%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC389+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 : n008.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 02:41:03 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 64
% Syntax : Number of formulae : 277 ( 15 unt; 48 def)
% Number of atoms : 1004 ( 136 equ)
% Maximal formula atoms : 22 ( 3 avg)
% Number of connectives : 1235 ( 508 ~; 508 |; 125 &)
% ( 63 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 59 ( 57 usr; 47 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-5 aty)
% Number of variables : 263 ( 215 !; 48 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/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/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(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
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(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(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,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(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(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] :
( ( ( singletonP(U)
| ~ neq(V,nil) )
& 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] :
( ( ( singletonP(U)
| ~ neq(V,nil) )
& 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(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
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(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(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(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(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(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
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(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(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] :
( ( ( ~ singletonP(U)
& neq(V,nil) )
| ~ 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] :
( ( ( ~ singletonP(U)
& neq(V,nil) )
| ~ 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] :
( ( ( ~ singletonP(U)
& neq(V,nil) )
| ~ 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,
( ( ( ~ singletonP(sK47_skl)
& neq(sK48_skl,nil) )
| ~ 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(f420,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f421,plain,
ssList(sK48_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,
( neq(sK48_skl,nil)
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
( ~ singletonP(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,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(f431,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,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) )
& ( ( ? [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)],[f431]) ).
fof(f433,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)],[f432]) ).
fof(f434,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))],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssList(sK52_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f437,plain,
! [X0,X1,X2] :
( ssList(sK53_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f438,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f439,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)],[f434]) ).
fof(f451,definition,
( sQ0_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f451,f454]) ).
fof(f458,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f451,f458]) ).
fof(f462,definition,
( sQ3_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ3_spl
| ~ segmentP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,definition,
( sQ4_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ4_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f428,f462,f465]) ).
fof(f469,definition,
( sQ5_spl
<=> singletonP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f472,plain,
( ~ sQ5_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f429,f462,f469]) ).
fof(f476,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f477,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f478,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f479,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(f488,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f489,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f488]) ).
fof(f512,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f452]) ).
fof(f513,plain,
( ~ sQ0_spl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f512]) ).
fof(f514,plain,
( ~ sQ0_spl
| ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f513,f435]) ).
fof(f521,plain,
( ~ sQ0_spl
| cons(sK51_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f438,f513]) ).
fof(f522,plain,
( ~ sQ0_spl
| ~ ssItem(sK51_skl)
| singletonP(sK47_skl)
| ~ ssList(cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f521,f476]) ).
fof(f524,definition,
( sQ6_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( sQ6_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f527,definition,
( sQ7_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( sQ7_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,plain,
( ~ sQ0_spl
| ~ sQ7_spl
| sQ5_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f522,f524,f469,f527,f451]) ).
fof(f534,definition,
( sQ9_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ9_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f538,plain,
( ~ sQ1_spl
| nil = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f424,f455]) ).
fof(f539,plain,
( ~ sQ2_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f425,f459]) ).
fof(f540,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ segmentP(nil,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f538,f464]) ).
fof(f562,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ segmentP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f539,f540]) ).
fof(f563,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f562,f323]) ).
fof(f565,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f563,f223]) ).
fof(f566,plain,
( sQ3_spl
| ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f567,plain,
( ~ sQ0_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f514,f529]) ).
fof(f568,plain,
( ~ sQ0_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f567]) ).
fof(f570,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f123,f295]) ).
fof(f572,definition,
! [X0] :
( sQ14_spl
<=> ( ~ ssList(X0)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( ~ sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f570,f572,f534]) ).
fof(f577,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f536,f223]) ).
fof(f578,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f577]) ).
fof(f603,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| neq(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f538,f466]) ).
fof(f604,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f603,f489]) ).
fof(f605,plain,
( ~ sQ4_spl
| ~ sQ1_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f604,f534,f454,f465]) ).
fof(f615,plain,
( sQ6_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f526,f222]) ).
fof(f616,plain,
( sQ6_spl
| ~ sQ7_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f615,f534,f527,f524]) ).
fof(f619,definition,
( sQ17_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( sQ17_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f619]) ).
fof(f630,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f621,f420]) ).
fof(f631,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f630]) ).
fof(f636,plain,
( ~ sQ0_spl
| app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)) = sK48_skl ),
inference(resolution,[status(thm)],[f513,f439]) ).
fof(f647,plain,
! [X0] :
( app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f309,f129]) ).
fof(f648,definition,
! [X0] :
( sQ20_spl
<=> ( app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f651,plain,
( ~ sQ9_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f647,f648,f534]) ).
fof(f661,plain,
app(nil,sK47_skl) = sK47_skl,
inference(resolution,[status(thm)],[f249,f420]) ).
fof(f662,plain,
app(nil,sK48_skl) = sK48_skl,
inference(resolution,[status(thm)],[f249,f421]) ).
fof(f670,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f671,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f661,f478]) ).
fof(f672,plain,
( ~ ssList(sK47_skl)
| frontsegP(app(nil,sK47_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f661,f477]) ).
fof(f673,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f661,f479]) ).
fof(f674,definition,
( sQ21_spl
<=> rearsegP(app(nil,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f675,plain,
( ~ sQ21_spl
| rearsegP(app(nil,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f674]) ).
fof(f677,plain,
( ~ sQ9_spl
| sQ21_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f671,f619,f674,f534]) ).
fof(f678,definition,
( sQ22_spl
<=> frontsegP(app(nil,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f679,plain,
( ~ sQ22_spl
| frontsegP(app(nil,sK47_skl),nil) ),
inference(component_clause,[status(thm)],[f678]) ).
fof(f681,plain,
( sQ22_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f672,f619,f534,f678]) ).
fof(f682,definition,
! [X0] :
( sQ23_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f685,plain,
( ~ sQ9_spl
| ~ sQ17_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f673,f682,f619,f534]) ).
fof(f686,plain,
( ~ sQ21_spl
| rearsegP(sK47_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f661,f675]) ).
fof(f687,plain,
( ~ sQ22_spl
| frontsegP(sK47_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f661,f679]) ).
fof(f689,plain,
( ~ sQ21_spl
| app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f686,f129]) ).
fof(f690,definition,
( sQ24_spl
<=> app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f691,plain,
( ~ sQ24_spl
| app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f690]) ).
fof(f693,plain,
( ~ sQ21_spl
| sQ24_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f689,f619,f690,f674]) ).
fof(f694,plain,
( ~ sQ22_spl
| app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f687,f123]) ).
fof(f695,definition,
( sQ25_spl
<=> app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f696,plain,
( ~ sQ25_spl
| app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f695]) ).
fof(f698,plain,
( ~ sQ22_spl
| sQ25_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f694,f619,f534,f695,f678]) ).
fof(f699,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK48_skl),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f662,f478]) ).
fof(f700,plain,
( ~ ssList(sK48_skl)
| frontsegP(app(nil,sK48_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f662,f477]) ).
fof(f701,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f662,f479]) ).
fof(f702,definition,
( sQ26_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f704,plain,
( sQ26_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f702]) ).
fof(f705,definition,
( sQ27_spl
<=> rearsegP(app(nil,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f706,plain,
( ~ sQ27_spl
| rearsegP(app(nil,sK48_skl),sK48_skl) ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f708,plain,
( ~ sQ9_spl
| sQ27_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f699,f702,f705,f534]) ).
fof(f709,definition,
( sQ28_spl
<=> frontsegP(app(nil,sK48_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( ~ sQ28_spl
| frontsegP(app(nil,sK48_skl),nil) ),
inference(component_clause,[status(thm)],[f709]) ).
fof(f712,plain,
( sQ28_spl
| ~ sQ9_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f700,f702,f534,f709]) ).
fof(f713,definition,
! [X0] :
( sQ29_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f716,plain,
( ~ sQ9_spl
| ~ sQ26_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f701,f713,f702,f534]) ).
fof(f717,plain,
( sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f704,f421]) ).
fof(f718,plain,
sQ26_spl,
inference(contradiction_clause,[status(thm)],[f717]) ).
fof(f719,plain,
( ~ sQ27_spl
| rearsegP(sK48_skl,sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f662,f706]) ).
fof(f720,plain,
( ~ sQ28_spl
| frontsegP(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f662,f710]) ).
fof(f723,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(f725,definition,
! [X0] :
( sQ30_spl
<=> ( ~ ssList(X0)
| app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f728,plain,
( ~ sQ9_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f723,f725,f534]) ).
fof(f734,plain,
( ~ sQ27_spl
| app(sK6_skl(sK48_skl,sK48_skl),sK48_skl) = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f719,f129]) ).
fof(f735,definition,
( sQ31_spl
<=> app(sK6_skl(sK48_skl,sK48_skl),sK48_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f736,plain,
( ~ sQ31_spl
| app(sK6_skl(sK48_skl,sK48_skl),sK48_skl) = sK48_skl ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f738,plain,
( ~ sQ27_spl
| sQ31_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f734,f702,f735,f705]) ).
fof(f739,plain,
( ~ sQ28_spl
| app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f720,f123]) ).
fof(f740,definition,
( sQ32_spl
<=> app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( ~ sQ32_spl
| app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f743,plain,
( ~ sQ28_spl
| sQ32_spl
| ~ sQ9_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f739,f702,f534,f740,f709]) ).
fof(f757,plain,
( ~ ssList(nil)
| rearsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f670,f478]) ).
fof(f758,plain,
( ~ ssList(nil)
| frontsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f670,f477]) ).
fof(f759,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f670,f479]) ).
fof(f760,definition,
( sQ33_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f761,plain,
( ~ sQ33_spl
| rearsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f760]) ).
fof(f763,plain,
( sQ33_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f757,f534,f760]) ).
fof(f764,definition,
( sQ34_spl
<=> frontsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f765,plain,
( ~ sQ34_spl
| frontsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f767,plain,
( sQ34_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f758,f534,f764]) ).
fof(f768,definition,
! [X0] :
( sQ35_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f771,plain,
( ~ sQ9_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f759,f768,f534]) ).
fof(f772,plain,
( ~ sQ33_spl
| rearsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f670,f761]) ).
fof(f773,plain,
( ~ sQ34_spl
| frontsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f670,f765]) ).
fof(f775,plain,
( ~ sQ33_spl
| app(sK6_skl(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f772,f129]) ).
fof(f776,definition,
( sQ36_spl
<=> app(sK6_skl(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f779,plain,
( ~ sQ33_spl
| sQ36_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f775,f534,f776,f760]) ).
fof(f780,plain,
( ~ sQ34_spl
| app(nil,sK5_skl(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f773,f123]) ).
fof(f781,definition,
( sQ37_spl
<=> app(nil,sK5_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f784,plain,
( ~ sQ34_spl
| sQ37_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f780,f534,f781,f764]) ).
fof(f808,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f420]) ).
fof(f809,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f421]) ).
fof(f819,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f808,f479]) ).
fof(f821,definition,
! [X0] :
( sQ38_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f824,plain,
( ~ sQ17_spl
| ~ sQ9_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f819,f821,f534,f619]) ).
fof(f827,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK48_skl)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f809,f479]) ).
fof(f829,definition,
! [X0] :
( sQ39_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f832,plain,
( ~ sQ26_spl
| ~ sQ9_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f827,f829,f534,f702]) ).
fof(f986,plain,
! [X0,X1] :
( ~ ssItem(X0)
| memberP(X1,X0)
| ~ memberP(app(X1,nil),X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f270,f279]) ).
fof(f990,definition,
! [X0,X1] :
( sQ48_spl
<=> ( ~ ssItem(X0)
| memberP(X1,X0)
| ~ memberP(app(X1,nil),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f993,plain,
( ~ sQ9_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f986,f990,f534]) ).
fof(f1050,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f326,f323]) ).
fof(f1052,definition,
( sQ52_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1055,plain,
( sQ52_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1050,f534,f1052]) ).
fof(f1109,plain,
! [X0] :
( ~ sQ24_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK47_skl,sK47_skl))
| segmentP(app(app(sK6_skl(sK47_skl,sK47_skl),sK47_skl),X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f691,f479]) ).
fof(f1110,definition,
( sQ58_spl
<=> ssList(sK6_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1114,definition,
! [X0] :
( sQ59_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(sK47_skl,sK47_skl),sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1117,plain,
( ~ sQ24_spl
| ~ sQ58_spl
| ~ sQ17_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f1109,f1114,f619,f1110,f690]) ).
fof(f1120,plain,
! [X0] :
( ~ sQ25_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK5_skl(nil,sK47_skl)),X0),sK5_skl(nil,sK47_skl))
| ~ ssList(sK5_skl(nil,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f696,f479]) ).
fof(f1121,definition,
( sQ60_spl
<=> ssList(sK5_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1123,plain,
( sQ60_spl
| ~ ssList(sK5_skl(nil,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1121]) ).
fof(f1125,definition,
! [X0] :
( sQ61_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK5_skl(nil,sK47_skl)),X0),sK5_skl(nil,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1128,plain,
( ~ sQ25_spl
| ~ sQ9_spl
| ~ sQ60_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f1120,f1125,f1121,f534,f695]) ).
fof(f1129,plain,
( sQ60_spl
| ~ frontsegP(sK47_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1123,f122]) ).
fof(f1130,definition,
( sQ62_spl
<=> frontsegP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1132,plain,
( sQ62_spl
| ~ frontsegP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f1130]) ).
fof(f1133,plain,
( sQ60_spl
| ~ sQ62_spl
| ~ sQ9_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1129,f619,f534,f1130,f1121]) ).
fof(f1135,plain,
( sQ62_spl
| ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1132,f687]) ).
fof(f1136,plain,
( sQ62_spl
| ~ sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1135]) ).
fof(f1153,plain,
! [X0] :
( ~ sQ31_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK48_skl,sK48_skl))
| segmentP(app(app(sK6_skl(sK48_skl,sK48_skl),sK48_skl),X0),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f736,f479]) ).
fof(f1154,definition,
( sQ63_spl
<=> ssList(sK6_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1158,definition,
! [X0] :
( sQ64_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(sK48_skl,sK48_skl),sK48_skl),X0),sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1161,plain,
( ~ sQ31_spl
| ~ sQ63_spl
| ~ sQ26_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f1153,f1158,f702,f1154,f735]) ).
fof(f1164,plain,
! [X0] :
( ~ sQ32_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK5_skl(nil,sK48_skl)),X0),sK5_skl(nil,sK48_skl))
| ~ ssList(sK5_skl(nil,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f741,f479]) ).
fof(f1165,definition,
( sQ65_spl
<=> ssList(sK5_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1167,plain,
( sQ65_spl
| ~ ssList(sK5_skl(nil,sK48_skl)) ),
inference(component_clause,[status(thm)],[f1165]) ).
fof(f1169,definition,
! [X0] :
( sQ66_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK5_skl(nil,sK48_skl)),X0),sK5_skl(nil,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1172,plain,
( ~ sQ32_spl
| ~ sQ9_spl
| ~ sQ65_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1164,f1169,f1165,f534,f740]) ).
fof(f1173,plain,
( sQ65_spl
| ~ frontsegP(sK48_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1167,f122]) ).
fof(f1174,definition,
( sQ67_spl
<=> frontsegP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1176,plain,
( sQ67_spl
| ~ frontsegP(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f1174]) ).
fof(f1177,plain,
( sQ65_spl
| ~ sQ67_spl
| ~ sQ9_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1173,f702,f534,f1174,f1165]) ).
fof(f1179,plain,
( sQ67_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1176,f720]) ).
fof(f1180,plain,
( sQ67_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f1179]) ).
fof(f1209,plain,
( ~ sQ0_spl
| ~ ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl))
| ~ ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl))
| segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f636,f479]) ).
fof(f1212,definition,
( sQ68_spl
<=> segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1213,plain,
( ~ sQ68_spl
| segmentP(app(app(sK52_skl(sK51_skl,sK48_skl,sK47_skl),sK47_skl),sK53_skl(sK51_skl,sK48_skl,sK47_skl)),sK47_skl) ),
inference(component_clause,[status(thm)],[f1212]) ).
fof(f1215,definition,
( sQ69_spl
<=> ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1217,plain,
( sQ69_spl
| ~ ssList(sK52_skl(sK51_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1215]) ).
fof(f1218,definition,
( sQ70_spl
<=> ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1220,plain,
( sQ70_spl
| ~ ssList(sK53_skl(sK51_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1218]) ).
fof(f1221,plain,
( ~ sQ0_spl
| ~ sQ70_spl
| ~ sQ69_spl
| sQ68_spl
| ~ sQ17_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f1209,f702,f619,f1212,f1215,f1218,f451]) ).
fof(f1230,plain,
( sQ70_spl
| ~ sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f1220,f437]) ).
fof(f1231,plain,
( sQ70_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1230,f513]) ).
fof(f1232,plain,
( sQ70_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1231]) ).
fof(f1233,plain,
( ~ sQ68_spl
| ~ sQ0_spl
| segmentP(sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f636,f1213]) ).
fof(f1234,plain,
( ~ sQ68_spl
| ~ sQ0_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1233,f464]) ).
fof(f1235,plain,
( ~ sQ68_spl
| ~ sQ0_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f1234]) ).
fof(f1247,plain,
( sQ69_spl
| ~ sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f1217,f436]) ).
fof(f1248,plain,
( sQ69_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1247,f513]) ).
fof(f1249,plain,
( sQ69_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1248]) ).
fof(f1250,plain,
$false,
inference(sat_refutation,[status(thm)],[f457,f461,f468,f472,f530,f566,f568,f575,f578,f605,f616,f631,f651,f677,f681,f685,f693,f698,f708,f712,f716,f718,f728,f738,f743,f763,f767,f771,f779,f784,f824,f832,f993,f1055,f1117,f1128,f1133,f1136,f1161,f1172,f1177,f1180,f1221,f1232,f1235,f1249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC389+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n008.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:21:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.39 % Drodi V4.1.1
% 0.10/0.46 % Refutation found
% 0.10/0.46 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.48 % Elapsed time: 0.106654 seconds
% 0.10/0.48 % CPU time: 0.551309 seconds
% 0.10/0.48 % Total memory used: 119.055 MB
% 0.10/0.48 % Net memory used: 118.339 MB
%------------------------------------------------------------------------------