51_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f679,f505]) ).
fof(f684,plain,
( ~ sQ32_spl
| neq(sK51_skl,nil) ),
inference(backward_demodulation,[status(thm)],[f679,f462]) ).
fof(f764,plain,
( sQ7_spl
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f498,f658]) ).
fof(f765,plain,
( sQ7_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f764,f474,f496]) ).
fof(f937,plain,
! [X0,X1,X2] :
( ~ ssList(X0)
| segmentP(app(app(X1,X0),X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f321,f319]) ).
fof(f951,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X0),X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f937]) ).
fof(f1033,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f435,f245]) ).
fof(f1038,plain,
( ~ ssList(nil)
| rearsegP(sK51_skl,sK51_skl)
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f541,f1033]) ).
fof(f1053,definition,
( sQ81_spl
<=> rearsegP(sK51_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1054,plain,
( ~ sQ81_spl
| rearsegP(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1053]) ).
fof(f1056,plain,
( ~ sQ11_spl
| sQ81_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1038,f474,f1053,f522]) ).
fof(f1071,plain,
( ~ sQ81_spl
| app(sK6_skl(sK51_skl,sK51_skl),sK51_skl) = sK51_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f1054,f129]) ).
fof(f1072,plain,
( ~ sQ81_spl
| ssList(sK6_skl(sK51_skl,sK51_skl))
| ~ ssList(sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f1054,f128]) ).
fof(f1073,definition,
( sQ84_spl
<=> app(sK6_skl(sK51_skl,sK51_skl),sK51_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1074,plain,
( ~ sQ84_spl
| app(sK6_skl(sK51_skl,sK51_skl),sK51_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f1073]) ).
fof(f1076,plain,
( ~ sQ81_spl
| sQ84_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1071,f474,f1073,f1053]) ).
fof(f1077,definition,
( sQ85_spl
<=> ssList(sK6_skl(sK51_skl,sK51_skl)) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1080,plain,
( ~ sQ81_spl
| sQ85_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1072,f474,f1077,f1053]) ).
fof(f2628,definition,
( sQ213_spl
<=> sK1_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2629,plain,
( ~ sQ213_spl
| sK1_skl = sK0_skl ),
inference(component_clause,[status(thm)],[f2628]) ).
fof(f2646,plain,
( ~ sQ213_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2629,f105]) ).
fof(f2647,plain,
~ sQ213_spl,
inference(contradiction_clause,[status(thm)],[f2646]) ).
fof(f2806,plain,
( ~ sQ6_spl
| ~ ssList(nil)
| segmentP(app(sK49_skl,nil),sK53_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f616,f502]) ).
fof(f2815,definition,
( sQ219_spl
<=> segmentP(app(sK49_skl,nil),sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2816,plain,
( ~ sQ219_spl
| segmentP(app(sK49_skl,nil),sK53_skl) ),
inference(component_clause,[status(thm)],[f2815]) ).
fof(f2818,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| sQ219_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2806,f483,f2815,f522,f493]) ).
fof(f2819,plain,
( ~ sQ219_spl
| segmentP(sK49_skl,sK53_skl) ),
inference(forward_demodulation,[status(thm)],[f616,f2816]) ).
fof(f2820,plain,
( ~ sQ219_spl
| sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2819,f653]) ).
fof(f2821,plain,
( ~ sQ219_spl
| sQ31_spl ),
inference(contradiction_clause,[status(thm)],[f2820]) ).
fof(f2890,plain,
( ~ sQ32_spl
| ~ segmentP(sK49_skl,sK51_skl)
| ~ segmentP(sK51_skl,sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f684,f683]) ).
fof(f2891,definition,
( sQ223_spl
<=> segmentP(sK51_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2894,definition,
( sQ224_spl
<=> segmentP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2897,plain,
( ~ sQ32_spl
| ~ sQ224_spl
| ~ sQ223_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f2890,f474,f2891,f2894,f666]) ).
fof(f2978,plain,
nil != cons(sK1_skl,nil),
inference(resolution,[status(thm)],[f567,f223]) ).
fof(f3041,plain,
nil != cons(sK0_skl,nil),
inference(resolution,[status(thm)],[f568,f223]) ).
fof(f3703,plain,
( ~ sQ7_spl
| app(app(sK51_skl,sK52_skl),nil) = app(sK51_skl,sK52_skl) ),
inference(resolution,[status(thm)],[f497,f389]) ).
fof(f3706,plain,
( ~ sQ7_spl
| ~ sQ32_spl
| sK49_skl = app(sK51_skl,sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f674,f3703]) ).
fof(f4983,plain,
! [X0] :
( ~ sQ84_spl
| segmentP(app(sK51_skl,X0),sK51_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK51_skl,sK51_skl))
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1074,f951]) ).
fof(f5019,definition,
! [X0] :
( sQ391_spl
<=> ( segmentP(app(sK51_skl,X0),sK51_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f5020,plain,
! [X0] :
( ~ sQ391_spl
| segmentP(app(sK51_skl,X0),sK51_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f5019]) ).
fof(f5022,plain,
( ~ sQ84_spl
| sQ391_spl
| ~ sQ85_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f4983,f474,f1077,f5019,f1073]) ).
fof(f5859,definition,
( sQ420_spl
<=> ssItem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f5861,plain,
( sQ420_spl
| ~ ssItem(sK1_skl) ),
inference(component_clause,[status(thm)],[f5859]) ).
fof(f5915,definition,
( sQ425_spl
<=> nil = cons(sK1_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f5916,plain,
( ~ sQ425_spl
| nil = cons(sK1_skl,nil) ),
inference(component_clause,[status(thm)],[f5915]) ).
fof(f5923,plain,
( sQ420_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5861,f104]) ).
fof(f5924,plain,
sQ420_spl,
inference(contradiction_clause,[status(thm)],[f5923]) ).
fof(f5925,plain,
( ~ sQ425_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5916,f2978]) ).
fof(f5926,plain,
~ sQ425_spl,
inference(contradiction_clause,[status(thm)],[f5925]) ).
fof(f5965,definition,
( sQ428_spl
<=> ssItem(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f5967,plain,
( sQ428_spl
| ~ ssItem(sK0_skl) ),
inference(component_clause,[status(thm)],[f5965]) ).
fof(f6021,definition,
( sQ433_spl
<=> nil = cons(sK0_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f6022,plain,
( ~ sQ433_spl
| nil = cons(sK0_skl,nil) ),
inference(component_clause,[status(thm)],[f6021]) ).
fof(f6029,plain,
( sQ428_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5967,f103]) ).
fof(f6030,plain,
sQ428_spl,
inference(contradiction_clause,[status(thm)],[f6029]) ).
fof(f6031,plain,
( ~ sQ433_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6022,f3041]) ).
fof(f6032,plain,
~ sQ433_spl,
inference(contradiction_clause,[status(thm)],[f6031]) ).
fof(f11228,plain,
( ~ sQ391_spl
| segmentP(sK51_skl,sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f613,f5020]) ).
fof(f11229,plain,
( ~ sQ7_spl
| ~ sQ32_spl
| ~ sQ391_spl
| segmentP(sK49_skl,sK51_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f3706,f5020]) ).
fof(f11310,plain,
( ~ sQ391_spl
| sQ223_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f11228,f522,f2891,f5019]) ).
fof(f11311,plain,
( ~ sQ7_spl
| ~ sQ32_spl
| ~ sQ391_spl
| sQ224_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f11229,f486,f2894,f5019,f666,f496]) ).
fof(f11312,plain,
$false,
inference(sat_refutation,[status(thm)],[f477,f479,f499,f501,f520,f533,f581,f584,f640,f654,f669,f765,f1056,f1076,f1080,f2647,f2818,f2821,f2897,f5022,f5924,f5926,f6030,f6032,f11310,f11311]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC083+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:56:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 11.87/1.96 % Refutation found
% 11.87/1.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 11.87/1.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.48/2.01 % Elapsed time: 1.638133 seconds
% 5.48/2.01 % CPU time: 12.659389 seconds
% 5.48/2.01 % Total memory used: 212.020 MB
% 5.48/2.01 % Net memory used: 202.116 MB
%------------------------------------------------------------------------------