%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC204+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 : n004.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 02:40:22 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 55
% Syntax : Number of formulae : 239 ( 10 unt; 35 def)
% Number of atoms : 1011 ( 223 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1346 ( 574 ~; 575 |; 101 &)
% ( 53 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 44 ( 42 usr; 35 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 294 ( 260 !; 34 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(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(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(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(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = 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] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( neq(U,nil)
| ? [Y] :
( ? [Z] :
( neq(nil,X)
& app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ 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)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( neq(U,nil)
| ? [Y] :
( ? [Z] :
( neq(nil,X)
& app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f106,plain,
! [U] :
( ! [V] :
( ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f107,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ( app(sK2_skl(V,U),cons(V,sK3_skl(V,U))) = U
& ssList(sK3_skl(V,U))
& ssList(sK2_skl(V,U)) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107]) ).
fof(f111,plain,
! [X0,X1] :
( app(sK2_skl(X1,X0),cons(X1,sK3_skl(X1,X0))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
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(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(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ 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(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(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f236,plain,
! [U] :
( ssItem(hd(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f237,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f240,plain,
! [U] :
( ssList(tl(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f241,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
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(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f299,plain,
! [X0] :
( nil != X0
| frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f310,plain,
! [U] :
( ( rearsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f311,plain,
! [U] :
( ( ( nil != U
| rearsegP(nil,U) )
& ( nil = U
| ~ rearsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f310]) ).
fof(f313,plain,
! [X0] :
( nil != X0
| rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f327,plain,
! [X0] :
( nil != X0
| segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f373,plain,
! [U] :
( cons(hd(U),tl(U)) = U
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f374,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f387,plain,
! [X0,X1] :
( nil != X0
| nil != X1
| nil = app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
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] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ~ neq(U,nil)
& ! [Y] :
( ! [Z] :
( ~ neq(nil,X)
| app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ 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,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ~ neq(U,nil)
& ! [Y] :
( ! [Z] :
( ~ neq(nil,X)
| app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_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)],[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)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( neq(U,nil)
| ? [Y] :
( ? [Z] :
( neq(nil,X)
& app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ~ neq(U,nil)
& ! [Y] :
( ! [Z] :
( ~ neq(nil,X)
| app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( neq(U,nil)
| ? [Y] :
( neq(nil,X)
& ? [Z] :
( app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ~ neq(U,nil)
& ! [Y] :
( ~ neq(nil,X)
| ! [Z] :
( app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( neq(U,nil)
| ( neq(nil,X)
& app(W,sK52_skl(X,W,V,U)) = sK51_skl(X,W,V,U)
& tl(X) = sK52_skl(X,W,V,U)
& ssList(sK52_skl(X,W,V,U))
& X != sK51_skl(X,W,V,U)
& ssList(sK51_skl(X,W,V,U)) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ~ neq(U,nil)
& ! [Y] :
( ~ neq(nil,X)
| ! [Z] :
( app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Y,sK51_skl(X,W,V,U)),skolemize(Z,sK52_skl(X,W,V,U))],[f428]) ).
fof(f430,plain,
! [X0,X1,X2,X3] :
( neq(X2,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ neq(nil,X0)
| app(X1,X5) != X4
| tl(X0) != X5
| ~ ssList(X5)
| X0 = X4
| ~ ssList(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ~ neq(X3,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f439,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f439,f442]) ).
fof(f446,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f439,f446]) ).
fof(f465,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f466,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f465]) ).
fof(f471,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f299]) ).
fof(f472,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f313]) ).
fof(f473,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f327]) ).
fof(f476,plain,
( nil = app(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f387]) ).
fof(f477,plain,
( nil = app(nil,nil)
| ~ ssList(nil) ),
inference(duplicate_literals_removal,[status(thm)],[f476]) ).
fof(f480,plain,
! [X0,X1,X2,X3] :
( ~ neq(nil,X0)
| ~ ssList(tl(X0))
| X0 = app(X1,tl(X0))
| ~ ssList(app(X1,tl(X0)))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f431]) ).
fof(f483,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f440]) ).
fof(f484,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f483]) ).
fof(f485,plain,
( ~ sQ0_spl
| neq(sK50_skl,nil) ),
inference(resolution,[status(thm)],[f430,f484]) ).
fof(f486,plain,
( ~ sQ0_spl
| ~ neq(sK49_skl,nil) ),
inference(resolution,[status(thm)],[f432,f484]) ).
fof(f491,plain,
( ~ sQ0_spl
| sK49_skl = nil
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f486,f220]) ).
fof(f493,definition,
( sQ3_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ3_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f498,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f496]) ).
fof(f499,definition,
( sQ5_spl
<=> sK49_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( ~ sQ5_spl
| sK49_skl = nil ),
inference(component_clause,[status(thm)],[f499]) ).
fof(f502,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f491,f493,f496,f499,f439]) ).
fof(f510,plain,
( ~ sQ1_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f443]) ).
fof(f522,plain,
! [X0] :
( ~ sQ5_spl
| app(X0,sK49_skl) = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f500,f389]) ).
fof(f523,plain,
! [X0] :
( ~ sQ5_spl
| app(sK49_skl,X0) = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f500,f249]) ).
fof(f534,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f421]) ).
fof(f535,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f498,f223]) ).
fof(f537,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f536]) ).
fof(f548,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| neq(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f500,f485]) ).
fof(f553,definition,
( sQ8_spl
<=> sK49_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f571,plain,
! [X0] :
( ~ sQ5_spl
| ssList(tl(X0))
| sK49_skl = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f500,f241]) ).
fof(f576,plain,
! [X0] :
( ~ sQ5_spl
| cons(hd(X0),tl(X0)) = X0
| sK49_skl = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f500,f374]) ).
fof(f604,definition,
! [X1] :
( sQ10_spl
<=> neq(sK49_skl,X1) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f605,plain,
! [X0] :
( ~ sQ10_spl
| neq(sK49_skl,X0) ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f623,plain,
! [X0,X1,X2,X3] :
( ~ sQ5_spl
| ~ neq(sK49_skl,X0)
| ~ ssList(tl(X0))
| X0 = app(X1,tl(X0))
| ~ ssList(app(X1,tl(X0)))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(forward_demodulation,[status(thm)],[f500,f480]) ).
fof(f624,plain,
! [X0,X1,X2,X3] :
( ~ sQ5_spl
| ~ ssList(tl(X0))
| ~ ssList(X1)
| ~ neq(sK49_skl,X0)
| ~ ssList(tl(X0))
| X0 = app(X1,tl(X0))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f623,f245]) ).
fof(f625,plain,
! [X0,X1,X2,X3] :
( ~ sQ5_spl
| ~ ssList(X1)
| ~ neq(sK49_skl,X0)
| ~ ssList(tl(X0))
| X0 = app(X1,tl(X0))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(duplicate_literals_removal,[status(thm)],[f624]) ).
fof(f626,plain,
! [X0,X1] :
( ~ sQ5_spl
| nil = X1
| sK49_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f500,f385]) ).
fof(f627,plain,
! [X0,X1] :
( ~ sQ5_spl
| sK49_skl = X1
| sK49_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f500,f626]) ).
fof(f628,plain,
( ~ sQ5_spl
| ~ ssList(sK49_skl)
| sK49_skl = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f627,f523]) ).
fof(f629,plain,
! [X0] :
( ~ sQ5_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ ssList(sK49_skl)
| sK49_skl = cons(X0,sK3_skl(X0,sK49_skl))
| ~ ssList(cons(X0,sK3_skl(X0,sK49_skl)))
| ~ ssList(sK2_skl(X0,sK49_skl)) ),
inference(resolution,[status(thm)],[f627,f111]) ).
fof(f630,plain,
! [X0] :
( ~ sQ5_spl
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| sK49_skl = sK5_skl(X0,sK49_skl)
| ~ ssList(sK5_skl(X0,sK49_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f627,f123]) ).
fof(f632,plain,
( ~ sQ5_spl
| sQ8_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f628,f493,f553,f499]) ).
fof(f633,definition,
! [X0] :
( sQ13_spl
<=> ( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| sK49_skl = cons(X0,sK3_skl(X0,sK49_skl))
| ~ ssList(cons(X0,sK3_skl(X0,sK49_skl)))
| ~ ssList(sK2_skl(X0,sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f629,f633,f493,f499]) ).
fof(f637,definition,
! [X0] :
( sQ14_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| sK49_skl = sK5_skl(X0,sK49_skl)
| ~ ssList(sK5_skl(X0,sK49_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f638,plain,
! [X0] :
( ~ sQ14_spl
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| sK49_skl = sK5_skl(X0,sK49_skl)
| ~ ssList(sK5_skl(X0,sK49_skl))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f630,f637,f493,f499]) ).
fof(f642,plain,
! [X0] :
( ~ sQ14_spl
| ~ frontsegP(sK49_skl,X0)
| sK49_skl = sK5_skl(X0,sK49_skl)
| ~ ssList(sK5_skl(X0,sK49_skl))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f638]) ).
fof(f643,plain,
! [X0,X1] :
( ~ sQ5_spl
| nil = X0
| sK49_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f500,f386]) ).
fof(f644,plain,
! [X0,X1] :
( ~ sQ5_spl
| sK49_skl = X0
| sK49_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f500,f643]) ).
fof(f646,plain,
! [X0] :
( ~ sQ5_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ ssList(sK49_skl)
| sK49_skl = sK2_skl(X0,sK49_skl)
| ~ ssList(cons(X0,sK3_skl(X0,sK49_skl)))
| ~ ssList(sK2_skl(X0,sK49_skl)) ),
inference(resolution,[status(thm)],[f644,f111]) ).
fof(f647,plain,
! [X0] :
( ~ sQ5_spl
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| sK49_skl = X0
| ~ ssList(sK5_skl(X0,sK49_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f644,f123]) ).
fof(f650,definition,
! [X0] :
( sQ15_spl
<=> ( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| sK49_skl = sK2_skl(X0,sK49_skl)
| ~ ssList(cons(X0,sK3_skl(X0,sK49_skl)))
| ~ ssList(sK2_skl(X0,sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f653,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f646,f650,f493,f499]) ).
fof(f654,definition,
! [X0] :
( sQ16_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| sK49_skl = X0
| ~ ssList(sK5_skl(X0,sK49_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f655,plain,
! [X0] :
( ~ sQ16_spl
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| sK49_skl = X0
| ~ ssList(sK5_skl(X0,sK49_skl))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f657,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f647,f654,f493,f499]) ).
fof(f659,plain,
! [X0] :
( ~ sQ16_spl
| ~ frontsegP(sK49_skl,X0)
| sK49_skl = X0
| ~ ssList(sK5_skl(X0,sK49_skl))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f655]) ).
fof(f661,plain,
! [X0] :
( ~ sQ16_spl
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ frontsegP(sK49_skl,X0)
| sK49_skl = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f659,f122]) ).
fof(f662,definition,
! [X0] :
( sQ17_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,X0)
| sK49_skl = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f665,plain,
( ~ sQ16_spl
| ~ sQ3_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f661,f662,f493,f654]) ).
fof(f671,plain,
! [X0] :
( ~ sQ5_spl
| ~ ssList(app(X0,sK49_skl))
| app(X0,sK49_skl) = X0
| ~ ssList(app(X0,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f522]) ).
fof(f674,definition,
! [X0] :
( sQ18_spl
<=> ( ~ ssList(app(X0,sK49_skl))
| app(X0,sK49_skl) = X0
| ~ ssList(app(X0,sK49_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f671,f674,f493,f499]) ).
fof(f687,plain,
! [X0] :
( ~ sQ5_spl
| ~ ssList(app(sK49_skl,X0))
| app(sK49_skl,X0) = X0
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f378,f523]) ).
fof(f692,definition,
! [X0] :
( sQ21_spl
<=> ( ~ ssList(app(sK49_skl,X0))
| app(sK49_skl,X0) = X0
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f687,f692,f493,f499]) ).
fof(f704,plain,
! [X0] :
( ~ sQ14_spl
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ frontsegP(sK49_skl,X0)
| sK49_skl = sK5_skl(X0,sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f642,f122]) ).
fof(f705,definition,
! [X0] :
( sQ22_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,X0)
| sK49_skl = sK5_skl(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( ~ sQ14_spl
| ~ sQ3_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f704,f705,f493,f637]) ).
fof(f719,plain,
! [X0] :
( ~ sQ5_spl
| sK49_skl = sK6_skl(X0,sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f129,f644]) ).
fof(f720,plain,
! [X0] :
( ~ sQ5_spl
| sK49_skl = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f129,f627]) ).
fof(f725,definition,
! [X0] :
( sQ23_spl
<=> ( sK49_skl = sK6_skl(X0,sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f726,plain,
! [X0] :
( ~ sQ23_spl
| sK49_skl = sK6_skl(X0,sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f725]) ).
fof(f728,plain,
( ~ sQ5_spl
| sQ23_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f719,f493,f725,f499]) ).
fof(f729,definition,
! [X0] :
( sQ24_spl
<=> ( sK49_skl = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f730,plain,
! [X0] :
( ~ sQ24_spl
| sK49_skl = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f729]) ).
fof(f732,plain,
( ~ sQ5_spl
| sQ24_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f720,f493,f729,f499]) ).
fof(f733,plain,
! [X0] :
( ~ sQ23_spl
| sK49_skl = sK6_skl(X0,sK49_skl)
| ~ ssList(sK6_skl(X0,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f726]) ).
fof(f734,plain,
! [X0] :
( ~ sQ24_spl
| sK49_skl = X0
| ~ ssList(sK6_skl(X0,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f730]) ).
fof(f735,plain,
! [X0] :
( ~ sQ24_spl
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| sK49_skl = X0
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f734,f128]) ).
fof(f736,definition,
! [X0] :
( sQ25_spl
<=> ( ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0)
| sK49_skl = X0
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f739,plain,
( ~ sQ24_spl
| ~ sQ3_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f735,f736,f493,f729]) ).
fof(f745,plain,
! [X0] :
( ~ sQ23_spl
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| sK49_skl = sK6_skl(X0,sK49_skl)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f733,f128]) ).
fof(f746,definition,
! [X0] :
( sQ26_spl
<=> ( ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0)
| sK49_skl = sK6_skl(X0,sK49_skl)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f749,plain,
( ~ sQ23_spl
| ~ sQ3_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f745,f746,f493,f725]) ).
fof(f751,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ ssList(sK49_skl)
| ~ neq(sK49_skl,sK50_skl)
| ~ ssList(tl(sK50_skl))
| sK50_skl = app(sK49_skl,tl(sK50_skl)) ),
inference(resolution,[status(thm)],[f625,f484]) ).
fof(f753,definition,
( sQ27_spl
<=> sK50_skl = app(sK49_skl,tl(sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( ~ sQ27_spl
| sK50_skl = app(sK49_skl,tl(sK50_skl)) ),
inference(component_clause,[status(thm)],[f753]) ).
fof(f756,definition,
( sQ28_spl
<=> ssList(tl(sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f758,plain,
( sQ28_spl
| ~ ssList(tl(sK50_skl)) ),
inference(component_clause,[status(thm)],[f756]) ).
fof(f759,definition,
( sQ29_spl
<=> neq(sK49_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( sQ29_spl
| ~ neq(sK49_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f759]) ).
fof(f762,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ3_spl
| ~ sQ29_spl
| ~ sQ28_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f751,f753,f756,f759,f493,f499,f439]) ).
fof(f784,plain,
( ~ sQ10_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f605,f466]) ).
fof(f786,plain,
( ~ sQ10_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f784,f493,f604]) ).
fof(f787,plain,
( sQ29_spl
| sK49_skl = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f761,f220]) ).
fof(f789,definition,
( sQ33_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f791,plain,
( sQ33_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f789]) ).
fof(f792,definition,
( sQ34_spl
<=> sK49_skl = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( ~ sQ34_spl
| sK49_skl = sK50_skl ),
inference(component_clause,[status(thm)],[f792]) ).
fof(f795,plain,
( sQ29_spl
| sQ34_spl
| ~ sQ33_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f787,f493,f789,f792,f759]) ).
fof(f800,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f791,f422]) ).
fof(f801,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f800]) ).
fof(f856,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ34_spl
| neq(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f793,f548]) ).
fof(f857,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ34_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f856,f466]) ).
fof(f859,plain,
( ~ sQ0_spl
| ~ sQ5_spl
| ~ sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f857,f789,f792,f499,f439]) ).
fof(f889,plain,
( ~ sQ27_spl
| ~ sQ5_spl
| sK50_skl = tl(sK50_skl)
| ~ ssList(tl(sK50_skl)) ),
inference(paramodulation,[status(thm)],[f754,f523]) ).
fof(f899,definition,
( sQ36_spl
<=> sK50_skl = tl(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f900,plain,
( ~ sQ36_spl
| sK50_skl = tl(sK50_skl) ),
inference(component_clause,[status(thm)],[f899]) ).
fof(f902,plain,
( ~ sQ27_spl
| ~ sQ5_spl
| sQ36_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f889,f756,f899,f499,f753]) ).
fof(f945,plain,
( sQ28_spl
| ~ sQ5_spl
| sK49_skl = sK50_skl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f571,f758]) ).
fof(f946,plain,
( sQ28_spl
| ~ sQ5_spl
| sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f945,f789,f792,f499,f756]) ).
fof(f1052,plain,
! [X0] :
( ~ sQ5_spl
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| sK49_skl = app(sK7_skl(X0,sK49_skl),X0)
| ~ ssList(sK8_skl(X0,sK49_skl))
| ~ ssList(app(sK7_skl(X0,sK49_skl),X0)) ),
inference(resolution,[status(thm)],[f644,f136]) ).
fof(f1072,definition,
! [X0] :
( sQ60_spl
<=> ( ~ segmentP(sK49_skl,X0)
| ~ ssList(X0)
| sK49_skl = app(sK7_skl(X0,sK49_skl),X0)
| ~ ssList(sK8_skl(X0,sK49_skl))
| ~ ssList(app(sK7_skl(X0,sK49_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1075,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1052,f1072,f493,f499]) ).
fof(f1083,plain,
! [X0] :
( ~ sQ5_spl
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| sK49_skl = sK8_skl(X0,sK49_skl)
| ~ ssList(sK8_skl(X0,sK49_skl))
| ~ ssList(app(sK7_skl(X0,sK49_skl),X0)) ),
inference(resolution,[status(thm)],[f627,f136]) ).
fof(f1094,definition,
! [X0] :
( sQ62_spl
<=> ( ~ segmentP(sK49_skl,X0)
| ~ ssList(X0)
| sK49_skl = sK8_skl(X0,sK49_skl)
| ~ ssList(sK8_skl(X0,sK49_skl))
| ~ ssList(app(sK7_skl(X0,sK49_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1097,plain,
( ~ sQ5_spl
| ~ sQ3_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f1083,f1094,f493,f499]) ).
fof(f1102,plain,
( ~ sQ36_spl
| ~ sQ5_spl
| cons(hd(sK50_skl),sK50_skl) = sK50_skl
| sK49_skl = sK50_skl
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f900,f576]) ).
fof(f1103,definition,
( sQ63_spl
<=> cons(hd(sK50_skl),sK50_skl) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1104,plain,
( ~ sQ63_spl
| cons(hd(sK50_skl),sK50_skl) = sK50_skl ),
inference(component_clause,[status(thm)],[f1103]) ).
fof(f1106,plain,
( ~ sQ36_spl
| ~ sQ5_spl
| sQ63_spl
| sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1102,f789,f792,f1103,f499,f899]) ).
fof(f1114,definition,
( sQ65_spl
<=> ssItem(hd(sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1116,plain,
( sQ65_spl
| ~ ssItem(hd(sK50_skl)) ),
inference(component_clause,[status(thm)],[f1114]) ).
fof(f1135,plain,
( ~ sQ63_spl
| ~ ssItem(hd(sK50_skl))
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f225,f1104]) ).
fof(f1138,plain,
( ~ sQ63_spl
| ~ sQ65_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1135,f789,f1114,f1103]) ).
fof(f1151,plain,
! [X0] :
( ~ sQ5_spl
| ssItem(hd(X0))
| sK49_skl = X0
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f500,f237]) ).
fof(f1152,plain,
( sQ65_spl
| ~ sQ5_spl
| sK49_skl = sK50_skl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1151,f1116]) ).
fof(f1153,plain,
( sQ65_spl
| ~ sQ5_spl
| sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f1152,f789,f792,f499,f1114]) ).
fof(f1154,definition,
( sQ71_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1157,plain,
( sQ71_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f473,f496,f1154]) ).
fof(f1158,definition,
( sQ72_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1161,plain,
( sQ72_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f472,f496,f1158]) ).
fof(f1162,definition,
( sQ73_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1165,plain,
( sQ73_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f471,f496,f1162]) ).
fof(f1166,definition,
( sQ74_spl
<=> nil = app(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1169,plain,
( sQ74_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f477,f496,f1166]) ).
fof(f1170,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f510,f446,f442]) ).
fof(f1174,plain,
$false,
inference(sat_refutation,[status(thm)],[f445,f449,f502,f535,f537,f632,f636,f640,f653,f657,f665,f677,f695,f708,f728,f732,f739,f749,f762,f786,f795,f801,f859,f902,f946,f1075,f1097,f1106,f1138,f1153,f1157,f1161,f1165,f1169,f1170]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC204+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:04:19 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.44 % Elapsed time: 0.071635 seconds
% 0.09/0.44 % CPU time: 0.227713 seconds
% 0.09/0.44 % Total memory used: 112.066 MB
% 0.09/0.44 % Net memory used: 111.717 MB
%------------------------------------------------------------------------------