TSTP Solution File: NUM457+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM457+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:09:49 EDT 2022
% Result : Theorem 0.16s 0.36s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 41
% Syntax : Number of formulae : 90 ( 24 unt; 5 typ; 0 def)
% Number of atoms : 898 ( 520 equ)
% Maximal formula atoms : 28 ( 10 avg)
% Number of connectives : 1213 ( 465 ~; 572 |; 64 &)
% ( 69 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 65 ( 65 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 3 ( 2 >; 1 *; 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 : 223 ( 210 !; 0 ?; 223 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xn_type,type,
xn: $i ).
tff(xm_type,type,
xm: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
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,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) = sdtasdt0(xm,xn) )
& ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) = sdtasdt0(xm,xn) )
& ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) = sdtasdt0(xm,xn) )
& ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) = sdtasdt0(xm,xn) )
& ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
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(rewrite,[status(thm)],]) ).
tff(12,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(13,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)],[12]) ).
tff(14,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
tff(15,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) = sdtasdt0(xm,xn) )
& ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ),
inference(modus_ponens,[status(thm)],[16,10]) ).
tff(18,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) = sdtasdt0(xm,xn) )
& ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ),
inference(modus_ponens,[status(thm)],[18,8]) ).
tff(20,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) ),
inference(modus_ponens,[status(thm)],[19,6]) ).
tff(21,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),xn) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),xn) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),xn) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(23,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),W0) ) ) )
| ~ aNaturalNumber0(xn)
| ~ ( ( sdtasdt0(xn,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),xn) ) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
~ ( ( sdtasdt0(xn,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),xn) ) ),
inference(unit_resolution,[status(thm)],[23,20,4]) ).
tff(25,plain,
( ( sdtasdt0(xn,sdtasdt0(xm,xn)) != sdtasdt0(xm,xn) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) ) ),
inference(tautology,[status(thm)],]) ).
tff(26,plain,
sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) )
| ( sdtasdt0(xm,xn) != sdtasdt0(sdtasdt0(xm,xn),xn) ) ),
inference(tautology,[status(thm)],]) ).
tff(28,plain,
( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( ( xn != sz00 )
<=> ( xn != sdtasdt0(xm,xn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( xn != sz00 )
<=> ( xn != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
( ~ ( ( sdtasdt0(xm,xn) = sz00 )
=> ( ( xm = sz00 )
| ( xn = sz00 ) ) )
<=> ~ ( ( xn = sz00 )
| ( xm = sz00 )
| ( sdtasdt0(xm,xn) != sz00 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
~ ( ( sdtasdt0(xm,xn) = sz00 )
=> ( ( xm = sz00 )
| ( xn = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(33,plain,
~ ( ( xn = sz00 )
| ( xm = sz00 )
| ( sdtasdt0(xm,xn) != sz00 ) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
xn != sz00,
inference(or_elim,[status(thm)],[33]) ).
tff(35,plain,
xn != sz00,
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
xn != sdtasdt0(xm,xn),
inference(modus_ponens,[status(thm)],[35,29]) ).
tff(37,plain,
^ [W0: $i] :
refl(
( ( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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(38,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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)],[37]) ).
tff(39,plain,
^ [W0: $i] :
rewrite(
( ( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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(40,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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)],[39]) ).
tff(41,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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)],[40,38]) ).
tff(42,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) ) )),
( ( ~ 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 = sdtasdt0(xm,xn) ) )
<=> ( ~ 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 = sdtasdt0(xm,xn) ) ) )),
rewrite(
( ( ~ 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 = sdtasdt0(xm,xn) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) ) )),
( ( ~ 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 = sdtasdt0(xm,xn) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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(43,plain,
( ! [W0: $i] :
( ~ 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 = sdtasdt0(xm,xn) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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)],[42]) ).
tff(44,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( W0 = sz00 )
<=> ( W0 = sdtasdt0(xm,xn) ) )),
( ( ( 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 = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(W0)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) ) ) )),
rewrite(
( ( ( W0 = sdtasdt0(xm,xn) )
| ~ 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)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
| ( W0 = sdtasdt0(xm,xn) ) ) )),
( ( ( 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)
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ ( aNaturalNumber0(W1)
& aNaturalNumber0(W2) )
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) ) )
| ( W0 = sdtasdt0(xm,xn) ) ) )),
inference(bind,[status(th)],]) ).
tff(45,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] :
( ~ 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 = sdtasdt0(xm,xn) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,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(47,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(48,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)],[47]) ).
tff(49,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(50,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)],[49,48]) ).
tff(51,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)],[50,46]) ).
tff(52,plain,
! [W0: $i] :
( ~ 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 = sdtasdt0(xm,xn) ) ),
inference(modus_ponens,[status(thm)],[51,45]) ).
tff(53,plain,
! [W0: $i] :
( ~ 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 = sdtasdt0(xm,xn) ) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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)],[53,43]) ).
tff(55,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [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)],[54,41]) ).
tff(56,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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(57,plain,
( ( ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) )
| ~ aNaturalNumber0(W1) ) )
<=> ( ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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(58,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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)],[57]) ).
tff(59,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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)],[58,56]) ).
tff(60,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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(61,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( W0 = sdtasdt0(xm,xn) )
| ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ ( ( sdtasdt0(W0,W1) = sdtasdt0(W0,W2) )
| ( sdtasdt0(W1,W0) = sdtasdt0(W2,W0) ) )
| ~ aNaturalNumber0(W1) ) )
| ~ aNaturalNumber0(xn)
| ( xn = sdtasdt0(xm,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)],[60,59]) ).
tff(62,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)],[61,55,4,36]) ).
tff(63,plain,
( ( xm != sz00 )
<=> ( xm != sdtasdt0(xm,xn) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( xm != sz00 )
<=> ( xm != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
xm != sz00,
inference(or_elim,[status(thm)],[33]) ).
tff(66,plain,
xm != sz00,
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
xm != sdtasdt0(xm,xn),
inference(modus_ponens,[status(thm)],[66,63]) ).
tff(68,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[2]) ).
tff(70,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( aNaturalNumber0(sz00)
<=> aNaturalNumber0(sdtasdt0(xm,xn)) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( aNaturalNumber0(sz00)
<=> aNaturalNumber0(sz00) ),
inference(rewrite,[status(thm)],]) ).
tff(73,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
tff(74,plain,
aNaturalNumber0(sz00),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
aNaturalNumber0(sdtasdt0(xm,xn)),
inference(modus_ponens,[status(thm)],[74,71]) ).
tff(76,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ( ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) )
<=> ( ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) ) )
<=> ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) ) ) )
<=> ( ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) ) ) )
<=> ( ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) ) ),
inference(monotonicity,[status(thm)],[80]) ).
tff(82,plain,
( ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) ) ) )
<=> ( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) ) ),
inference(transitivity,[status(thm)],[81,76]) ).
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) ) ) )
| ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) )
| ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
( ~ ! [W1: $i,W2: $i] :
( ( W1 = W2 )
| ~ aNaturalNumber0(W2)
| ~ aNaturalNumber0(W1)
| ~ ( ( sdtasdt0(xn,W1) = sdtasdt0(xn,W2) )
| ( sdtasdt0(W1,xn) = sdtasdt0(W2,xn) ) ) )
| ( xm = sdtasdt0(xm,xn) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(sdtasdt0(xm,xn))
| ~ ( ( sdtasdt0(xm,xn) = sdtasdt0(sdtasdt0(xm,xn),xn) )
| ( sdtasdt0(xn,xm) = sdtasdt0(xn,sdtasdt0(xm,xn)) ) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
$false,
inference(unit_resolution,[status(thm)],[84,75,70,67,62,28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : NUM457+1 : TPTP v8.1.0. Released v4.0.0.
% 0.05/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Sep 2 10:28:18 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.10/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.31 Usage: tptp [options] [-file:]file
% 0.10/0.31 -h, -? prints this message.
% 0.10/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.31 -m, -model generate model.
% 0.10/0.31 -p, -proof generate proof.
% 0.10/0.31 -c, -core generate unsat core of named formulas.
% 0.10/0.31 -st, -statistics display statistics.
% 0.10/0.31 -t:timeout set timeout (in second).
% 0.10/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.31 -<param>:<value> configuration parameter and value.
% 0.10/0.31 -o:<output-file> file to place output in.
% 0.16/0.36 % SZS status Theorem
% 0.16/0.36 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------