%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM482+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:08 AM UTC 2025
% Result : Theorem 0.24s 0.44s
% Output : Proof 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 35
% Syntax : Number of formulae : 85 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 781 ( 204 equ)
% Maximal formula atoms : 31 ( 9 avg)
% Number of connectives : 1400 ( 750 ~; 467 |; 104 &)
% ( 68 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 46 ( 46 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 186 ( 147 !; 25 ?; 186 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(sz10_type,type,
sz10: $i ).
tff(xk_type,type,
xk: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(isPrime0_type,type,
isPrime0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( aNaturalNumber0(xk)
<=> aNaturalNumber0(xk) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
aNaturalNumber0(xk),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1716) ).
tff(3,plain,
aNaturalNumber0(xk),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulUnit) ).
tff(12,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz10) = W0 )
& ( W0 = sdtasdt0(sz10,W0) ) ) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz10) != W0 )
| ( W0 != sdtasdt0(sz10,W0) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ ( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) ) ),
inference(unit_resolution,[status(thm)],[19,16,3]) ).
tff(21,plain,
( ( sdtasdt0(xk,sz10) != xk )
| ( xk != sdtasdt0(sz10,xk) )
| ( sdtasdt0(xk,sz10) = xk ) ),
inference(tautology,[status(thm)],[]) ).
tff(22,plain,
sdtasdt0(xk,sz10) = xk,
inference(unit_resolution,[status(thm)],[21,20]) ).
tff(23,plain,
xk = sdtasdt0(xk,sz10),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
trans(monotonicity(rewrite(( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
<=> ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) ) )),
rewrite(( ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
rewrite(( ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
( ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) )
<=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiv) ).
tff(35,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [W0: $i,W1: $i] :
( ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
| ( ( ~ doDivides0(W0,W1)
| ( aNaturalNumber0(tptp_fun_W2_1(W1,W0))
& ( W1 = sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
& ( doDivides0(W0,W1)
| ! [W2: $i] :
~ ( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,28]) ).
tff(40,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ( ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) )
| ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) )
| ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) )
| ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) )
| ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) )
| ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[45,40]) ).
tff(47,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) )
| ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0)
| ~ ( ~ ( ~ doDivides0(W0,W1)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(W1,W0))
| ( W1 != sdtasdt0(W0,tptp_fun_W2_1(W1,W0)) ) ) )
| ~ ( doDivides0(W0,W1)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( W1 != sdtasdt0(W0,W2) ) ) ) ) )
| ~ aNaturalNumber0(xk)
| ~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) ) ),
inference(unit_resolution,[status(thm)],[48,39,3]) ).
tff(50,plain,
( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ~ ( ~ doDivides0(xk,xk)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xk,xk))
| ( xk != sdtasdt0(xk,tptp_fun_W2_1(xk,xk)) ) ) )
| doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) )
<=> ( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) )
<=> ~ ( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ) )),
( ~ ( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) )
<=> ~ ~ ( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ) )),
rewrite(( ~ ~ ( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) )
<=> ( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ) )),
( ~ ( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) )
<=> ( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [W0: $i] :
~ ( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) )
<=> ~ ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ( isPrime0(xk)
=> ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ) )
<=> ~ ( ~ isPrime0(xk)
| ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,axiom,
~ ( isPrime0(xk)
=> ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(59,plain,
~ ( ~ isPrime0(xk)
| ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
inference(or_elim,[status(thm)],[59]) ).
tff(61,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
inference(modus_ponens,[status(thm)],[60,56]) ).
tff(62,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
inference(modus_ponens,[status(thm)],[61,56]) ).
tff(63,plain,
~ ? [W0: $i] :
( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
inference(modus_ponens,[status(thm)],[62,56]) ).
tff(64,plain,
^ [W0: $i] :
refl($oeq(~ ( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
~ ( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ))),
inference(bind,[status(th)],[]) ).
tff(65,plain,
! [W0: $i] :
~ ( aNaturalNumber0(W0)
& doDivides0(W0,xk)
& isPrime0(W0) ),
inference(nnf-neg,[status(sab)],[63,64]) ).
tff(66,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ),
inference(modus_ponens,[status(thm)],[65,55]) ).
tff(67,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) ),
inference(modus_ponens,[status(thm)],[66,53]) ).
tff(68,plain,
( isPrime0(xk)
<=> isPrime0(xk) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
isPrime0(xk),
inference(or_elim,[status(thm)],[59]) ).
tff(70,plain,
isPrime0(xk),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) )
| ~ aNaturalNumber0(xk)
| ~ isPrime0(xk)
| ~ doDivides0(xk,xk) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) )
| ~ aNaturalNumber0(xk)
| ~ isPrime0(xk)
| ~ doDivides0(xk,xk) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) )
| ~ aNaturalNumber0(xk)
| ~ isPrime0(xk)
| ~ doDivides0(xk,xk) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ isPrime0(W0)
| ~ doDivides0(W0,xk) )
| ~ aNaturalNumber0(xk)
| ~ isPrime0(xk)
| ~ doDivides0(xk,xk) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
~ doDivides0(xk,xk),
inference(unit_resolution,[status(thm)],[73,3,70,67]) ).
tff(75,plain,
( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(76,plain,
( ~ ( doDivides0(xk,xk)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) )
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) ),
inference(unit_resolution,[status(thm)],[76,51]) ).
tff(78,plain,
( aNaturalNumber0(sz10)
<=> aNaturalNumber0(sz10) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
( aNaturalNumber0(sz10)
& ( sz10 != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSortsC_01) ).
tff(80,plain,
aNaturalNumber0(sz10),
inference(and_elim,[status(thm)],[79]) ).
tff(81,plain,
aNaturalNumber0(sz10),
inference(modus_ponens,[status(thm)],[80,78]) ).
tff(82,plain,
( ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) )
| ~ aNaturalNumber0(sz10)
| ( xk != sdtasdt0(xk,sz10) ) )
<=> ( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) )
| ~ aNaturalNumber0(sz10)
| ( xk != sdtasdt0(xk,sz10) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) )
| ~ aNaturalNumber0(sz10)
| ( xk != sdtasdt0(xk,sz10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xk != sdtasdt0(xk,W2) ) )
| ~ aNaturalNumber0(sz10)
| ( xk != sdtasdt0(xk,sz10) ) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
$false,
inference(unit_resolution,[status(thm)],[84,81,77,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.15 % Problem : NUM482+1 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.15 % Command : run_E %s %d THM
% 0.15/0.37 % Computer : n016.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Fri Jun 20 01:16:17 EDT 2025
% 0.15/0.37 % CPUTime :
% 0.24/0.44 % SZS status Theorem
% 0.24/0.44 % SZS output start Proof
% See solution above
% 0.24/0.46 % E exiting
%------------------------------------------------------------------------------