%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWX029+1 : TPTP v9.3.1. Released v9.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n003.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 : Fri Sep 25 03:32:35 PM UTC 2026
% Result : Theorem 163.72s 25.54s
% Output : CNFRefutation 163.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 31
% Syntax : Number of formulae : 250 ( 70 unt; 6 def)
% Number of atoms : 817 ( 209 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 586 ( 232 ~; 260 |; 67 &)
% ( 6 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 340 ( 0 sgn 312 !; 28 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] : '0' != s(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id1) ).
fof(f7,axiom,
! [X0,X1] : nil != cons(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id7) ).
fof(f8,axiom,
! [X0,X1,X2,X3] :
( cons(X0,X1) = cons(X2,X3)
=> X1 = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id8) ).
fof(f73,axiom,
! [X0,X1,X2] :
( split_succeeds(X0,X1,X2)
<=> ( ( X2 = nil
& X1 = nil
& X0 = nil )
| ? [X3,X4,X5] :
( split_succeeds(X4,X2,X5)
& X1 = cons(X3,X5)
& X0 = cons(X3,X4) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id73) ).
fof(f118,axiom,
! [X0,X1] :
( '@=<_succeeds'(X0,X1)
<=> ( X0 = '0'
| ? [X2,X3] :
( '@=<_succeeds'(X2,X3)
& X1 = s(X3)
& X0 = s(X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',id118) ).
fof(f156,axiom,
! [X0] :
( nat_succeeds(X0)
=> '@+'(X0,'0') = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(plus:zero)_001') ).
fof(f187,axiom,
! [X0] :
( nat_succeeds(X0)
=> '@<_succeeds'(X0,s(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(less:one)') ).
fof(f190,axiom,
! [X0] :
( ( X0 != '0'
& nat_succeeds(X0) )
=> '@<_succeeds'('0',X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(less:different:zero)') ).
fof(f192,axiom,
! [X0,X1] :
( '@=<_succeeds'(X0,X1)
=> nat_succeeds(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(leq:types)') ).
fof(f202,axiom,
! [X0,X1] :
( ( nat_succeeds(X1)
& '@=<_succeeds'(X0,X1) )
=> ( X0 = X1
| '@<_succeeds'(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(leq:less)') ).
fof(f203,axiom,
! [X0,X1,X2] :
( ( '@<_succeeds'(X1,X2)
& '@=<_succeeds'(X0,X1) )
=> '@<_succeeds'(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(leq:less:transitive)') ).
fof(f209,axiom,
! [X0,X1,X2] :
( ( '@<_succeeds'(X1,X2)
& nat_succeeds(X0) )
=> '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(less:plus:second)') ).
fof(f212,axiom,
! [X0,X1] :
( ( nat_succeeds(X1)
& nat_succeeds(X0)
& '@<_succeeds'('0',X1) )
=> '@<_succeeds'(X0,'@+'(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(less:plus:first)_010') ).
fof(f213,axiom,
! [X0,X1,X2] :
( ( '@=<_succeeds'(X1,X2)
& nat_succeeds(X0) )
=> '@=<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(leq:plus:second)') ).
fof(f232,axiom,
! [X0,X1] :
( list_succeeds(cons(X0,X1))
=> list_succeeds(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(list:cons)') ).
fof(f256,axiom,
! [X0,X1] :
( length_succeeds(X0,X1)
=> ( nat_succeeds(X1)
& list_succeeds(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(length:types)') ).
fof(f261,axiom,
lh(nil) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(lh:nil)') ).
fof(f262,axiom,
! [X0,X1] :
( list_succeeds(X1)
=> lh(cons(X0,X1)) = s(lh(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(lh:cons)') ).
fof(f263,axiom,
! [X0] :
( list_succeeds(X0)
=> nat_succeeds(lh(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(lh:types)') ).
fof(f264,axiom,
! [X0] :
( ( lh(X0) = '0'
& list_succeeds(X0) )
=> X0 = nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(lh:zero)') ).
fof(f269,axiom,
! [X0,X1] :
( list_succeeds(X1)
=> '@=<_succeeds'(lh(X1),lh(cons(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','axiom-(lh:cons:leq)') ).
fof(f361,axiom,
! [X0,X1] :
( list_succeeds(X0)
=> ( lh(X0) = X1
<=> length_succeeds(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lh/1') ).
fof(f365,axiom,
! [X0,X1,X2] :
( split_succeeds(X0,X1,X2)
=> ( list_succeeds(X2)
& list_succeeds(X1)
& list_succeeds(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(split:types)') ).
fof(f366,axiom,
! [X0,X1,X2] :
( split_succeeds(X0,X1,X2)
=> lh(X0) = '@+'(lh(X1),lh(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(split:length)') ).
fof(f374,conjecture,
! [X0,X1,X2,X3,X4] :
( split_succeeds(cons(X0,cons(X1,X2)),X3,X4)
=> ( '@<_succeeds'(lh(X4),lh(cons(X0,cons(X1,X2))))
& '@<_succeeds'(lh(X3),lh(cons(X0,cons(X1,X2)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','lemma-(split:length:less)') ).
fof(f375,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( split_succeeds(cons(X0,cons(X1,X2)),X3,X4)
=> ( '@<_succeeds'(lh(X4),lh(cons(X0,cons(X1,X2))))
& '@<_succeeds'(lh(X3),lh(cons(X0,cons(X1,X2)))) ) ),
inference(negated_conjecture,[status(cth)],[f374]) ).
fof(f410,plain,
! [X0,X1,X2,X3] :
( cons(X0,X1) != cons(X2,X3)
| X1 = X3 ),
inference(ennf_transformation,[],[f8]) ).
fof(f510,plain,
! [X0] :
( ~ nat_succeeds(X0)
| '@+'(X0,'0') = X0 ),
inference(ennf_transformation,[],[f156]) ).
fof(f558,plain,
! [X0] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(X0,s(X0)) ),
inference(ennf_transformation,[],[f187]) ).
fof(f563,plain,
! [X0] :
( '0' = X0
| ~ nat_succeeds(X0)
| '@<_succeeds'('0',X0) ),
inference(ennf_transformation,[],[f190]) ).
fof(f564,plain,
! [X0] :
( '0' = X0
| ~ nat_succeeds(X0)
| '@<_succeeds'('0',X0) ),
inference(flattening,[],[f563]) ).
fof(f566,plain,
! [X0,X1] :
( ~ '@=<_succeeds'(X0,X1)
| nat_succeeds(X0) ),
inference(ennf_transformation,[],[f192]) ).
fof(f579,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ '@=<_succeeds'(X0,X1)
| X0 = X1
| '@<_succeeds'(X0,X1) ),
inference(ennf_transformation,[],[f202]) ).
fof(f580,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ '@=<_succeeds'(X0,X1)
| X0 = X1
| '@<_succeeds'(X0,X1) ),
inference(flattening,[],[f579]) ).
fof(f581,plain,
! [X0,X1,X2] :
( ~ '@<_succeeds'(X1,X2)
| ~ '@=<_succeeds'(X0,X1)
| '@<_succeeds'(X0,X2) ),
inference(ennf_transformation,[],[f203]) ).
fof(f582,plain,
! [X0,X1,X2] :
( ~ '@<_succeeds'(X1,X2)
| ~ '@=<_succeeds'(X0,X1)
| '@<_succeeds'(X0,X2) ),
inference(flattening,[],[f581]) ).
fof(f591,plain,
! [X0,X1,X2] :
( ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(ennf_transformation,[],[f209]) ).
fof(f592,plain,
! [X0,X1,X2] :
( ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(flattening,[],[f591]) ).
fof(f596,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| ~ '@<_succeeds'('0',X1)
| '@<_succeeds'(X0,'@+'(X1,X0)) ),
inference(ennf_transformation,[],[f212]) ).
fof(f597,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| ~ '@<_succeeds'('0',X1)
| '@<_succeeds'(X0,'@+'(X1,X0)) ),
inference(flattening,[],[f596]) ).
fof(f598,plain,
! [X0,X1,X2] :
( ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@=<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(ennf_transformation,[],[f213]) ).
fof(f599,plain,
! [X0,X1,X2] :
( ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@=<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(flattening,[],[f598]) ).
fof(f629,plain,
! [X0,X1] :
( ~ list_succeeds(cons(X0,X1))
| list_succeeds(X1) ),
inference(ennf_transformation,[],[f232]) ).
fof(f666,plain,
! [X0,X1] :
( ~ length_succeeds(X0,X1)
| ( nat_succeeds(X1)
& list_succeeds(X0) ) ),
inference(ennf_transformation,[],[f256]) ).
fof(f672,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| lh(cons(X0,X1)) = s(lh(X1)) ),
inference(ennf_transformation,[],[f262]) ).
fof(f673,plain,
! [X0] :
( ~ list_succeeds(X0)
| nat_succeeds(lh(X0)) ),
inference(ennf_transformation,[],[f263]) ).
fof(f674,plain,
! [X0] :
( '0' != lh(X0)
| ~ list_succeeds(X0)
| X0 = nil ),
inference(ennf_transformation,[],[f264]) ).
fof(f675,plain,
! [X0] :
( '0' != lh(X0)
| ~ list_succeeds(X0)
| X0 = nil ),
inference(flattening,[],[f674]) ).
fof(f684,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| '@=<_succeeds'(lh(X1),lh(cons(X0,X1))) ),
inference(ennf_transformation,[],[f269]) ).
fof(f829,plain,
! [X0,X1] :
( ~ list_succeeds(X0)
| ( lh(X0) = X1
<=> length_succeeds(X0,X1) ) ),
inference(ennf_transformation,[],[f361]) ).
fof(f833,plain,
! [X0,X1,X2] :
( ~ split_succeeds(X0,X1,X2)
| ( list_succeeds(X2)
& list_succeeds(X1)
& list_succeeds(X0) ) ),
inference(ennf_transformation,[],[f365]) ).
fof(f834,plain,
! [X0,X1,X2] :
( ~ split_succeeds(X0,X1,X2)
| lh(X0) = '@+'(lh(X1),lh(X2)) ),
inference(ennf_transformation,[],[f366]) ).
fof(f846,plain,
? [X0,X1,X2,X3,X4] :
( split_succeeds(cons(X0,cons(X1,X2)),X3,X4)
& ( ~ '@<_succeeds'(lh(X4),lh(cons(X0,cons(X1,X2))))
| ~ '@<_succeeds'(lh(X3),lh(cons(X0,cons(X1,X2)))) ) ),
inference(ennf_transformation,[],[f375]) ).
fof(f927,plain,
! [X0,X1,X2] :
( ( ~ split_succeeds(X0,X1,X2)
| sP6(X0,X1,X2)
| ? [X3,X4,X5] :
( split_succeeds(X4,X2,X5)
& X1 = cons(X3,X5)
& X0 = cons(X3,X4) ) )
& ( ( ~ sP6(X0,X1,X2)
& ! [X3,X4,X5] :
( ~ split_succeeds(X4,X2,X5)
| cons(X3,X5) != X1
| cons(X3,X4) != X0 ) )
| split_succeeds(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f857]) ).
fof(f928,plain,
! [X0,X1,X2] :
( ( ~ split_succeeds(X0,X1,X2)
| sP6(X0,X1,X2)
| ? [X3,X4,X5] :
( split_succeeds(X4,X2,X5)
& X1 = cons(X3,X5)
& X0 = cons(X3,X4) ) )
& ( ( ~ sP6(X0,X1,X2)
& ! [X3,X4,X5] :
( ~ split_succeeds(X4,X2,X5)
| cons(X3,X5) != X1
| cons(X3,X4) != X0 ) )
| split_succeeds(X0,X1,X2) ) ),
inference(flattening,[],[f927]) ).
fof(f929,plain,
! [X0,X1,X2] :
( ( ~ split_succeeds(X0,X1,X2)
| sP6(X0,X1,X2)
| ? [X6,X7,X8] :
( split_succeeds(X7,X2,X8)
& cons(X6,X8) = X1
& cons(X6,X7) = X0 ) )
& ( ( ~ sP6(X0,X1,X2)
& ! [X3,X4,X5] :
( ~ split_succeeds(X4,X2,X5)
| cons(X3,X5) != X1
| cons(X3,X4) != X0 ) )
| split_succeeds(X0,X1,X2) ) ),
inference(rectify,[],[f928]) ).
fof(f930,plain,
! [X0,X1,X2] :
( ( ~ split_succeeds(X0,X1,X2)
| sP6(X0,X1,X2)
| ( split_succeeds(sK71(X0,X1,X2),X2,sK72(X0,X1,X2))
& cons(sK70(X0,X1,X2),sK72(X0,X1,X2)) = X1
& cons(sK70(X0,X1,X2),sK71(X0,X1,X2)) = X0 ) )
& ( ( ~ sP6(X0,X1,X2)
& ! [X3,X4,X5] :
( ~ split_succeeds(X4,X2,X5)
| cons(X3,X5) != X1
| cons(X3,X4) != X0 ) )
| split_succeeds(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK70,sK71,sK72]),skolemize(X6,sK70(X0,X1,X2)),skolemize(X7,sK71(X0,X1,X2)),skolemize(X8,sK72(X0,X1,X2))],[f929]) ).
fof(f1100,plain,
! [X0,X1] :
( ( ~ '@=<_succeeds'(X0,X1)
| X0 = '0'
| ? [X2,X3] :
( '@=<_succeeds'(X2,X3)
& X1 = s(X3)
& X0 = s(X2) ) )
& ( ( '0' != X0
& ! [X2,X3] :
( ~ '@=<_succeeds'(X2,X3)
| s(X3) != X1
| s(X2) != X0 ) )
| '@=<_succeeds'(X0,X1) ) ),
inference(nnf_transformation,[],[f118]) ).
fof(f1101,plain,
! [X0,X1] :
( ( ~ '@=<_succeeds'(X0,X1)
| X0 = '0'
| ? [X2,X3] :
( '@=<_succeeds'(X2,X3)
& X1 = s(X3)
& X0 = s(X2) ) )
& ( ( '0' != X0
& ! [X2,X3] :
( ~ '@=<_succeeds'(X2,X3)
| s(X3) != X1
| s(X2) != X0 ) )
| '@=<_succeeds'(X0,X1) ) ),
inference(flattening,[],[f1100]) ).
fof(f1102,plain,
! [X0,X1] :
( ( ~ '@=<_succeeds'(X0,X1)
| X0 = '0'
| ? [X4,X5] :
( '@=<_succeeds'(X4,X5)
& s(X5) = X1
& s(X4) = X0 ) )
& ( ( '0' != X0
& ! [X2,X3] :
( ~ '@=<_succeeds'(X2,X3)
| s(X3) != X1
| s(X2) != X0 ) )
| '@=<_succeeds'(X0,X1) ) ),
inference(rectify,[],[f1101]) ).
fof(f1103,plain,
! [X0,X1] :
( ( ~ '@=<_succeeds'(X0,X1)
| X0 = '0'
| ( '@=<_succeeds'(sK191(X0,X1),sK192(X0,X1))
& s(sK192(X0,X1)) = X1
& s(sK191(X0,X1)) = X0 ) )
& ( ( '0' != X0
& ! [X2,X3] :
( ~ '@=<_succeeds'(X2,X3)
| s(X3) != X1
| s(X2) != X0 ) )
| '@=<_succeeds'(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK191,sK192]),skolemize(X4,sK191(X0,X1)),skolemize(X5,sK192(X0,X1))],[f1102]) ).
fof(f1156,plain,
! [X0,X1] :
( ~ list_succeeds(X0)
| ( ( lh(X0) != X1
| length_succeeds(X0,X1) )
& ( ~ length_succeeds(X0,X1)
| lh(X0) = X1 ) ) ),
inference(nnf_transformation,[],[f829]) ).
fof(f1161,plain,
( split_succeeds(cons(sK231,cons(sK232,sK233)),sK234,sK235)
& ( ~ '@<_succeeds'(lh(sK235),lh(cons(sK231,cons(sK232,sK233))))
| ~ '@<_succeeds'(lh(sK234),lh(cons(sK231,cons(sK232,sK233)))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK231,sK232,sK233,sK234,sK235]),skolemize(X0,sK231),skolemize(X1,sK232),skolemize(X2,sK233),skolemize(X3,sK234),skolemize(X4,sK235)],[f846]) ).
fof(f1162,plain,
! [X0] : '0' != s(X0),
inference(cnf_transformation,[],[f1]) ).
fof(f1168,plain,
! [X0,X1] : nil != cons(X0,X1),
inference(cnf_transformation,[],[f7]) ).
fof(f1169,plain,
! [X2,X3,X0,X1] :
( cons(X0,X1) != cons(X2,X3)
| X1 = X3 ),
inference(cnf_transformation,[],[f410]) ).
fof(f1329,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| sP6(X0,X1,X2)
| split_succeeds(sK71(X0,X1,X2),X2,sK72(X0,X1,X2)) ),
inference(cnf_transformation,[],[f930]) ).
fof(f1330,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| sP6(X0,X1,X2)
| cons(sK70(X0,X1,X2),sK72(X0,X1,X2)) = X1 ),
inference(cnf_transformation,[],[f930]) ).
fof(f1331,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| sP6(X0,X1,X2)
| cons(sK70(X0,X1,X2),sK71(X0,X1,X2)) = X0 ),
inference(cnf_transformation,[],[f930]) ).
fof(f1619,plain,
! [X0,X1] :
( '0' != X0
| '@=<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f1103]) ).
fof(f1690,plain,
! [X0] :
( ~ nat_succeeds(X0)
| '@+'(X0,'0') = X0 ),
inference(cnf_transformation,[],[f510]) ).
fof(f1721,plain,
! [X0] :
( ~ nat_succeeds(X0)
| '@<_succeeds'(X0,s(X0)) ),
inference(cnf_transformation,[],[f558]) ).
fof(f1724,plain,
! [X0] :
( '0' = X0
| ~ nat_succeeds(X0)
| '@<_succeeds'('0',X0) ),
inference(cnf_transformation,[],[f564]) ).
fof(f1726,plain,
! [X0,X1] :
( ~ '@=<_succeeds'(X0,X1)
| nat_succeeds(X0) ),
inference(cnf_transformation,[],[f566]) ).
fof(f1736,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ '@=<_succeeds'(X0,X1)
| X0 = X1
| '@<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f580]) ).
fof(f1737,plain,
! [X2,X0,X1] :
( ~ '@<_succeeds'(X1,X2)
| ~ '@=<_succeeds'(X0,X1)
| '@<_succeeds'(X0,X2) ),
inference(cnf_transformation,[],[f582]) ).
fof(f1743,plain,
! [X2,X0,X1] :
( ~ '@<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(cnf_transformation,[],[f592]) ).
fof(f1746,plain,
! [X0,X1] :
( ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| ~ '@<_succeeds'('0',X1)
| '@<_succeeds'(X0,'@+'(X1,X0)) ),
inference(cnf_transformation,[],[f597]) ).
fof(f1747,plain,
! [X2,X0,X1] :
( ~ '@=<_succeeds'(X1,X2)
| ~ nat_succeeds(X0)
| '@=<_succeeds'('@+'(X0,X1),'@+'(X0,X2)) ),
inference(cnf_transformation,[],[f599]) ).
fof(f1766,plain,
! [X0,X1] :
( ~ list_succeeds(cons(X0,X1))
| list_succeeds(X1) ),
inference(cnf_transformation,[],[f629]) ).
fof(f1794,plain,
! [X0,X1] :
( ~ length_succeeds(X0,X1)
| list_succeeds(X0) ),
inference(cnf_transformation,[],[f666]) ).
fof(f1799,plain,
'0' = lh(nil),
inference(cnf_transformation,[],[f261]) ).
fof(f1800,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| lh(cons(X0,X1)) = s(lh(X1)) ),
inference(cnf_transformation,[],[f672]) ).
fof(f1801,plain,
! [X0] :
( ~ list_succeeds(X0)
| nat_succeeds(lh(X0)) ),
inference(cnf_transformation,[],[f673]) ).
fof(f1802,plain,
! [X0] :
( '0' != lh(X0)
| ~ list_succeeds(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f675]) ).
fof(f1807,plain,
! [X0,X1] :
( ~ list_succeeds(X1)
| '@=<_succeeds'(lh(X1),lh(cons(X0,X1))) ),
inference(cnf_transformation,[],[f684]) ).
fof(f1908,plain,
! [X0,X1] :
( ~ list_succeeds(X0)
| lh(X0) != X1
| length_succeeds(X0,X1) ),
inference(cnf_transformation,[],[f1156]) ).
fof(f1909,plain,
! [X0,X1] :
( ~ list_succeeds(X0)
| ~ length_succeeds(X0,X1)
| lh(X0) = X1 ),
inference(cnf_transformation,[],[f1156]) ).
fof(f1916,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| list_succeeds(X2) ),
inference(cnf_transformation,[],[f833]) ).
fof(f1917,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| list_succeeds(X1) ),
inference(cnf_transformation,[],[f833]) ).
fof(f1918,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| list_succeeds(X0) ),
inference(cnf_transformation,[],[f833]) ).
fof(f1919,plain,
! [X2,X0,X1] :
( ~ split_succeeds(X0,X1,X2)
| lh(X0) = '@+'(lh(X1),lh(X2)) ),
inference(cnf_transformation,[],[f834]) ).
fof(f1927,plain,
split_succeeds(cons(sK231,cons(sK232,sK233)),sK234,sK235),
inference(cnf_transformation,[],[f1161]) ).
fof(f1928,plain,
( ~ '@<_succeeds'(lh(sK235),lh(cons(sK231,cons(sK232,sK233))))
| ~ '@<_succeeds'(lh(sK234),lh(cons(sK231,cons(sK232,sK233)))) ),
inference(cnf_transformation,[],[f1161]) ).
fof(f2100,plain,
! [X1] : '@=<_succeeds'('0',X1),
inference(equality_resolution,[],[f1619]) ).
fof(f2126,plain,
! [X0] :
( ~ list_succeeds(X0)
| length_succeeds(X0,lh(X0)) ),
inference(equality_resolution,[],[f1908]) ).
tcf(c_49,plain,
! [X0: $i] : s(X0) != '0',
inference(cnf_transformation,[],[f1162]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] : cons(X0,X1) != nil,
inference(cnf_transformation,[],[f1168]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ( cons(X0,X1) != cons(X2,X3) ) ),
inference(cnf_transformation,[],[f1169]) ).
tcf(c_218,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP6(X0,X1,X2)
| ( cons(sK70(X0,X1,X2),sK71(X0,X1,X2)) = X0 )
| ~ split_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f1331]) ).
tcf(c_219,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP6(X0,X1,X2)
| ( cons(sK70(X0,X1,X2),sK72(X0,X1,X2)) = X1 )
| ~ split_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f1330]) ).
tcf(c_220,plain,
! [X0: $i,X1: $i,X2: $i] :
( sP6(X0,X1,X2)
| split_succeeds(sK71(X0,X1,X2),X2,sK72(X0,X1,X2))
| ~ split_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f1329]) ).
tcf(c_504,plain,
! [X0: $i] : '@=<_succeeds'('0',X0),
inference(cnf_transformation,[],[f2100]) ).
tcf(c_577,plain,
! [X0: $i] :
( ( '@+'(X0,'0') = X0 )
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f1690]) ).
tcf(c_608,plain,
! [X0: $i] :
( '@<_succeeds'(X0,s(X0))
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f1721]) ).
tcf(c_611,plain,
! [X0: $i] :
( '@<_succeeds'('0',X0)
| ( X0 = '0' )
| ~ nat_succeeds(X0) ),
inference(cnf_transformation,[],[f1724]) ).
tcf(c_613,plain,
! [X0: $i,X1: $i] :
( nat_succeeds(X0)
| ~ '@=<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f1726]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i] :
( '@<_succeeds'(X0,X1)
| ( X0 = X1 )
| ~ nat_succeeds(X1)
| ~ '@=<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f1736]) ).
tcf(c_624,plain,
! [X0: $i,X1: $i,X2: $i] :
( '@<_succeeds'(X0,X2)
| ~ '@<_succeeds'(X1,X2)
| ~ '@=<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f1737]) ).
tcf(c_630,plain,
! [X0: $i,X1: $i,X2: $i] :
( '@<_succeeds'('@+'(X2,X0),'@+'(X2,X1))
| ~ nat_succeeds(X2)
| ~ '@<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f1743]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i] :
( '@<_succeeds'(X1,'@+'(X0,X1))
| ~ nat_succeeds(X1)
| ~ nat_succeeds(X0)
| ~ '@<_succeeds'('0',X0) ),
inference(cnf_transformation,[],[f1746]) ).
tcf(c_634,plain,
! [X0: $i,X1: $i,X2: $i] :
( '@=<_succeeds'('@+'(X2,X0),'@+'(X2,X1))
| ~ nat_succeeds(X2)
| ~ '@=<_succeeds'(X0,X1) ),
inference(cnf_transformation,[],[f1747]) ).
tcf(c_653,plain,
! [X0: $i,X1: $i] :
( list_succeeds(X1)
| ~ list_succeeds(cons(X0,X1)) ),
inference(cnf_transformation,[],[f1766]) ).
tcf(c_680,plain,
! [X0: $i,X1: $i] :
( list_succeeds(X0)
| ~ length_succeeds(X0,X1) ),
inference(cnf_transformation,[],[f1794]) ).
tcf(c_686,plain,
lh(nil) = '0',
inference(cnf_transformation,[],[f1799]) ).
tcf(c_687,plain,
! [X0: $i,X1: $i] :
( ( lh(cons(X1,X0)) = s(lh(X0)) )
| ~ list_succeeds(X0) ),
inference(cnf_transformation,[],[f1800]) ).
tcf(c_688,plain,
! [X0: $i] :
( nat_succeeds(lh(X0))
| ~ list_succeeds(X0) ),
inference(cnf_transformation,[],[f1801]) ).
tcf(c_689,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ list_succeeds(X0)
| ( lh(X0) != '0' ) ),
inference(cnf_transformation,[],[f1802]) ).
tcf(c_694,plain,
! [X0: $i,X1: $i] :
( '@=<_succeeds'(lh(X0),lh(cons(X1,X0)))
| ~ list_succeeds(X0) ),
inference(cnf_transformation,[],[f1807]) ).
tcf(c_795,plain,
! [X0: $i,X1: $i] :
( ( lh(X0) = X1 )
| ~ list_succeeds(X0)
| ~ length_succeeds(X0,X1) ),
inference(cnf_transformation,[],[f1909]) ).
tcf(c_796,plain,
! [X0: $i] :
( length_succeeds(X0,lh(X0))
| ~ list_succeeds(X0) ),
inference(cnf_transformation,[],[f2126]) ).
tcf(c_803,plain,
! [X0: $i,X1: $i,X2: $i] :
( list_succeeds(X0)
| ~ split_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f1918]) ).
tcf(c_804,plain,
! [X0: $i,X1: $i,X2: $i] :
( list_succeeds(X1)
| ~ split_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f1917]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i,X2: $i] :
( list_succeeds(X2)
| ~ split_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f1916]) ).
tcf(c_806,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( '@+'(lh(X1),lh(X2)) = lh(X0) )
| ~ split_succeeds(X0,X1,X2) ),
inference(cnf_transformation,[],[f1919]) ).
tcf(c_814,negated_conjecture,
( ~ '@<_succeeds'(lh(sK235),lh(cons(sK231,cons(sK232,sK233))))
| ~ '@<_succeeds'(lh(sK234),lh(cons(sK231,cons(sK232,sK233)))) ),
inference(cnf_transformation,[],[f1928]) ).
tcf(c_815,negated_conjecture,
split_succeeds(cons(sK231,cons(sK232,sK233)),sK234,sK235),
inference(cnf_transformation,[],[f1927]) ).
tcf(c_1364,plain,
! [X0: $i,X1: $i] :
( ( lh(X0) = X1 )
| ~ length_succeeds(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_795,c_680,c_795]) ).
tcf(c_37257,plain,
! [X0: $i,X1: $i] :
( ( lh(X0) = X1 )
| ~ length_succeeds(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_1364]) ).
tcf(c_54167,definition,
iPr_def_10 = cons(sK232,sK233),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_54168,definition,
iPr_def_11 = cons(sK231,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_54169,definition,
iPr_def_12 = lh(sK234),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_54170,definition,
iPr_def_13 = lh(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_54171,definition,
iPr_def_14 = lh(sK235),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_54172,negated_conjecture,
split_succeeds(iPr_def_11,sK234,sK235),
inference(demodulation,[status(thm)],[c_815,c_54167,c_54168]) ).
tcf(c_54173,negated_conjecture,
( ~ '@<_succeeds'(iPr_def_14,iPr_def_13)
| ~ '@<_succeeds'(iPr_def_12,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_814,c_54171,c_54170,c_54169]) ).
tcf(c_66452,plain,
( nat_succeeds(iPr_def_12)
| ~ list_succeeds(sK234) ),
inference(superposition,[status(thm)],[c_54169,c_688]) ).
tcf(c_66453,plain,
( nat_succeeds(iPr_def_14)
| ~ list_succeeds(sK235) ),
inference(superposition,[status(thm)],[c_54171,c_688]) ).
tcf(c_66454,plain,
( nat_succeeds(iPr_def_13)
| ~ list_succeeds(iPr_def_11) ),
inference(superposition,[status(thm)],[c_54170,c_688]) ).
tcf(c_66510,plain,
nil != iPr_def_11,
inference(superposition,[status(thm)],[c_54168,c_55]) ).
tcf(c_66814,plain,
( list_succeeds(sK233)
| ~ list_succeeds(iPr_def_10) ),
inference(superposition,[status(thm)],[c_54167,c_653]) ).
tcf(c_66815,plain,
( list_succeeds(iPr_def_10)
| ~ list_succeeds(iPr_def_11) ),
inference(superposition,[status(thm)],[c_54168,c_653]) ).
tcf(c_66939,plain,
( length_succeeds(sK234,iPr_def_12)
| ~ list_succeeds(sK234) ),
inference(superposition,[status(thm)],[c_54169,c_796]) ).
tcf(c_66940,plain,
( length_succeeds(sK235,iPr_def_14)
| ~ list_succeeds(sK235) ),
inference(superposition,[status(thm)],[c_54171,c_796]) ).
tcf(c_66941,plain,
( length_succeeds(iPr_def_11,iPr_def_13)
| ~ list_succeeds(iPr_def_11) ),
inference(superposition,[status(thm)],[c_54170,c_796]) ).
tcf(c_66976,plain,
list_succeeds(iPr_def_11),
inference(superposition,[status(thm)],[c_54172,c_803]) ).
tcf(c_66977,plain,
length_succeeds(iPr_def_11,iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_66941,c_66976]) ).
tcf(c_66978,plain,
list_succeeds(iPr_def_10),
inference(backward_subsumption_resolution,[status(thm)],[c_66815,c_66976]) ).
tcf(c_66981,plain,
nat_succeeds(iPr_def_13),
inference(backward_subsumption_resolution,[status(thm)],[c_66454,c_66976]) ).
tcf(c_66982,plain,
list_succeeds(sK233),
inference(backward_subsumption_resolution,[status(thm)],[c_66814,c_66978]) ).
tcf(c_67002,plain,
list_succeeds(sK234),
inference(superposition,[status(thm)],[c_54172,c_804]) ).
tcf(c_67003,plain,
length_succeeds(sK234,iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_66939,c_67002]) ).
tcf(c_67006,plain,
nat_succeeds(iPr_def_12),
inference(backward_subsumption_resolution,[status(thm)],[c_66452,c_67002]) ).
tcf(c_67011,plain,
list_succeeds(sK235),
inference(superposition,[status(thm)],[c_54172,c_805]) ).
tcf(c_67012,plain,
length_succeeds(sK235,iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_66940,c_67011]) ).
tcf(c_67015,plain,
nat_succeeds(iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_66453,c_67011]) ).
tcf(c_67933,plain,
'@+'(iPr_def_12,'0') = iPr_def_12,
inference(superposition,[status(thm)],[c_67006,c_577]) ).
tcf(c_68370,plain,
lh(sK234) = iPr_def_12,
inference(superposition,[status(thm)],[c_67003,c_37257]) ).
tcf(c_68371,plain,
lh(sK235) = iPr_def_14,
inference(superposition,[status(thm)],[c_67012,c_37257]) ).
tcf(c_68372,plain,
lh(iPr_def_11) = iPr_def_13,
inference(superposition,[status(thm)],[c_66977,c_37257]) ).
tcf(c_70161,plain,
( '@=<_succeeds'(lh(sK233),lh(iPr_def_10))
| ~ list_succeeds(sK233) ),
inference(superposition,[status(thm)],[c_54167,c_694]) ).
tcf(c_70163,plain,
( '@=<_succeeds'(lh(iPr_def_10),lh(iPr_def_11))
| ~ list_succeeds(iPr_def_10) ),
inference(superposition,[status(thm)],[c_54168,c_694]) ).
tcf(c_70172,plain,
( '@=<_succeeds'(lh(iPr_def_10),iPr_def_13)
| ~ list_succeeds(iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_70163,c_68372]) ).
tcf(c_70173,plain,
'@=<_succeeds'(lh(iPr_def_10),iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_70172,c_66978]) ).
tcf(c_70174,plain,
'@=<_succeeds'(lh(sK233),lh(iPr_def_10)),
inference(forward_subsumption_resolution,[status(thm)],[c_70161,c_66982]) ).
tcf(c_70250,plain,
nat_succeeds(lh(iPr_def_10)),
inference(superposition,[status(thm)],[c_70173,c_613]) ).
tcf(c_71171,plain,
! [X0: $i,X1: $i] :
( '@<_succeeds'('0',X1)
| ~ '@<_succeeds'(X0,X1) ),
inference(superposition,[status(thm)],[c_504,c_624]) ).
tcf(c_71193,plain,
! [X0: $i] :
( '@<_succeeds'(lh(sK233),X0)
| ~ '@<_succeeds'(lh(iPr_def_10),X0) ),
inference(superposition,[status(thm)],[c_70174,c_624]) ).
tcf(c_73752,plain,
( '@<_succeeds'(lh(sK233),s(lh(iPr_def_10)))
| ~ nat_succeeds(lh(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_608,c_71193]) ).
tcf(c_73760,plain,
'@<_succeeds'(lh(sK233),s(lh(iPr_def_10))),
inference(forward_subsumption_resolution,[status(thm)],[c_73752,c_70250]) ).
tcf(c_75071,plain,
! [X0: $i] : lh(cons(X0,iPr_def_10)) = s(lh(iPr_def_10)),
inference(superposition,[status(thm)],[c_66978,c_687]) ).
tcf(c_75338,plain,
s(lh(iPr_def_10)) = lh(iPr_def_11),
inference(superposition,[status(thm)],[c_54168,c_75071]) ).
tcf(c_75347,plain,
s(lh(iPr_def_10)) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_75338,c_68372]) ).
tcf(c_75357,plain,
'@<_succeeds'(lh(sK233),iPr_def_13),
inference(demodulation,[status(thm)],[c_73760,c_75347]) ).
tcf(c_75475,plain,
'@<_succeeds'('0',iPr_def_13),
inference(superposition,[status(thm)],[c_75357,c_71171]) ).
tcf(c_75708,plain,
'0' != iPr_def_13,
inference(superposition,[status(thm)],[c_75347,c_49]) ).
tcf(c_80982,plain,
( length_succeeds(sK235,iPr_def_14)
| ~ list_succeeds(sK235) ),
inference(superposition,[status(thm)],[c_54171,c_796]) ).
tcf(c_80999,plain,
( ( nil = sK234 )
| ~ list_succeeds(sK234)
| ( '0' != iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_68370,c_689]) ).
tcf(c_81001,plain,
( ( nil = sK235 )
| ~ list_succeeds(sK235)
| ( '0' != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_68371,c_689]) ).
tcf(c_81009,plain,
( ( nil = sK235 )
| ( '0' != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_81001,c_67011]) ).
tcf(c_81012,plain,
( ( nil = sK234 )
| ( '0' != iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_80999,c_67002]) ).
tcf(c_81303,plain,
list_succeeds(sK235),
inference(superposition,[status(thm)],[c_54172,c_805]) ).
tcf(c_81393,plain,
length_succeeds(sK235,iPr_def_14),
inference(global_subsumption_just,[status(thm)],[c_80982,c_66940,c_67011]) ).
tcf(c_86088,plain,
! [X0: $i] :
( '@<_succeeds'(iPr_def_12,'@+'(iPr_def_12,X0))
| ~ nat_succeeds(iPr_def_12)
| ~ '@<_succeeds'('0',X0) ),
inference(superposition,[status(thm)],[c_67933,c_630]) ).
tcf(c_86142,plain,
! [X0: $i] :
( '@<_succeeds'(iPr_def_12,'@+'(iPr_def_12,X0))
| ~ '@<_succeeds'('0',X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_86088,c_67006]) ).
tcf(c_86464,plain,
! [X0: $i] :
( '@=<_succeeds'(iPr_def_12,'@+'(iPr_def_12,X0))
| ~ nat_succeeds(iPr_def_12)
| ~ '@=<_succeeds'('0',X0) ),
inference(superposition,[status(thm)],[c_67933,c_634]) ).
tcf(c_86511,plain,
! [X0: $i] : '@=<_succeeds'(iPr_def_12,'@+'(iPr_def_12,X0)),
inference(forward_subsumption_resolution,[status(thm)],[c_86464,c_67006,c_504]) ).
tcf(c_87761,plain,
'@+'(lh(sK234),lh(sK235)) = lh(iPr_def_11),
inference(superposition,[status(thm)],[c_54172,c_806]) ).
tcf(c_87769,plain,
'@+'(iPr_def_12,iPr_def_14) = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_87761,c_68370,c_68371,c_68372]) ).
tcf(c_87967,plain,
'@=<_succeeds'(iPr_def_12,iPr_def_13),
inference(superposition,[status(thm)],[c_87769,c_86511]) ).
tcf(c_87968,plain,
( '@<_succeeds'(iPr_def_12,iPr_def_13)
| ~ '@<_succeeds'('0',iPr_def_14) ),
inference(superposition,[status(thm)],[c_87769,c_86142]) ).
tcf(c_88023,plain,
( '@<_succeeds'(iPr_def_12,iPr_def_13)
| ( iPr_def_12 = iPr_def_13 )
| ~ nat_succeeds(iPr_def_13) ),
inference(superposition,[status(thm)],[c_87967,c_623]) ).
tcf(c_88042,plain,
( '@<_succeeds'(iPr_def_12,iPr_def_13)
| ( iPr_def_12 = iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88023,c_66981]) ).
tcf(c_88411,plain,
( '@<_succeeds'(iPr_def_12,iPr_def_13)
| ( '0' = iPr_def_14 )
| ~ nat_succeeds(iPr_def_14) ),
inference(superposition,[status(thm)],[c_611,c_87968]) ).
tcf(c_88412,plain,
( '@<_succeeds'(iPr_def_12,iPr_def_13)
| ( '0' = iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_88411,c_67015]) ).
tcf(c_88430,plain,
( ( iPr_def_12 = iPr_def_13 )
| ~ '@<_succeeds'(iPr_def_14,iPr_def_13) ),
inference(superposition,[status(thm)],[c_88042,c_54173]) ).
tcf(c_88954,plain,
( ( '0' = iPr_def_14 )
| ~ '@<_succeeds'(iPr_def_14,iPr_def_13) ),
inference(superposition,[status(thm)],[c_88412,c_54173]) ).
tcf(c_88986,plain,
lh(sK235) = iPr_def_14,
inference(superposition,[status(thm)],[c_81393,c_37257]) ).
tcf(c_95742,plain,
( '@<_succeeds'(iPr_def_14,iPr_def_13)
| ~ nat_succeeds(iPr_def_14)
| ~ nat_succeeds(iPr_def_12)
| ~ '@<_succeeds'('0',iPr_def_12) ),
inference(superposition,[status(thm)],[c_87769,c_633]) ).
tcf(c_95766,plain,
( '@<_succeeds'(iPr_def_14,iPr_def_13)
| ~ '@<_succeeds'('0',iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_95742,c_67015,c_67006]) ).
tcf(c_97380,plain,
( '@<_succeeds'(iPr_def_14,iPr_def_13)
| ( '0' = iPr_def_12 )
| ~ nat_succeeds(iPr_def_12) ),
inference(superposition,[status(thm)],[c_611,c_95766]) ).
tcf(c_97382,plain,
( '@<_succeeds'(iPr_def_14,iPr_def_13)
| ( '0' = iPr_def_12 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_97380,c_67006]) ).
tcf(c_97858,plain,
( ( '0' = iPr_def_14 )
| ( '0' = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_97382,c_88954]) ).
tcf(c_97859,plain,
( ( iPr_def_12 = iPr_def_13 )
| ( '0' = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_97382,c_88430]) ).
tcf(c_97894,plain,
( ( nil = sK235 )
| ( '0' = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_97858,c_81009]) ).
tcf(c_98728,plain,
( ( iPr_def_12 = iPr_def_13 )
| ( nil = sK234 ) ),
inference(superposition,[status(thm)],[c_97859,c_81012]) ).
tcf(c_99839,plain,
( split_succeeds(iPr_def_11,sK234,nil)
| ( '0' = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_97894,c_54172]) ).
tcf(c_101260,plain,
( split_succeeds(iPr_def_11,nil,sK235)
| ( iPr_def_12 = iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_98728,c_54172]) ).
tcf(c_129490,plain,
( sP6(iPr_def_11,sK234,nil)
| ( '0' = iPr_def_12 )
| ( cons(sK70(iPr_def_11,sK234,nil),sK71(iPr_def_11,sK234,nil)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_99839,c_218]) ).
tcf(c_129656,plain,
( sP6(iPr_def_11,nil,sK235)
| ( iPr_def_12 = iPr_def_13 )
| ( cons(sK70(iPr_def_11,nil,sK235),sK72(iPr_def_11,nil,sK235)) = nil ) ),
inference(superposition,[status(thm)],[c_101260,c_219]) ).
tcf(c_129659,plain,
( sP6(iPr_def_11,nil,sK235)
| ( iPr_def_12 = iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_129656,c_55]) ).
tcf(c_144299,plain,
( ( nil = sK235 )
| ~ list_succeeds(sK235)
| ( '0' != iPr_def_14 ) ),
inference(superposition,[status(thm)],[c_88986,c_689]) ).
tcf(c_144306,plain,
( ( nil = sK235 )
| ( '0' != iPr_def_14 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_144299,c_81303]) ).
tcf(c_163272,plain,
nil != iPr_def_10,
inference(superposition,[status(thm)],[c_54167,c_55]) ).
tcf(c_163273,plain,
nil != iPr_def_11,
inference(superposition,[status(thm)],[c_54168,c_55]) ).
tcf(c_163616,plain,
( length_succeeds(sK235,iPr_def_14)
| ~ list_succeeds(sK235) ),
inference(superposition,[status(thm)],[c_54171,c_796]) ).
tcf(c_163659,plain,
list_succeeds(sK235),
inference(superposition,[status(thm)],[c_54172,c_805]) ).
tcf(c_163667,plain,
length_succeeds(sK235,iPr_def_14),
inference(global_subsumption_just,[status(thm)],[c_163616,c_66940,c_67011]) ).
tcf(c_164910,plain,
lh(sK235) = iPr_def_14,
inference(superposition,[status(thm)],[c_163667,c_37257]) ).
fof(f856,definition,
! [X0,X1,X2] :
( sP6(X0,X1,X2)
<=> ( X2 = nil
& X1 = nil
& X0 = nil ) ),
introduced(definition,[new_symbols(definition,[sP6])],[predicate_definition_introduction]) ).
fof(f857,plain,
! [X0,X1,X2] :
( split_succeeds(X0,X1,X2)
<=> ( sP6(X0,X1,X2)
| ? [X3,X4,X5] :
( split_succeeds(X4,X2,X5)
& X1 = cons(X3,X5)
& X0 = cons(X3,X4) ) ) ),
inference(definition_folding,[],[f73,f856]) ).
fof(f925,plain,
! [X0,X1,X2] :
( ( ~ sP6(X0,X1,X2)
| ( X2 = nil
& X1 = nil
& X0 = nil ) )
& ( nil != X2
| nil != X1
| nil != X0
| sP6(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f856]) ).
fof(f926,plain,
! [X0,X1,X2] :
( ( ~ sP6(X0,X1,X2)
| ( X2 = nil
& X1 = nil
& X0 = nil ) )
& ( nil != X2
| nil != X1
| nil != X0
| sP6(X0,X1,X2) ) ),
inference(flattening,[],[f925]) ).
fof(f1327,plain,
! [X2,X0,X1] :
( ~ sP6(X0,X1,X2)
| nil = X0 ),
inference(cnf_transformation,[],[f926]) ).
tcf(c_213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = nil )
| ~ sP6(X0,X1,X2) ),
inference(cnf_transformation,[],[f1327]) ).
tcf(c_132190,plain,
( ( nil = iPr_def_11 )
| ( '0' = iPr_def_12 )
| ( cons(sK70(iPr_def_11,sK234,nil),sK71(iPr_def_11,sK234,nil)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_129490,c_213]) ).
tcf(c_132191,plain,
( ( '0' = iPr_def_12 )
| ( cons(sK70(iPr_def_11,sK234,nil),sK71(iPr_def_11,sK234,nil)) = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_132190,c_66510]) ).
tcf(c_132574,plain,
( ( iPr_def_12 = iPr_def_13 )
| ( nil = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_129659,c_213]) ).
tcf(c_132575,plain,
iPr_def_12 = iPr_def_13,
inference(forward_subsumption_resolution,[status(thm)],[c_132574,c_66510]) ).
tcf(c_132735,plain,
'0' != iPr_def_12,
inference(demodulation,[status(thm)],[c_75708,c_132575]) ).
tcf(c_132751,plain,
'@<_succeeds'('0',iPr_def_12),
inference(demodulation,[status(thm)],[c_75475,c_132575]) ).
tcf(c_144312,plain,
nil = sK235,
inference(global_subsumption_just,[status(thm)],[c_144306,c_81009,c_88954,c_95766,c_132751]) ).
tcf(c_144331,plain,
lh(nil) = iPr_def_14,
inference(demodulation,[status(thm)],[c_54171,c_144312]) ).
tcf(c_144341,plain,
'0' = iPr_def_14,
inference(demodulation,[status(thm)],[c_686,c_144331]) ).
tcf(c_184127,plain,
! [X0: $i] :
( ( X0 = nil )
| ~ list_succeeds(X0)
| ( lh(X0) != iPr_def_14 ) ),
inference(light_normalisation,[status(thm)],[c_689,c_144341]) ).
tcf(c_184140,plain,
( ( nil = sK235 )
| ~ list_succeeds(sK235) ),
inference(superposition,[status(thm)],[c_164910,c_184127]) ).
tcf(c_184145,plain,
nil = sK235,
inference(forward_subsumption_resolution,[status(thm)],[c_184140,c_163659]) ).
tcf(c_184219,plain,
split_succeeds(iPr_def_11,sK234,nil),
inference(demodulation,[status(thm)],[c_54172,c_184145]) ).
tcf(c_251339,plain,
( sP6(iPr_def_11,sK234,nil)
| ( cons(sK70(iPr_def_11,sK234,nil),sK71(iPr_def_11,sK234,nil)) = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_184219,c_218]) ).
tcf(c_251588,plain,
cons(sK70(iPr_def_11,sK234,nil),sK71(iPr_def_11,sK234,nil)) = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_251339,c_132191,c_132735]) ).
tcf(c_251651,plain,
! [X0: $i,X1: $i] :
( ( sK71(iPr_def_11,sK234,nil) = X1 )
| ( cons(X0,X1) != iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_251588,c_56]) ).
tcf(c_253355,plain,
sK71(iPr_def_11,sK234,nil) = iPr_def_10,
inference(superposition,[status(thm)],[c_54168,c_251651]) ).
tcf(c_260400,plain,
( sP6(iPr_def_11,sK234,nil)
| split_succeeds(iPr_def_10,nil,sK72(iPr_def_11,sK234,nil))
| ~ split_succeeds(iPr_def_11,sK234,nil) ),
inference(superposition,[status(thm)],[c_253355,c_220]) ).
tcf(c_260401,plain,
( sP6(iPr_def_11,sK234,nil)
| split_succeeds(iPr_def_10,nil,sK72(iPr_def_11,sK234,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_260400,c_184219]) ).
tcf(c_260408,plain,
( sP6(iPr_def_11,sK234,nil)
| sP6(iPr_def_10,nil,sK72(iPr_def_11,sK234,nil))
| ( cons(sK70(iPr_def_10,nil,sK72(iPr_def_11,sK234,nil)),sK72(iPr_def_10,nil,sK72(iPr_def_11,sK234,nil))) = nil ) ),
inference(superposition,[status(thm)],[c_260401,c_219]) ).
tcf(c_260428,plain,
( sP6(iPr_def_11,sK234,nil)
| sP6(iPr_def_10,nil,sK72(iPr_def_11,sK234,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_260408,c_55]) ).
tcf(c_262786,plain,
( sP6(iPr_def_11,sK234,nil)
| ( nil = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_260428,c_213]) ).
tcf(c_262787,plain,
sP6(iPr_def_11,sK234,nil),
inference(forward_subsumption_resolution,[status(thm)],[c_262786,c_163272]) ).
tcf(c_262942,plain,
nil = iPr_def_11,
inference(superposition,[status(thm)],[c_262787,c_213]) ).
tcf(c_262943,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_262942,c_163273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWX029+1 : TPTP v9.3.1. Released v9.1.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n003.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 23:22:23 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.41
% 0.12/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.41
% 0.12/0.41 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 163.72/25.54 % SZS status Started for theBenchmark.p
% 163.72/25.54 % SZS status Theorem for theBenchmark.p
% 163.72/25.54
% 163.72/25.54 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 163.72/25.54
% 163.72/25.54 % ------ iProver source info
% 163.72/25.54
% 163.72/25.54 % git: date: 2026-07-19 20:42:38 +0200
% 163.72/25.54 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 163.72/25.54 % git: non_committed_changes: false
% 163.72/25.54
% 163.72/25.54 % ------ Parsing...
% 163.72/25.54 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 163.72/25.54
% 163.72/25.54 % ------ Preprocessing... sup_sim: 0 sf_s rm: 12 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 163.72/25.54
% 163.72/25.54 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 163.72/25.54
% 163.72/25.54 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 163.72/25.54 % ------ Proving...
% 163.72/25.54 % ------ Problem Properties
% 163.72/25.54
% 163.72/25.54 %
% 163.72/25.54 % clauses 671
% 163.72/25.54 % conjectures 2
% 163.72/25.54 % EPR 229
% 163.72/25.54 % Horn 444
% 163.72/25.54 % unary 64
% 163.72/25.54 % binary 273
% 163.72/25.54 % lits 1724
% 163.72/25.54 % lits eq 372
% 163.72/25.54 % fd_pure 0
% 163.72/25.54 % fd_pseudo 0
% 163.72/25.54 % fd_cond 59
% 163.72/25.54 % fd_pseudo_cond 43
% 163.72/25.54 % AC symbols 0
% 163.72/25.54
% 163.72/25.54 % ------ Schedule dynamic 5 is on
% 163.72/25.54
% 163.72/25.54 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 163.72/25.54
% 163.72/25.54
% 163.72/25.54 % ------
% 163.72/25.54 % Current options:
% 163.72/25.54 % ------
% 163.72/25.54
% 163.72/25.54
% 163.72/25.54 %
% 163.72/25.54
% 163.72/25.54 % ------ Proving...
% 163.72/25.54 % Proof_search_loop: time out after: 5392 full_loop iterations
% 163.72/25.54
% 163.72/25.54 % ------ Input Options"1. --res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 163.72/25.54
% 163.72/25.54
% 163.72/25.54 % ------
% 163.72/25.54 % Current options:
% 163.72/25.54 % ------
% 163.72/25.54
% 163.72/25.54
% 163.72/25.54 %
% 163.72/25.54
% 163.72/25.54 % ------ Proving...
% 163.72/25.54 %
% 163.72/25.54
% 163.72/25.54 % SZS status Theorem for theBenchmark.p
% 163.72/25.54
% 163.72/25.54 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 163.72/25.55
% 163.72/25.55
%------------------------------------------------------------------------------