%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC254+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 : n014.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 0.09s 0.42s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 66
% Syntax : Number of formulae : 270 ( 25 unt; 50 def)
% Number of atoms : 908 ( 164 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 1098 ( 460 ~; 447 |; 87 &)
% ( 62 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 59 ( 57 usr; 50 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-4 aty)
% Number of variables : 278 ( 245 !; 33 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(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(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(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(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( singletonP(U)
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ 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] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f99,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f100,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
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(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
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(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(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(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(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(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(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ~ singletonP(U)
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(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] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(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] :
( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W
| ~ ssList(Z) )
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ~ singletonP(U)
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(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] :
( ! [Z] :
( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W
| ~ ssList(Z) )
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ~ singletonP(U)
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( singletonP(U)
| ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W
| ~ ssList(Z) )
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ~ singletonP(U)
& app(sK52_skl(X,W,V,U),cons(sK51_skl(X,W,V,U),nil)) = X
& cons(sK51_skl(X,W,V,U),nil) = W
& ssList(sK52_skl(X,W,V,U))
& ssItem(sK51_skl(X,W,V,U))
& 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(f431,plain,
! [X0,X1,X2,X3] :
( ssItem(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( cons(sK51_skl(X0,X1,X2,X3),nil) = X1
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f435,plain,
! [X0,X1,X2,X3] :
( ~ singletonP(X3)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f437,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f438,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f437,f440]) ).
fof(f444,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f437,f444]) ).
fof(f448,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f100]) ).
fof(f449,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f448]) ).
fof(f451,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f452,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f453,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f454,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f463,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f464,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f463]) ).
fof(f480,plain,
! [X0] :
( X0 = sK0_skl
| neq(X0,sK0_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f103,f101]) ).
fof(f481,plain,
~ neq(sK0_skl,sK0_skl),
inference(resolution,[status(thm)],[f103,f449]) ).
fof(f482,plain,
! [X0] :
( X0 = sK1_skl
| neq(X0,sK1_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f104,f101]) ).
fof(f483,plain,
~ neq(sK1_skl,sK1_skl),
inference(resolution,[status(thm)],[f104,f449]) ).
fof(f493,plain,
~ neq(nil,nil),
inference(resolution,[status(thm)],[f464,f223]) ).
fof(f494,plain,
~ neq(sK48_skl,sK48_skl),
inference(resolution,[status(thm)],[f464,f420]) ).
fof(f495,plain,
~ neq(sK47_skl,sK47_skl),
inference(resolution,[status(thm)],[f464,f419]) ).
fof(f497,plain,
! [X0,X1,X2,X3] :
( ~ sP0_prd(X1,X2,X3,cons(X0,nil))
| ~ ssItem(X0)
| ~ ssList(cons(X0,nil)) ),
inference(resolution,[status(thm)],[f451,f435]) ).
fof(f500,plain,
! [X0] :
( X0 = nil
| neq(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f220,f223]) ).
fof(f501,plain,
! [X0] :
( X0 = sK48_skl
| neq(X0,sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f220,f420]) ).
fof(f502,plain,
! [X0] :
( X0 = sK47_skl
| neq(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f220,f419]) ).
fof(f507,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f438]) ).
fof(f508,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f507]) ).
fof(f513,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f514,plain,
app(nil,sK48_skl) = sK48_skl,
inference(resolution,[status(thm)],[f249,f420]) ).
fof(f515,plain,
app(nil,sK47_skl) = sK47_skl,
inference(resolution,[status(thm)],[f249,f419]) ).
fof(f549,plain,
( ~ ssList(sK47_skl)
| frontsegP(app(nil,sK47_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f515,f452]) ).
fof(f550,plain,
( ~ ssList(sK48_skl)
| frontsegP(app(nil,sK48_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f514,f452]) ).
fof(f551,plain,
( ~ ssList(nil)
| frontsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f513,f452]) ).
fof(f552,definition,
( sQ3_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ3_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f557,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f555]) ).
fof(f558,definition,
( sQ5_spl
<=> frontsegP(app(nil,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f549,f552,f555,f558]) ).
fof(f562,definition,
( sQ6_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( sQ6_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f565,definition,
( sQ7_spl
<=> frontsegP(app(nil,sK48_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f568,plain,
( sQ7_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f550,f562,f555,f565]) ).
fof(f569,definition,
( sQ8_spl
<=> frontsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( sQ8_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f551,f555,f569]) ).
fof(f573,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f223]) ).
fof(f574,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f573]) ).
fof(f576,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f419]) ).
fof(f577,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f578,plain,
( sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f564,f420]) ).
fof(f579,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f595,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f420]) ).
fof(f596,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f419]) ).
fof(f597,plain,
( ~ ssList(nil)
| frontsegP(app(sK48_skl,nil),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f595,f452]) ).
fof(f598,definition,
( sQ9_spl
<=> frontsegP(app(sK48_skl,nil),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ4_spl
| sQ9_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f597,f562,f598,f555]) ).
fof(f603,plain,
( ~ ssList(nil)
| frontsegP(app(sK47_skl,nil),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f596,f452]) ).
fof(f604,definition,
( sQ10_spl
<=> frontsegP(app(sK47_skl,nil),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( ~ sQ4_spl
| sQ10_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f603,f552,f604,f555]) ).
fof(f609,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f610,definition,
! [X0] :
( sQ11_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f611,plain,
! [X0] :
( ~ sQ11_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f610]) ).
fof(f613,definition,
! [X1] :
( sQ12_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f609,f610,f613]) ).
fof(f617,plain,
! [X0] :
( ~ sQ11_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f611]) ).
fof(f627,plain,
( ~ sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f223,f617]) ).
fof(f630,plain,
~ sQ11_spl,
inference(contradiction_clause,[status(thm)],[f627]) ).
fof(f639,plain,
( ~ ssList(sK47_skl)
| rearsegP(app(sK47_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f596,f453]) ).
fof(f640,plain,
( ~ ssList(sK48_skl)
| rearsegP(app(sK48_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f595,f453]) ).
fof(f641,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f515,f453]) ).
fof(f642,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK48_skl),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f514,f453]) ).
fof(f643,plain,
( ~ ssList(nil)
| rearsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f513,f453]) ).
fof(f644,definition,
( sQ15_spl
<=> rearsegP(app(sK47_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f647,plain,
( sQ15_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f639,f552,f555,f644]) ).
fof(f648,definition,
( sQ16_spl
<=> rearsegP(app(sK48_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f651,plain,
( sQ16_spl
| ~ sQ4_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f640,f562,f555,f648]) ).
fof(f652,definition,
( sQ17_spl
<=> rearsegP(app(nil,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( ~ sQ4_spl
| sQ17_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f641,f552,f652,f555]) ).
fof(f656,definition,
( sQ18_spl
<=> rearsegP(app(nil,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( ~ sQ4_spl
| sQ18_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f642,f562,f656,f555]) ).
fof(f660,definition,
( sQ19_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f663,plain,
( sQ19_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f643,f555,f660]) ).
fof(f669,plain,
( ~ sQ0_spl
| cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil) = sK47_skl ),
inference(resolution,[status(thm)],[f433,f508]) ).
fof(f670,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f453,f245]) ).
fof(f733,plain,
! [X0] :
( sK47_skl = X0
| sK47_skl != app(X0,nil)
| ~ ssList(sK47_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f596,f376]) ).
fof(f734,plain,
! [X0] :
( sK48_skl = X0
| sK48_skl != app(X0,nil)
| ~ ssList(sK48_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f595,f376]) ).
fof(f735,plain,
! [X0] :
( nil = X0
| sK47_skl != app(X0,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f515,f376]) ).
fof(f736,plain,
! [X0] :
( nil = X0
| sK48_skl != app(X0,sK48_skl)
| ~ ssList(nil)
| ~ ssList(sK48_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f514,f376]) ).
fof(f737,plain,
! [X0] :
( nil = X0
| nil != app(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f513,f376]) ).
fof(f744,definition,
! [X0] :
( sQ20_spl
<=> ( sK47_skl = X0
| sK47_skl != app(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f747,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f733,f744,f555,f552]) ).
fof(f748,definition,
! [X0] :
( sQ21_spl
<=> ( sK48_skl = X0
| sK48_skl != app(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f751,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f734,f748,f555,f562]) ).
fof(f752,definition,
! [X0] :
( sQ22_spl
<=> ( nil = X0
| sK47_skl != app(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f755,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f735,f752,f552,f555]) ).
fof(f756,definition,
! [X0] :
( sQ23_spl
<=> ( nil = X0
| sK48_skl != app(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f759,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f736,f756,f562,f555]) ).
fof(f760,definition,
! [X0] :
( sQ24_spl
<=> ( nil = X0
| nil != app(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f763,plain,
( ~ sQ4_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f737,f760,f555]) ).
fof(f784,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f596,f454]) ).
fof(f785,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK48_skl)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f595,f454]) ).
fof(f786,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f515,f454]) ).
fof(f787,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f514,f454]) ).
fof(f788,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f513,f454]) ).
fof(f791,definition,
! [X0] :
( sQ26_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f794,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f784,f791,f555,f552]) ).
fof(f795,definition,
! [X0] :
( sQ27_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f798,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f785,f795,f555,f562]) ).
fof(f799,definition,
! [X0] :
( sQ28_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f802,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f786,f799,f552,f555]) ).
fof(f803,definition,
! [X0] :
( sQ29_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f806,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| sQ29_spl ),
inference(split_clause,[status(thm)],[f787,f803,f562,f555]) ).
fof(f807,definition,
! [X0] :
( sQ30_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f810,plain,
( ~ sQ4_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f788,f807,f555]) ).
fof(f821,plain,
( sK48_skl = sK48_skl
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f501,f494]) ).
fof(f822,definition,
( sQ31_spl
<=> sK48_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f825,plain,
( sQ31_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f821,f562,f822]) ).
fof(f826,plain,
( sK47_skl = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f502,f495]) ).
fof(f827,definition,
( sQ32_spl
<=> sK47_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f830,plain,
( sQ32_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f826,f552,f827]) ).
fof(f832,plain,
( sK0_skl = sK0_skl
| ~ ssItem(sK0_skl) ),
inference(resolution,[status(thm)],[f480,f481]) ).
fof(f833,definition,
( sQ33_spl
<=> ssItem(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f835,plain,
( sQ33_spl
| ~ ssItem(sK0_skl) ),
inference(component_clause,[status(thm)],[f833]) ).
fof(f836,definition,
( sQ34_spl
<=> sK0_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f839,plain,
( sQ34_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f832,f833,f836]) ).
fof(f840,plain,
( sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f835,f103]) ).
fof(f841,plain,
sQ33_spl,
inference(contradiction_clause,[status(thm)],[f840]) ).
fof(f842,plain,
( sK1_skl = sK1_skl
| ~ ssItem(sK1_skl) ),
inference(resolution,[status(thm)],[f482,f483]) ).
fof(f843,definition,
( sQ35_spl
<=> ssItem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f845,plain,
( sQ35_spl
| ~ ssItem(sK1_skl) ),
inference(component_clause,[status(thm)],[f843]) ).
fof(f846,definition,
( sQ36_spl
<=> sK1_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f849,plain,
( sQ36_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f842,f843,f846]) ).
fof(f850,plain,
( sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f845,f104]) ).
fof(f851,plain,
sQ35_spl,
inference(contradiction_clause,[status(thm)],[f850]) ).
fof(f852,plain,
( nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f500,f493]) ).
fof(f854,definition,
( sQ37_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f857,plain,
( sQ37_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f852,f555,f854]) ).
fof(f865,plain,
! [X0] :
( nil = X0
| sK47_skl != app(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f596,f378]) ).
fof(f866,plain,
! [X0] :
( nil = X0
| sK48_skl != app(sK48_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK48_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f595,f378]) ).
fof(f867,plain,
! [X0] :
( sK47_skl = X0
| sK47_skl != app(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f515,f378]) ).
fof(f868,plain,
! [X0] :
( sK48_skl = X0
| sK48_skl != app(nil,X0)
| ~ ssList(sK48_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f514,f378]) ).
fof(f869,plain,
! [X0] :
( nil = X0
| nil != app(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f513,f378]) ).
fof(f876,definition,
! [X0] :
( sQ38_spl
<=> ( nil = X0
| sK47_skl != app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f879,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f865,f876,f552,f555]) ).
fof(f880,definition,
! [X0] :
( sQ39_spl
<=> ( nil = X0
| sK48_skl != app(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f883,plain,
( ~ sQ4_spl
| ~ sQ6_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f866,f880,f562,f555]) ).
fof(f884,definition,
! [X0] :
( sQ40_spl
<=> ( sK47_skl = X0
| sK47_skl != app(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f887,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f867,f884,f555,f552]) ).
fof(f888,definition,
! [X0] :
( sQ41_spl
<=> ( sK48_skl = X0
| sK48_skl != app(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f891,plain,
( ~ sQ6_spl
| ~ sQ4_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f868,f888,f555,f562]) ).
fof(f892,definition,
! [X0] :
( sQ42_spl
<=> ( nil = X0
| nil != app(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f895,plain,
( ~ sQ4_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f869,f892,f555]) ).
fof(f1002,plain,
! [X0] :
( rearsegP(app(sK47_skl,X0),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f670,f419]) ).
fof(f1003,plain,
! [X0] :
( rearsegP(app(sK48_skl,X0),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f670,f420]) ).
fof(f1004,plain,
! [X0] :
( rearsegP(app(nil,X0),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f670,f223]) ).
fof(f1070,plain,
( rearsegP(sK47_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f596,f1002]) ).
fof(f1071,definition,
( sQ46_spl
<=> rearsegP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1074,plain,
( sQ46_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1070,f555,f1071]) ).
fof(f1075,plain,
( rearsegP(sK48_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f595,f1003]) ).
fof(f1076,definition,
( sQ47_spl
<=> rearsegP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1079,plain,
( sQ47_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1075,f555,f1076]) ).
fof(f1084,plain,
( rearsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f515,f1004]) ).
fof(f1085,plain,
( rearsegP(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f514,f1004]) ).
fof(f1086,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f513,f1004]) ).
fof(f1087,definition,
( sQ48_spl
<=> rearsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1090,plain,
( sQ48_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1084,f552,f1087]) ).
fof(f1091,definition,
( sQ49_spl
<=> rearsegP(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1094,plain,
( sQ49_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f1085,f562,f1091]) ).
fof(f1095,definition,
( sQ50_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1098,plain,
( sQ50_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1086,f555,f1095]) ).
fof(f1295,plain,
( ~ sQ0_spl
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))
| singletonP(sK47_skl)
| ~ ssList(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)) ),
inference(paramodulation,[status(thm)],[f669,f451]) ).
fof(f1312,definition,
( sQ51_spl
<=> ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1314,plain,
( sQ51_spl
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1312]) ).
fof(f1323,definition,
( sQ54_spl
<=> ssList(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1325,plain,
( sQ54_spl
| ~ ssList(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)) ),
inference(component_clause,[status(thm)],[f1323]) ).
fof(f1326,definition,
( sQ55_spl
<=> singletonP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1327,plain,
( ~ sQ55_spl
| singletonP(sK47_skl) ),
inference(component_clause,[status(thm)],[f1326]) ).
fof(f1329,plain,
( ~ sQ0_spl
| ~ sQ51_spl
| sQ55_spl
| ~ sQ54_spl ),
inference(split_clause,[status(thm)],[f1295,f1323,f1326,f1312,f437]) ).
fof(f1379,plain,
( sQ51_spl
| ~ sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f1314,f431]) ).
fof(f1380,plain,
( sQ51_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1379,f508]) ).
fof(f1381,plain,
( sQ51_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1380]) ).
fof(f1382,plain,
( sQ2_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f446]) ).
fof(f1386,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1382,f441]) ).
fof(f1387,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1386]) ).
fof(f1470,plain,
( sQ54_spl
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1325,f222]) ).
fof(f1471,plain,
( sQ54_spl
| ~ sQ51_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1470,f555,f1312,f1323]) ).
fof(f1475,plain,
! [X0,X1,X2] :
( ~ sQ55_spl
| ~ sP0_prd(X0,X1,X2,sK47_skl) ),
inference(resolution,[status(thm)],[f1327,f435]) ).
fof(f1538,plain,
! [X0,X1,X2,X3] :
( ~ ssItem(X0)
| ~ ssList(nil)
| ~ sP0_prd(X1,X2,X3,cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f497,f222]) ).
fof(f1539,definition,
! [X0,X1,X2,X3] :
( sQ67_spl
<=> ( ~ ssItem(X0)
| ~ sP0_prd(X1,X2,X3,cons(X0,nil))
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1542,plain,
( ~ sQ4_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1538,f1539,f555]) ).
fof(f1566,plain,
( ~ sQ0_spl
| ~ sQ55_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f508,f1475]) ).
fof(f1567,plain,
( ~ sQ0_spl
| ~ sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f1566]) ).
fof(f1568,plain,
$false,
inference(sat_refutation,[status(thm)],[f443,f447,f561,f568,f572,f574,f577,f579,f601,f607,f616,f630,f647,f651,f655,f659,f663,f747,f751,f755,f759,f763,f794,f798,f802,f806,f810,f825,f830,f839,f841,f849,f851,f857,f879,f883,f887,f891,f895,f1074,f1079,f1090,f1094,f1098,f1329,f1381,f1387,f1471,f1542,f1567]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC254+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 08:08:49 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.09/0.42 % Refutation found
% 0.09/0.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.45 % Elapsed time: 0.076877 seconds
% 0.09/0.45 % CPU time: 0.369457 seconds
% 0.09/0.45 % Total memory used: 70.709 MB
% 0.09/0.45 % Net memory used: 70.327 MB
%------------------------------------------------------------------------------