TSTP Solution File: DAT100_1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : DAT100_1 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 14:36:44 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 54
% Syntax : Number of formulae : 130 ( 51 unt; 7 typ; 0 def)
% Number of atoms : 1298 ( 479 equ)
% Maximal formula atoms : 48 ( 10 avg)
% Number of connectives : 2163 (1041 ~; 868 |; 170 &)
% ( 84 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of FOOLs : 53 ( 53 fml; 0 var)
% Number arithmetic : 3675 ( 404 atm; 352 fun;2721 num; 198 var)
% Number of types : 2 ( 0 usr; 1 ari)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 14 ( 9 usr; 2 prp; 0-3 aty)
% Number of functors : 14 ( 6 usr; 7 con; 0-2 aty)
% Number of variables : 396 ( 332 !; 38 ?; 396 :)
% Comments :
%------------------------------------------------------------------------------
tff(tptp_fun_K_1_type,type,
tptp_fun_K_1: ( list * $int ) > $int ).
tff(tptp_fun_T_0_type,type,
tptp_fun_T_0: ( list * $int ) > list ).
tff(cons_type,type,
cons: ( $int * list ) > list ).
tff(nil_type,type,
nil: list ).
tff(inRange_type,type,
inRange: ( $int * list ) > $o ).
tff(tail_type,type,
tail: list > list ).
tff(head_type,type,
head: list > $int ).
tff(1,plain,
^ [N: $int,L: list] :
refl(
( ~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
<=> ~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
<=> ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [N: $int,L: list] :
rewrite(
( ~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
<=> ~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
<=> ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
<=> ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [N: $int,L: list] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) )
<=> ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )),
( ( ( L = nil )
| ~ inRange(N,L)
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
<=> ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) ) )),
rewrite(
( ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
<=> ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) ) )),
( ( ( L = nil )
| ~ inRange(N,L)
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
<=> ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) ) )),
trans(
monotonicity(
trans(
monotonicity(
quant_intro(
proof_bind(
^ [K: $int,T: list] :
trans(
monotonicity(
rewrite(
( ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) )
<=> ~ ( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) )),
( ~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) )
<=> ~ ~ ( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) )),
rewrite(
( ~ ~ ( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) )
<=> ( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) )),
( ~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) )
<=> ( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ))),
( ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) )
<=> ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) )),
( ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) )
<=> ( ( L != nil )
& ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) )),
rewrite(
( ( ( L != nil )
& ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) )
<=> ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) )),
( ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) )
<=> ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) )),
( ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) )
<=> ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )),
rewrite(
( ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) )
<=> ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )),
( ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) )
<=> ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )),
( ( ( ( L = nil )
| ~ inRange(N,L)
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) )
<=> ( ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) )),
rewrite(
( ( ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
<=> ~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) )),
( ( ( ( L = nil )
| ~ inRange(N,L)
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) )
<=> ~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [N: $int,L: list] :
( ( ( L = nil )
| ~ inRange(N,L)
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) )
<=> ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [N: $int,L: list] :
rewrite(
( ( ( ~ inRange(N,L)
| ( L = nil )
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $greatereq($sum(tptp_fun_K_1(L,N),$product(-1,N)),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) )
<=> ( ( ( L = nil )
| ~ inRange(N,L)
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [N: $int,L: list] :
( ( ~ inRange(N,L)
| ( L = nil )
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $greatereq($sum(tptp_fun_K_1(L,N),$product(-1,N)),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) )
<=> ! [N: $int,L: list] :
( ( ( L = nil )
| ~ inRange(N,L)
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [N: $int,L: list] :
rewrite(
( ( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $lesseq($sum(N,$product(-1,K)),0)
& inRange(N,T) ) ) )
<=> ( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $lesseq($sum(N,$product(-1,K)),0)
& inRange(N,T) ) ) )
<=> ! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [N: $int,L: list] :
rewrite(
( ( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& ~ $lesseq(N,K)
& inRange(N,T) ) ) )
<=> ( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $lesseq($sum(N,$product(-1,K)),0)
& inRange(N,T) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& ~ $lesseq(N,K)
& inRange(N,T) ) ) )
<=> ! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $lesseq($sum(N,$product(-1,K)),0)
& inRange(N,T) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& ~ $lesseq(N,K)
& inRange(N,T) ) ) )
<=> ! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& ~ $lesseq(N,K)
& inRange(N,T) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
^ [N: $int,L: list] :
rewrite(
( ( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& $less(K,N)
& inRange(N,T) ) ) )
<=> ( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& ~ $lesseq(N,K)
& inRange(N,T) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& $less(K,N)
& inRange(N,T) ) ) )
<=> ! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& ~ $lesseq(N,K)
& inRange(N,T) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,axiom,
! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& $less(K,N)
& inRange(N,T) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange) ).
tff(18,plain,
! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& ~ $lesseq(N,K)
& inRange(N,T) ) ) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $lesseq(0,K)
& ~ $lesseq(N,K)
& inRange(N,T) ) ) ),
inference(modus_ponens,[status(thm)],[18,14]) ).
tff(20,plain,
! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $lesseq($sum(N,$product(-1,K)),0)
& inRange(N,T) ) ) ),
inference(modus_ponens,[status(thm)],[19,13]) ).
tff(21,plain,
! [N: $int,L: list] :
( inRange(N,L)
<=> ( ( L = nil )
| ? [K: $int,T: list] :
( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ),
inference(modus_ponens,[status(thm)],[20,11]) ).
tff(22,plain,
! [N: $int,L: list] :
( ( ~ inRange(N,L)
| ( L = nil )
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $greatereq($sum(tptp_fun_K_1(L,N),$product(-1,N)),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [N: $int,L: list] :
( ( ( L = nil )
| ~ inRange(N,L)
| ( ( L = cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
& $greatereq(tptp_fun_K_1(L,N),0)
& ~ $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
& inRange(N,tptp_fun_T_0(L,N)) ) )
& ( inRange(N,L)
| ( ( L != nil )
& ! [K: $int,T: list] :
~ ( ( L = cons(K,T) )
& $greatereq(K,0)
& ~ $greatereq($sum(K,$product(-1,N)),0)
& inRange(N,T) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,9]) ).
tff(24,plain,
! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,7]) ).
tff(25,plain,
! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,5]) ).
tff(26,plain,
( ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ~ inRange(4,T)
| $greatereq(K,4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) ) ) ) ) ) )
<=> ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ~ inRange(4,T)
| $greatereq(K,4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( ~ ( ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| $lesseq($sum(4,$product(-1,tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))),0)
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,4)),0)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(4,T) ) ) ) )
<=> ~ ( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ~ inRange(4,T)
| $greatereq(K,4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| $lesseq($sum(4,$product(-1,tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))),0)
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,4)),0)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(4,T) ) ) ) ) )
<=> ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ~ inRange(4,T)
| $greatereq(K,4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| $lesseq($sum(4,$product(-1,tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))),0)
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,4)),0)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(4,T) ) ) ) ) )
<=> ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ~ inRange(4,T)
| $greatereq(K,4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| $lesseq($sum(4,$product(-1,tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))),0)
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,4)),0)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(4,T) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ~ inRange(4,T)
| $greatereq(K,4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ ( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ~ inRange(4,T)
| $greatereq(K,4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[31,25]) ).
tff(33,plain,
( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ ( inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ~ inRange(4,T)
| $greatereq(K,4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(K,T) ) ) ) )
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) ),
inference(tautology,[status(thm)],]) ).
tff(34,plain,
( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
^ [K: $int,L: list] :
refl(
( ( tail(cons(K,L)) = L )
<=> ( tail(cons(K,L)) = L ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [K: $int,L: list] : ( tail(cons(K,L)) = L )
<=> ! [K: $int,L: list] : ( tail(cons(K,L)) = L ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
( ! [K: $int,L: list] : ( tail(cons(K,L)) = L )
<=> ! [K: $int,L: list] : ( tail(cons(K,L)) = L ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
! [K: $int,L: list] : ( tail(cons(K,L)) = L ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).
tff(39,plain,
! [K: $int,L: list] : ( tail(cons(K,L)) = L ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [K: $int,L: list] : ( tail(cons(K,L)) = L ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [K: $int,L: list] : ( tail(cons(K,L)) = L ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ~ ! [K: $int,L: list] : ( tail(cons(K,L)) = L )
| ( tail(cons(1,cons(5,cons(2,nil)))) = cons(5,cons(2,nil)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
tail(cons(1,cons(5,cons(2,nil)))) = cons(5,cons(2,nil)),
inference(unit_resolution,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ inRange(4,T)
| $greatereq(K,4) ) ) ) ) )
<=> ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ inRange(4,T)
| $greatereq(K,4) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ( ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| $lesseq($sum(4,$product(-1,tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4))),0)
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,4)),0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(4,T) ) ) ) )
<=> ~ ( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ inRange(4,T)
| $greatereq(K,4) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| $lesseq($sum(4,$product(-1,tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4))),0)
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,4)),0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(4,T) ) ) ) ) )
<=> ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ inRange(4,T)
| $greatereq(K,4) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| $lesseq($sum(4,$product(-1,tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4))),0)
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,4)),0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(4,T) ) ) ) ) )
<=> ( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ inRange(4,T)
| $greatereq(K,4) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| $lesseq($sum(4,$product(-1,tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4))),0)
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,4)),0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(4,T) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [N: $int,L: list] :
~ ( ~ ( ( L = nil )
| ~ inRange(N,L)
| ~ ( ( L != cons(tptp_fun_K_1(L,N),tptp_fun_T_0(L,N)) )
| $lesseq($sum(N,$product(-1,tptp_fun_K_1(L,N))),0)
| ~ $greatereq(tptp_fun_K_1(L,N),0)
| ~ inRange(N,tptp_fun_T_0(L,N)) ) )
| ~ ( inRange(N,L)
| ~ ( ( L = nil )
| ~ ! [K: $int,T: list] :
( $greatereq($sum(K,$product(-1,N)),0)
| ( L != cons(K,T) )
| ~ $greatereq(K,0)
| ~ inRange(N,T) ) ) ) )
| ~ ( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ inRange(4,T)
| $greatereq(K,4) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ ( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ inRange(4,T)
| $greatereq(K,4) ) ) ) ),
inference(unit_resolution,[status(thm)],[49,25]) ).
tff(51,plain,
( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( inRange(4,cons(1,cons(5,cons(2,nil))))
| ~ ( ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ! [K: $int,T: list] :
( ~ $greatereq(K,0)
| ( cons(1,cons(5,cons(2,nil))) != cons(K,T) )
| ~ inRange(4,T)
| $greatereq(K,4) ) ) )
| ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) ),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
^ [K: $int,L: list] :
refl(
( ( cons(K,L) != nil )
<=> ( cons(K,L) != nil ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [K: $int,L: list] : ( cons(K,L) != nil )
<=> ! [K: $int,L: list] : ( cons(K,L) != nil ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [K: $int,L: list] : ( cons(K,L) != nil )
<=> ! [K: $int,L: list] : ( cons(K,L) != nil ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
! [K: $int,L: list] : ( cons(K,L) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
tff(57,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [K: $int,L: list] : ( cons(K,L) != nil ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [K: $int,L: list] : ( cons(K,L) != nil )
| ( cons(1,cons(5,cons(2,nil))) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(61,plain,
cons(1,cons(5,cons(2,nil))) != nil,
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
( inRange(4,cons(1,cons(5,cons(2,nil))))
<=> inRange(4,cons(1,cons(5,cons(2,nil)))) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ~ ~ inRange(4,cons(1,cons(5,cons(2,nil))))
<=> inRange(4,cons(1,cons(5,cons(2,nil)))) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
~ ~ inRange(4,cons(1,cons(5,cons(2,nil)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).
tff(65,plain,
inRange(4,cons(1,cons(5,cons(2,nil)))),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
inRange(4,cons(1,cons(5,cons(2,nil)))),
inference(modus_ponens,[status(thm)],[65,62]) ).
tff(67,plain,
( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) ),
inference(tautology,[status(thm)],]) ).
tff(68,plain,
( ~ ( ~ inRange(4,cons(1,cons(5,cons(2,nil))))
| ( cons(1,cons(5,cons(2,nil))) = nil )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) )
| ~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ) ),
inference(unit_resolution,[status(thm)],[67,66,61]) ).
tff(69,plain,
~ ( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4) ),
inference(unit_resolution,[status(thm)],[68,52]) ).
tff(70,plain,
( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4)
| ( cons(1,cons(5,cons(2,nil))) = cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) ) ),
inference(tautology,[status(thm)],]) ).
tff(71,plain,
cons(1,cons(5,cons(2,nil))) = cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) = cons(1,cons(5,cons(2,nil))),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
tail(cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))) = tail(cons(1,cons(5,cons(2,nil)))),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ~ ! [K: $int,L: list] : ( tail(cons(K,L)) = L )
| ( tail(cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))) = tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
tail(cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))) = tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),
inference(unit_resolution,[status(thm)],[74,41]) ).
tff(76,plain,
tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = tail(cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = cons(5,cons(2,nil)),
inference(transitivity,[status(thm)],[76,73,43]) ).
tff(78,plain,
( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
<=> ( cons(5,cons(2,nil)) = nil ) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ( cons(5,cons(2,nil)) = nil )
<=> ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil ) ),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( ( cons(5,cons(2,nil)) != nil )
<=> ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != nil ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [K: $int,L: list] : ( cons(K,L) != nil )
| ( cons(5,cons(2,nil)) != nil ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
cons(5,cons(2,nil)) != nil,
inference(unit_resolution,[status(thm)],[81,59]) ).
tff(83,plain,
tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != nil,
inference(modus_ponens,[status(thm)],[82,80]) ).
tff(84,plain,
( ( cons(1,cons(5,cons(2,nil))) != cons(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) )
| ~ $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),0)
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| $greatereq(tptp_fun_K_1(cons(1,cons(5,cons(2,nil))),4),4)
| inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4)),
inference(unit_resolution,[status(thm)],[84,69]) ).
tff(86,plain,
( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) ),
inference(tautology,[status(thm)],]) ).
tff(87,plain,
( ~ ( ~ inRange(4,tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4))
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) )
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = nil )
| ~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ) ),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
~ ( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ),
inference(unit_resolution,[status(thm)],[87,83,34]) ).
tff(89,plain,
( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4)
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
^ [K: $int,L: list] :
refl(
( ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
<=> ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
<=> ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
^ [K: $int,L: list] :
trans(
monotonicity(rewrite($sum(head(cons(K,L)),$product(-1,K)) = $sum($product(-1,K),head(cons(K,L)))),
( ( $sum(head(cons(K,L)),$product(-1,K)) = 0 )
<=> ( $sum($product(-1,K),head(cons(K,L))) = 0 ) )),
rewrite(
( ( $sum($product(-1,K),head(cons(K,L))) = 0 )
<=> ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) )),
( ( $sum(head(cons(K,L)),$product(-1,K)) = 0 )
<=> ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [K: $int,L: list] : ( $sum(head(cons(K,L)),$product(-1,K)) = 0 )
<=> ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
^ [K: $int,L: list] :
rewrite(
( ( head(cons(K,L)) = K )
<=> ( $sum(head(cons(K,L)),$product(-1,K)) = 0 ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [K: $int,L: list] : ( head(cons(K,L)) = K )
<=> ! [K: $int,L: list] : ( $sum(head(cons(K,L)),$product(-1,K)) = 0 ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
( ! [K: $int,L: list] : ( head(cons(K,L)) = K )
<=> ! [K: $int,L: list] : ( head(cons(K,L)) = K ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,axiom,
! [K: $int,L: list] : ( head(cons(K,L)) = K ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
tff(99,plain,
! [K: $int,L: list] : ( head(cons(K,L)) = K ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [K: $int,L: list] : ( $sum(head(cons(K,L)),$product(-1,K)) = 0 ),
inference(modus_ponens,[status(thm)],[99,96]) ).
tff(101,plain,
! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ),
inference(modus_ponens,[status(thm)],[100,94]) ).
tff(102,plain,
! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 ),
inference(modus_ponens,[status(thm)],[102,92]) ).
tff(104,plain,
( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( $sum(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),$product(-1,head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
$sum(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),$product(-1,head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))))) = 0,
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
( ( $sum(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),$product(-1,head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))))) != 0 )
| $greatereq($sum(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),$product(-1,head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))))),0) ),
inference(theory_lemma,[status(thm)],]) ).
tff(107,plain,
$greatereq($sum(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),$product(-1,head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))))),0),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
( ( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( head(cons(5,cons(2,nil))) = 5 ) )
<=> ( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( head(cons(5,cons(2,nil))) = 5 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( $sum(5,$product(-1,head(cons(5,cons(2,nil))))) = 0 )
<=> ( head(cons(5,cons(2,nil))) = 5 ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( $sum(5,$product(-1,head(cons(5,cons(2,nil))))) = 0 ) )
<=> ( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( head(cons(5,cons(2,nil))) = 5 ) ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( $sum(5,$product(-1,head(cons(5,cons(2,nil))))) = 0 ) )
<=> ( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( head(cons(5,cons(2,nil))) = 5 ) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( $sum(5,$product(-1,head(cons(5,cons(2,nil))))) = 0 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [K: $int,L: list] : ( $sum(K,$product(-1,head(cons(K,L)))) = 0 )
| ( head(cons(5,cons(2,nil))) = 5 ) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
head(cons(5,cons(2,nil))) = 5,
inference(unit_resolution,[status(thm)],[113,103]) ).
tff(115,plain,
( ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) != cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) )
| ~ $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),0)
| ~ inRange(4,tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))
| $greatereq(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),4)
| ( tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) ) ),
inference(tautology,[status(thm)],]) ).
tff(116,plain,
tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4) = cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)),
inference(unit_resolution,[status(thm)],[115,88]) ).
tff(117,plain,
cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) = tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4)) = cons(5,cons(2,nil)),
inference(transitivity,[status(thm)],[117,76,73,43]) ).
tff(119,plain,
head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))) = head(cons(5,cons(2,nil))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))) = 5,
inference(transitivity,[status(thm)],[119,114]) ).
tff(121,plain,
( ( head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))) != 5 )
| $greatereq(head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))),5) ),
inference(theory_lemma,[status(thm)],]) ).
tff(122,plain,
$greatereq(head(cons(tptp_fun_K_1(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4),tptp_fun_T_0(tptp_fun_T_0(cons(1,cons(5,cons(2,nil))),4),4))),5),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
$false,
inference(theory_lemma,[status(thm)],[122,107,90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : DAT100_1 : TPTP v8.1.0. Released v6.1.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 31 01:44:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.39 % SZS status Theorem
% 0.12/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------