TSTP Solution File: NUM443+4 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM443+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:09:44 EDT 2022
% Result : Theorem 0.19s 0.47s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 61
% Syntax : Number of formulae : 132 ( 30 unt; 16 typ; 0 def)
% Number of atoms : 2122 ( 336 equ)
% Maximal formula atoms : 68 ( 18 avg)
% Number of connectives : 3507 (1606 ~;1301 |; 470 &)
% ( 96 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 105 ( 105 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 11 >; 7 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 345 ( 286 !; 33 ?; 345 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(xq_type,type,
xq: $i ).
tff(xc_type,type,
xc: $i ).
tff(xb_type,type,
xb: $i ).
tff(aDivisorOf0_type,type,
aDivisorOf0: ( $i * $i ) > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(aInteger0_type,type,
aInteger0: $i > $o ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(stldt0_type,type,
stldt0: $i > $i ).
tff(szAzrzSzezqlpdtcmdtrp0_type,type,
szAzrzSzezqlpdtcmdtrp0: ( $i * $i ) > $i ).
tff(xa_type,type,
xa: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sz00_type,type,
sz00: $i ).
tff(tptp_fun_W1_15_type,type,
tptp_fun_W1_15: $i > $i ).
tff(1,plain,
( sdteqdtlpzmzozddtrp0(xc,xb,xq)
<=> sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb)) ) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) )
<=> ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
| ~ ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb)) ) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb)) ) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) )
=> ( ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
=> ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ( aInteger0(W0)
& ( ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
=> aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
=> ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| aElementOf0(xc,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
| ~ ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) )
| ~ ( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb)) ) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
& ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
& aElementOf0(xb,stldt0(szAzrzSzezqlpdtcmdtrp0(xa,xq)))
& ? [W0: $i] :
( aInteger0(W0)
& ( sdtasdt0(xq,W0) = sdtpldt0(xc,smndt0(xb)) ) )
& aDivisorOf0(xq,sdtpldt0(xc,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(and_elim,[status(thm)],[5]) ).
tff(7,plain,
sdteqdtlpzmzozddtrp0(xc,xb,xq),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
( aInteger0(xc)
<=> aInteger0(xc) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
( aInteger0(xb)
& aInteger0(xc) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2010) ).
tff(10,plain,
aInteger0(xc),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aInteger0(xc),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
( aInteger0(xb)
<=> aInteger0(xb) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
aInteger0(xb),
inference(and_elim,[status(thm)],[9]) ).
tff(14,plain,
aInteger0(xb),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
( ( xq != sz00 )
<=> ( xq != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
( aInteger0(xa)
& aInteger0(xq)
& ( xq != sz00 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1962) ).
tff(17,plain,
xq != sz00,
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
xq != sz00,
inference(modus_ponens,[status(thm)],[17,15]) ).
tff(19,plain,
( aInteger0(xq)
<=> aInteger0(xq) ),
inference(rewrite,[status(thm)],]) ).
tff(20,plain,
( aInteger0(xa)
& aInteger0(xq) ),
inference(and_elim,[status(thm)],[16]) ).
tff(21,plain,
aInteger0(xq),
inference(and_elim,[status(thm)],[20]) ).
tff(22,plain,
aInteger0(xq),
inference(modus_ponens,[status(thm)],[21,19]) ).
tff(23,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(
( ( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,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) ) )),
( ( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) )
<=> ( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )),
rewrite(
( ( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ( W2 = sz00 )
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) )
<=> ( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) )
<=> ( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,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 ) ) )),
rewrite(
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) )
<=> ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| sdteqdtlpzmzozddtrp0(W1,W0,W2) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) )
<=> ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ) )),
rewrite(
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| sdteqdtlpzmzozddtrp0(W1,W0,W2) ) )
<=> ( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) )
<=> ( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
=> sdteqdtlpzmzozddtrp0(W1,W0,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModSym) ).
tff(31,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [W0: $i,W1: $i,W2: $i] :
( sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 ) )
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[34,24]) ).
tff(36,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ( xq = sz00 )
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ aInteger0(xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq)
| ~ aInteger0(xb)
| ~ aInteger0(xc) )
<=> ( ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ aInteger0(xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq)
| ~ aInteger0(xb)
| ~ aInteger0(xc) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ aInteger0(xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq)
| ~ aInteger0(xb)
| ~ aInteger0(xc) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ aInteger0(xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq)
| ~ aInteger0(xb)
| ~ aInteger0(xc) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W1,W0,W2)
| ~ aInteger0(W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xb,xq) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
sdteqdtlpzmzozddtrp0(xb,xc,xq),
inference(unit_resolution,[status(thm)],[41,35,22,18,14,11,7]) ).
tff(43,plain,
^ [W0: $i] :
refl(
( ~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
<=> ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) ) )),
trans(
monotonicity(
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
trans(
monotonicity(
rewrite(
( ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
<=> ~ ( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) )),
( ~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
<=> ~ ~ ( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) )),
rewrite(
( ~ ~ ( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) )
<=> ( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) )),
( ~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
<=> ( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ))),
( ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
<=> ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) )),
( ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) )
<=> ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) )),
rewrite(
( ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) )
<=> ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) )),
( ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) )
<=> ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) )),
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
<=> ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )),
rewrite(
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) )
<=> ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )),
( ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
<=> ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )),
( ( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) )),
rewrite(
( ( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) )),
( ( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [W0: $i] :
rewrite(
( ( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
<=> ( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( aSet0(szAzrzSzezqlpdtcmdtrp0(xa,xq))
& ! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(54,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
inference(and_elim,[status(thm)],[53]) ).
tff(55,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ ( aInteger0(W0)
& ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ? [W1: $i] :
( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
inference(modus_ponens,[status(thm)],[54,52]) ).
tff(56,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) )
| aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ) ),
inference(skolemize,[status(sab)],[55]) ).
tff(57,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ( aInteger0(W0)
& aInteger0(tptp_fun_W1_15(W0))
& ( sdtasdt0(xq,tptp_fun_W1_15(W0)) = sdtpldt0(W0,smndt0(xa)) )
& aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& sdteqdtlpzmzozddtrp0(W0,xa,xq) ) )
& ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ( ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
& ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
& ! [W1: $i] :
~ ( aInteger0(W1)
& ( sdtasdt0(xq,W1) = sdtpldt0(W0,smndt0(xa)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[56,51]) ).
tff(58,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[57,49]) ).
tff(59,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[58,47]) ).
tff(60,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( sdteqdtlpzmzozddtrp0(xc,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( sdteqdtlpzmzozddtrp0(xc,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( sdteqdtlpzmzozddtrp0(xc,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[62,60]) ).
tff(64,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( sdteqdtlpzmzozddtrp0(xc,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
~ ( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[65,59]) ).
tff(67,plain,
( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xc)
| ~ ( aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xc,smndt0(xa)) ) ) ) )
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(68,plain,
( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) ),
inference(unit_resolution,[status(thm)],[67,66]) ).
tff(69,plain,
( aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
<=> aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(or_elim,[status(thm)],[4]) ).
tff(71,plain,
aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(73,plain,
( ~ ( ~ aElementOf0(xc,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) )
| ~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
~ ( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) ) ),
inference(unit_resolution,[status(thm)],[73,68]) ).
tff(75,plain,
( ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xc,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xc))
| ( sdtasdt0(xq,tptp_fun_W1_15(xc)) != sdtpldt0(xc,smndt0(xa)) )
| sdteqdtlpzmzozddtrp0(xc,xa,xq) ),
inference(tautology,[status(thm)],]) ).
tff(76,plain,
sdteqdtlpzmzozddtrp0(xc,xa,xq),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
( ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[79,77]) ).
tff(81,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( sdteqdtlpzmzozddtrp0(xb,xa,xq)
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(82,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(W0))
| ( sdtasdt0(xq,tptp_fun_W1_15(W0)) != sdtpldt0(W0,smndt0(xa)) ) ) )
| ~ ( aElementOf0(W0,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(W0)
| ~ ( sdteqdtlpzmzozddtrp0(W0,xa,xq)
| aDivisorOf0(xq,sdtpldt0(W0,smndt0(xa)))
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(W0,smndt0(xa)) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ ( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[82,59]) ).
tff(84,plain,
( ~ ( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ ( ~ aInteger0(xb)
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| ~ aInteger0(tptp_fun_W1_15(xb))
| ( sdtasdt0(xq,tptp_fun_W1_15(xb)) != sdtpldt0(xb,smndt0(xa)) ) ) )
| ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(85,plain,
( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
<=> ~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(and_elim,[status(thm)],[5]) ).
tff(88,plain,
~ aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq)),
inference(modus_ponens,[status(thm)],[87,86]) ).
tff(89,plain,
( ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
( ~ ( aElementOf0(xb,szAzrzSzezqlpdtcmdtrp0(xa,xq))
| ~ aInteger0(xb)
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) )
| ~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ) ),
inference(unit_resolution,[status(thm)],[89,14,88]) ).
tff(91,plain,
~ ( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) ) ),
inference(unit_resolution,[status(thm)],[90,85]) ).
tff(92,plain,
( aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ ! [W1: $i] :
( ~ aInteger0(W1)
| ( sdtasdt0(xq,W1) != sdtpldt0(xb,smndt0(xa)) ) )
| ~ sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(tautology,[status(thm)],]) ).
tff(93,plain,
~ sdteqdtlpzmzozddtrp0(xb,xa,xq),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
( aInteger0(xa)
<=> aInteger0(xa) ),
inference(rewrite,[status(thm)],]) ).
tff(95,plain,
aInteger0(xa),
inference(and_elim,[status(thm)],[20]) ).
tff(96,plain,
aInteger0(xa),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
refl(
( ( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
<=> ( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
<=> ~ ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2) ) )),
( ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
<=> ~ ~ ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2) ) )),
rewrite(
( ~ ~ ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2) )
<=> ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2) ) )),
( ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
<=> ( ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2) ) )),
trans(
monotonicity(
rewrite(
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
<=> ~ ( ( W2 = sz00 )
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
<=> ~ ~ ( ( W2 = sz00 )
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ~ ~ ( ( W2 = sz00 )
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( W2 = sz00 )
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
<=> ( ( W2 = sz00 )
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
( ( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) )
<=> ( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ( W2 = sz00 )
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) ) )),
rewrite(
( ( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ( W2 = sz00 )
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ aInteger0(W0) )
<=> ( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) ) )),
( ( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) )
<=> ( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(100,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
^ [W0: $i,W1: $i,W2: $i,W3: $i] :
trans(
monotonicity(
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 )
& aInteger0(W3) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) )),
rewrite(
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) )),
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
<=> ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) )),
rewrite(
( ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) )
<=> ( ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| sdteqdtlpzmzozddtrp0(W0,W3,W2) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) )
<=> ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
=> ( ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ) )),
rewrite(
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
=> ( ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| sdteqdtlpzmzozddtrp0(W0,W3,W2) ) )
<=> ( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) ) )),
( ( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) )
<=> ( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) )
=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
=> sdteqdtlpzmzozddtrp0(W0,W3,W2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquModTrn) ).
tff(105,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
& sdteqdtlpzmzozddtrp0(W1,W3,W2) )
| ~ ( aInteger0(W0)
& aInteger0(W1)
& aInteger0(W2)
& ( W2 != sz00 )
& aInteger0(W3) ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) ),
inference(modus_ponens,[status(thm)],[108,98]) ).
tff(110,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( ( xq = sz00 )
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aInteger0(xb) )
<=> ( ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ),
inference(monotonicity,[status(thm)],[111]) ).
tff(113,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aInteger0(xb) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ),
inference(transitivity,[status(thm)],[112,110]) ).
tff(114,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ aInteger0(xa)
| ~ aInteger0(xq)
| ~ aInteger0(xc)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ aInteger0(xb) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( ~ ! [W0: $i,W1: $i,W2: $i,W3: $i] :
( ( W2 = sz00 )
| sdteqdtlpzmzozddtrp0(W0,W3,W2)
| ~ aInteger0(W3)
| ~ aInteger0(W2)
| ~ aInteger0(W1)
| ~ sdteqdtlpzmzozddtrp0(W0,W1,W2)
| ~ sdteqdtlpzmzozddtrp0(W1,W3,W2)
| ~ aInteger0(W0) )
| ( xq = sz00 )
| ~ aInteger0(xb)
| ~ aInteger0(xc)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| sdteqdtlpzmzozddtrp0(xb,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xc,xa,xq)
| ~ sdteqdtlpzmzozddtrp0(xb,xc,xq) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
$false,
inference(unit_resolution,[status(thm)],[115,109,96,22,18,14,11,93,76,42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM443+4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 10:34:14 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.47 % SZS status Theorem
% 0.19/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------