%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC330+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 : n026.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 02:40:48 PM UTC 2026
% Result : Theorem 0.27s 0.88s
% Output : CNFRefutation 3.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 77
% Syntax : Number of formulae : 305 ( 17 unt; 57 def)
% Number of atoms : 1106 ( 134 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 1362 ( 561 ~; 574 |; 116 &)
% ( 68 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 67 ( 65 usr; 56 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-5 aty)
% Number of variables : 310 ( 265 !; 45 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/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/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(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
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(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
equalelemsP(nil),
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] :
( ( equalelemsP(U)
& segmentP(V,U) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) ) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( equalelemsP(U)
& segmentP(V,U) )
| ( ( nil != W
| nil != X )
& ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] :
( lt(Y,X2)
& memberP(Z,X2)
& ssItem(X2) )
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) ) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(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(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| 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(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(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(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(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
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(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f314,plain,
! [U] :
( ! [V] :
( ! [W] :
( segmentP(U,W)
| ~ segmentP(V,W)
| ~ segmentP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f315,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f316,plain,
! [U] :
( ! [V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f317,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
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(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
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(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f360,plain,
! [U] :
( equalelemsP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f361,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f360]) ).
fof(f362,plain,
equalelemsP(nil),
inference(cnf_transformation,[status(thm)],[f74]) ).
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] :
( ( ~ equalelemsP(U)
| ~ segmentP(V,U) )
& ( ( nil = W
& nil = X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] :
( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) )
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ equalelemsP(U)
| ~ segmentP(V,U) )
& ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ( ~ equalelemsP(U)
| ~ segmentP(V,U) )
& ? [X] :
( ( ( nil = W
& nil = X )
| ? [Y] : sP0_prd(Y,X,W) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f417]) ).
fof(f419,plain,
( ( ~ equalelemsP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) )
& ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK51_skl,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,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f418]) ).
fof(f422,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f423,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f424,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f426,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
( ~ equalelemsP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,definition,
! [Y,Z,X2] :
( sP1_prd(X2,Z,Y)
<=> ( ~ lt(Y,X2)
| ~ memberP(Z,X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f430,plain,
! [W,X,Y] :
( sP0_prd(Y,X,W)
<=> ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) ) ),
inference(formula_renaming,[status(thm)],[f416,f429]) ).
fof(f431,plain,
! [W,X,Y] :
( ( ! [Z] :
( ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] : ~ sP1_prd(X2,Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ( ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f430]) ).
fof(f432,plain,
( ! [W,X,Y] :
( ! [Z] :
( ! [X1] :
( ? [X3] :
( lt(X3,Y)
& memberP(X1,X3)
& ssItem(X3) )
| ? [X2] : ~ sP1_prd(X2,Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ? [Z] :
( ? [X1] :
( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,Z,Y)
& app(app(Z,W),X1) = X
& cons(Y,nil) = W
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(miniscoping,[status(thm)],[f431]) ).
fof(f433,plain,
( ! [W,X,Y] :
( ! [Z] :
( ! [X1] :
( ( lt(sK55_skl(X1,Z,Y,X,W),Y)
& memberP(X1,sK55_skl(X1,Z,Y,X,W))
& ssItem(sK55_skl(X1,Z,Y,X,W)) )
| ~ sP1_prd(sK54_skl(X1,Z,Y,X,W),Z,Y)
| app(app(Z,W),X1) != X
| cons(Y,nil) != W
| ~ ssList(X1) )
| ~ ssList(Z) )
| ~ ssItem(Y)
| sP0_prd(Y,X,W) )
& ! [W,X,Y] :
( ( ! [X3] :
( ~ lt(X3,Y)
| ~ memberP(sK53_skl(Y,X,W),X3)
| ~ ssItem(X3) )
& ! [X2] : sP1_prd(X2,sK52_skl(Y,X,W),Y)
& app(app(sK52_skl(Y,X,W),W),sK53_skl(Y,X,W)) = X
& cons(Y,nil) = W
& ssList(sK53_skl(Y,X,W))
& ssList(sK52_skl(Y,X,W))
& ssItem(Y) )
| ~ sP0_prd(Y,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(Z,sK52_skl(Y,X,W)),skolemize(X1,sK53_skl(Y,X,W)),skolemize(X2,sK54_skl(X1,Z,Y,X,W)),skolemize(X3,sK55_skl(X1,Z,Y,X,W))],[f432]) ).
fof(f434,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ssList(sK52_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssList(sK53_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f437,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f438,plain,
! [X0,X1,X2] :
( app(app(sK52_skl(X0,X1,X2),X2),sK53_skl(X0,X1,X2)) = X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f450,definition,
( sQ0_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f450]) ).
fof(f453,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f450,f453]) ).
fof(f457,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f450,f457]) ).
fof(f461,definition,
( sQ3_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( sQ3_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,definition,
( sQ4_spl
<=> equalelemsP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( sQ4_spl
| ~ equalelemsP(sK47_skl) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f428,f461,f464]) ).
fof(f472,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f473,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f474,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(f504,plain,
( sQ3_spl
| ~ segmentP(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f463]) ).
fof(f505,plain,
( sQ3_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f504]) ).
fof(f531,plain,
app(nil,sK50_skl) = sK50_skl,
inference(resolution,[status(thm)],[f249,f423]) ).
fof(f532,plain,
app(nil,sK49_skl) = sK49_skl,
inference(resolution,[status(thm)],[f249,f422]) ).
fof(f534,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f535,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f472,f245]) ).
fof(f536,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f245,f474]) ).
fof(f539,plain,
! [X0,X1,X2] :
( ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f536]) ).
fof(f540,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| segmentP(app(app(X2,X1),X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f245]) ).
fof(f551,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f245]) ).
fof(f556,plain,
( ~ ssList(nil)
| rearsegP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f531,f551]) ).
fof(f558,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK50_skl),X0),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f531,f474]) ).
fof(f559,definition,
( sQ5_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( sQ5_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f559]) ).
fof(f562,definition,
( sQ6_spl
<=> rearsegP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f563,plain,
( ~ sQ6_spl
| rearsegP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f565,definition,
( sQ7_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( sQ7_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f565]) ).
fof(f568,plain,
( ~ sQ7_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f556,f559,f562,f565]) ).
fof(f570,definition,
! [X0] :
( sQ8_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK50_skl),X0),sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f558,f570,f559,f565]) ).
fof(f574,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f567,f223]) ).
fof(f575,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f574]) ).
fof(f576,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f561,f423]) ).
fof(f577,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f579,plain,
( ~ sQ0_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f437,f451]) ).
fof(f580,plain,
( ~ sQ6_spl
| app(sK6_skl(sK50_skl,sK50_skl),sK50_skl) = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f563,f129]) ).
fof(f581,definition,
( sQ9_spl
<=> app(sK6_skl(sK50_skl,sK50_skl),sK50_skl) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f584,plain,
( ~ sQ6_spl
| sQ9_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f580,f559,f581,f562]) ).
fof(f585,plain,
( ~ ssList(nil)
| rearsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f532,f551]) ).
fof(f587,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f532,f474]) ).
fof(f588,definition,
( sQ10_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f590,plain,
( sQ10_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f588]) ).
fof(f591,definition,
( sQ11_spl
<=> rearsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( ~ sQ11_spl
| rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f594,plain,
( ~ sQ7_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f585,f588,f591,f565]) ).
fof(f596,definition,
! [X0] :
( sQ12_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f587,f596,f588,f565]) ).
fof(f600,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f590,f422]) ).
fof(f601,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f600]) ).
fof(f603,plain,
( ~ sQ11_spl
| app(sK6_skl(sK49_skl,sK49_skl),sK49_skl) = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f592,f129]) ).
fof(f604,definition,
( sQ13_spl
<=> app(sK6_skl(sK49_skl,sK49_skl),sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( ~ sQ11_spl
| sQ13_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f603,f588,f604,f591]) ).
fof(f608,plain,
! [X0] :
( app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f295,f123]) ).
fof(f609,definition,
! [X0] :
( sQ14_spl
<=> ( app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f612,plain,
( ~ sQ7_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f608,f609,f565]) ).
fof(f614,plain,
! [X0] :
( app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f309,f129]) ).
fof(f615,definition,
! [X0] :
( sQ15_spl
<=> ( app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( ~ sQ7_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f614,f615,f565]) ).
fof(f621,plain,
! [X0] :
( ~ ssList(X0)
| app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f136,f323]) ).
fof(f623,definition,
! [X0] :
( sQ16_spl
<=> ( ~ ssList(X0)
| app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f626,plain,
( ~ sQ7_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f621,f623,f565]) ).
fof(f635,definition,
( sQ17_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f637,plain,
( sQ17_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f641,definition,
( sQ19_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f643,plain,
( sQ19_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f641]) ).
fof(f662,plain,
( ~ sQ0_spl
| app(app(sK52_skl(sK51_skl,sK50_skl,sK49_skl),sK49_skl),sK53_skl(sK51_skl,sK50_skl,sK49_skl)) = sK50_skl ),
inference(resolution,[status(thm)],[f438,f451]) ).
fof(f663,plain,
! [X0,X1] :
( sQ19_spl
| ~ sP0_prd(sK51_skl,X0,X1) ),
inference(resolution,[status(thm)],[f643,f434]) ).
fof(f664,plain,
( ~ sQ0_spl
| sQ19_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f451,f663]) ).
fof(f665,plain,
( ~ sQ0_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f664]) ).
fof(f666,plain,
! [X0] :
( memberP(sK49_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f532,f270]) ).
fof(f667,plain,
! [X0] :
( memberP(sK50_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssList(sK50_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f531,f270]) ).
fof(f668,definition,
! [X0] :
( sQ24_spl
<=> ( memberP(sK49_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f671,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f666,f668,f565,f588]) ).
fof(f672,definition,
! [X0] :
( sQ25_spl
<=> ( memberP(sK50_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f675,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f667,f672,f565,f559]) ).
fof(f694,plain,
( ~ sQ1_spl
| equalelemsP(sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f454,f362]) ).
fof(f697,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| sK49_skl = sK50_skl ),
inference(backward_demodulation,[status(thm)],[f458,f454]) ).
fof(f708,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| equalelemsP(sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f697,f694]) ).
fof(f717,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ segmentP(sK49_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f697,f505]) ).
fof(f756,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f717,f319]) ).
fof(f761,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f756,f588,f457,f453,f461]) ).
fof(f762,plain,
( sQ4_spl
| ~ equalelemsP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f466]) ).
fof(f763,plain,
( sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f762,f708]) ).
fof(f764,plain,
( sQ4_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f763]) ).
fof(f770,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f326,f315]) ).
fof(f771,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f326,f319]) ).
fof(f772,definition,
! [X0,X1] :
( sQ27_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f775,plain,
( ~ sQ7_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f770,f772,f565]) ).
fof(f776,definition,
( sQ28_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f779,plain,
( sQ28_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f771,f565,f776]) ).
fof(f1030,plain,
! [X0] :
( memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f534,f270]) ).
fof(f1031,plain,
( ~ ssList(nil)
| rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f534,f551]) ).
fof(f1033,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f534,f474]) ).
fof(f1034,definition,
! [X0] :
( sQ41_spl
<=> ( memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1037,plain,
( ~ sQ7_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1030,f1034,f565]) ).
fof(f1038,definition,
( sQ42_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1039,plain,
( ~ sQ42_spl
| rearsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1038]) ).
fof(f1041,plain,
( sQ42_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1031,f565,f1038]) ).
fof(f1043,definition,
! [X0] :
( sQ43_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1046,plain,
( ~ sQ7_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f1033,f1043,f565]) ).
fof(f1048,plain,
( ~ sQ42_spl
| app(sK6_skl(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1039,f129]) ).
fof(f1049,definition,
( sQ44_spl
<=> app(sK6_skl(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1052,plain,
( ~ sQ42_spl
| sQ44_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1048,f565,f1049,f1038]) ).
fof(f1053,plain,
( sQ17_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f637,f222]) ).
fof(f1054,plain,
( sQ17_spl
| ~ sQ19_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1053,f565,f641,f635]) ).
fof(f1127,plain,
( ~ sQ0_spl
| equalelemsP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f579,f361]) ).
fof(f1143,definition,
( sQ48_spl
<=> equalelemsP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1144,plain,
( ~ sQ48_spl
| equalelemsP(sK49_skl) ),
inference(component_clause,[status(thm)],[f1143]) ).
fof(f1146,plain,
( ~ sQ0_spl
| sQ48_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1127,f641,f1143,f450]) ).
fof(f1257,plain,
app(sK50_skl,nil) = sK50_skl,
inference(resolution,[status(thm)],[f389,f423]) ).
fof(f1274,plain,
app(sK49_skl,nil) = sK49_skl,
inference(resolution,[status(thm)],[f389,f422]) ).
fof(f1317,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X0),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f323,f321]) ).
fof(f1318,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f323,f317]) ).
fof(f1319,plain,
! [X0,X1] :
( segmentP(X1,nil)
| ~ segmentP(X1,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f323,f315]) ).
fof(f1322,definition,
! [X0,X1,X2] :
( sQ67_spl
<=> ( segmentP(app(app(X1,X0),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1325,plain,
( ~ sQ7_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1317,f1322,f565]) ).
fof(f1326,definition,
! [X0] :
( sQ68_spl
<=> ( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1329,plain,
( ~ sQ7_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f1318,f1326,f565]) ).
fof(f1330,definition,
! [X0,X1] :
( sQ69_spl
<=> ( segmentP(X1,nil)
| ~ segmentP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1333,plain,
( ~ sQ7_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1319,f1330,f565]) ).
fof(f1339,plain,
( ~ ssList(sK50_skl)
| frontsegP(sK50_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f531,f535]) ).
fof(f1340,plain,
( ~ ssList(sK49_skl)
| frontsegP(sK49_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f532,f535]) ).
fof(f1341,plain,
( ~ ssList(nil)
| frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f534,f535]) ).
fof(f1344,definition,
( sQ70_spl
<=> frontsegP(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1345,plain,
( ~ sQ70_spl
| frontsegP(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f1344]) ).
fof(f1347,plain,
( ~ sQ5_spl
| sQ70_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1339,f565,f1344,f559]) ).
fof(f1348,definition,
( sQ71_spl
<=> frontsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1349,plain,
( ~ sQ71_spl
| frontsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f1348]) ).
fof(f1351,plain,
( ~ sQ10_spl
| sQ71_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1340,f565,f1348,f588]) ).
fof(f1352,definition,
( sQ72_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1353,plain,
( ~ sQ72_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1352]) ).
fof(f1355,plain,
( sQ72_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1341,f565,f1352]) ).
fof(f1360,plain,
( ~ sQ70_spl
| app(nil,sK5_skl(nil,sK50_skl)) = sK50_skl
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1345,f123]) ).
fof(f1361,definition,
( sQ73_spl
<=> app(nil,sK5_skl(nil,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1364,plain,
( ~ sQ70_spl
| sQ73_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1360,f559,f565,f1361,f1344]) ).
fof(f1365,plain,
( ~ sQ71_spl
| app(nil,sK5_skl(nil,sK49_skl)) = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1349,f123]) ).
fof(f1366,definition,
( sQ74_spl
<=> app(nil,sK5_skl(nil,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1369,plain,
( ~ sQ71_spl
| sQ74_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1365,f588,f565,f1366,f1348]) ).
fof(f1370,plain,
( ~ sQ72_spl
| app(nil,sK5_skl(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1353,f123]) ).
fof(f1371,definition,
( sQ75_spl
<=> app(nil,sK5_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1374,plain,
( ~ sQ72_spl
| sQ75_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1370,f565,f1371,f1352]) ).
fof(f1381,plain,
( ~ ssList(nil)
| frontsegP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f1257,f535]) ).
fof(f1383,plain,
( ~ ssList(sK50_skl)
| rearsegP(sK50_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1257,f551]) ).
fof(f1385,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK50_skl)
| segmentP(app(app(sK50_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1257,f474]) ).
fof(f1386,definition,
( sQ76_spl
<=> frontsegP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1387,plain,
( ~ sQ76_spl
| frontsegP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f1386]) ).
fof(f1389,plain,
( ~ sQ7_spl
| sQ76_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1381,f559,f1386,f565]) ).
fof(f1391,definition,
( sQ77_spl
<=> rearsegP(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1392,plain,
( ~ sQ77_spl
| rearsegP(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f1391]) ).
fof(f1394,plain,
( ~ sQ5_spl
| sQ77_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1383,f565,f1391,f559]) ).
fof(f1396,definition,
! [X0] :
( sQ78_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK50_skl,nil),X0),nil)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1399,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f1385,f1396,f565,f559]) ).
fof(f1405,plain,
( ~ sQ76_spl
| app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1387,f123]) ).
fof(f1406,definition,
( sQ79_spl
<=> app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1409,plain,
( ~ sQ76_spl
| sQ79_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1405,f559,f1406,f1386]) ).
fof(f1410,plain,
( ~ sQ77_spl
| app(sK6_skl(nil,sK50_skl),nil) = sK50_skl
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1392,f129]) ).
fof(f1411,definition,
( sQ80_spl
<=> app(sK6_skl(nil,sK50_skl),nil) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1414,plain,
( ~ sQ77_spl
| sQ80_spl
| ~ sQ7_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1410,f559,f565,f1411,f1391]) ).
fof(f1439,plain,
( ~ ssList(nil)
| frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1274,f535]) ).
fof(f1441,plain,
( ~ ssList(sK49_skl)
| rearsegP(sK49_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1274,f551]) ).
fof(f1443,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK49_skl)
| segmentP(app(app(sK49_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1274,f474]) ).
fof(f1444,definition,
( sQ81_spl
<=> frontsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1445,plain,
( ~ sQ81_spl
| frontsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1444]) ).
fof(f1447,plain,
( ~ sQ7_spl
| sQ81_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1439,f588,f1444,f565]) ).
fof(f1449,definition,
( sQ82_spl
<=> rearsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1450,plain,
( ~ sQ82_spl
| rearsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f1449]) ).
fof(f1452,plain,
( ~ sQ10_spl
| sQ82_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1441,f565,f1449,f588]) ).
fof(f1454,definition,
! [X0] :
( sQ83_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK49_skl,nil),X0),nil)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1457,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f1443,f1454,f565,f588]) ).
fof(f1459,plain,
( ~ sQ81_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1445,f123]) ).
fof(f1460,definition,
( sQ84_spl
<=> app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1463,plain,
( ~ sQ81_spl
| sQ84_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1459,f588,f1460,f1444]) ).
fof(f1464,plain,
( ~ sQ82_spl
| app(sK6_skl(nil,sK49_skl),nil) = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1450,f129]) ).
fof(f1465,definition,
( sQ85_spl
<=> app(sK6_skl(nil,sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1468,plain,
( ~ sQ82_spl
| sQ85_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1464,f588,f565,f1465,f1449]) ).
fof(f1801,plain,
( ~ sQ0_spl
| ~ ssList(sK53_skl(sK51_skl,sK50_skl,sK49_skl))
| ~ ssList(sK52_skl(sK51_skl,sK50_skl,sK49_skl))
| segmentP(app(app(sK52_skl(sK51_skl,sK50_skl,sK49_skl),sK49_skl),sK53_skl(sK51_skl,sK50_skl,sK49_skl)),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f662,f474]) ).
fof(f1807,definition,
( sQ108_spl
<=> segmentP(app(app(sK52_skl(sK51_skl,sK50_skl,sK49_skl),sK49_skl),sK53_skl(sK51_skl,sK50_skl,sK49_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1808,plain,
( ~ sQ108_spl
| segmentP(app(app(sK52_skl(sK51_skl,sK50_skl,sK49_skl),sK49_skl),sK53_skl(sK51_skl,sK50_skl,sK49_skl)),sK49_skl) ),
inference(component_clause,[status(thm)],[f1807]) ).
fof(f1810,definition,
( sQ109_spl
<=> ssList(sK52_skl(sK51_skl,sK50_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1812,plain,
( sQ109_spl
| ~ ssList(sK52_skl(sK51_skl,sK50_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1810]) ).
fof(f1813,definition,
( sQ110_spl
<=> ssList(sK53_skl(sK51_skl,sK50_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1815,plain,
( sQ110_spl
| ~ ssList(sK53_skl(sK51_skl,sK50_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1813]) ).
fof(f1816,plain,
( ~ sQ0_spl
| ~ sQ110_spl
| ~ sQ109_spl
| sQ108_spl
| ~ sQ10_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1801,f559,f588,f1807,f1810,f1813,f450]) ).
fof(f1879,plain,
( sQ110_spl
| ~ sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(resolution,[status(thm)],[f1815,f436]) ).
fof(f1880,plain,
( sQ110_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1879,f450,f1813]) ).
fof(f1881,plain,
( ~ sQ108_spl
| ~ sQ0_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f662,f1808]) ).
fof(f1882,plain,
( ~ sQ108_spl
| ~ sQ0_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1881,f505]) ).
fof(f1883,plain,
( ~ sQ108_spl
| ~ sQ0_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1882]) ).
fof(f1884,plain,
( sQ4_spl
| ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f762,f1144]) ).
fof(f1885,plain,
( sQ4_spl
| ~ sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f1884]) ).
fof(f1904,plain,
! [X0] :
( ~ ssList(sK49_skl)
| segmentP(app(sK49_skl,X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1274,f540]) ).
fof(f1905,plain,
! [X0] :
( ~ ssList(sK50_skl)
| segmentP(app(sK50_skl,X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1257,f540]) ).
fof(f1906,plain,
! [X0] :
( ~ ssList(nil)
| segmentP(app(sK50_skl,X0),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f531,f540]) ).
fof(f1907,plain,
! [X0] :
( ~ ssList(nil)
| segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f532,f540]) ).
fof(f1908,plain,
! [X0] :
( ~ ssList(nil)
| segmentP(app(nil,X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f534,f540]) ).
fof(f1921,definition,
! [X0] :
( sQ122_spl
<=> ( segmentP(app(sK49_skl,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1924,plain,
( ~ sQ10_spl
| ~ sQ7_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f1904,f1921,f565,f588]) ).
fof(f1925,definition,
! [X0] :
( sQ123_spl
<=> ( segmentP(app(sK50_skl,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1928,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f1905,f1925,f565,f559]) ).
fof(f1929,definition,
! [X0] :
( sQ124_spl
<=> ( segmentP(app(sK50_skl,X0),sK50_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1932,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1906,f1929,f559,f565]) ).
fof(f1933,definition,
! [X0] :
( sQ125_spl
<=> ( segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1936,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f1907,f1933,f588,f565]) ).
fof(f1937,definition,
! [X0] :
( sQ126_spl
<=> ( segmentP(app(nil,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1940,plain,
( ~ sQ7_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1908,f1937,f565]) ).
fof(f1972,plain,
( sQ109_spl
| ~ sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(resolution,[status(thm)],[f1812,f435]) ).
fof(f1973,plain,
( sQ109_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1972,f450,f1810]) ).
fof(f1974,plain,
$false,
inference(sat_refutation,[status(thm)],[f456,f460,f467,f568,f573,f575,f577,f584,f594,f599,f601,f607,f612,f618,f626,f665,f671,f675,f761,f764,f775,f779,f1037,f1041,f1046,f1052,f1054,f1146,f1325,f1329,f1333,f1347,f1351,f1355,f1364,f1369,f1374,f1389,f1394,f1399,f1409,f1414,f1447,f1452,f1457,f1463,f1468,f1816,f1880,f1883,f1885,f1924,f1928,f1932,f1936,f1940,f1973]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWC330+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Mon Sep 21 08:18:36 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.46 % Drodi V4.1.1
% 0.27/0.88 % Refutation found
% 0.27/0.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.27/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.05/0.91 % Elapsed time: 0.460229 seconds
% 3.05/0.91 % CPU time: 3.249707 seconds
% 3.05/0.91 % Total memory used: 140.296 MB
% 3.05/0.91 % Net memory used: 137.809 MB
%------------------------------------------------------------------------------