%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC377+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:41:00 PM UTC 2026
% Result : Theorem 0.03s 0.33s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 81
% Syntax : Number of formulae : 335 ( 13 unt; 59 def)
% Number of atoms : 1307 ( 194 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 1740 ( 768 ~; 764 |; 77 &)
% ( 75 <=>; 56 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 69 ( 67 usr; 60 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-2 aty)
% Number of variables : 309 ( 285 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( V = U
& W = X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> cons(W,app(V,U)) = app(cons(W,V),U) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(X1,cons(Z,nil)) != X
| app(cons(Z,nil),X1) != W ) ) ) )
| ( nil = X
& nil != W )
| ! [Y] :
( ssItem(Y)
=> ( ( memberP(U,Y)
& memberP(V,Y) )
| ( ~ memberP(U,Y)
& ~ memberP(V,Y) ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( neq(X,nil)
& ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ( app(X1,cons(Z,nil)) != X
| app(cons(Z,nil),X1) != W ) ) ) )
| ( nil = X
& nil != W )
| ! [Y] :
( ssItem(Y)
=> ( ( memberP(U,Y)
& memberP(V,Y) )
| ( ~ memberP(U,Y)
& ~ memberP(V,Y) ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
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(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,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(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( V = U
& W = X )
| cons(W,U) != cons(X,V)
| ~ ssItem(X) )
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f246,plain,
! [U] :
( ! [V] :
( ! [W] :
( cons(W,app(V,U)) = app(cons(W,V),U)
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f247,plain,
! [X0,X1,X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
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(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f273,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f274,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& U != V )
| memberP(cons(V,W),U) )
& ( memberP(W,U)
| U = V
| ~ memberP(cons(V,W),U) ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f276,plain,
! [X0,X1,X2] :
( X0 != X1
| memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f277,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
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(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f379,plain,
! [U] :
( ! [V] :
( cons(V,U) = app(cons(V,nil),U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f380,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [Z] :
( ? [X1] :
( app(X1,cons(Z,nil)) = X
& app(cons(Z,nil),X1) = W
& ssList(X1) )
& ssItem(Z) ) )
& ( nil != X
| nil = W )
& ? [Y] :
( ( ~ memberP(U,Y)
| ~ memberP(V,Y) )
& ( memberP(U,Y)
| memberP(V,Y) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,plain,
( ( ~ neq(sK50_skl,nil)
| ( app(sK53_skl,cons(sK52_skl,nil)) = sK50_skl
& app(cons(sK52_skl,nil),sK53_skl) = sK49_skl
& ssList(sK53_skl)
& ssItem(sK52_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ( ~ memberP(sK47_skl,sK51_skl)
| ~ memberP(sK48_skl,sK51_skl) )
& ( memberP(sK47_skl,sK51_skl)
| memberP(sK48_skl,sK51_skl) )
& ssItem(sK51_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,sK52_skl,sK53_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl)],[f415]) ).
fof(f420,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f421,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f422,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f423,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f424,plain,
( memberP(sK47_skl,sK51_skl)
| memberP(sK48_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f425,plain,
( ~ memberP(sK47_skl,sK51_skl)
| ~ memberP(sK48_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f426,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK52_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK53_skl) ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| app(cons(sK52_skl,nil),sK53_skl) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ~ neq(sK50_skl,nil)
| app(sK53_skl,cons(sK52_skl,nil)) = sK50_skl ),
inference(cnf_transformation,[status(thm)],[f416]) ).
fof(f431,definition,
( sQ0_spl
<=> memberP(sK48_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f432,plain,
( ~ sQ0_spl
| memberP(sK48_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f433,plain,
( sQ0_spl
| ~ memberP(sK48_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f431]) ).
fof(f434,definition,
( sQ1_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f435,plain,
( ~ sQ1_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f436,plain,
( sQ1_spl
| ~ memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f424,f431,f434]) ).
fof(f438,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f431,f434]) ).
fof(f439,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
( sQ3_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ3_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f426,f439,f442]) ).
fof(f446,definition,
( sQ4_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f449,definition,
( sQ5_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( sQ5_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f427,f446,f449]) ).
fof(f453,definition,
( sQ6_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ6_spl
| ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( ~ sQ5_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f428,f453,f449]) ).
fof(f457,definition,
( sQ7_spl
<=> app(cons(sK52_skl,nil),sK53_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ7_spl
| app(cons(sK52_skl,nil),sK53_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,plain,
( ~ sQ5_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f429,f457,f449]) ).
fof(f461,definition,
( sQ8_spl
<=> app(sK53_skl,cons(sK52_skl,nil)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ8_spl
| app(sK53_skl,cons(sK52_skl,nil)) = sK50_skl ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,plain,
( ~ sQ5_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f430,f461,f449]) ).
fof(f468,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f469,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f470,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f482,plain,
! [X1,X2] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f483,plain,
! [X0,X1] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f482]) ).
fof(f499,plain,
( sQ0_spl
| ~ memberP(sK50_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f421,f433]) ).
fof(f500,plain,
( ~ sQ1_spl
| memberP(sK49_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f435]) ).
fof(f501,plain,
! [X0] :
( ~ sQ2_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f440,f279]) ).
fof(f502,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f501,f500]) ).
fof(f503,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f502,f423]) ).
fof(f504,plain,
( ~ sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f505,plain,
( sQ1_spl
| ~ memberP(sK49_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f422,f436]) ).
fof(f506,plain,
( ~ sQ0_spl
| memberP(sK50_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f421,f432]) ).
fof(f517,plain,
( sQ5_spl
| sK50_skl = nil
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f220,f451]) ).
fof(f520,definition,
( sQ11_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ11_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ12_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( sQ12_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
( sQ5_spl
| sQ3_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f517,f520,f523,f442,f449]) ).
fof(f527,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f420]) ).
fof(f528,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f527]) ).
fof(f529,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f530,definition,
! [X0] :
( sQ13_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f531,plain,
! [X0] :
( ~ sQ13_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,definition,
! [X1] :
( sQ14_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f536,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f529,f530,f533]) ).
fof(f537,plain,
! [X0] :
( ~ sQ13_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f531]) ).
fof(f539,definition,
! [X0] :
( sQ15_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f542,definition,
! [X1] :
( sQ16_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f543,plain,
! [X0] :
( ~ sQ16_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f546,plain,
( ~ sQ6_spl
| ~ sQ13_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f454,f537]) ).
fof(f550,plain,
( ~ sQ6_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f546]) ).
fof(f560,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f223]) ).
fof(f561,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f560]) ).
fof(f566,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f222,f468]) ).
fof(f567,definition,
! [X0] :
( sQ19_spl
<=> ( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f570,plain,
( sQ19_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f566,f523,f567]) ).
fof(f574,plain,
( ~ sQ7_spl
| ssList(sK49_skl)
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK52_skl,nil)) ),
inference(paramodulation,[status(thm)],[f458,f245]) ).
fof(f575,definition,
( sQ20_spl
<=> ssList(cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f577,plain,
( sQ20_spl
| ~ ssList(cons(sK52_skl,nil)) ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f578,definition,
( sQ21_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( ~ sQ7_spl
| sQ21_spl
| ~ sQ6_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f574,f575,f453,f578,f457]) ).
fof(f582,plain,
( sQ20_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f577,f222]) ).
fof(f583,plain,
( sQ20_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f582,f523,f446,f575]) ).
fof(f584,plain,
! [X0] :
( ~ sQ7_spl
| cons(X0,sK49_skl) = app(cons(X0,cons(sK52_skl,nil)),sK53_skl)
| ~ ssItem(X0)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f458,f247]) ).
fof(f585,definition,
! [X0] :
( sQ22_spl
<=> ( cons(X0,sK49_skl) = app(cons(X0,cons(sK52_skl,nil)),sK53_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f588,plain,
( ~ sQ7_spl
| sQ22_spl
| ~ sQ20_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f584,f453,f575,f585,f457]) ).
fof(f589,plain,
! [X0] :
( ~ sQ7_spl
| memberP(sK53_skl,X0)
| memberP(cons(sK52_skl,nil),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f458,f270]) ).
fof(f590,definition,
! [X0] :
( sQ23_spl
<=> ( memberP(sK53_skl,X0)
| memberP(cons(sK52_skl,nil),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ20_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f589,f590,f575,f453,f457]) ).
fof(f594,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f245]) ).
fof(f595,plain,
( ~ sQ7_spl
| ~ ssList(sK53_skl)
| frontsegP(sK49_skl,cons(sK52_skl,nil))
| ~ ssList(cons(sK52_skl,nil)) ),
inference(paramodulation,[status(thm)],[f458,f594]) ).
fof(f596,definition,
( sQ24_spl
<=> frontsegP(sK49_skl,cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| sQ24_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f595,f575,f596,f453,f457]) ).
fof(f600,plain,
( ~ sQ8_spl
| ~ ssList(cons(sK52_skl,nil))
| frontsegP(sK50_skl,sK53_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f462,f594]) ).
fof(f601,plain,
! [X0] :
( ~ sQ8_spl
| memberP(cons(sK52_skl,nil),X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f462,f270]) ).
fof(f602,plain,
! [X0] :
( ~ sQ8_spl
| cons(X0,sK50_skl) = app(cons(X0,sK53_skl),cons(sK52_skl,nil))
| ~ ssItem(X0)
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK52_skl,nil)) ),
inference(paramodulation,[status(thm)],[f462,f247]) ).
fof(f604,definition,
( sQ25_spl
<=> frontsegP(sK50_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| sQ25_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f600,f453,f604,f575,f461]) ).
fof(f608,definition,
! [X0] :
( sQ26_spl
<=> ( memberP(cons(sK52_skl,nil),X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f609,plain,
! [X0] :
( ~ sQ26_spl
| memberP(cons(sK52_skl,nil),X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ6_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f601,f608,f453,f575,f461]) ).
fof(f612,definition,
! [X0] :
( sQ27_spl
<=> ( cons(X0,sK50_skl) = app(cons(X0,sK53_skl),cons(sK52_skl,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ8_spl
| sQ27_spl
| ~ sQ6_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f602,f575,f453,f612,f461]) ).
fof(f617,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f385,f249]) ).
fof(f618,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f385,f123]) ).
fof(f622,definition,
( sQ28_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( sQ28_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f617,f523,f622]) ).
fof(f626,definition,
! [X0] :
( sQ29_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f629,plain,
( ~ sQ12_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f618,f626,f523]) ).
fof(f631,definition,
( sQ30_spl
<=> nil = cons(sK52_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f632,plain,
( ~ sQ30_spl
| nil = cons(sK52_skl,nil) ),
inference(component_clause,[status(thm)],[f631]) ).
fof(f647,plain,
( ~ sQ30_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f632,f235]) ).
fof(f662,plain,
( ~ sQ30_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f647,f523,f446,f631]) ).
fof(f721,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f386,f123]) ).
fof(f723,plain,
( ~ sQ7_spl
| nil = cons(sK52_skl,nil)
| nil != sK49_skl
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK52_skl,nil)) ),
inference(paramodulation,[status(thm)],[f458,f386]) ).
fof(f726,definition,
! [X0] :
( sQ40_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f727,plain,
! [X0] :
( ~ sQ40_spl
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,plain,
( ~ sQ12_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f721,f726,f523]) ).
fof(f731,plain,
( ~ sQ7_spl
| sQ30_spl
| ~ sQ2_spl
| ~ sQ6_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f723,f575,f453,f439,f631,f457]) ).
fof(f733,plain,
! [X0] :
( ~ sQ40_spl
| ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f727]) ).
fof(f734,plain,
( ~ sQ7_spl
| cons(sK52_skl,sK53_skl) = sK49_skl
| ~ ssItem(sK52_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f458,f380]) ).
fof(f735,definition,
( sQ41_spl
<=> cons(sK52_skl,sK53_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f736,plain,
( ~ sQ41_spl
| cons(sK52_skl,sK53_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f735]) ).
fof(f738,plain,
( ~ sQ7_spl
| sQ41_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f734,f453,f446,f735,f457]) ).
fof(f740,plain,
! [X0] :
( ~ sQ7_spl
| ~ memberP(cons(sK52_skl,nil),X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f458,f271]) ).
fof(f741,plain,
! [X0] :
( ~ sQ8_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f462,f271]) ).
fof(f742,definition,
! [X0] :
( sQ42_spl
<=> ( ~ memberP(cons(sK52_skl,nil),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f743,plain,
! [X0] :
( ~ sQ42_spl
| ~ memberP(cons(sK52_skl,nil),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f742]) ).
fof(f745,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ20_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f740,f742,f575,f453,f457]) ).
fof(f746,definition,
! [X0] :
( sQ43_spl
<=> ( ~ memberP(sK53_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f747,plain,
! [X0] :
( ~ sQ43_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f746]) ).
fof(f749,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ6_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f741,f746,f453,f575,f461]) ).
fof(f752,plain,
! [X0] :
( ~ sQ8_spl
| ~ memberP(cons(sK52_skl,nil),X0)
| memberP(sK50_skl,X0)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f462,f272]) ).
fof(f753,definition,
! [X0] :
( sQ44_spl
<=> ( ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f754,plain,
! [X0] :
( ~ sQ44_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f753]) ).
fof(f757,definition,
! [X0] :
( sQ45_spl
<=> ( ~ memberP(cons(sK52_skl,nil),X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f758,plain,
! [X0] :
( ~ sQ45_spl
| ~ memberP(cons(sK52_skl,nil),X0)
| memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f757]) ).
fof(f760,plain,
( ~ sQ8_spl
| ~ sQ20_spl
| ~ sQ6_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f752,f757,f453,f575,f461]) ).
fof(f761,plain,
( ~ sQ41_spl
| memberP(sK49_skl,sK52_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl) ),
inference(paramodulation,[status(thm)],[f736,f483]) ).
fof(f764,plain,
( ~ sQ41_spl
| sK49_skl != sK53_skl
| ~ ssItem(sK52_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f736,f225]) ).
fof(f765,definition,
( sQ46_spl
<=> memberP(sK49_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f768,plain,
( ~ sQ41_spl
| sQ46_spl
| ~ sQ6_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f761,f446,f453,f765,f735]) ).
fof(f771,definition,
( sQ47_spl
<=> sK49_skl = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f774,plain,
( ~ sQ41_spl
| ~ sQ47_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f764,f453,f446,f771,f735]) ).
fof(f775,plain,
! [X0] :
( nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f129,f386]) ).
fof(f776,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f129,f385]) ).
fof(f777,definition,
! [X0] :
( sQ48_spl
<=> ( nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f780,plain,
( sQ48_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f775,f523,f777]) ).
fof(f781,definition,
! [X0] :
( sQ49_spl
<=> ( nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f782,plain,
! [X0] :
( ~ sQ49_spl
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f781]) ).
fof(f784,plain,
( sQ49_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f776,f523,f781]) ).
fof(f786,plain,
! [X0] :
( ~ sQ49_spl
| nil = X0
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f782]) ).
fof(f787,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f470,f245]) ).
fof(f788,plain,
( ~ sQ7_spl
| ~ ssList(cons(sK52_skl,nil))
| rearsegP(sK49_skl,sK53_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f458,f787]) ).
fof(f789,plain,
( ~ sQ8_spl
| ~ ssList(sK53_skl)
| rearsegP(sK50_skl,cons(sK52_skl,nil))
| ~ ssList(cons(sK52_skl,nil)) ),
inference(paramodulation,[status(thm)],[f462,f787]) ).
fof(f790,definition,
( sQ50_spl
<=> rearsegP(sK49_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( ~ sQ7_spl
| ~ sQ20_spl
| sQ50_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f788,f453,f790,f575,f457]) ).
fof(f794,definition,
( sQ51_spl
<=> rearsegP(sK50_skl,cons(sK52_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f797,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| sQ51_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f789,f575,f794,f453,f461]) ).
fof(f800,plain,
! [X0] :
( ~ sQ42_spl
| ~ sQ26_spl
| memberP(sK49_skl,X0)
| ~ ssItem(X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f609,f743]) ).
fof(f801,plain,
! [X0] :
( ~ sQ42_spl
| ~ sQ26_spl
| memberP(sK49_skl,X0)
| memberP(sK53_skl,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f800]) ).
fof(f802,plain,
! [X0] :
( ~ sQ42_spl
| ~ sQ26_spl
| ~ sQ44_spl
| memberP(sK49_skl,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f801,f754]) ).
fof(f804,plain,
( ~ sQ45_spl
| ~ ssList(nil)
| ~ ssItem(sK52_skl)
| memberP(sK50_skl,sK52_skl)
| ~ ssItem(sK52_skl) ),
inference(resolution,[status(thm)],[f758,f483]) ).
fof(f805,definition,
( sQ52_spl
<=> memberP(sK50_skl,sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f806,plain,
( ~ sQ52_spl
| memberP(sK50_skl,sK52_skl) ),
inference(component_clause,[status(thm)],[f805]) ).
fof(f808,plain,
( ~ sQ45_spl
| ~ sQ12_spl
| sQ52_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f804,f446,f805,f523,f757]) ).
fof(f811,plain,
! [X0] :
( ~ sQ40_spl
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f733,f122]) ).
fof(f812,definition,
! [X0] :
( sQ53_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f815,plain,
( ~ sQ40_spl
| ~ sQ12_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f811,f812,f523,f726]) ).
fof(f821,plain,
! [X0] :
( ~ sQ49_spl
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f786,f128]) ).
fof(f822,definition,
! [X0] :
( sQ54_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f825,plain,
( ~ sQ49_spl
| ~ sQ12_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f821,f822,f523,f781]) ).
fof(f832,plain,
! [X0] :
( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f389]) ).
fof(f835,plain,
! [X0] :
( ~ sQ7_spl
| cons(sK52_skl,nil) = X0
| sK49_skl != app(X0,sK53_skl)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f458,f376]) ).
fof(f836,plain,
! [X0] :
( ~ sQ8_spl
| sK53_skl = X0
| sK50_skl != app(X0,cons(sK52_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK52_skl,nil))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f462,f376]) ).
fof(f839,plain,
! [X0,X1] :
( X0 = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f376]) ).
fof(f842,definition,
! [X0] :
( sQ55_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f845,plain,
( ~ sQ12_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f832,f842,f523]) ).
fof(f849,definition,
! [X0] :
( sQ56_spl
<=> ( cons(sK52_skl,nil) = X0
| sK49_skl != app(X0,sK53_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f850,plain,
! [X0] :
( ~ sQ56_spl
| cons(sK52_skl,nil) = X0
| sK49_skl != app(X0,sK53_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f849]) ).
fof(f852,plain,
( ~ sQ7_spl
| ~ sQ20_spl
| ~ sQ6_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f835,f849,f453,f575,f457]) ).
fof(f853,definition,
! [X0] :
( sQ57_spl
<=> ( sK53_skl = X0
| sK50_skl != app(X0,cons(sK52_skl,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f856,plain,
( ~ sQ8_spl
| ~ sQ6_spl
| ~ sQ20_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f836,f853,f575,f453,f461]) ).
fof(f859,definition,
! [X1] :
( sQ58_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f860,plain,
! [X0] :
( ~ sQ58_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f859]) ).
fof(f862,plain,
( sQ58_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f839,f539,f859]) ).
fof(f864,plain,
( ~ sQ56_spl
| ~ ssItem(sK52_skl)
| ~ ssList(nil)
| sK49_skl != app(nil,sK53_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f850,f225]) ).
fof(f865,plain,
! [X0] :
( ~ sQ56_spl
| ~ ssItem(X0)
| ~ ssList(cons(sK52_skl,nil))
| sK49_skl != app(cons(X0,cons(sK52_skl,nil)),sK53_skl)
| ~ ssList(cons(X0,cons(sK52_skl,nil))) ),
inference(resolution,[status(thm)],[f850,f225]) ).
fof(f868,definition,
( sQ59_spl
<=> sK49_skl = app(nil,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f871,plain,
( ~ sQ56_spl
| ~ sQ4_spl
| ~ sQ59_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f864,f523,f868,f446,f849]) ).
fof(f872,definition,
! [X0] :
( sQ60_spl
<=> ( ~ ssItem(X0)
| sK49_skl != app(cons(X0,cons(sK52_skl,nil)),sK53_skl)
| ~ ssList(cons(X0,cons(sK52_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f875,plain,
( ~ sQ56_spl
| ~ sQ20_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f865,f872,f575,f849]) ).
fof(f878,plain,
! [X0] :
( ~ sQ26_spl
| memberP(sK53_skl,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0)
| memberP(nil,X0)
| X0 = sK52_skl
| ~ ssList(nil)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f275,f609]) ).
fof(f880,plain,
! [X0] :
( ~ sQ41_spl
| memberP(sK53_skl,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f736,f275]) ).
fof(f881,definition,
! [X0] :
( sQ61_spl
<=> ( memberP(sK53_skl,X0)
| ~ memberP(sK50_skl,X0)
| ~ ssItem(X0)
| memberP(nil,X0)
| X0 = sK52_skl
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f884,plain,
( ~ sQ26_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f878,f881,f446,f523,f608]) ).
fof(f885,definition,
! [X0] :
( sQ62_spl
<=> ( memberP(sK53_skl,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f886,plain,
! [X0] :
( ~ sQ62_spl
| memberP(sK53_skl,X0)
| X0 = sK52_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f885]) ).
fof(f888,plain,
( ~ sQ41_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f880,f885,f446,f453,f735]) ).
fof(f891,plain,
! [X0] :
( ~ sQ45_spl
| memberP(sK50_skl,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f277,f758]) ).
fof(f892,plain,
! [X0] :
( ~ sQ42_spl
| memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f277,f743]) ).
fof(f894,plain,
! [X0] :
( ~ sQ41_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssItem(sK52_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f736,f277]) ).
fof(f895,definition,
! [X0] :
( sQ63_spl
<=> ( memberP(sK50_skl,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f898,plain,
( ~ sQ45_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f891,f895,f446,f523,f757]) ).
fof(f899,definition,
! [X0] :
( sQ64_spl
<=> ( memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f902,plain,
( ~ sQ42_spl
| ~ sQ12_spl
| ~ sQ4_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f892,f899,f446,f523,f742]) ).
fof(f903,plain,
( ~ sQ41_spl
| ~ sQ6_spl
| ~ sQ4_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f894,f753,f446,f453,f735]) ).
fof(f906,plain,
! [X0] :
( nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0))
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f136,f386]) ).
fof(f907,plain,
! [X0] :
( nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0))
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f136,f385]) ).
fof(f908,definition,
! [X0] :
( sQ65_spl
<=> ( nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0))
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f911,plain,
( sQ65_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f906,f523,f908]) ).
fof(f912,definition,
! [X0] :
( sQ66_spl
<=> ( nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0))
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f915,plain,
( sQ66_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f907,f523,f912]) ).
fof(f917,plain,
( ~ sQ1_spl
| ~ sQ62_spl
| memberP(sK53_skl,sK51_skl)
| sK51_skl = sK52_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f886,f500]) ).
fof(f925,definition,
( sQ69_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f927,plain,
( sQ69_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f925]) ).
fof(f928,definition,
( sQ70_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f929,plain,
( ~ sQ70_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f928]) ).
fof(f931,definition,
( sQ71_spl
<=> memberP(sK53_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( ~ sQ71_spl
| memberP(sK53_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f931]) ).
fof(f934,plain,
( ~ sQ1_spl
| ~ sQ62_spl
| sQ71_spl
| sQ70_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f917,f925,f928,f931,f885,f434]) ).
fof(f998,plain,
( ~ sQ44_spl
| ~ sQ71_spl
| memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f932,f754]) ).
fof(f999,plain,
( ~ sQ43_spl
| ~ sQ71_spl
| memberP(sK50_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f932,f747]) ).
fof(f1000,definition,
( sQ73_spl
<=> memberP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1001,plain,
( ~ sQ73_spl
| memberP(sK49_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1000]) ).
fof(f1003,plain,
( ~ sQ44_spl
| ~ sQ71_spl
| sQ73_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f998,f925,f1000,f931,f753]) ).
fof(f1004,definition,
( sQ74_spl
<=> memberP(sK50_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
( ~ sQ74_spl
| memberP(sK50_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1004]) ).
fof(f1007,plain,
( ~ sQ43_spl
| ~ sQ71_spl
| sQ74_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f999,f925,f1004,f931,f746]) ).
fof(f1008,plain,
( sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f927,f423]) ).
fof(f1009,plain,
sQ69_spl,
inference(contradiction_clause,[status(thm)],[f1008]) ).
fof(f1010,plain,
( ~ sQ74_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1005,f499]) ).
fof(f1011,plain,
( ~ sQ74_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1010]) ).
fof(f1012,plain,
( ~ sQ42_spl
| ~ sQ26_spl
| ~ sQ44_spl
| ~ sQ0_spl
| memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f506,f802]) ).
fof(f1013,plain,
( ~ sQ42_spl
| ~ sQ26_spl
| ~ sQ44_spl
| ~ sQ0_spl
| sQ73_spl
| ~ sQ69_spl ),
inference(split_clause,[status(thm)],[f1012,f925,f1000,f431,f753,f608,f742]) ).
fof(f1014,plain,
( ~ sQ73_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1001,f505]) ).
fof(f1015,plain,
( ~ sQ73_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1014]) ).
fof(f1028,plain,
( sQ0_spl
| ~ sQ70_spl
| ~ memberP(sK50_skl,sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f929,f499]) ).
fof(f1029,plain,
( sQ0_spl
| ~ sQ70_spl
| ~ sQ52_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1028,f806]) ).
fof(f1030,plain,
( sQ0_spl
| ~ sQ70_spl
| ~ sQ52_spl ),
inference(contradiction_clause,[status(thm)],[f1029]) ).
fof(f1031,plain,
! [X0] :
( ~ sQ16_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f543]) ).
fof(f1032,plain,
( ~ sQ58_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f223,f860]) ).
fof(f1035,plain,
~ sQ58_spl,
inference(contradiction_clause,[status(thm)],[f1032]) ).
fof(f1036,plain,
( ~ sQ16_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f104,f1031]) ).
fof(f1038,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f1036]) ).
fof(f1052,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sK49_skl = sK50_skl ),
inference(forward_demodulation,[status(thm)],[f440,f443]) ).
fof(f1070,plain,
( sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ memberP(sK50_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f1052,f505]) ).
fof(f1071,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f506,f1070]) ).
fof(f1072,plain,
( ~ sQ0_spl
| sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1071]) ).
fof(f1073,plain,
$false,
inference(sat_refutation,[status(thm)],[f437,f438,f445,f452,f456,f460,f464,f504,f526,f528,f536,f550,f561,f570,f581,f583,f588,f593,f599,f607,f611,f615,f625,f629,f662,f729,f731,f738,f745,f749,f760,f768,f774,f780,f784,f793,f797,f808,f815,f825,f845,f852,f856,f862,f871,f875,f884,f888,f898,f902,f903,f911,f915,f934,f1003,f1007,f1009,f1011,f1013,f1015,f1030,f1035,f1038,f1072]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWC377+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 21 08:19:21 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.31 % Drodi V4.1.1
% 0.03/0.33 % Refutation found
% 0.03/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.03/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.34 % Elapsed time: 0.039443 seconds
% 0.07/0.34 % CPU time: 0.132407 seconds
% 0.07/0.34 % Total memory used: 91.655 MB
% 0.07/0.34 % Net memory used: 91.431 MB
%------------------------------------------------------------------------------