%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM459+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:21:02 AM UTC 2025
% Result : Theorem 0.85s 1.02s
% Output : Proof 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 107
% Syntax : Number of formulae : 292 ( 71 unt; 0 typ; 0 def)
% Number of atoms : 2734 ( 976 equ)
% Maximal formula atoms : 32 ( 9 avg)
% Number of connectives : 4485 (2218 ~;1609 |; 279 &)
% ( 320 <=>; 59 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 175 ( 175 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 : 647 ( 576 !; 15 ?; 647 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xm_type,type,
xm: $i ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(1,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__745) ).
tff(3,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_AddZero) ).
tff(13,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtpldt0(W0,sz00) = W0 )
& ( W0 = sdtpldt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[16,6]) ).
tff(18,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
~ ( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) ) ),
inference(unit_resolution,[status(thm)],[20,17,4]) ).
tff(22,plain,
( ( sdtpldt0(xm,sz00) != xm )
| ( xm != sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sz00) = xm ) ),
inference(tautology,[status(thm)],[]) ).
tff(23,plain,
sdtpldt0(xm,sz00) = xm,
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
xm = sdtpldt0(xm,sz00),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[2]) ).
tff(27,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,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(29,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)],[28]) ).
tff(30,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(31,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)],[30]) ).
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(transitivity,[status(thm)],[31,29]) ).
tff(33,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(34,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)],[33]) ).
tff(35,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(36,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(37,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)],[36]) ).
tff(38,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(39,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)],[38,37]) ).
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)],[39,35]) ).
tff(41,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)],[40]) ).
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 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
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)],[42,32]) ).
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 ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ) ) )
<=> ( ~ ! [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(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) )
| ~ ( sdtlseqdt0(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,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(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) )
| ~ ( sdtlseqdt0(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) ) ) )
<=> ( ~ ! [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(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,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(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) )
| ~ ( sdtlseqdt0(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) ) ) )
<=> ( ~ ! [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(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,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(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) )
| ~ ( sdtlseqdt0(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,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(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ ( ~ ( sdtlseqdt0(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ) ),
inference(unit_resolution,[status(thm)],[49,43,4,27]) ).
tff(51,plain,
( ~ ( sdtlseqdt0(xn,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) )
| ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(52,plain,
( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
( sdtlseqdt0(xn,xm)
<=> sdtlseqdt0(xn,xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,plain,
( ~ ( ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) )
=> ( xm = xn ) )
<=> ~ ( ~ ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) )
| ( xm = xn ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
~ ( ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) )
=> ( xm = xn ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(56,plain,
~ ( ~ ( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) )
| ( xm = xn ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( sdtlseqdt0(xm,xn)
& sdtlseqdt0(xn,xm) ),
inference(or_elim,[status(thm)],[56]) ).
tff(58,plain,
sdtlseqdt0(xn,xm),
inference(and_elim,[status(thm)],[57]) ).
tff(59,plain,
sdtlseqdt0(xn,xm),
inference(modus_ponens,[status(thm)],[58,53]) ).
tff(60,plain,
( ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) )
| ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(61,plain,
( ~ ( ~ sdtlseqdt0(xn,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) ),
inference(unit_resolution,[status(thm)],[61,52]) ).
tff(63,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm )
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) = xm ) ),
inference(tautology,[status(thm)],[]) ).
tff(64,plain,
sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) = xm,
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,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(66,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(67,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(68,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)],[67]) ).
tff(69,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)],[68,66]) ).
tff(70,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)],[69]) ).
tff(71,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)],[70,65]) ).
tff(72,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(73,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)],[72,71]) ).
tff(74,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)],[73,43,4,27]) ).
tff(75,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(76,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)],[75,74]) ).
tff(77,plain,
( sdtlseqdt0(xm,xn)
<=> sdtlseqdt0(xm,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
sdtlseqdt0(xm,xn),
inference(and_elim,[status(thm)],[57]) ).
tff(79,plain,
sdtlseqdt0(xm,xn),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,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(81,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)],[80,79]) ).
tff(82,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ( sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) != xn ) ),
inference(unit_resolution,[status(thm)],[81,76]) ).
tff(83,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(84,plain,
sdtpldt0(xm,tptp_fun_W2_0(xn,xm)) = xn,
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xn,tptp_fun_W2_0(xm,xn)),
inference(monotonicity,[status(thm)],[84]) ).
tff(86,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm )
| aNaturalNumber0(tptp_fun_W2_0(xm,xn)) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
aNaturalNumber0(tptp_fun_W2_0(xm,xn)),
inference(unit_resolution,[status(thm)],[86,62]) ).
tff(88,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(89,plain,
aNaturalNumber0(tptp_fun_W2_0(xn,xm)),
inference(unit_resolution,[status(thm)],[88,82]) ).
tff(90,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(91,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)],[90]) ).
tff(92,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(93,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)],[92]) ).
tff(94,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(95,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(96,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)],[95]) ).
tff(97,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/sandbox2/benchmark/theBenchmark.p',mAddAsso) ).
tff(98,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)],[97,96]) ).
tff(99,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)],[98,94]) ).
tff(100,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)],[99]) ).
tff(101,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)],[100,93]) ).
tff(102,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)],[101,91]) ).
tff(103,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(xm,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,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(xm,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,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(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,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(xm,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) ) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,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(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,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(xm,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) ) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,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(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ~ aNaturalNumber0(tptp_fun_W2_0(xn,xm))
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,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(xm,xn))
| ( sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))),
inference(unit_resolution,[status(thm)],[108,102,4,89,87]) ).
tff(110,plain,
sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))) = sdtpldt0(sdtpldt0(xm,tptp_fun_W2_0(xn,xm)),tptp_fun_W2_0(xm,xn)),
inference(symmetry,[status(thm)],[109]) ).
tff(111,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(112,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)],[111]) ).
tff(113,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(114,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)],[113]) ).
tff(115,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)],[114,112]) ).
tff(116,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(117,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)],[116]) ).
tff(118,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(119,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(120,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)],[119]) ).
tff(121,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/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
tff(122,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)],[121,120]) ).
tff(123,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)],[122,118]) ).
tff(124,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)],[123]) ).
tff(125,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)],[124,117]) ).
tff(126,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)],[125,115]) ).
tff(127,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(xn,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,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(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,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)
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,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(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) ) ) ),
inference(monotonicity,[status(thm)],[128]) ).
tff(130,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)
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,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(xm)
| ~ aNaturalNumber0(xn)
| ~ sdtlseqdt0(xn,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) ) ) ),
inference(transitivity,[status(thm)],[129,127]) ).
tff(131,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)
| ~ sdtlseqdt0(xn,xm)
| ~ aNaturalNumber0(xn)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(132,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(xn,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) ) ),
inference(modus_ponens,[status(thm)],[131,130]) ).
tff(133,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) ),
inference(unit_resolution,[status(thm)],[132,126,4,27,59]) ).
tff(134,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) )
<=> ( tptp_fun_W2_0(xm,xn) = sdtmndt0(xm,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) )
<=> ( tptp_fun_W2_0(xm,xn) = sdtmndt0(xm,xn) ) ),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) )
<=> ( tptp_fun_W2_0(xm,xn) = sdtmndt0(xm,xn) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm )
| ( tptp_fun_W2_0(xm,xn) = sdtmndt0(xm,xn) ) ),
inference(tautology,[status(thm)],[]) ).
tff(137,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(xm,xn)) != xm ) )
<=> ( tptp_fun_W2_0(xm,xn) = sdtmndt0(xm,xn) ) )
| ( tptp_fun_W2_0(xm,xn) = sdtmndt0(xm,xn) ) ),
inference(unit_resolution,[status(thm)],[136,62]) ).
tff(138,plain,
tptp_fun_W2_0(xm,xn) = sdtmndt0(xm,xn),
inference(unit_resolution,[status(thm)],[137,135]) ).
tff(139,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(140,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(141,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)],[140]) ).
tff(142,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)],[141,139]) ).
tff(143,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(144,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)],[143,142]) ).
tff(145,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xm,W2) != xn ) )
<=> ( W2 = sdtmndt0(xn,xm) ) ),
inference(unit_resolution,[status(thm)],[144,126,4,27,79]) ).
tff(146,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(147,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)],[146,145]) ).
tff(148,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(149,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)],[148,82]) ).
tff(150,plain,
tptp_fun_W2_0(xn,xm) = sdtmndt0(xn,xm),
inference(unit_resolution,[status(thm)],[149,147]) ).
tff(151,plain,
sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)),
inference(monotonicity,[status(thm)],[150,138]) ).
tff(152,plain,
sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn)),
inference(symmetry,[status(thm)],[151]) ).
tff(153,plain,
sdtmndt0(xm,xn) = tptp_fun_W2_0(xm,xn),
inference(symmetry,[status(thm)],[138]) ).
tff(154,plain,
( aNaturalNumber0(sdtmndt0(xm,xn))
<=> aNaturalNumber0(tptp_fun_W2_0(xm,xn)) ),
inference(monotonicity,[status(thm)],[153]) ).
tff(155,plain,
( aNaturalNumber0(tptp_fun_W2_0(xm,xn))
<=> aNaturalNumber0(sdtmndt0(xm,xn)) ),
inference(symmetry,[status(thm)],[154]) ).
tff(156,plain,
aNaturalNumber0(sdtmndt0(xm,xn)),
inference(modus_ponens,[status(thm)],[87,155]) ).
tff(157,plain,
sdtmndt0(xn,xm) = tptp_fun_W2_0(xn,xm),
inference(symmetry,[status(thm)],[150]) ).
tff(158,plain,
( aNaturalNumber0(sdtmndt0(xn,xm))
<=> aNaturalNumber0(tptp_fun_W2_0(xn,xm)) ),
inference(monotonicity,[status(thm)],[157]) ).
tff(159,plain,
( aNaturalNumber0(tptp_fun_W2_0(xn,xm))
<=> aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
aNaturalNumber0(sdtmndt0(xn,xm)),
inference(modus_ponens,[status(thm)],[89,159]) ).
tff(161,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,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(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(164,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddComm) ).
tff(169,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[169,165]) ).
tff(171,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[170]) ).
tff(172,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[171,164]) ).
tff(173,plain,
! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[172,162]) ).
tff(174,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
( ( ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) )
<=> ( ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) ) ) ),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) ) ) ),
inference(transitivity,[status(thm)],[176,174]) ).
tff(178,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtpldt0(W0,W1) = sdtpldt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) ) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
( ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) ) ),
inference(unit_resolution,[status(thm)],[179,173]) ).
tff(181,plain,
sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)),
inference(unit_resolution,[status(thm)],[180,160,156]) ).
tff(182,plain,
sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) = sdtpldt0(sdtmndt0(xn,xm),sdtmndt0(xm,xn)),
inference(symmetry,[status(thm)],[181]) ).
tff(183,plain,
sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) = sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),
inference(monotonicity,[status(thm)],[153,157]) ).
tff(184,plain,
sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn)),
inference(transitivity,[status(thm)],[184,182,152]) ).
tff(186,plain,
sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xn,xm),tptp_fun_W2_0(xm,xn))),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00),
inference(transitivity,[status(thm)],[186,110,85,64,24]) ).
tff(188,plain,
( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) != sdtpldt0(xm,sz00) ) ),
inference(tautology,[status(thm)],[]) ).
tff(189,plain,
( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ),
inference(unit_resolution,[status(thm)],[188,187]) ).
tff(190,plain,
( ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) = sz00 )
<=> ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 ) ),
inference(monotonicity,[status(thm)],[183]) ).
tff(191,plain,
( ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
<=> ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) != sz00 ) ),
inference(monotonicity,[status(thm)],[190]) ).
tff(192,plain,
( ( sdtmndt0(xm,xn) = sz00 )
<=> ( sz00 = sdtmndt0(xm,xn) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(193,plain,
( ( sz00 = sdtmndt0(xm,xn) )
<=> ( sdtmndt0(xm,xn) = sz00 ) ),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
( ( sz00 != sdtmndt0(xm,xn) )
<=> ( sdtmndt0(xm,xn) != sz00 ) ),
inference(monotonicity,[status(thm)],[193]) ).
tff(195,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,xn) ) )
| ~ ( ( ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xn,sz00) != xm ) )
<=> ( sz00 = sdtmndt0(xm,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(196,plain,
~ ( ( ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xn,sz00) != xm ) )
<=> ( sz00 = sdtmndt0(xm,xn) ) ),
inference(unit_resolution,[status(thm)],[195,133]) ).
tff(197,plain,
( ( xn = xm )
<=> ( xm = xn ) ),
inference(commutativity,[status(thm)],[]) ).
tff(198,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtpldt0(xn,sz00) != xn )
| ( xn != sdtpldt0(sz00,xn) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtpldt0(xn,sz00) != xn )
| ( xn != sdtpldt0(sz00,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtpldt0(xn,sz00) != xn )
| ( xn != sdtpldt0(sz00,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(200,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W0,sz00) != W0 )
| ( W0 != sdtpldt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtpldt0(xn,sz00) != xn )
| ( xn != sdtpldt0(sz00,xn) ) ) ),
inference(modus_ponens,[status(thm)],[199,198]) ).
tff(201,plain,
~ ( ( sdtpldt0(xn,sz00) != xn )
| ( xn != sdtpldt0(sz00,xn) ) ),
inference(unit_resolution,[status(thm)],[200,17,27]) ).
tff(202,plain,
( ( sdtpldt0(xn,sz00) != xn )
| ( xn != sdtpldt0(sz00,xn) )
| ( sdtpldt0(xn,sz00) = xn ) ),
inference(tautology,[status(thm)],[]) ).
tff(203,plain,
sdtpldt0(xn,sz00) = xn,
inference(unit_resolution,[status(thm)],[202,201]) ).
tff(204,plain,
( ( sdtpldt0(xn,sz00) = xm )
<=> ( xn = xm ) ),
inference(monotonicity,[status(thm)],[203]) ).
tff(205,plain,
( ( sdtpldt0(xn,sz00) = xm )
<=> ( xm = xn ) ),
inference(transitivity,[status(thm)],[204,197]) ).
tff(206,plain,
( ( xm = xn )
<=> ( sdtpldt0(xn,sz00) = xm ) ),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ( xm != xn )
<=> ( sdtpldt0(xn,sz00) != xm ) ),
inference(monotonicity,[status(thm)],[206]) ).
tff(208,plain,
( ( xm != xn )
<=> ( xm != xn ) ),
inference(rewrite,[status(thm)],[]) ).
tff(209,plain,
xm != xn,
inference(or_elim,[status(thm)],[56]) ).
tff(210,plain,
xm != xn,
inference(modus_ponens,[status(thm)],[209,208]) ).
tff(211,plain,
sdtpldt0(xn,sz00) != xm,
inference(modus_ponens,[status(thm)],[210,207]) ).
tff(212,plain,
( ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xn,sz00) != xm )
| ( sdtpldt0(xn,sz00) = xm ) ),
inference(tautology,[status(thm)],[]) ).
tff(213,plain,
( ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xn,sz00) != xm ) ),
inference(unit_resolution,[status(thm)],[212,211]) ).
tff(214,plain,
( ( ( ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xn,sz00) != xm ) )
<=> ( sz00 = sdtmndt0(xm,xn) ) )
| ~ ( ~ aNaturalNumber0(sz00)
| ( sdtpldt0(xn,sz00) != xm ) )
| ( sz00 != sdtmndt0(xm,xn) ) ),
inference(tautology,[status(thm)],[]) ).
tff(215,plain,
sz00 != sdtmndt0(xm,xn),
inference(unit_resolution,[status(thm)],[214,213,196]) ).
tff(216,plain,
sdtmndt0(xm,xn) != sz00,
inference(modus_ponens,[status(thm)],[215,194]) ).
tff(217,plain,
( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 )
| ( sdtmndt0(xm,xn) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(218,plain,
( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ),
inference(unit_resolution,[status(thm)],[217,216]) ).
tff(219,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(220,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[219]) ).
tff(221,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
<=> ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )),
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) ) )),
( ( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) )
<=> ( ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtpldt0(W0,W1) != sz00 ) ) )),
rewrite(( ( ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtpldt0(W0,W1) != sz00 ) )
<=> ( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) ) )),
( ( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) )
<=> ( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(222,plain,
( ! [W0: $i,W1: $i] :
( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[221]) ).
tff(223,plain,
( ! [W0: $i,W1: $i] :
( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) )
<=> ! [W0: $i,W1: $i] :
( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(224,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( sdtpldt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) )
<=> ( ( sdtpldt0(W0,W1) != sz00 )
| ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) != sz00 )
| ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) != sz00 )
| ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) )
<=> ( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) )
<=> ( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) ) )),
inference(bind,[status(th)],[]) ).
tff(225,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) ) ),
inference(quant_intro,[status(thm)],[224]) ).
tff(226,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( sdtpldt0(W0,W1) = sz00 )
=> ( ( W0 = sz00 )
& ( W1 = sz00 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroAdd) ).
tff(227,plain,
! [W0: $i,W1: $i] :
( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) ),
inference(modus_ponens,[status(thm)],[226,225]) ).
tff(228,plain,
! [W0: $i,W1: $i] :
( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) ),
inference(modus_ponens,[status(thm)],[227,223]) ).
tff(229,plain,
! [W0: $i,W1: $i] :
( ( ( W0 = sz00 )
& ( W1 = sz00 ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtpldt0(W0,W1) != sz00 ) ),
inference(skolemize,[status(sab)],[228]) ).
tff(230,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[229,222]) ).
tff(231,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[230,220]) ).
tff(232,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(233,plain,
( ( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) )
<=> ( ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(234,plain,
( ~ ( ( sdtmndt0(xn,xm) != sz00 )
| ( sdtmndt0(xm,xn) != sz00 ) )
<=> ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(235,plain,
( ( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ ( ( sdtmndt0(xn,xm) != sz00 )
| ( sdtmndt0(xm,xn) != sz00 ) ) )
<=> ( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ) ),
inference(monotonicity,[status(thm)],[234]) ).
tff(236,plain,
( ( ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ ( ( sdtmndt0(xn,xm) != sz00 )
| ( sdtmndt0(xm,xn) != sz00 ) ) )
<=> ( ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ) ),
inference(transitivity,[status(thm)],[235,233]) ).
tff(237,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ ( ( sdtmndt0(xn,xm) != sz00 )
| ( sdtmndt0(xm,xn) != sz00 ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ) ),
inference(monotonicity,[status(thm)],[236]) ).
tff(238,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ ( ( sdtmndt0(xn,xm) != sz00 )
| ( sdtmndt0(xm,xn) != sz00 ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ) ),
inference(transitivity,[status(thm)],[237,232]) ).
tff(239,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ ( ( sdtmndt0(xn,xm) != sz00 )
| ( sdtmndt0(xm,xn) != sz00 ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ( sdtpldt0(W0,W1) != sz00 )
| ~ aNaturalNumber0(W0)
| ~ ( ( W1 != sz00 )
| ( W0 != sz00 ) ) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[239,238]) ).
tff(241,plain,
( ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ( sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00 )
| ~ ( ( sdtmndt0(xm,xn) != sz00 )
| ( sdtmndt0(xn,xm) != sz00 ) ) ),
inference(unit_resolution,[status(thm)],[240,231]) ).
tff(242,plain,
sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)) != sz00,
inference(unit_resolution,[status(thm)],[241,160,156,218]) ).
tff(243,plain,
sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) != sz00,
inference(modus_ponens,[status(thm)],[242,191]) ).
tff(244,plain,
( aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)))
<=> aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) ),
inference(monotonicity,[status(thm)],[183]) ).
tff(245,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(246,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)],[245]) ).
tff(247,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(248,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)],[247]) ).
tff(249,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(250,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(251,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)],[250]) ).
tff(252,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsB) ).
tff(253,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[252,251]) ).
tff(254,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[253,249]) ).
tff(255,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[254]) ).
tff(256,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[255,248]) ).
tff(257,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[256,246]) ).
tff(258,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(259,plain,
( ( aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ~ aNaturalNumber0(sdtmndt0(xm,xn)) )
<=> ( ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(260,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ~ aNaturalNumber0(sdtmndt0(xm,xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ) ),
inference(monotonicity,[status(thm)],[259]) ).
tff(261,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ~ aNaturalNumber0(sdtmndt0(xm,xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ) ),
inference(transitivity,[status(thm)],[260,258]) ).
tff(262,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm)))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| ~ aNaturalNumber0(sdtmndt0(xm,xn)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(263,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtpldt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ),
inference(modus_ponens,[status(thm)],[262,261]) ).
tff(264,plain,
( ~ aNaturalNumber0(sdtmndt0(xm,xn))
| ~ aNaturalNumber0(sdtmndt0(xn,xm))
| aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))) ),
inference(unit_resolution,[status(thm)],[263,257]) ).
tff(265,plain,
aNaturalNumber0(sdtpldt0(sdtmndt0(xm,xn),sdtmndt0(xn,xm))),
inference(unit_resolution,[status(thm)],[264,160,156]) ).
tff(266,plain,
aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))),
inference(modus_ponens,[status(thm)],[265,244]) ).
tff(267,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(268,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[267]) ).
tff(269,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) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) )),
rewrite(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(270,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[269]) ).
tff(271,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(272,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) ) )),
trans(monotonicity(rewrite(( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
<=> ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) )),
( ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
=> ( W1 = W2 ) ) )),
rewrite(( ( ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ( W1 = W2 ) ) )),
( ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ( W1 = W2 ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ( W1 = W2 ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(273,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ) ),
inference(quant_intro,[status(thm)],[272]) ).
tff(274,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) )
| ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) ) )
=> ( W1 = W2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mAddCanc) ).
tff(275,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ),
inference(modus_ponens,[status(thm)],[274,273]) ).
tff(276,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ),
inference(modus_ponens,[status(thm)],[275,271]) ).
tff(277,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) ) ),
inference(skolemize,[status(sab)],[276]) ).
tff(278,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[277,270]) ).
tff(279,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[278,268]) ).
tff(280,plain,
( aNaturalNumber0(sz00)
<=> aNaturalNumber0(sz00) ),
inference(rewrite,[status(thm)],[]) ).
tff(281,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC) ).
tff(282,plain,
aNaturalNumber0(sz00),
inference(modus_ponens,[status(thm)],[281,280]) ).
tff(283,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(284,plain,
( ( ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(285,plain,
( ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) )
<=> ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(286,plain,
( ( ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ~ aNaturalNumber0(xm) )
<=> ( ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ~ aNaturalNumber0(xm) ) ),
inference(monotonicity,[status(thm)],[285]) ).
tff(287,plain,
( ( ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ) ) ),
inference(transitivity,[status(thm)],[286,284]) ).
tff(288,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ) ) ),
inference(monotonicity,[status(thm)],[287]) ).
tff(289,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ) ) ),
inference(transitivity,[status(thm)],[288,283]) ).
tff(290,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) )
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(291,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtpldt0(W1,W0) = sdtpldt0(W2,W0) )
| ( sdtpldt0(W0,W1) = sdtpldt0(W0,W2) ) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)))
| ( sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)) = sz00 )
| ~ ( ( sdtpldt0(sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm)),xm) = sdtpldt0(sz00,xm) )
| ( sdtpldt0(xm,sdtpldt0(tptp_fun_W2_0(xm,xn),tptp_fun_W2_0(xn,xm))) = sdtpldt0(xm,sz00) ) ) ),
inference(modus_ponens,[status(thm)],[290,289]) ).
tff(292,plain,
$false,
inference(unit_resolution,[status(thm)],[291,282,279,4,266,243,189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM459+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:13:09 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.85/1.02 % SZS status Theorem
% 0.85/1.02 % SZS output start Proof
% See solution above
% 0.85/1.05 % E exiting
%------------------------------------------------------------------------------