%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC253+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 : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:40:31 PM UTC 2026
% Result : Theorem 202.32s 26.09s
% Output : CNFRefutation 202.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 112
% Syntax : Number of formulae : 441 ( 18 unt; 82 def)
% Number of atoms : 1640 ( 286 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 2123 ( 924 ~; 941 |; 92 &)
% ( 92 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 91 ( 89 usr; 82 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 431 ( 404 !; 27 ?)
% 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(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f22,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssItem(hd(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(V,W)
& frontsegP(U,V) )
=> frontsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( rearsegP(U,V)
=> rearsegP(app(W,U),V) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> app(app(U,V),W) = app(U,app(V,W)) ) ) ),
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(f86,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> tl(app(U,V)) = app(tl(U),V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( singletonP(U)
| ? [Y] :
( ? [Z] :
( neq(nil,X)
& app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( singletonP(U)
| ? [Y] :
( ? [Z] :
( neq(nil,X)
& app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(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(X1)
| ~ ssList(X0)
| ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| ~ ssList(X1)
| X0 = app(X1,sK5_skl(X1,X0))
| ~ 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] :
( ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ssList(sK6_skl(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( ~ ssList(X1)
| app(sK6_skl(X0,X1),X0) = X1
| ~ rearsegP(X1,X0)
| ~ 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(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| X1 = X0
| neq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(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(f228,plain,
! [X0,X1,X2,X3] :
( X1 = X3
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f236,plain,
! [U] :
( ssItem(hd(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f237,plain,
! [X0] :
( ssItem(hd(X0))
| ~ ssList(X0)
| nil = X0 ),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f240,plain,
! [U] :
( ssList(tl(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f241,plain,
! [X0] :
( ssList(tl(X0))
| ~ ssList(X0)
| X0 = nil ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ~ ssList(X1)
| ssList(app(X0,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] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,app(X1,X2)) = app(cons(X0,X1),X2) ),
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] :
( X0 = app(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f280,plain,
~ singletonP(nil),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f281,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(U,W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f282,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X2,X0)
| ~ ssList(X2)
| frontsegP(X2,X1)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f287,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(app(U,W),V)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f288,plain,
! [X0,X1,X2] :
( frontsegP(app(X1,X0),X2)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( ~ ssList(X0)
| frontsegP(X0,nil) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f306,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(app(W,U),V)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f307,plain,
! [X0,X1,X2] :
( rearsegP(app(X2,X1),X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f316,plain,
! [U] :
( ! [V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f317,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| X1 = X0
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
fof(f320,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( segmentP(app(app(W,U),X),V)
| ~ segmentP(U,V)
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| segmentP(app(app(X3,X2),X0),X1)
| ~ ssList(X2)
| ~ segmentP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f373,plain,
! [U] :
( cons(hd(U),tl(U)) = U
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f374,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| X0 = cons(hd(X0),tl(X0)) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| X1 = X0
| app(X2,X1) != app(X2,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f381,plain,
! [U] :
( ! [V] :
( ! [W] :
( app(app(U,V),W) = app(U,app(V,W))
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f382,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| app(X1,app(X2,X0)) = app(app(X1,X2),X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
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] :
( X0 = nil
| nil != app(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X1)
| nil != app(X0,X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f387,plain,
! [X0,X1] :
( nil != X0
| nil != X1
| nil = app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( ~ ssList(X0)
| X0 = app(X0,nil) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f392,plain,
! [U] :
( ! [V] :
( tl(app(U,V)) = app(tl(U),V)
| nil = U
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f393,plain,
! [X0,X1] :
( X0 = nil
| ~ ssList(X0)
| ~ ssList(X1)
| tl(app(X0,X1)) = app(tl(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ~ singletonP(U)
& ! [Y] :
( ! [Z] :
( ~ neq(nil,X)
| app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ~ singletonP(U)
& ! [Y] :
( ! [Z] :
( ~ neq(nil,X)
| app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( singletonP(U)
| ? [Y] :
( ? [Z] :
( neq(nil,X)
& app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ~ singletonP(U)
& ! [Y] :
( ! [Z] :
( ~ neq(nil,X)
| app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( singletonP(U)
| ? [Y] :
( neq(nil,X)
& ? [Z] :
( app(W,Z) = Y
& tl(X) = Z
& ssList(Z) )
& X != Y
& ssList(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ~ singletonP(U)
& ! [Y] :
( ~ neq(nil,X)
| ! [Z] :
( app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( singletonP(U)
| ( neq(nil,X)
& app(W,sK52_skl(X,W,V,U)) = sK51_skl(X,W,V,U)
& tl(X) = sK52_skl(X,W,V,U)
& ssList(sK52_skl(X,W,V,U))
& X != sK51_skl(X,W,V,U)
& ssList(sK51_skl(X,W,V,U)) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ~ singletonP(U)
& ! [Y] :
( ~ neq(nil,X)
| ! [Z] :
( app(W,Z) != Y
| tl(X) != Z
| ~ ssList(Z) )
| X = Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Y,sK51_skl(X,W,V,U)),skolemize(Z,sK52_skl(X,W,V,U))],[f428]) ).
fof(f430,plain,
! [X0,X1,X2,X3] :
( neq(X2,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ neq(nil,X0)
| app(X1,X5) != X4
| tl(X0) != X5
| ~ ssList(X5)
| X0 = X4
| ~ ssList(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X1,X2,X3,X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f438,plain,
! [X0,X1,X2,X3] :
( ~ neq(X3,nil)
| neq(nil,X1)
| sP0_prd(X1,X2,X3,X0)
| singletonP(X0) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f439,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f439,f442]) ).
fof(f446,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ2_spl
| neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f448,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f439,f446]) ).
fof(f455,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f457,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f424,f440]) ).
fof(f458,plain,
ssList(sK49_skl),
inference(backward_demodulation,[status(thm)],[f424,f419]) ).
fof(f461,plain,
( nil = app(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(destructive_equality_resolution,[status(thm)],[f387]) ).
fof(f462,plain,
( ~ ssList(nil)
| nil = app(nil,nil) ),
inference(duplicate_literals_removal,[status(thm)],[f461]) ).
fof(f465,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f466,plain,
app(nil,nil) = nil,
inference(backward_subsumption_resolution,[status(thm)],[f462,f223]) ).
fof(f467,plain,
! [X0,X1,X2,X3] :
( ~ ssList(tl(X1))
| ~ sP0_prd(X1,X0,X2,X3)
| app(X0,tl(X1)) = X1
| ~ neq(nil,X1)
| ~ ssList(app(X0,tl(X1))) ),
inference(destructive_equality_resolution,[status(thm)],[f431]) ).
fof(f470,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f471,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f470]) ).
fof(f475,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f465,f245]) ).
fof(f476,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f423,f457]) ).
fof(f481,plain,
! [X2,X1] :
( ~ ssList(X2)
| rearsegP(app(X2,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f482,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| rearsegP(app(X0,X1),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f481,f245]) ).
fof(f489,definition,
! [X0] :
( sQ3_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| X0 = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f496,plain,
! [X0] :
( app(X0,nil) != nil
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0)
| nil = X0 ),
inference(paramodulation,[status(thm)],[f466,f376]) ).
fof(f498,definition,
! [X0] :
( sQ5_spl
<=> ( app(X0,nil) != nil
| ~ ssList(X0)
| nil = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f499,plain,
! [X0] :
( ~ sQ5_spl
| nil != app(X0,nil)
| X0 = nil
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ6_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ6_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f496,f498,f501]) ).
fof(f506,plain,
( ~ sQ0_spl
| ~ singletonP(sK49_skl) ),
inference(resolution,[status(thm)],[f476,f432]) ).
fof(f507,plain,
( ~ sQ0_spl
| ~ ssList(app(sK49_skl,tl(sK48_skl)))
| ~ ssList(tl(sK48_skl))
| ~ neq(nil,sK48_skl)
| app(sK49_skl,tl(sK48_skl)) = sK48_skl ),
inference(resolution,[status(thm)],[f476,f467]) ).
fof(f508,definition,
( sQ7_spl
<=> app(sK49_skl,tl(sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( ~ sQ7_spl
| app(sK49_skl,tl(sK48_skl)) = sK48_skl ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,definition,
( sQ8_spl
<=> neq(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ8_spl
| ~ neq(nil,sK48_skl) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,definition,
( sQ9_spl
<=> ssList(tl(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f516,plain,
( sQ9_spl
| ~ ssList(tl(sK48_skl)) ),
inference(component_clause,[status(thm)],[f514]) ).
fof(f517,definition,
( sQ10_spl
<=> ssList(app(sK49_skl,tl(sK48_skl))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ10_spl
| ~ ssList(app(sK49_skl,tl(sK48_skl))) ),
inference(component_clause,[status(thm)],[f517]) ).
fof(f520,plain,
( ~ sQ0_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f507,f508,f511,f514,f517,f439]) ).
fof(f521,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(X0,nil))
| X0 = app(X0,nil)
| ~ ssList(app(X0,nil)) ),
inference(resolution,[status(thm)],[f389,f376]) ).
fof(f523,plain,
( nil = nil
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f389]) ).
fof(f524,definition,
! [X0] :
( sQ11_spl
<=> ( ~ ssList(X0)
| ~ ssList(app(X0,nil))
| X0 = app(X0,nil)
| ~ ssList(app(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( ~ sQ6_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f521,f524,f501]) ).
fof(f529,definition,
( sQ12_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ12_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f523,f501,f529]) ).
fof(f534,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f503,f223]) ).
fof(f535,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f538,plain,
( ~ sQ0_spl
| neq(sK48_skl,nil) ),
inference(resolution,[status(thm)],[f430,f476]) ).
fof(f539,plain,
! [X0,X1,X2] :
( neq(X2,nil)
| ~ neq(X2,nil)
| singletonP(X1)
| neq(nil,X0) ),
inference(resolution,[status(thm)],[f438,f430]) ).
fof(f540,plain,
! [X0,X1,X2] :
( ~ singletonP(X1)
| ~ neq(X2,nil)
| singletonP(X1)
| neq(nil,X0) ),
inference(resolution,[status(thm)],[f438,f432]) ).
fof(f541,plain,
! [X0,X1,X2,X3] :
( ~ ssList(app(X3,tl(X0)))
| ~ ssList(tl(X0))
| ~ neq(nil,X0)
| app(X3,tl(X0)) = X0
| ~ neq(X2,nil)
| singletonP(X1)
| neq(nil,X0) ),
inference(resolution,[status(thm)],[f438,f467]) ).
fof(f542,definition,
! [X0,X3] :
( sQ13_spl
<=> ( ~ ssList(app(X3,tl(X0)))
| ~ ssList(tl(X0))
| ~ neq(nil,X0)
| app(X3,tl(X0)) = X0
| neq(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f545,definition,
! [X1] :
( sQ14_spl
<=> singletonP(X1) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f546,plain,
! [X0] :
( ~ sQ14_spl
| singletonP(X0) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,definition,
! [X2] :
( sQ15_spl
<=> ~ neq(X2,nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f549,plain,
! [X0] :
( ~ sQ15_spl
| ~ neq(X0,nil) ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f551,plain,
( sQ15_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f541,f542,f545,f548]) ).
fof(f552,definition,
! [X0] :
( sQ16_spl
<=> neq(nil,X0) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f553,plain,
! [X0] :
( ~ sQ16_spl
| neq(nil,X0) ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,definition,
! [X2] :
( sQ17_spl
<=> ( neq(X2,nil)
| ~ neq(X2,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( sQ17_spl
| sQ14_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f539,f552,f545,f555]) ).
fof(f559,definition,
! [X1] :
( sQ18_spl
<=> ( ~ singletonP(X1)
| singletonP(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( sQ15_spl
| sQ18_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f540,f552,f559,f548]) ).
fof(f563,plain,
! [X0,X1,X2,X3] :
( ~ sQ15_spl
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f430,f549]) ).
fof(f565,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f476,f563]) ).
fof(f566,plain,
( ~ sQ0_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f567,plain,
( sQ2_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f448]) ).
fof(f568,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f567,f443]) ).
fof(f569,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f571,plain,
( ~ sQ14_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f280,f546]) ).
fof(f574,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f571]) ).
fof(f575,plain,
( ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f538,f442,f439]) ).
fof(f576,plain,
( ~ sQ2_spl
| neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f447]) ).
fof(f577,plain,
( ~ sQ16_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f553,f471]) ).
fof(f579,plain,
( ~ sQ16_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f577,f501,f552]) ).
fof(f588,plain,
( sQ10_spl
| ~ ssList(tl(sK48_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f245,f519]) ).
fof(f590,definition,
( sQ19_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f592,plain,
( sQ19_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f590]) ).
fof(f593,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f588,f590,f514,f517]) ).
fof(f595,plain,
( sQ9_spl
| nil = sK48_skl
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f516,f241]) ).
fof(f596,definition,
( sQ20_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f598,plain,
( sQ20_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f596]) ).
fof(f599,definition,
( sQ21_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( ~ sQ21_spl
| nil = sK48_skl ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f601,plain,
( sQ21_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f599]) ).
fof(f602,plain,
( sQ9_spl
| sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f595,f596,f599,f514]) ).
fof(f603,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f592,f458]) ).
fof(f604,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f603]) ).
fof(f605,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f598,f420]) ).
fof(f606,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f605]) ).
fof(f614,plain,
( ~ sQ2_spl
| ~ sQ21_spl
| neq(sK48_skl,sK48_skl) ),
inference(backward_demodulation,[status(thm)],[f600,f576]) ).
fof(f680,plain,
( ~ sQ2_spl
| ~ sQ21_spl
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f614,f471]) ).
fof(f682,plain,
( ~ sQ2_spl
| ~ sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f680,f596,f599,f446]) ).
fof(f686,plain,
! [X0] :
( ~ sQ7_spl
| sK48_skl != app(X0,tl(sK48_skl))
| ~ ssList(X0)
| ~ ssList(tl(sK48_skl))
| ~ ssList(sK49_skl)
| X0 = sK49_skl ),
inference(paramodulation,[status(thm)],[f509,f376]) ).
fof(f687,definition,
! [X0] :
( sQ22_spl
<=> ( sK48_skl != app(X0,tl(sK48_skl))
| ~ ssList(X0)
| X0 = sK49_skl ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f688,plain,
! [X0] :
( ~ sQ22_spl
| sK48_skl != app(X0,tl(sK48_skl))
| ~ ssList(X0)
| sK49_skl = X0 ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ19_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f686,f687,f590,f514,f508]) ).
fof(f706,plain,
( ~ sQ7_spl
| ~ sQ22_spl
| sK49_skl = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f688,f509]) ).
fof(f708,definition,
( sQ23_spl
<=> sK49_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f711,definition,
( sQ24_spl
<=> sK48_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f713,plain,
( sQ24_spl
| sK48_skl != sK48_skl ),
inference(component_clause,[status(thm)],[f711]) ).
fof(f715,plain,
( ~ sQ7_spl
| ~ sQ22_spl
| sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f706,f590,f708,f687,f508]) ).
fof(f716,plain,
( sQ8_spl
| ~ ssList(nil)
| ~ ssList(sK48_skl)
| sK48_skl = nil ),
inference(resolution,[status(thm)],[f513,f220]) ).
fof(f717,plain,
( sQ8_spl
| ~ sQ6_spl
| ~ sQ20_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f716,f599,f596,f501,f511]) ).
fof(f737,plain,
( ~ sQ7_spl
| ~ ssList(tl(sK48_skl))
| frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f509,f475]) ).
fof(f738,plain,
( ~ ssList(nil)
| frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f475]) ).
fof(f739,definition,
( sQ25_spl
<=> frontsegP(sK48_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f740,plain,
( ~ sQ25_spl
| frontsegP(sK48_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f742,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ25_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f737,f590,f739,f514,f508]) ).
fof(f743,definition,
( sQ26_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f744,plain,
( ~ sQ26_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f743]) ).
fof(f746,plain,
( sQ26_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f738,f501,f743]) ).
fof(f747,plain,
( ~ sQ7_spl
| ~ ssList(tl(sK48_skl))
| rearsegP(sK48_skl,tl(sK48_skl))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f509,f482]) ).
fof(f748,plain,
( ~ ssList(nil)
| rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f482]) ).
fof(f749,definition,
( sQ27_spl
<=> rearsegP(sK48_skl,tl(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f752,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ27_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f747,f590,f749,f514,f508]) ).
fof(f753,definition,
( sQ28_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f756,plain,
( sQ28_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f748,f501,f753]) ).
fof(f767,plain,
! [X0] :
( ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(sK5_skl(X0,nil))
| nil = sK5_skl(X0,nil) ),
inference(resolution,[status(thm)],[f385,f123]) ).
fof(f771,definition,
! [X0] :
( sQ29_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(sK5_skl(X0,nil))
| nil = sK5_skl(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f774,plain,
( ~ sQ6_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f767,f771,f501]) ).
fof(f787,plain,
! [X0] :
( ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| X0 = nil ),
inference(resolution,[status(thm)],[f386,f123]) ).
fof(f790,definition,
! [X0] :
( sQ31_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| X0 = nil ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( ~ sQ6_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f787,f790,f501]) ).
fof(f796,definition,
( sQ32_spl
<=> sK49_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f797,plain,
( ~ sQ32_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f796]) ).
fof(f805,plain,
! [X0,X1,X2,X3] :
( ~ ssList(tl(X0))
| ~ ssList(X1)
| ~ sP0_prd(X0,X1,X2,X3)
| ~ neq(nil,X0)
| app(X1,tl(X0)) = X0
| ~ ssList(tl(X0)) ),
inference(resolution,[status(thm)],[f467,f245]) ).
fof(f809,plain,
! [X0,X1,X2,X3] :
( ~ ssList(tl(X0))
| app(X1,tl(X0)) = X0
| ~ neq(nil,X0)
| ~ ssList(X1)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(duplicate_literals_removal,[status(thm)],[f805]) ).
fof(f815,plain,
! [X0,X1,X2,X3] :
( neq(nil,X1)
| ~ neq(X3,nil)
| singletonP(X2)
| ~ neq(nil,X1)
| X1 = app(X0,tl(X1))
| ~ ssList(tl(X1))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f809,f438]) ).
fof(f816,definition,
! [X0,X1] :
( sQ34_spl
<=> ( neq(nil,X1)
| ~ neq(nil,X1)
| X1 = app(X0,tl(X1))
| ~ ssList(tl(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f819,plain,
( sQ15_spl
| sQ14_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f815,f816,f545,f548]) ).
fof(f822,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| ~ ssList(X0)
| ~ ssList(app(nil,X0))
| X0 = app(nil,X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f378,f249]) ).
fof(f826,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(X0)
| nil != app(nil,X0)
| nil = X0
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f378]) ).
fof(f827,plain,
! [X0] :
( ~ sQ7_spl
| ~ ssList(X0)
| ~ ssList(tl(sK48_skl))
| app(sK49_skl,X0) != sK48_skl
| X0 = tl(sK48_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f509,f378]) ).
fof(f830,definition,
! [X0] :
( sQ35_spl
<=> ( ~ ssList(X0)
| nil != app(nil,X0)
| nil = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f831,plain,
! [X0] :
( ~ sQ35_spl
| ~ ssList(X0)
| nil != app(nil,X0)
| X0 = nil ),
inference(component_clause,[status(thm)],[f830]) ).
fof(f833,plain,
( sQ35_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f826,f501,f830]) ).
fof(f836,definition,
! [X0] :
( sQ36_spl
<=> ( ~ ssList(app(nil,X0))
| ~ ssList(X0)
| ~ ssList(app(nil,X0))
| X0 = app(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f839,plain,
( sQ36_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f822,f501,f836]) ).
fof(f841,definition,
! [X0] :
( sQ37_spl
<=> ( ~ ssList(X0)
| app(sK49_skl,X0) != sK48_skl
| X0 = tl(sK48_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f842,plain,
! [X0] :
( ~ sQ37_spl
| ~ ssList(X0)
| sK48_skl != app(sK49_skl,X0)
| X0 = tl(sK48_skl) ),
inference(component_clause,[status(thm)],[f841]) ).
fof(f844,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ37_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f827,f590,f841,f514,f508]) ).
fof(f850,plain,
( ~ sQ7_spl
| ~ sQ37_spl
| tl(sK48_skl) = tl(sK48_skl)
| ~ ssList(tl(sK48_skl)) ),
inference(resolution,[status(thm)],[f842,f509]) ).
fof(f851,plain,
( ~ sQ37_spl
| ~ ssList(sK48_skl)
| ~ frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl)
| tl(sK48_skl) = sK5_skl(sK49_skl,sK48_skl)
| ~ ssList(sK5_skl(sK49_skl,sK48_skl)) ),
inference(resolution,[status(thm)],[f842,f123]) ).
fof(f853,definition,
( sQ38_spl
<=> tl(sK48_skl) = tl(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f856,plain,
( ~ sQ7_spl
| ~ sQ37_spl
| sQ38_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f850,f514,f853,f841,f508]) ).
fof(f858,definition,
( sQ39_spl
<=> ssList(sK5_skl(sK49_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( sQ39_spl
| ~ ssList(sK5_skl(sK49_skl,sK48_skl)) ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f861,definition,
( sQ40_spl
<=> tl(sK48_skl) = sK5_skl(sK49_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f862,plain,
( ~ sQ40_spl
| tl(sK48_skl) = sK5_skl(sK49_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f861]) ).
fof(f864,plain,
( ~ sQ37_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ19_spl
| sQ40_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f851,f858,f861,f590,f739,f596,f841]) ).
fof(f867,plain,
( ~ sQ35_spl
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(sK5_skl(nil,nil))
| nil = sK5_skl(nil,nil) ),
inference(resolution,[status(thm)],[f831,f123]) ).
fof(f874,definition,
( sQ41_spl
<=> nil = sK5_skl(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f877,definition,
( sQ42_spl
<=> ssList(sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f879,plain,
( sQ42_spl
| ~ ssList(sK5_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f877]) ).
fof(f880,plain,
( ~ sQ35_spl
| ~ sQ26_spl
| ~ sQ6_spl
| ~ sQ42_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f867,f874,f877,f501,f743,f830]) ).
fof(f881,plain,
! [X0] :
( ~ sQ7_spl
| ~ ssList(tl(sK48_skl))
| app(sK49_skl,app(tl(sK48_skl),X0)) = app(sK48_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f509,f382]) ).
fof(f882,plain,
! [X0] :
( ~ ssList(nil)
| app(nil,app(nil,X0)) = app(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f382]) ).
fof(f883,definition,
! [X0] :
( sQ43_spl
<=> ( app(sK49_skl,app(tl(sK48_skl),X0)) = app(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f886,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ43_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f881,f590,f883,f514,f508]) ).
fof(f887,definition,
! [X0] :
( sQ44_spl
<=> ( app(nil,app(nil,X0)) = app(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f888,plain,
! [X0] :
( ~ sQ44_spl
| app(nil,app(nil,X0)) = app(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f887]) ).
fof(f890,plain,
( sQ44_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f882,f501,f887]) ).
fof(f892,definition,
( sQ45_spl
<=> app(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f897,plain,
! [X0] :
( ~ sQ44_spl
| ~ ssList(X0)
| ~ ssList(app(nil,X0))
| X0 = app(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f888,f378]) ).
fof(f898,plain,
( ~ sQ44_spl
| app(nil,nil) = app(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f888]) ).
fof(f899,definition,
( sQ46_spl
<=> app(nil,nil) = app(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f902,plain,
( ~ sQ44_spl
| sQ46_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f898,f501,f899,f887]) ).
fof(f903,definition,
! [X0] :
( sQ47_spl
<=> ( ~ ssList(X0)
| ~ ssList(app(nil,X0))
| X0 = app(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f906,plain,
( ~ sQ44_spl
| ~ sQ6_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f897,f903,f501,f887]) ).
fof(f910,plain,
( ~ sQ7_spl
| ~ ssList(sK49_skl)
| sK49_skl = nil
| app(tl(sK49_skl),tl(sK48_skl)) = tl(sK48_skl)
| ~ ssList(tl(sK48_skl)) ),
inference(paramodulation,[status(thm)],[f509,f393]) ).
fof(f912,definition,
( sQ48_spl
<=> app(tl(sK49_skl),tl(sK48_skl)) = tl(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f913,plain,
( ~ sQ48_spl
| app(tl(sK49_skl),tl(sK48_skl)) = tl(sK48_skl) ),
inference(component_clause,[status(thm)],[f912]) ).
fof(f915,plain,
( ~ sQ7_spl
| ~ sQ19_spl
| sQ32_spl
| sQ48_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f910,f514,f912,f796,f590,f508]) ).
fof(f941,plain,
! [X0] :
( ~ sQ32_spl
| ~ ssList(X0)
| sK49_skl = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(backward_demodulation,[status(thm)],[f797,f374]) ).
fof(f950,plain,
! [X0] :
( ~ sQ32_spl
| ~ ssList(X0)
| app(sK49_skl,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f797,f249]) ).
fof(f1014,plain,
! [X0] :
( ~ sQ7_spl
| app(cons(X0,sK49_skl),tl(sK48_skl)) = cons(X0,sK48_skl)
| ~ ssList(tl(sK48_skl))
| ~ ssItem(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f509,f247]) ).
fof(f1015,definition,
! [X0] :
( sQ50_spl
<=> ( app(cons(X0,sK49_skl),tl(sK48_skl)) = cons(X0,sK48_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1018,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ50_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1014,f590,f1015,f514,f508]) ).
fof(f1046,definition,
( sQ55_spl
<=> sK49_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1088,plain,
( sQ24_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f713]) ).
fof(f1089,plain,
sQ24_spl,
inference(contradiction_clause,[status(thm)],[f1088]) ).
fof(f1091,plain,
( ~ sQ37_spl
| ~ sQ32_spl
| tl(sK48_skl) = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f950,f842]) ).
fof(f1098,definition,
( sQ64_spl
<=> tl(sK48_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1099,plain,
( ~ sQ64_spl
| sK48_skl = tl(sK48_skl) ),
inference(component_clause,[status(thm)],[f1098]) ).
fof(f1101,plain,
( ~ sQ37_spl
| ~ sQ32_spl
| sQ64_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1091,f596,f1098,f796,f841]) ).
fof(f1109,plain,
! [X0] :
( app(cons(X0,nil),nil) = cons(X0,nil)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f247]) ).
fof(f1124,definition,
! [X0] :
( sQ66_spl
<=> ( app(cons(X0,nil),nil) = cons(X0,nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1127,plain,
( sQ66_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1109,f501,f1124]) ).
fof(f1174,plain,
( ~ sQ7_spl
| ~ sQ64_spl
| app(sK49_skl,sK48_skl) = sK48_skl ),
inference(backward_demodulation,[status(thm)],[f1099,f509]) ).
fof(f1183,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ64_spl
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| sK48_skl != app(sK49_skl,X0)
| sK48_skl = X0
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1174,f378]) ).
fof(f1209,definition,
! [X0] :
( sQ75_spl
<=> ( ~ ssList(X0)
| sK48_skl != app(sK49_skl,X0)
| sK48_skl = X0 ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1210,plain,
! [X0] :
( ~ sQ75_spl
| X0 = sK48_skl
| app(sK49_skl,X0) != sK48_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1209]) ).
fof(f1212,plain,
( ~ sQ7_spl
| ~ sQ64_spl
| ~ sQ20_spl
| sQ75_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1183,f590,f1209,f596,f1098,f508]) ).
fof(f1256,plain,
( ~ sQ75_spl
| ~ ssList(sK48_skl)
| ~ frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK49_skl)
| sK5_skl(sK49_skl,sK48_skl) = sK48_skl
| ~ ssList(sK5_skl(sK49_skl,sK48_skl)) ),
inference(resolution,[status(thm)],[f1210,f123]) ).
fof(f1259,definition,
( sQ76_spl
<=> sK5_skl(sK49_skl,sK48_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1260,plain,
( ~ sQ76_spl
| sK5_skl(sK49_skl,sK48_skl) = sK48_skl ),
inference(component_clause,[status(thm)],[f1259]) ).
fof(f1262,plain,
( ~ sQ75_spl
| ~ sQ20_spl
| ~ sQ25_spl
| ~ sQ19_spl
| sQ76_spl
| ~ sQ39_spl ),
inference(split_clause,[status(thm)],[f1256,f858,f1259,f590,f739,f596,f1209]) ).
fof(f1279,plain,
! [X0] :
( ~ sQ48_spl
| tl(sK48_skl) != app(X0,tl(sK48_skl))
| ~ ssList(X0)
| ~ ssList(tl(sK48_skl))
| ~ ssList(tl(sK49_skl))
| X0 = tl(sK49_skl) ),
inference(paramodulation,[status(thm)],[f913,f376]) ).
fof(f1280,definition,
( sQ77_spl
<=> ssList(tl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1282,plain,
( sQ77_spl
| ~ ssList(tl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f1280]) ).
fof(f1293,definition,
! [X0] :
( sQ80_spl
<=> ( tl(sK48_skl) != app(X0,tl(sK48_skl))
| ~ ssList(X0)
| X0 = tl(sK49_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1294,plain,
! [X0] :
( ~ sQ80_spl
| tl(sK48_skl) != app(X0,tl(sK48_skl))
| X0 = tl(sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1293]) ).
fof(f1296,plain,
( ~ sQ48_spl
| ~ sQ9_spl
| ~ sQ77_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f1279,f1293,f1280,f514,f912]) ).
fof(f1311,plain,
( sQ77_spl
| ~ ssList(sK49_skl)
| sK49_skl = nil ),
inference(resolution,[status(thm)],[f1282,f241]) ).
fof(f1312,plain,
( sQ77_spl
| ~ sQ19_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1311,f796,f590,f1280]) ).
fof(f1313,plain,
( sQ39_spl
| ~ frontsegP(sK48_skl,sK49_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f122,f860]) ).
fof(f1314,plain,
( sQ42_spl
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f122,f879]) ).
fof(f1315,plain,
( sQ42_spl
| ~ sQ26_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1314,f501,f743,f877]) ).
fof(f1316,plain,
( sQ39_spl
| ~ sQ25_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1313,f590,f596,f739,f858]) ).
fof(f1363,plain,
! [X0,X1] :
( ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(X0)
| X0 = X0 ),
inference(equality_resolution,[status(thm)],[f228]) ).
fof(f1364,definition,
! [X1] :
( sQ90_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1365,plain,
! [X0] :
( ~ sQ90_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1364]) ).
fof(f1367,plain,
( sQ90_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f1363,f489,f1364]) ).
fof(f1373,plain,
( ~ sQ90_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f104,f1388]) ).
fof(f1388,plain,
! [X0] :
( ~ sQ90_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1365]) ).
fof(f1389,plain,
~ sQ90_spl,
inference(contradiction_clause,[status(thm)],[f1373]) ).
fof(f1418,plain,
! [X0] :
( ~ sQ26_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f282,f744]) ).
fof(f1419,plain,
! [X0] :
( ~ sQ25_spl
| frontsegP(X0,sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(sK48_skl)
| ~ frontsegP(X0,sK48_skl) ),
inference(resolution,[status(thm)],[f282,f740]) ).
fof(f1421,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f282,f295]) ).
fof(f1427,definition,
! [X0] :
( sQ92_spl
<=> ( frontsegP(X0,sK49_skl)
| ~ ssList(X0)
| ~ frontsegP(X0,sK48_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1428,plain,
! [X0] :
( ~ sQ92_spl
| frontsegP(X0,sK49_skl)
| ~ ssList(X0)
| ~ frontsegP(X0,sK48_skl) ),
inference(component_clause,[status(thm)],[f1427]) ).
fof(f1430,plain,
( ~ sQ25_spl
| ~ sQ19_spl
| ~ sQ20_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f1419,f1427,f596,f590,f739]) ).
fof(f1431,definition,
! [X0] :
( sQ93_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1434,plain,
( ~ sQ26_spl
| ~ sQ6_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1418,f1431,f501,f743]) ).
fof(f1437,definition,
! [X0,X1] :
( sQ94_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1440,plain,
( ~ sQ6_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1421,f1437,f501]) ).
fof(f1442,plain,
! [X0] :
( ~ sQ92_spl
| ~ ssList(X0)
| ~ ssList(sK48_skl)
| frontsegP(app(sK48_skl,X0),sK49_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(resolution,[status(thm)],[f1428,f475]) ).
fof(f1444,definition,
! [X0] :
( sQ95_spl
<=> ( ~ ssList(X0)
| frontsegP(app(sK48_skl,X0),sK49_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1445,plain,
! [X0] :
( ~ sQ95_spl
| ~ ssList(app(sK48_skl,X0))
| ~ ssList(X0)
| frontsegP(app(sK48_skl,X0),sK49_skl) ),
inference(component_clause,[status(thm)],[f1444]) ).
fof(f1447,plain,
( ~ sQ92_spl
| ~ sQ20_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f1442,f1444,f596,f1427]) ).
fof(f1468,definition,
( sQ96_spl
<=> nil = tl(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1469,plain,
( ~ sQ96_spl
| tl(sK49_skl) = nil ),
inference(component_clause,[status(thm)],[f1468]) ).
fof(f1486,plain,
( ~ sQ96_spl
| ~ ssList(sK49_skl)
| nil = sK49_skl
| sK49_skl = cons(hd(sK49_skl),nil) ),
inference(paramodulation,[status(thm)],[f1469,f374]) ).
fof(f1491,definition,
( sQ97_spl
<=> sK49_skl = cons(hd(sK49_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1492,plain,
( ~ sQ97_spl
| cons(hd(sK49_skl),nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f1491]) ).
fof(f1494,plain,
( ~ sQ96_spl
| ~ sQ19_spl
| sQ32_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1486,f1491,f796,f590,f1468]) ).
fof(f1518,plain,
! [X0] :
( ~ sQ7_spl
| ~ rearsegP(tl(sK48_skl),X0)
| ~ ssList(sK49_skl)
| rearsegP(sK48_skl,X0)
| ~ ssList(X0)
| ~ ssList(tl(sK48_skl)) ),
inference(paramodulation,[status(thm)],[f509,f307]) ).
fof(f1519,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(nil)
| rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f307]) ).
fof(f1520,definition,
! [X0] :
( sQ103_spl
<=> ( ~ rearsegP(nil,X0)
| rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1523,plain,
( sQ103_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1519,f501,f1520]) ).
fof(f1524,definition,
! [X0] :
( sQ104_spl
<=> ( ~ rearsegP(tl(sK48_skl),X0)
| rearsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1525,plain,
! [X0] :
( ~ sQ104_spl
| ~ ssList(X0)
| rearsegP(sK48_skl,X0)
| ~ rearsegP(tl(sK48_skl),X0) ),
inference(component_clause,[status(thm)],[f1524]) ).
fof(f1527,plain,
( ~ sQ7_spl
| ~ sQ19_spl
| sQ104_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f1518,f514,f1524,f590,f508]) ).
fof(f1528,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f1530,definition,
! [X0] :
( sQ105_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1533,plain,
( ~ sQ6_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1528,f1530,f501]) ).
fof(f1541,definition,
( sQ107_spl
<=> ssItem(hd(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1543,plain,
( sQ107_spl
| ~ ssItem(hd(sK49_skl)) ),
inference(component_clause,[status(thm)],[f1541]) ).
fof(f1632,plain,
( ~ sQ104_spl
| ~ ssList(tl(sK48_skl))
| ~ ssList(nil)
| rearsegP(sK48_skl,nil) ),
inference(resolution,[status(thm)],[f1525,f309]) ).
fof(f1636,definition,
( sQ110_spl
<=> rearsegP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1639,plain,
( ~ sQ104_spl
| ~ sQ9_spl
| ~ sQ6_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1632,f1636,f501,f514,f1524]) ).
fof(f1642,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ ssList(tl(sK48_skl))
| ~ segmentP(tl(sK48_skl),X1)
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| segmentP(app(sK48_skl,X0),X1)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f509,f321]) ).
fof(f1643,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ segmentP(nil,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| segmentP(app(nil,X0),X1)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f466,f321]) ).
fof(f1648,definition,
! [X0,X1] :
( sQ112_spl
<=> ( ~ segmentP(nil,X1)
| ~ ssList(X1)
| segmentP(app(nil,X0),X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1651,plain,
( ~ sQ6_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f1643,f1648,f501]) ).
fof(f1652,definition,
! [X0,X1] :
( sQ113_spl
<=> ( ~ segmentP(tl(sK48_skl),X1)
| ~ ssList(X1)
| segmentP(app(sK48_skl,X0),X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1655,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ19_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f1642,f1652,f590,f514,f508]) ).
fof(f1695,plain,
! [X0,X1] :
( ~ sQ92_spl
| frontsegP(app(X0,X1),sK49_skl)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(sK48_skl)
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f288,f1428]) ).
fof(f1698,plain,
! [X0] :
( ~ sQ7_spl
| ~ ssList(tl(sK48_skl))
| ~ ssList(X0)
| frontsegP(sK48_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f509,f288]) ).
fof(f1699,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(X0)
| frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f466,f288]) ).
fof(f1708,definition,
! [X0] :
( sQ119_spl
<=> ( ~ ssList(X0)
| frontsegP(nil,X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1711,plain,
( sQ119_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1699,f501,f1708]) ).
fof(f1712,definition,
! [X0,X1] :
( sQ120_spl
<=> ( frontsegP(app(X0,X1),sK49_skl)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1715,plain,
( ~ sQ92_spl
| ~ sQ20_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f1695,f1712,f596,f1427]) ).
fof(f1716,definition,
! [X0] :
( sQ121_spl
<=> ( ~ ssList(X0)
| frontsegP(sK48_skl,X0)
| ~ frontsegP(sK49_skl,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1717,plain,
! [X0] :
( ~ sQ121_spl
| frontsegP(sK48_skl,X0)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,X0) ),
inference(component_clause,[status(thm)],[f1716]) ).
fof(f1719,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| sQ121_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1698,f590,f1716,f514,f508]) ).
fof(f1728,plain,
( ~ sQ121_spl
| ~ ssList(sK49_skl)
| frontsegP(sK48_skl,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1717,f295]) ).
fof(f1731,definition,
( sQ122_spl
<=> frontsegP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1732,plain,
( ~ sQ122_spl
| frontsegP(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f1731]) ).
fof(f1734,plain,
( ~ sQ121_spl
| ~ sQ19_spl
| sQ122_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1728,f501,f1731,f590,f1716]) ).
fof(f1736,plain,
( ~ sQ5_spl
| sK6_skl(nil,nil) = nil
| ~ ssList(sK6_skl(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(nil,nil) ),
inference(resolution,[status(thm)],[f129,f499]) ).
fof(f1737,plain,
! [X0] :
( nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f129,f386]) ).
fof(f1738,plain,
! [X0] :
( X0 = nil
| ~ ssList(sK6_skl(X0,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f129,f385]) ).
fof(f1741,definition,
! [X0] :
( sQ123_spl
<=> ( X0 = nil
| ~ ssList(sK6_skl(X0,nil))
| ~ ssList(X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1744,plain,
( ~ sQ6_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f1738,f1741,f501]) ).
fof(f1745,definition,
( sQ124_spl
<=> ssList(sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1747,plain,
( sQ124_spl
| ~ ssList(sK6_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1745]) ).
fof(f1748,definition,
( sQ125_spl
<=> sK6_skl(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1749,plain,
( ~ sQ125_spl
| nil = sK6_skl(nil,nil) ),
inference(component_clause,[status(thm)],[f1748]) ).
fof(f1751,plain,
( ~ sQ5_spl
| sQ125_spl
| ~ sQ124_spl
| ~ sQ6_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f1736,f753,f501,f1745,f1748,f498]) ).
fof(f1759,definition,
! [X0] :
( sQ128_spl
<=> ( nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1762,plain,
( ~ sQ6_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f1737,f1759,f501]) ).
fof(f1773,plain,
! [X0] :
( ~ sQ122_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK48_skl)
| ~ frontsegP(X0,sK48_skl) ),
inference(resolution,[status(thm)],[f1732,f282]) ).
fof(f1774,definition,
! [X0] :
( sQ129_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,sK48_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1777,plain,
( ~ sQ122_spl
| ~ sQ6_spl
| ~ sQ20_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1773,f1774,f596,f501,f1731]) ).
fof(f1789,plain,
( sQ124_spl
| ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1747,f128]) ).
fof(f1790,plain,
( sQ124_spl
| ~ sQ28_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1789,f501,f753,f1745]) ).
fof(f1797,plain,
( ~ sQ125_spl
| ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(nil,nil)
| nil = app(nil,nil) ),
inference(paramodulation,[status(thm)],[f1749,f129]) ).
fof(f1800,plain,
( ~ sQ125_spl
| ~ sQ6_spl
| ~ sQ28_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1797,f892,f753,f501,f1748]) ).
fof(f1801,plain,
! [X0,X1] :
( ~ sQ95_spl
| frontsegP(X1,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK48_skl,X0))
| ~ frontsegP(X1,app(sK48_skl,X0))
| ~ ssList(app(sK48_skl,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1445,f282]) ).
fof(f1802,definition,
! [X0,X1] :
( sQ132_spl
<=> ( frontsegP(X1,sK49_skl)
| ~ ssList(X1)
| ~ ssList(app(sK48_skl,X0))
| ~ frontsegP(X1,app(sK48_skl,X0))
| ~ ssList(app(sK48_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1805,plain,
( ~ sQ95_spl
| ~ sQ19_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f1801,f1802,f590,f1444]) ).
fof(f1829,plain,
( ~ sQ80_spl
| ~ ssList(tl(sK48_skl))
| nil = tl(sK49_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1294,f249]) ).
fof(f1839,plain,
( ~ sQ80_spl
| ~ sQ9_spl
| sQ96_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1829,f501,f1468,f514,f1293]) ).
fof(f1882,plain,
( ~ sQ97_spl
| singletonP(cons(hd(sK49_skl),nil))
| ~ ssList(sK49_skl)
| ~ ssItem(hd(sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1492,f455]) ).
fof(f1921,definition,
( sQ145_spl
<=> singletonP(cons(hd(sK49_skl),nil)) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1922,plain,
( ~ sQ145_spl
| singletonP(cons(hd(sK49_skl),nil)) ),
inference(component_clause,[status(thm)],[f1921]) ).
fof(f1924,plain,
( ~ sQ97_spl
| sQ145_spl
| ~ sQ19_spl
| ~ sQ107_spl ),
inference(split_clause,[status(thm)],[f1882,f1541,f590,f1921,f1491]) ).
fof(f1927,plain,
( ~ sQ145_spl
| ~ sQ97_spl
| singletonP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1492,f1922]) ).
fof(f1928,plain,
( ~ sQ145_spl
| ~ sQ97_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1927,f506]) ).
fof(f1929,plain,
( ~ sQ145_spl
| ~ sQ97_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1928]) ).
fof(f2136,plain,
( sQ107_spl
| ~ ssList(sK49_skl)
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f237,f1543]) ).
fof(f2137,plain,
( sQ107_spl
| ~ sQ19_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f2136,f796,f590,f1541]) ).
fof(f2138,plain,
! [X0] :
( ~ sQ32_spl
| sK49_skl = X0
| ~ ssList(X0)
| ssItem(hd(X0)) ),
inference(backward_demodulation,[status(thm)],[f797,f237]) ).
fof(f2200,plain,
( sQ21_spl
| ~ sQ32_spl
| sK49_skl != sK48_skl ),
inference(backward_demodulation,[status(thm)],[f797,f601]) ).
fof(f2386,plain,
( ~ sQ40_spl
| ~ sQ76_spl
| sK48_skl = tl(sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f1260,f862]) ).
fof(f2507,plain,
( ~ sQ40_spl
| ~ sQ76_spl
| ~ sQ32_spl
| ~ ssList(sK48_skl)
| sK49_skl = sK48_skl
| cons(hd(sK48_skl),sK48_skl) = sK48_skl ),
inference(paramodulation,[status(thm)],[f2386,f941]) ).
fof(f2509,definition,
( sQ168_spl
<=> cons(hd(sK48_skl),sK48_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f2510,plain,
( ~ sQ168_spl
| sK48_skl = cons(hd(sK48_skl),sK48_skl) ),
inference(component_clause,[status(thm)],[f2509]) ).
fof(f2512,plain,
( ~ sQ40_spl
| ~ sQ76_spl
| ~ sQ32_spl
| ~ sQ20_spl
| sQ55_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f2507,f2509,f1046,f596,f796,f1259,f861]) ).
fof(f2513,plain,
( ~ sQ168_spl
| ~ ssItem(hd(sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2510,f225]) ).
fof(f2521,definition,
( sQ170_spl
<=> ssItem(hd(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f2523,plain,
( sQ170_spl
| ~ ssItem(hd(sK48_skl)) ),
inference(component_clause,[status(thm)],[f2521]) ).
fof(f2526,plain,
( ~ sQ168_spl
| ~ sQ170_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2513,f596,f2521,f2509]) ).
fof(f2529,plain,
( ~ sQ32_spl
| sQ170_spl
| sK49_skl = sK48_skl
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2523,f2138]) ).
fof(f2530,plain,
( ~ sQ32_spl
| sQ170_spl
| sQ55_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2529,f596,f1046,f2521,f796]) ).
fof(f2531,plain,
( sQ21_spl
| ~ sQ32_spl
| ~ sQ55_spl ),
inference(split_clause,[status(thm)],[f2200,f1046,f796,f599]) ).
fof(f2576,plain,
$false,
inference(sat_refutation,[status(thm)],[f445,f449,f504,f520,f527,f532,f535,f551,f558,f562,f566,f569,f574,f575,f579,f593,f602,f604,f606,f682,f690,f715,f717,f742,f746,f752,f756,f774,f793,f819,f833,f839,f844,f856,f864,f880,f886,f890,f902,f906,f915,f1018,f1089,f1101,f1127,f1212,f1262,f1296,f1312,f1315,f1316,f1367,f1389,f1430,f1434,f1440,f1447,f1494,f1523,f1527,f1533,f1639,f1651,f1655,f1711,f1715,f1719,f1734,f1744,f1751,f1762,f1777,f1790,f1800,f1805,f1839,f1924,f1929,f2137,f2512,f2526,f2530,f2531]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC253+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.42 % Computer : n009.cluster.edu
% 0.18/0.42 % Model : x86_64 x86_64
% 0.18/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.42 % Memory : 8046.5625MB
% 0.18/0.42 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 08:08:42 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.45 % Drodi V4.1.1
% 202.32/26.09 % Refutation found
% 202.32/26.09 % SZS status Theorem for theBenchmark: Theorem is valid
% 202.32/26.09 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 202.32/26.14 % Elapsed time: 25.691232 seconds
% 202.32/26.14 % CPU time: 202.866675 seconds
% 202.32/26.14 % Total memory used: 473.037 MB
% 202.32/26.14 % Net memory used: 439.014 MB
%------------------------------------------------------------------------------