%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM460+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 : Sat Jun 21 05:21:03 AM UTC 2025
% Result : Theorem 0.72s 0.91s
% Output : Proof 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 68
% Syntax : Number of formulae : 185 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 1892 ( 497 equ)
% Maximal formula atoms : 32 ( 10 avg)
% Number of connectives : 3352 (1750 ~;1172 |; 169 &)
% ( 233 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 105 ( 105 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 485 ( 438 !; 15 ?; 485 :)
% Comments :
%------------------------------------------------------------------------------
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xl_type,type,
xl: $i ).
tff(xm_type,type,
xm: $i ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(1,plain,
( sdtlseqdt0(xn,xl)
<=> sdtlseqdt0(xn,xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xl) )
=> sdtlseqdt0(xm,xl) )
<=> ~ ( ~ ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xl) )
| sdtlseqdt0(xm,xl) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xl) )
=> sdtlseqdt0(xm,xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ~ ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xl) )
| sdtlseqdt0(xm,xl) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xl) ),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
sdtlseqdt0(xn,xl),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
sdtlseqdt0(xn,xl),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
( aNaturalNumber0(xl)
<=> aNaturalNumber0(xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn)
& aNaturalNumber0(xl) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__773) ).
tff(10,plain,
aNaturalNumber0(xl),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aNaturalNumber0(xl),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
inference(and_elim,[status(thm)],[9]) ).
tff(14,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[14,12]) ).
tff(16,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
trans(trans(monotonicity(rewrite(( ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) )),
rewrite(( ( ( W2 = sdtmndt0(W1,W0) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
rewrite(( ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
( ( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
<=> ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )),
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) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(( ( ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
( ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ~ sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(27,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[30,20]) ).
tff(32,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
( ( ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) ) ),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) ) ),
inference(transitivity,[status(thm)],[34,32]) ).
tff(36,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xl)
| ~ sdtlseqdt0(xn,xl)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) ),
inference(unit_resolution,[status(thm)],[37,31,15,11,7]) ).
tff(39,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) )
<=> ( W2 = sdtmndt0(xl,xn) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) )
<=> ( tptp_fun_W2_0(xl,xn) = sdtmndt0(xl,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(40,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) )
<=> ( tptp_fun_W2_0(xl,xn) = sdtmndt0(xl,xn) ) ),
inference(unit_resolution,[status(thm)],[39,38]) ).
tff(41,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(42,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)],[41]) ).
tff(43,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(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 ) ) ) ) )
<=> ! [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)],[43]) ).
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 ) ) ) ) )
<=> ! [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)],[44,42]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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(49,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(50,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)],[49]) ).
tff(51,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
tff(52,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)],[51,50]) ).
tff(53,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)],[52,48]) ).
tff(54,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)],[53]) ).
tff(55,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)],[54,47]) ).
tff(56,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)],[55,45]) ).
tff(57,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(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ) ) )
<=> ( ~ ! [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(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) )
| ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,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(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) )
| ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) ) ) )
<=> ( ~ ! [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(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,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(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) )
| ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) ) ) )
<=> ( ~ ! [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(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ) ) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,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(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) )
| ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,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(xl)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ ( ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ) ),
inference(unit_resolution,[status(thm)],[62,56,15,11]) ).
tff(64,plain,
( ~ ( sdtlseqdt0(xn,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) )
| ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(65,plain,
( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) )
| ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(67,plain,
( ~ ( ~ sdtlseqdt0(xn,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ) ),
inference(unit_resolution,[status(thm)],[66,7]) ).
tff(68,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) ),
inference(unit_resolution,[status(thm)],[67,65]) ).
tff(69,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) )
<=> ( tptp_fun_W2_0(xl,xn) = sdtmndt0(xl,xn) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl )
| ( tptp_fun_W2_0(xl,xn) = sdtmndt0(xl,xn) ) ),
inference(tautology,[status(thm)],[]) ).
tff(70,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl ) )
<=> ( tptp_fun_W2_0(xl,xn) = sdtmndt0(xl,xn) ) )
| ( tptp_fun_W2_0(xl,xn) = sdtmndt0(xl,xn) ) ),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
tptp_fun_W2_0(xl,xn) = sdtmndt0(xl,xn),
inference(unit_resolution,[status(thm)],[70,40]) ).
tff(72,plain,
sdtmndt0(xl,xn) = tptp_fun_W2_0(xl,xn),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( sdtlseqdt0(xm,xn)
<=> sdtlseqdt0(xm,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
sdtlseqdt0(xm,xn),
inference(and_elim,[status(thm)],[5]) ).
tff(75,plain,
sdtlseqdt0(xm,xn),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[13]) ).
tff(78,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ~ aNaturalNumber0(xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xm,xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ),
inference(unit_resolution,[status(thm)],[84,31,78,15,75]) ).
tff(86,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) )
<=> ( tptp_fun_W2_0(xn,xm) = sdtmndt0(xn,xm) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) )
<=> ( tptp_fun_W2_0(xn,xm) = sdtmndt0(xn,xm) ) ),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,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(xn)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,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(xn)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ~ ( ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) ) )
<=> ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) ) ),
inference(transitivity,[status(thm)],[91,89]) ).
tff(93,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(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != 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(xn)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,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(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != 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(xn)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) ) ),
inference(transitivity,[status(thm)],[93,88]) ).
tff(95,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(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,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(xn)
| ~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
~ ( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ) ),
inference(unit_resolution,[status(thm)],[96,56,78,15]) ).
tff(98,plain,
( ~ ( sdtlseqdt0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) ) )
| ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(99,plain,
( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(101,plain,
( ~ ( ~ sdtlseqdt0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ) ),
inference(unit_resolution,[status(thm)],[100,75]) ).
tff(102,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ),
inference(unit_resolution,[status(thm)],[101,99]) ).
tff(103,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) )
<=> ( tptp_fun_W2_0(xn,xm) = sdtmndt0(xn,xm) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn )
| ( tptp_fun_W2_0(xn,xm) = sdtmndt0(xn,xm) ) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) )
<=> ( tptp_fun_W2_0(xn,xm) = sdtmndt0(xn,xm) ) )
| ( tptp_fun_W2_0(xn,xm) = sdtmndt0(xn,xm) ) ),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
tptp_fun_W2_0(xn,xm) = sdtmndt0(xn,xm),
inference(unit_resolution,[status(thm)],[104,87]) ).
tff(106,plain,
sdtmndt0(xn,xm) = tptp_fun_W2_0(xn,xm),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)) = sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn)),
inference(monotonicity,[status(thm)],[106,72]) ).
tff(108,plain,
( aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
<=> aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn)))
<=> aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))) ),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn)))
<=> ~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl )
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) = xl ) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) = xl,
inference(unit_resolution,[status(thm)],[111,68]) ).
tff(113,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn )
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) = xn ) ),
inference(tautology,[status(thm)],[]) ).
tff(114,plain,
sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) = xn,
inference(unit_resolution,[status(thm)],[113,102]) ).
tff(115,plain,
sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xn,tptp_fun_W2_0(xl,xn)),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xl,xn)) != xl )
| aNaturalNumber0(tptp_fun_W2_0(xl,xn)) ),
inference(tautology,[status(thm)],[]) ).
tff(117,plain,
aNaturalNumber0(tptp_fun_W2_0(xl,xn)),
inference(unit_resolution,[status(thm)],[116,68]) ).
tff(118,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn )
| aNaturalNumber0(tptp_fun_W2_0(xn,xm)) ),
inference(tautology,[status(thm)],[]) ).
tff(119,plain,
aNaturalNumber0(tptp_fun_W2_0(xn,xm)),
inference(unit_resolution,[status(thm)],[118,102]) ).
tff(120,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(121,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[120]) ).
tff(122,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(123,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(126,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
tff(128,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(modus_ponens,[status(thm)],[128,124]) ).
tff(130,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) ) ),
inference(skolemize,[status(sab)],[129]) ).
tff(131,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[130,123]) ).
tff(132,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[131,121]) ).
tff(133,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ( ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) ) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) ) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdtpldt0(sdtpldt0(W0,W1),W2) = sdtpldt0(W0,sdtpldt0(W1,W2)) )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_0(xl,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))),
inference(unit_resolution,[status(thm)],[138,132,78,119,117]) ).
tff(140,plain,
sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) = sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xl,xn)),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) = xl,
inference(transitivity,[status(thm)],[140,115,112]) ).
tff(142,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(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) ) ) )
<=> ( ~ ! [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(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) )
| ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) ) ) )
<=> ( ~ aNaturalNumber0(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,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(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) )
| ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) ) ) )
<=> ( ~ ! [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(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[143]) ).
tff(145,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(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) )
| ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) ) ) )
<=> ( ~ ! [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(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) ) ) ) ),
inference(transitivity,[status(thm)],[144,142]) ).
tff(146,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(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) )
| ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(147,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(xl)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) ) ) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
~ ( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) ) ),
inference(unit_resolution,[status(thm)],[147,56,78,11]) ).
tff(149,plain,
( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ~ ( ~ sdtlseqdt0(xm,xl)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xl,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xl,xm)) != xl ) ) )
| sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(150,plain,
( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) ),
inference(unit_resolution,[status(thm)],[149,148]) ).
tff(151,plain,
( ~ sdtlseqdt0(xm,xl)
<=> ~ sdtlseqdt0(xm,xl) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
~ sdtlseqdt0(xm,xl),
inference(or_elim,[status(thm)],[4]) ).
tff(153,plain,
~ sdtlseqdt0(xm,xl),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(155,plain,
( ~ ( sdtlseqdt0(xm,xl)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ) ),
inference(unit_resolution,[status(thm)],[154,153]) ).
tff(156,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) ),
inference(unit_resolution,[status(thm)],[155,150]) ).
tff(157,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn)))
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) != xl ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn)))
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) != xl ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(158,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn)))
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) != xl ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(159,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xl ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn)))
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))) != xl ) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xl,xn))),
inference(unit_resolution,[status(thm)],[159,156,141]) ).
tff(161,plain,
~ aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn))),
inference(modus_ponens,[status(thm)],[160,110]) ).
tff(162,plain,
( aNaturalNumber0(sdtmndt0(xl,xn))
<=> aNaturalNumber0(tptp_fun_W2_0(xl,xn)) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(163,plain,
( aNaturalNumber0(tptp_fun_W2_0(xl,xn))
<=> aNaturalNumber0(sdtmndt0(xl,xn)) ),
inference(symmetry,[status(thm)],[162]) ).
tff(164,plain,
aNaturalNumber0(sdtmndt0(xl,xn)),
inference(modus_ponens,[status(thm)],[117,163]) ).
tff(165,plain,
( aNaturalNumber0(sdtmndt0(xn,xm))
<=> aNaturalNumber0(tptp_fun_W2_0(xn,xm)) ),
inference(monotonicity,[status(thm)],[106]) ).
tff(166,plain,
( aNaturalNumber0(tptp_fun_W2_0(xn,xm))
<=> aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(symmetry,[status(thm)],[165]) ).
tff(167,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(modus_ponens,[status(thm)],[119,166]) ).
tff(168,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(169,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)],[168]) ).
tff(170,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(171,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)],[170]) ).
tff(172,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(173,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(174,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)],[173]) ).
tff(175,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(176,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[176,172]) ).
tff(178,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[177]) ).
tff(179,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[178,171]) ).
tff(180,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[179,169]) ).
tff(181,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(182,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(183,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(modus_ponens,[status(thm)],[182,181]) ).
tff(184,plain,
( aNaturalNumber0(sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xl,xn)))
| ~ aNaturalNumber0(sdtmndt0(xl,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(unit_resolution,[status(thm)],[183,180]) ).
tff(185,plain,
$false,
inference(unit_resolution,[status(thm)],[184,167,164,161]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM460+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n011.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 01:13:11 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.72/0.91 % SZS status Theorem
% 0.72/0.91 % SZS output start Proof
% See solution above
% 0.77/0.94 % E exiting
%------------------------------------------------------------------------------