%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM477+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:21:07 AM UTC 2025
% Result : Theorem 0.20s 0.44s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 38
% Syntax : Number of formulae : 100 ( 29 unt; 0 typ; 0 def)
% Number of atoms : 895 ( 256 equ)
% Maximal formula atoms : 32 ( 8 avg)
% Number of connectives : 1514 ( 775 ~; 546 |; 91 &)
% ( 82 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 56 ( 56 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 201 ( 169 !; 15 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
tff(sz00_type,type,
sz00: $i ).
tff(xn_type,type,
xn: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(aNaturalNumber0_type,type,
aNaturalNumber0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(doDivides0_type,type,
doDivides0: ( $i * $i ) > $o ).
tff(1,plain,
( aNaturalNumber0(xm)
<=> aNaturalNumber0(xm) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aNaturalNumber0(xm)
& aNaturalNumber0(xn) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1494) ).
tff(3,plain,
aNaturalNumber0(xm),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aNaturalNumber0(xm),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
refl(( ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
rewrite(( ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(( ( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) )
<=> ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W0: $i] :
( aNaturalNumber0(W0)
=> ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
tff(13,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ( ( sdtasdt0(W0,sz00) = sz00 )
& ( sz00 = sdtasdt0(sz00,W0) ) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) ),
inference(modus_ponens,[status(thm)],[16,6]) ).
tff(18,plain,
( ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xm,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xm) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xm,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xm) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xm,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xm) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [W0: $i] :
( ~ aNaturalNumber0(W0)
| ~ ( ( sdtasdt0(W0,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,W0) ) ) )
| ~ aNaturalNumber0(xm)
| ~ ( ( sdtasdt0(xm,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xm) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
~ ( ( sdtasdt0(xm,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xm) ) ),
inference(unit_resolution,[status(thm)],[20,17,4]) ).
tff(22,plain,
( ( sdtasdt0(xm,sz00) != sz00 )
| ( sz00 != sdtasdt0(sz00,xm) )
| ( sdtasdt0(xm,sz00) = sz00 ) ),
inference(tautology,[status(thm)],[]) ).
tff(23,plain,
sdtasdt0(xm,sz00) = sz00,
inference(unit_resolution,[status(thm)],[22,21]) ).
tff(24,plain,
( aNaturalNumber0(xn)
<=> aNaturalNumber0(xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
aNaturalNumber0(xn),
inference(and_elim,[status(thm)],[2]) ).
tff(26,plain,
aNaturalNumber0(xn),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,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(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(quant_intro,[status(thm)],[27]) ).
tff(29,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(30,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)],[29]) ).
tff(31,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)],[30,28]) ).
tff(32,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(33,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)],[32]) ).
tff(34,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(35,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(36,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)],[35]) ).
tff(37,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( doDivides0(W0,W1)
<=> ? [W2: $i] :
( aNaturalNumber0(W2)
& ( W1 = sdtasdt0(W0,W2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefDiv) ).
tff(38,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)],[37,36]) ).
tff(39,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)],[38,34]) ).
tff(40,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)],[39]) ).
tff(41,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)],[40,33]) ).
tff(42,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)],[41,31]) ).
tff(43,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(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) )
<=> ( ~ ! [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(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) )
<=> ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ aNaturalNumber0(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) ) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
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(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,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(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,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(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,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(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[48,43]) ).
tff(50,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(xn)
| ~ aNaturalNumber0(xm)
| ~ ( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,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(xm)
| ~ aNaturalNumber0(xn)
| ~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
~ ( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ) ),
inference(unit_resolution,[status(thm)],[51,42,4,26]) ).
tff(53,plain,
( ~ ( doDivides0(xm,xn)
| ! [W2: $i] :
( ~ aNaturalNumber0(W2)
| ( xn != sdtasdt0(xm,W2) ) ) )
| ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(54,plain,
( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( doDivides0(xm,xn)
<=> doDivides0(xm,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
( doDivides0(xm,xn)
& ( xn != sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1494_04) ).
tff(57,plain,
doDivides0(xm,xn),
inference(and_elim,[status(thm)],[56]) ).
tff(58,plain,
doDivides0(xm,xn),
inference(modus_ponens,[status(thm)],[57,55]) ).
tff(59,plain,
( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(60,plain,
( ~ ( ~ doDivides0(xm,xn)
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) )
| ~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
~ ( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ),
inference(unit_resolution,[status(thm)],[60,54]) ).
tff(62,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) )
| ( xn = sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
xn = sdtasdt0(xm,tptp_fun_W2_1(xn,xm)),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) = xn,
inference(symmetry,[status(thm)],[63]) ).
tff(65,plain,
( sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm)))
<=> sdtlseqdt0(xm,xn) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( sdtlseqdt0(xm,xn)
<=> sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) ),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ sdtlseqdt0(xm,xn)
<=> ~ sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
( ~ sdtlseqdt0(xm,xn)
<=> ~ sdtlseqdt0(xm,xn) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
~ sdtlseqdt0(xm,xn),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(70,plain,
~ sdtlseqdt0(xm,xn),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))),
inference(modus_ponens,[status(thm)],[70,67]) ).
tff(72,plain,
( ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( xn != sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) )
| aNaturalNumber0(tptp_fun_W2_1(xn,xm)) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
aNaturalNumber0(tptp_fun_W2_1(xn,xm)),
inference(unit_resolution,[status(thm)],[72,61]) ).
tff(74,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,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) ) )),
( ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
rewrite(( ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
<=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
( ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) )
<=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) )
<=> ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ) )),
rewrite(( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) )
<=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
( ( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) )
<=> ( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,axiom,
! [W0: $i,W1: $i] :
( ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) )
=> ( ( W0 != sz00 )
=> sdtlseqdt0(W1,sdtasdt0(W1,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMonMul2) ).
tff(82,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ ( aNaturalNumber0(W0)
& aNaturalNumber0(W1) ) ),
inference(skolemize,[status(sab)],[83]) ).
tff(85,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[84,77]) ).
tff(86,plain,
! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) ),
inference(modus_ponens,[status(thm)],[85,75]) ).
tff(87,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm)))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm)) )
<=> ( ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm)))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) ) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm)))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) ) ),
inference(transitivity,[status(thm)],[89,87]) ).
tff(91,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm)))
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = sz00 )
| sdtlseqdt0(W1,sdtasdt0(W1,W0))
| ~ aNaturalNumber0(W1)
| ~ aNaturalNumber0(W0) )
| ~ aNaturalNumber0(xm)
| ~ aNaturalNumber0(tptp_fun_W2_1(xn,xm))
| ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
( ( tptp_fun_W2_1(xn,xm) = sz00 )
| sdtlseqdt0(xm,sdtasdt0(xm,tptp_fun_W2_1(xn,xm))) ),
inference(unit_resolution,[status(thm)],[92,86,4,73]) ).
tff(94,plain,
tptp_fun_W2_1(xn,xm) = sz00,
inference(unit_resolution,[status(thm)],[93,71]) ).
tff(95,plain,
sdtasdt0(xm,tptp_fun_W2_1(xn,xm)) = sdtasdt0(xm,sz00),
inference(monotonicity,[status(thm)],[94]) ).
tff(96,plain,
xn = sz00,
inference(transitivity,[status(thm)],[63,95,23]) ).
tff(97,plain,
( ( xn != sz00 )
<=> ( xn != sz00 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
xn != sz00,
inference(and_elim,[status(thm)],[56]) ).
tff(99,plain,
xn != sz00,
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
$false,
inference(unit_resolution,[status(thm)],[99,96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM477+1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:13:38 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.20/0.44 % SZS status Theorem
% 0.20/0.44 % SZS output start Proof
% See solution above
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------