%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM465+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:21:04 AM UTC 2025
% Result : Theorem 0.38s 0.54s
% Output : Proof 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 80
% Syntax : Number of formulae : 207 ( 49 unt; 0 typ; 0 def)
% Number of atoms : 1975 ( 583 equ)
% Maximal formula atoms : 32 ( 9 avg)
% Number of connectives : 3384 (1741 ~;1167 |; 209 &)
% ( 231 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 125 ( 125 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 506 ( 450 !; 15 ?; 506 :)
% Comments :
%------------------------------------------------------------------------------
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(sz10_type,type,
sz10: $i ).
tff(xm_type,type,
xm: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( ( xm != sz00 )
<=> ( xm != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ( xm != sz00 )
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) )
<=> ~ ( ( xm = sz00 )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ( xm != sz00 )
=> sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ( xm = sz00 )
| sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
xm != sz00,
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
xm != sz00,
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ( ( xm = sz00 )
| sdtlseqdt0(sz10,xm) )
<=> ( ( xm = sz00 )
| sdtlseqdt0(sz10,xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
( ( ( xm != sz00 )
=> sdtlseqdt0(sz10,xm) )
<=> ( ( xm = sz00 )
| sdtlseqdt0(sz10,xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
( ( xm != sz00 )
=> sdtlseqdt0(sz10,xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1007) ).
tff(10,plain,
( ( xm = sz00 )
| sdtlseqdt0(sz10,xm) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
( ( xm = sz00 )
| sdtlseqdt0(sz10,xm) ),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,plain,
sdtlseqdt0(sz10,xm),
inference(unit_resolution,[status(thm)],[11,6]) ).
tff(13,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__987) ).
tff(15,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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(20,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,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)],[20,18]) ).
tff(22,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(23,plain,
( ! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,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(25,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(26,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)],[25]) ).
tff(27,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiff) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( ! [W2: $i] :
( ( W2 = sdtmndt0(W1,W0) )
<=> ( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) )
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,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)],[29]) ).
tff(31,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) ),
inference(modus_ponens,[status(thm)],[31,21]) ).
tff(33,plain,
( aNaturalNumber0(sz10)
<=> aNaturalNumber0(sz10) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
tff(35,plain,
aNaturalNumber0(sz10),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
aNaturalNumber0(sz10),
inference(modus_ponens,[status(thm)],[35,33]) ).
tff(37,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ aNaturalNumber0(W0)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) )
<=> ( W2 = sdtmndt0(W1,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) )
<=> ( ~ ! [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(sz10)
| ~ sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( ~ aNaturalNumber0(xm)
| ~ sdtlseqdt0(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,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(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) )
<=> ( ~ ! [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(sz10)
| ~ sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,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(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) )
<=> ( ~ ! [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(sz10)
| ~ sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,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(sz10,xm)
| ~ aNaturalNumber0(sz10)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,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(sz10)
| ~ sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) ),
inference(unit_resolution,[status(thm)],[42,36,32,16,12]) ).
tff(44,plain,
( ~ ! [W2: $i] :
~ ( ( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) )
<=> ( W2 = sdtmndt0(xm,sz10) ) )
| ~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) )
<=> ( tptp_fun_W2_0(xm,sz10) = sdtmndt0(xm,sz10) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
~ ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) )
<=> ( tptp_fun_W2_0(xm,sz10) = sdtmndt0(xm,sz10) ) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,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(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 ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
^ [W0: $i,W1: $i] :
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(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 ) ) ) ) )
<=> ! [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)],[48]) ).
tff(50,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
<=> ! [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)],[49,47]) ).
tff(51,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(52,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)],[51]) ).
tff(53,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(54,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(55,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)],[54]) ).
tff(56,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtlseqdt0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( sdtpldt0(W0,W2) = W1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefLE) ).
tff(57,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)],[56,55]) ).
tff(58,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)],[57,53]) ).
tff(59,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)],[58]) ).
tff(60,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[60,50]) ).
tff(62,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ sdtlseqdt0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(W1,W0))
| ( sdtpldt0(W0,tptp_fun_W2_0(W1,W0)) != W1 ) ) )
| ~ ( sdtlseqdt0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(W0,W2) != W1 ) ) ) ) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != 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(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ~ ( ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) ) )
<=> ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,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(sz10)
| ~ ( ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,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(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,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(sz10)
| ~ ( ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,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(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) ) ),
inference(transitivity,[status(thm)],[67,62]) ).
tff(69,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(sz10)
| ~ ( ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
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(xm)
| ~ aNaturalNumber0(sz10)
| ~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ ( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ) ),
inference(unit_resolution,[status(thm)],[70,36,61,16]) ).
tff(72,plain,
( ~ ( sdtlseqdt0(sz10,xm)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(sz10,W2) != xm ) ) )
| ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(75,plain,
( ~ ( ~ sdtlseqdt0(sz10,xm)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ) ),
inference(unit_resolution,[status(thm)],[74,12]) ).
tff(76,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) ),
inference(unit_resolution,[status(thm)],[75,73]) ).
tff(77,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) )
<=> ( tptp_fun_W2_0(xm,sz10) = sdtmndt0(xm,sz10) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm )
| ( tptp_fun_W2_0(xm,sz10) = sdtmndt0(xm,sz10) ) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
( ( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm ) )
<=> ( tptp_fun_W2_0(xm,sz10) = sdtmndt0(xm,sz10) ) )
| ( tptp_fun_W2_0(xm,sz10) = sdtmndt0(xm,sz10) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
tptp_fun_W2_0(xm,sz10) = sdtmndt0(xm,sz10),
inference(unit_resolution,[status(thm)],[78,45]) ).
tff(80,plain,
sdtmndt0(xm,sz10) = tptp_fun_W2_0(xm,sz10),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
sdtasdt0(sdtmndt0(xm,sz10),xn) = sdtasdt0(tptp_fun_W2_0(xm,sz10),xn),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn))
<=> aNaturalNumber0(sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( aNaturalNumber0(sdtmndt0(xm,sz10))
<=> aNaturalNumber0(tptp_fun_W2_0(xm,sz10)) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(84,plain,
( aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
<=> aNaturalNumber0(sdtmndt0(xm,sz10)) ),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm )
| aNaturalNumber0(tptp_fun_W2_0(xm,sz10)) ),
inference(tautology,[status(thm)],[]) ).
tff(86,plain,
aNaturalNumber0(tptp_fun_W2_0(xm,sz10)),
inference(unit_resolution,[status(thm)],[85,76]) ).
tff(87,plain,
aNaturalNumber0(sdtmndt0(xm,sz10)),
inference(modus_ponens,[status(thm)],[86,84]) ).
tff(88,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[14]) ).
tff(90,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
^ [W0: $i,W1: $i] :
refl(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,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(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(94,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> aNaturalNumber0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(99,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[102,92]) ).
tff(104,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10))
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10))
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,plain,
( ( aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10)) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10))
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10))
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn)) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10))
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn)) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn))
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtmndt0(xm,sz10))
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn)) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
( ~ aNaturalNumber0(sdtmndt0(xm,sz10))
| aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn)) ),
inference(unit_resolution,[status(thm)],[109,103,90]) ).
tff(111,plain,
aNaturalNumber0(sdtasdt0(sdtmndt0(xm,sz10),xn)),
inference(unit_resolution,[status(thm)],[110,87]) ).
tff(112,plain,
aNaturalNumber0(sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)),
inference(modus_ponens,[status(thm)],[111,82]) ).
tff(113,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(114,plain,
( ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,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) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(121,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[124,114]) ).
tff(126,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ( ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ) ),
inference(monotonicity,[status(thm)],[127]) ).
tff(129,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ) ),
inference(transitivity,[status(thm)],[128,126]) ).
tff(130,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm) ),
inference(quant_inst,[status(thm)],[]) ).
tff(131,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ( sdtasdt0(xm,xn) = sdtasdt0(xn,xm) ) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
sdtasdt0(xm,xn) = sdtasdt0(xn,xm),
inference(unit_resolution,[status(thm)],[131,125,16,90]) ).
tff(133,plain,
( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) != xm )
| ( sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) = xm ) ),
inference(tautology,[status(thm)],[]) ).
tff(134,plain,
sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)) = xm,
inference(unit_resolution,[status(thm)],[133,76]) ).
tff(135,plain,
sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) = sdtasdt0(xm,xn),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(137,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,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) ) )),
rewrite(( ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) )
<=> ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,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) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
tff(144,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[144,140]) ).
tff(146,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) = sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
& ( sdtasdt0(sdtpldt0(W1,W2),W0) = sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(skolemize,[status(sab)],[145]) ).
tff(147,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[146,139]) ).
tff(148,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) ),
inference(modus_ponens,[status(thm)],[147,137]) ).
tff(149,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
( ( ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(151,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) ) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) ) ),
inference(transitivity,[status(thm)],[151,149]) ).
tff(153,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtpldt0(W1,W2)) != sdtpldt0(sdtasdt0(W0,W1),sdtasdt0(W0,W2)) )
| ( sdtasdt0(sdtpldt0(W1,W2),W0) != sdtpldt0(sdtasdt0(W1,W0),sdtasdt0(W2,W0)) ) ) )
| ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sz10)
| ~ aNaturalNumber0(tptp_fun_W2_0(xm,sz10))
| ~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
~ ( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ),
inference(unit_resolution,[status(thm)],[154,36,148,90,86]) ).
tff(156,plain,
( ( sdtasdt0(xn,sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10))) != sdtpldt0(sdtasdt0(xn,sz10),sdtasdt0(xn,tptp_fun_W2_0(xm,sz10))) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) != sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) )
| ( sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) = sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(157,plain,
sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn) = sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)),
inference(unit_resolution,[status(thm)],[156,155]) ).
tff(158,plain,
sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) = sdtasdt0(sdtpldt0(sz10,tptp_fun_W2_0(xm,sz10)),xn),
inference(symmetry,[status(thm)],[157]) ).
tff(159,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(162,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[161]) ).
tff(163,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(164,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(165,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[164]) ).
tff(166,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
tff(167,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[167,163]) ).
tff(169,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(skolemize,[status(sab)],[168]) ).
tff(170,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[169,162]) ).
tff(171,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[170,160]) ).
tff(172,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sz10) != xn )
| ( xn != sdtasdt0(sz10,xn) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sz10) != xn )
| ( xn != sdtasdt0(sz10,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sz10) != xn )
| ( xn != sdtasdt0(sz10,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(174,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sz10) != xn )
| ( xn != sdtasdt0(sz10,xn) ) ) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
~ ( ( sdtasdt0(xn,sz10) != xn )
| ( xn != sdtasdt0(sz10,xn) ) ),
inference(unit_resolution,[status(thm)],[174,171,90]) ).
tff(176,plain,
( ( sdtasdt0(xn,sz10) != xn )
| ( xn != sdtasdt0(sz10,xn) )
| ( xn = sdtasdt0(sz10,xn) ) ),
inference(tautology,[status(thm)],[]) ).
tff(177,plain,
xn = sdtasdt0(sz10,xn),
inference(unit_resolution,[status(thm)],[176,175]) ).
tff(178,plain,
sdtpldt0(xn,sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) = sdtpldt0(sdtasdt0(sz10,xn),sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
sdtpldt0(xn,sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) = sdtasdt0(xn,xm),
inference(transitivity,[status(thm)],[178,158,135,132]) ).
tff(180,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
( ~ ! [W0: $i,W1: $i] :
( aNaturalNumber0(sdtasdt0(W0,W1))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
aNaturalNumber0(sdtasdt0(xn,xm)),
inference(unit_resolution,[status(thm)],[182,103,16,90]) ).
tff(184,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(sdtasdt0(xn,xm))
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(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(xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ~ ( ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) )
| ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) ) )
<=> ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(187,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) )
| ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) ) ) )
<=> ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[186]) ).
tff(188,plain,
( ( ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) )
| ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[187,185]) ).
tff(189,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(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) )
| ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(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(xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[188]) ).
tff(190,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(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) )
| ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(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(xn)
| ~ aNaturalNumber0(sdtasdt0(xn,xm))
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[189,184]) ).
tff(191,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(sdtasdt0(xn,xm))
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) )
| ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(192,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(sdtasdt0(xn,xm))
| ~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[191,190]) ).
tff(193,plain,
~ ( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) ) ),
inference(unit_resolution,[status(thm)],[192,61,90,183]) ).
tff(194,plain,
( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ~ ( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_0(sdtasdt0(xn,xm),xn))
| ( sdtpldt0(xn,tptp_fun_W2_0(sdtasdt0(xn,xm),xn)) != sdtasdt0(xn,xm) ) ) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(195,plain,
( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) ),
inference(unit_resolution,[status(thm)],[194,193]) ).
tff(196,plain,
( ~ sdtlseqdt0(xn,sdtasdt0(xn,xm))
<=> ~ sdtlseqdt0(xn,sdtasdt0(xn,xm)) ),
inference(rewrite,[status(thm)],[]) ).
tff(197,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(or_elim,[status(thm)],[4]) ).
tff(198,plain,
~ sdtlseqdt0(xn,sdtasdt0(xn,xm)),
inference(modus_ponens,[status(thm)],[197,196]) ).
tff(199,plain,
( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(200,plain,
( ~ ( sdtlseqdt0(xn,sdtasdt0(xn,xm))
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ) ),
inference(unit_resolution,[status(thm)],[199,198]) ).
tff(201,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) ),
inference(unit_resolution,[status(thm)],[200,195]) ).
tff(202,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) )
| ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_0(xm,sz10),xn))
| ( sdtpldt0(xn,sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) != sdtasdt0(xn,xm) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) )
| ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_0(xm,sz10),xn))
| ( sdtpldt0(xn,sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) != sdtasdt0(xn,xm) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(203,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) )
| ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_0(xm,sz10),xn))
| ( sdtpldt0(xn,sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) != sdtasdt0(xn,xm) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(204,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( sdtpldt0(xn,W2) != sdtasdt0(xn,xm) ) )
| ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_0(xm,sz10),xn))
| ( sdtpldt0(xn,sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) != sdtasdt0(xn,xm) ) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
( ~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_0(xm,sz10),xn))
| ( sdtpldt0(xn,sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)) != sdtasdt0(xn,xm) ) ),
inference(unit_resolution,[status(thm)],[204,201]) ).
tff(206,plain,
~ aNaturalNumber0(sdtasdt0(tptp_fun_W2_0(xm,sz10),xn)),
inference(unit_resolution,[status(thm)],[205,179]) ).
tff(207,plain,
$false,
inference(unit_resolution,[status(thm)],[206,112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM465+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:13:05 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.38/0.54 % SZS status Theorem
% 0.38/0.54 % SZS output start Proof
% See solution above
% 0.38/0.57 % E exiting
%------------------------------------------------------------------------------