%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM457+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 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 40
% Syntax : Number of formulae : 99 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 981 ( 533 equ)
% Maximal formula atoms : 28 ( 9 avg)
% Number of connectives : 1333 ( 524 ~; 619 |; 66 &)
% ( 78 <=>; 46 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 73 ( 73 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 253 ( 234 !; 0 ?; 253 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xm_type,type,
xm: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(1,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__624) ).
tff(3,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
tff(13,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[16,6]) ).
tff(18,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xn) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xn) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
~ ( ( sdtasdt0(xn,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xn) ) ),
inference(unit_resolution,[status(thm)],[20,17,4]) ).
tff(22,plain,
( ( sdtasdt0(xn,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xn) )
| ( sdtasdt0(xn,sz00) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(23,plain,
sdtasdt0(xn,sz00) = sz00,
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
sz00 = sdtasdt0(xn,sz00),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
( ( sdtasdt0(xm,xn) = sz00 )
<=> ( sdtasdt0(xm,xn) = sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ( ( sdtasdt0(xm,xn) = sz00 )
=> ( ( xm = sz00 )
| ( xn = sz00 ) ) )
<=> ~ ( ( xn = sz00 )
| ( xm = sz00 )
| ( sdtasdt0(xm,xn) != sz00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
~ ( ( sdtasdt0(xm,xn) = sz00 )
=> ( ( xm = sz00 )
| ( xn = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(28,plain,
~ ( ( xn = sz00 )
| ( xm = sz00 )
| ( sdtasdt0(xm,xn) != sz00 ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
sdtasdt0(xm,xn) = sz00,
inference(or_elim,[status(thm)],[28]) ).
tff(30,plain,
sdtasdt0(xm,xn) = sz00,
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[2]) ).
tff(33,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,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(35,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)],[34]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,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(40,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)],[39]) ).
tff(41,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
tff(42,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[45,35]) ).
tff(47,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [W0: $i,W1: $i] :
( ( sdtasdt0(W0,W1) = sdtasdt0(W1,W0) )
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
sdtasdt0(xn,xm) = sdtasdt0(xm,xn),
inference(unit_resolution,[status(thm)],[49,46,33,4]) ).
tff(51,plain,
sdtasdt0(xn,xm) = sdtasdt0(xn,sz00),
inference(transitivity,[status(thm)],[50,30,24]) ).
tff(52,plain,
( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) )
| ( sdtasdt0(xn,xm) != sdtasdt0(xn,sz00) ) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( ( xn != sz00 )
<=> ( xn != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
xn != sz00,
inference(or_elim,[status(thm)],[28]) ).
tff(56,plain,
xn != sz00,
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
^ [W0: $i] :
refl(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
^ [W0: $i] :
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
( ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
( ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
<=> ( ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1) ) )),
rewrite(( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
<=> ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
rewrite(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )),
( ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ))),
( ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )),
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
rewrite(( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
( ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
<=> ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )),
( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )),
rewrite(( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )),
( ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) )
<=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )),
( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
( ( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ))),
( ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )),
( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) )
<=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
rewrite(( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) )
<=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) )
<=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ) )),
rewrite(( ( aNaturalNumber0(W0)
=> ( ( W0 = sz00 )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
( ( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( W0 != sz00 )
=> ! [W1: $i,W2: $i] :
( ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
=> ( ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
=> ( W1 = W2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
tff(68,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ),
inference(skolemize,[status(sab)],[69]) ).
tff(71,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[70,63]) ).
tff(72,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[71,61]) ).
tff(73,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) )
<=> ( ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [W1: $i,W2: $i] :
rewrite(( ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) )
| ~ aNaturalNumber0(W1) )
<=> ( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) )
| ~ aNaturalNumber0(W1) )
<=> ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ( ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) ) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( ( ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) ) ),
inference(transitivity,[status(thm)],[77,74]) ).
tff(79,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) ) ),
inference(transitivity,[status(thm)],[79,73]) ).
tff(81,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) )
| ~ aNaturalNumber0(W1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ( xn = sz00 )
| ~ aNaturalNumber0(xn)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) ),
inference(unit_resolution,[status(thm)],[82,72,4,56]) ).
tff(84,plain,
( ( xm != sz00 )
<=> ( xm != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
xm != sz00,
inference(or_elim,[status(thm)],[28]) ).
tff(86,plain,
xm != sz00,
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( aNaturalNumber0(sz00)
<=> aNaturalNumber0(sz00) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(89,plain,
aNaturalNumber0(sz00),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) )
<=> ( ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) )
<=> ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(93,plain,
( ( ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) )
<=> ( ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
( ( ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) )
<=> ( ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ) ),
inference(transitivity,[status(thm)],[93,91]) ).
tff(95,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ) ),
inference(transitivity,[status(thm)],[95,90]) ).
tff(97,plain,
( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(sz00)
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(98,plain,
( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sz00 )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sz00)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sz00) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sz00,xn) ) ) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
$false,
inference(unit_resolution,[status(thm)],[98,89,33,86,83,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM457+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % 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 :
% 0.21/0.38 % SZS status Theorem
% 0.21/0.38 % SZS output start Proof
% See solution above
% 0.21/0.41 % E exiting
%------------------------------------------------------------------------------