%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM423+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:20:55 AM UTC 2025
% Result : Theorem 7.81s 8.02s
% Output : Proof 7.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 50
% Syntax : Number of formulae : 125 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 1381 ( 488 equ)
% Maximal formula atoms : 44 ( 11 avg)
% Number of connectives : 2273 (1064 ~; 853 |; 200 &)
% ( 138 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 47 ( 47 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 305 ( 267 !; 17 ?; 305 :)
% Comments :
%------------------------------------------------------------------------------
tff(sz00_type,type,
sz00: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xq_type,type,
xq: $i ).
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xa_type,type,
xa: $i ).
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(1,plain,
^ [W0: $i] :
refl(( ( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
<=> ( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
rewrite(( ( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
<=> ( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(( ( ~ aInteger0(W0)
| ! [W1: $i] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& ( W1 != sz00 )
& aInteger0(tptp_fun_W2_0(W1,W0))
& ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
~ ( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& ( W1 != sz00 )
& aInteger0(tptp_fun_W2_0(W1,W0))
& ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
~ ( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
rewrite(( ( ~ aInteger0(W0)
| ! [W1: $i] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& ( W1 != sz00 )
& aInteger0(tptp_fun_W2_0(W1,W0))
& ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| ( W1 = sz00 )
| ! [W2: $i] :
~ ( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ( ~ aInteger0(W0)
| ! [W1: $i] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& ( W1 != sz00 )
& aInteger0(tptp_fun_W2_0(W1,W0))
& ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
~ ( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& ( W1 != sz00 )
& aInteger0(tptp_fun_W2_0(W1,W0))
& ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| ( W1 = sz00 )
| ! [W2: $i] :
~ ( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& ( W1 != sz00 )
& aInteger0(tptp_fun_W2_0(W1,W0))
& ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
~ ( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) )
<=> ( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ))),
( ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) )
<=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )),
( ( aInteger0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ( aInteger0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ) )),
rewrite(( ( aInteger0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ( ~ aInteger0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ) )),
( ( aInteger0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ( ~ aInteger0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
tff(14,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( aDivisorOf0(W1,W0)
<=> ( aInteger0(W1)
& ( W1 != sz00 )
& ? [W2: $i] :
( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& ( W1 != sz00 )
& aInteger0(tptp_fun_W2_0(W1,W0))
& ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ~ aInteger0(W1)
| ( W1 = sz00 )
| ! [W2: $i] :
~ ( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
( ( ~ aDivisorOf0(W1,W0)
| ( aInteger0(W1)
& ( W1 != sz00 )
& aInteger0(tptp_fun_W2_0(W1,W0))
& ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) = W0 ) ) )
& ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
~ ( aInteger0(W2)
& ( sdtasdt0(W1,W2) = W0 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,5]) ).
tff(20,plain,
( aInteger0(sz00)
<=> aInteger0(sz00) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
tff(22,plain,
aInteger0(sz00),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
| ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
| ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ( ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,sz00))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 ) ) )
| ~ ( aDivisorOf0(W1,sz00)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) )
<=> ( ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
| ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,sz00))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 ) ) )
| ~ ( aDivisorOf0(W1,sz00)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
| ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
| ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,sz00))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 ) ) )
| ~ ( aDivisorOf0(W1,sz00)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
| ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
| ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,sz00))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 ) ) )
| ~ ( aDivisorOf0(W1,sz00)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,W0)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,W0))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,W0)) != W0 ) ) )
| ~ ( aDivisorOf0(W1,W0)
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != W0 ) ) ) ) )
| ~ aInteger0(sz00)
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) ),
inference(unit_resolution,[status(thm)],[28,22,19]) ).
tff(30,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sz00))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 ) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sz00))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 ) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(xq,sz00)) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) ) ) )
<=> ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sz00))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 ) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(xq,sz00)) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sz00))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 ) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ) ) ) ),
inference(monotonicity,[status(thm)],[31]) ).
tff(33,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(xq,sz00)) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sz00))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 ) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ) ) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(xq,sz00)) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sz00)
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sz00)) != sz00 )
| ~ aInteger0(tptp_fun_W2_0(W1,sz00)) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sz00)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sz00 ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sz00))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 ) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
~ ( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sz00))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 ) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ) ),
inference(unit_resolution,[status(thm)],[35,29]) ).
tff(37,plain,
( ~ ( ~ aDivisorOf0(xq,sz00)
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sz00))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sz00)) != sz00 ) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) )
| ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ),
inference(tautology,[status(thm)],[]) ).
tff(38,plain,
( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ),
inference(unit_resolution,[status(thm)],[37,36]) ).
tff(39,plain,
( aInteger0(xa)
<=> aInteger0(xa) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
( aInteger0(xa)
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__671) ).
tff(41,plain,
( aInteger0(xa)
& aInteger0(xq) ),
inference(and_elim,[status(thm)],[40]) ).
tff(42,plain,
aInteger0(xa),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
aInteger0(xa),
inference(modus_ponens,[status(thm)],[42,39]) ).
tff(44,plain,
^ [W0: $i] :
refl(( ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
^ [W0: $i] :
rewrite(( ( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [W0: $i] :
rewrite(( ( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
tff(52,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( sz00 = sdtpldt0(smndt0(W0),W0) ) ) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) ),
inference(modus_ponens,[status(thm)],[55,45]) ).
tff(57,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(59,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtpldt0(W0,smndt0(W0)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(W0),W0) ) ) )
| ~ aInteger0(xa)
| ~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ ( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) ) ),
inference(unit_resolution,[status(thm)],[59,56,43]) ).
tff(61,plain,
( ( sdtpldt0(xa,smndt0(xa)) != sz00 )
| ( sz00 != sdtpldt0(smndt0(xa),xa) )
| ( sdtpldt0(xa,smndt0(xa)) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(62,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
sz00 = sdtpldt0(xa,smndt0(xa)),
inference(symmetry,[status(thm)],[62]) ).
tff(64,plain,
( aDivisorOf0(xq,sz00)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
<=> aDivisorOf0(xq,sz00) ),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
<=> ~ aDivisorOf0(xq,sz00) ),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
( ( xq != sz00 )
<=> ( xq != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
xq != sz00,
inference(and_elim,[status(thm)],[40]) ).
tff(69,plain,
xq != sz00,
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( aInteger0(xq)
<=> aInteger0(xq) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
aInteger0(xq),
inference(and_elim,[status(thm)],[41]) ).
tff(72,plain,
aInteger0(xq),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
<=> ~ ( ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
<=> ~ ~ ( ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(( ~ ~ ( ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
<=> ( ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ( ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) )),
rewrite(( ( ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2) ) )),
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) ) )),
rewrite(( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) ) )),
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) )),
rewrite(( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
tff(81,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( ( xq = sz00 )
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xa) )
<=> ( ( xq = sz00 )
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xa) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xa) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xa) ),
inference(quant_inst,[status(thm)],[]) ).
tff(91,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aDivisorOf0(W2,sdtpldt0(W0,smndt0(W1))) )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ),
inference(unit_resolution,[status(thm)],[91,85,43,72,69]) ).
tff(93,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> ~ sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
inference(rewrite,[status(thm)],[]) ).
tff(94,axiom,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(95,plain,
~ sdteqdtlpzmzozddtrp0(xa,xa,xq),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
| sdteqdtlpzmzozddtrp0(xa,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ),
inference(tautology,[status(thm)],[]) ).
tff(97,plain,
( ~ ( sdteqdtlpzmzozddtrp0(xa,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
| ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) ),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))),
inference(unit_resolution,[status(thm)],[97,92]) ).
tff(99,plain,
~ aDivisorOf0(xq,sz00),
inference(modus_ponens,[status(thm)],[98,66]) ).
tff(100,plain,
( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) )
| ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ),
inference(tautology,[status(thm)],[]) ).
tff(101,plain,
( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) )
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| aDivisorOf0(xq,sz00) ),
inference(unit_resolution,[status(thm)],[100,72,69]) ).
tff(102,plain,
! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) ),
inference(unit_resolution,[status(thm)],[101,99,38]) ).
tff(103,plain,
^ [W0: $i] :
refl(( ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(104,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
^ [W0: $i] :
rewrite(( ( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
^ [W0: $i] :
rewrite(( ( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(109,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [W0: $i] :
( aInteger0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulZero) ).
tff(111,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[114,104]) ).
tff(116,plain,
( ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [W0: $i] :
( ~ aInteger0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aInteger0(xq)
| ~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
~ ( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) ) ),
inference(unit_resolution,[status(thm)],[118,115,72]) ).
tff(120,plain,
( ( sdtasdt0(xq,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xq) )
| ( sdtasdt0(xq,sz00) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(121,plain,
sdtasdt0(xq,sz00) = sz00,
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
( ( ~ ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| ~ aInteger0(sz00)
| ( sdtasdt0(xq,sz00) != sz00 ) )
<=> ( ~ ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| ~ aInteger0(sz00)
| ( sdtasdt0(xq,sz00) != sz00 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,plain,
( ~ ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| ~ aInteger0(sz00)
| ( sdtasdt0(xq,sz00) != sz00 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
( ~ ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sz00 ) )
| ~ aInteger0(sz00)
| ( sdtasdt0(xq,sz00) != sz00 ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
$false,
inference(unit_resolution,[status(thm)],[124,22,121,102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : NUM423+1 : TPTP v9.0.0. Released v4.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n006.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
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri Jun 20 01:02:50 EDT 2025
% 0.12/0.35 % CPUTime :
% 7.81/8.02 % SZS status Theorem
% 7.81/8.02 % SZS output start Proof
% See solution above
% 7.92/8.08 % E exiting
%------------------------------------------------------------------------------