%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM427+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:20:57 AM UTC 2025
% Result : Theorem 196.00s 196.24s
% Output : Proof 196.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 53
% Syntax : Number of formulae : 128 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 1424 ( 368 equ)
% Maximal formula atoms : 44 ( 11 avg)
% Number of connectives : 2270 (1032 ~; 879 |; 196 &)
% ( 145 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 58 ( 58 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 334 ( 294 !; 17 ?; 334 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xa_type,type,
xa: $i ).
tff(xb_type,type,
xb: $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(sz00_type,type,
sz00: $i ).
tff(tptp_fun_W2_0_type,type,
tptp_fun_W2_0: ( $i * $i ) > $i ).
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(xn_type,type,
xn: $i ).
tff(1,plain,
( aInteger0(xa)
<=> aInteger0(xa) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__704) ).
tff(3,plain,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xq) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
( aInteger0(xa)
& aInteger0(xb) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aInteger0(xa),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
aInteger0(xa),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [W0: $i] :
refl(( ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( aInteger0(W0)
=> aInteger0(smndt0(W0)) )
<=> ( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) )
<=> ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W0: $i] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
tff(13,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xa))
| ~ aInteger0(xa) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xa))
| ~ aInteger0(xa) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xa))
| ~ aInteger0(xa) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xa))
| ~ aInteger0(xa) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
aInteger0(smndt0(xa)),
inference(unit_resolution,[status(thm)],[19,16,6]) ).
tff(21,plain,
( aInteger0(xb)
<=> aInteger0(xb) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
aInteger0(xb),
inference(and_elim,[status(thm)],[4]) ).
tff(23,plain,
aInteger0(xb),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [W0: $i,W1: $i] :
refl(( ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(( ~ ~ ( ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1) )
<=> ( ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(( ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) )
<=> ( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [W0: $i,W1: $i] :
( ( aInteger0(W0)
& aInteger0(W1) )
=> aInteger0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
tff(32,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ ( aInteger0(W0)
& aInteger0(W1) ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[35,25]) ).
tff(37,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,plain,
( ( aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb) )
<=> ( ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ) ),
inference(monotonicity,[status(thm)],[38]) ).
tff(40,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ) ),
inference(transitivity,[status(thm)],[39,37]) ).
tff(41,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| aInteger0(sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(smndt0(xa))
| ~ aInteger0(xb) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [W0: $i,W1: $i] :
( aInteger0(sdtpldt0(W0,W1))
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ~ aInteger0(xb)
| ~ aInteger0(smndt0(xa))
| aInteger0(sdtpldt0(xb,smndt0(xa))) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
aInteger0(sdtpldt0(xb,smndt0(xa))),
inference(unit_resolution,[status(thm)],[42,36,23,20]) ).
tff(44,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(45,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)],[44]) ).
tff(46,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(47,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)],[46]) ).
tff(48,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)],[47,45]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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)],[51]) ).
tff(53,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(54,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(55,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)],[54]) ).
tff(56,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(57,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)],[56,55]) ).
tff(58,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)],[57,53]) ).
tff(59,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)],[58]) ).
tff(60,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)],[59,52]) ).
tff(61,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)],[60,50]) ).
tff(62,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)],[61,48]) ).
tff(63,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(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) )
<=> ( ~ ! [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(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) )
<=> ( ~ aInteger0(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,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(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) )
<=> ( ~ ! [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(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,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(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) )
<=> ( ~ ! [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(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,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(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ( W1 = sz00 )
| ~ aInteger0(W1)
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,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(sdtpldt0(xb,smndt0(xa)))
| ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ),
inference(unit_resolution,[status(thm)],[68,62,43]) ).
tff(70,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ( ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
<=> ~ ( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| ( sdtasdt0(W1,tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) )
| ~ aInteger0(tptp_fun_W2_0(W1,sdtpldt0(xb,smndt0(xa)))) ) )
| ~ ( ( W1 = sz00 )
| ~ aInteger0(W1)
| aDivisorOf0(W1,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(W1,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
~ ( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) ) ),
inference(unit_resolution,[status(thm)],[75,69]) ).
tff(77,plain,
( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| ~ aInteger0(tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa))))
| ( sdtasdt0(xq,tptp_fun_W2_0(xq,sdtpldt0(xb,smndt0(xa)))) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ( xq != sz00 )
<=> ( xq != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
xq != sz00,
inference(and_elim,[status(thm)],[2]) ).
tff(81,plain,
xq != sz00,
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( aInteger0(xq)
<=> aInteger0(xq) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
aInteger0(xq),
inference(and_elim,[status(thm)],[3]) ).
tff(84,plain,
aInteger0(xq),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,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(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) )
<=> ! [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)],[85]) ).
tff(87,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(88,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)],[87]) ).
tff(89,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(90,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(91,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)],[90]) ).
tff(92,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(93,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)],[92,91]) ).
tff(94,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)],[93,89]) ).
tff(95,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)],[94]) ).
tff(96,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)],[95,88]) ).
tff(97,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)],[96,86]) ).
tff(98,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(xb)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,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(xb)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
( ( ( xq = sz00 )
| ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb) )
<=> ( ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(100,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(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb) )
<=> ( ~ ! [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(xb)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(monotonicity,[status(thm)],[99]) ).
tff(101,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(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb) )
<=> ( ~ ! [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(xb)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ) ) ),
inference(transitivity,[status(thm)],[100,98]) ).
tff(102,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(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) )
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(xb) ),
inference(quant_inst,[status(thm)],[]) ).
tff(103,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(xb)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
inference(unit_resolution,[status(thm)],[103,97,6,23,84,81]) ).
tff(105,plain,
( ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> ~ sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(107,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) )
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
inference(tautology,[status(thm)],[]) ).
tff(109,plain,
( ~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
<=> aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) )
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) ),
inference(unit_resolution,[status(thm)],[108,107]) ).
tff(110,plain,
~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))),
inference(unit_resolution,[status(thm)],[109,104]) ).
tff(111,plain,
( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
( ~ ( ( xq = sz00 )
| ~ aInteger0(xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(unit_resolution,[status(thm)],[111,84,81,110]) ).
tff(113,plain,
! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) ),
inference(unit_resolution,[status(thm)],[112,78]) ).
tff(114,plain,
( aInteger0(xn)
<=> aInteger0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,axiom,
( aInteger0(xn)
& ( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__747) ).
tff(116,plain,
aInteger0(xn),
inference(and_elim,[status(thm)],[115]) ).
tff(117,plain,
aInteger0(xn),
inference(modus_ponens,[status(thm)],[116,114]) ).
tff(118,plain,
( ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) )
<=> ( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [W0: $i] :
( aInteger0(smndt0(W0))
| ~ aInteger0(W0) )
| aInteger0(smndt0(xn))
| ~ aInteger0(xn) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
aInteger0(smndt0(xn)),
inference(unit_resolution,[status(thm)],[120,16,117]) ).
tff(122,plain,
( ( sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)) )
<=> ( sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(123,axiom,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__767) ).
tff(124,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
( ( ~ ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) )
<=> ( ~ ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [W2: $i] :
( ~ aInteger0(W2)
| ( sdtasdt0(xq,W2) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ aInteger0(smndt0(xn))
| ( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa)) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,124,121,113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM427+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:04:27 EDT 2025
% 0.12/0.34 % CPUTime :
% 196.00/196.24 % SZS status Theorem
% 196.00/196.24 % SZS output start Proof
% See solution above
% 196.82/197.07 % E exiting
%------------------------------------------------------------------------------