TSTP Solution File: NUM472+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM472+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Sun Sep 18 13:09:55 EDT 2022
% Result : Theorem 0.23s 0.44s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 82 ( 15 unt; 7 typ; 0 def)
% Number of atoms : 755 ( 148 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 1343 ( 710 ~; 472 |; 76 &)
% ( 76 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 195 ( 166 !; 15 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xm_type,type,
xm: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(xl_type,type,
xl: $i ).
tff(1,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1324) ).
tff(3,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(6,plain,
( aNaturalNumber0(xl)
& aNaturalNumber0(xm) ),
inference(and_elim,[status(thm)],[2]) ).
tff(7,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[6]) ).
tff(8,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[7,5]) ).
tff(9,plain,
^ [W0: $i,W1: $i] :
refl(
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
tff(17,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[18]) ).
tff(20,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[19,12]) ).
tff(21,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[20,10]) ).
tff(22,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ( aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(monotonicity,[status(thm)],[23]) ).
tff(25,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| aNaturalNumber0(sdtpldt0(xm,xn)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
aNaturalNumber0(sdtpldt0(xm,xn)),
inference(unit_resolution,[status(thm)],[27,21,8,4]) ).
tff(29,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(
( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(
monotonicity(
rewrite(
( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) ) )),
rewrite(
( ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
( ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
rewrite(
( ( ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
rewrite(
( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
rewrite(
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).
tff(40,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ sdtlseqdt0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_0(W1,W0))
& ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) = W1 ) ) )
& ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[43,33]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) )
<=> ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[50,45]) ).
tff(52,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(xm,xn))
| ~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ ( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ) ),
inference(unit_resolution,[status(thm)],[53,44,8,28]) ).
tff(55,plain,
( ~ ( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtpldt0(xm,xn),xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(sdtpldt0(xm,xn),xm)) != sdtpldt0(xm,xn) ) ) )
| ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) )
| sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(56,plain,
( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ sdtlseqdt0(xm,sdtpldt0(xm,xn))
<=> ~ sdtlseqdt0(xm,sdtpldt0(xm,xn)) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(59,plain,
~ sdtlseqdt0(xm,sdtpldt0(xm,xn)),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
( ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) )
| sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(61,plain,
( ~ ( sdtlseqdt0(xm,sdtpldt0(xm,xn))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) ),
inference(unit_resolution,[status(thm)],[61,56]) ).
tff(63,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ~ aNaturalNumber0(xn)
| $false )
<=> ~ aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ $true
<=> $false ),
inference(rewrite,[status(thm)],]) ).
tff(66,plain,
( ( sdtpldt0(xm,xn) = sdtpldt0(xm,xn) )
<=> $true ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) )
<=> ~ $true ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) )
<=> $false ),
inference(transitivity,[status(thm)],[67,65]) ).
tff(69,plain,
( ( ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) )
<=> ( ~ aNaturalNumber0(xn)
| $false ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) )
<=> ~ aNaturalNumber0(xn) ),
inference(transitivity,[status(thm)],[69,64]) ).
tff(71,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) ) ),
inference(transitivity,[status(thm)],[71,63]) ).
tff(73,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn)
| ( sdtpldt0(xm,xn) != sdtpldt0(xm,xn) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != sdtpldt0(xm,xn) ) )
| ~ aNaturalNumber0(xn) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
$false,
inference(unit_resolution,[status(thm)],[74,4,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM472+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.15/0.36 % Computer : n026.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Sep 2 11:05:53 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.36 Usage: tptp [options] [-file:]file
% 0.15/0.36 -h, -? prints this message.
% 0.15/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.36 -m, -model generate model.
% 0.15/0.36 -p, -proof generate proof.
% 0.15/0.36 -c, -core generate unsat core of named formulas.
% 0.15/0.36 -st, -statistics display statistics.
% 0.15/0.36 -t:timeout set timeout (in second).
% 0.15/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.36 -<param>:<value> configuration parameter and value.
% 0.15/0.36 -o:<output-file> file to place output in.
% 0.23/0.44 % SZS status Theorem
% 0.23/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------