TSTP Solution File: RNG124+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG124+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 : Tue Sep 20 03:18:33 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 39
% Syntax : Number of formulae : 73 ( 16 unt; 16 typ; 0 def)
% Number of atoms : 624 ( 198 equ)
% Maximal formula atoms : 24 ( 10 avg)
% Number of connectives : 958 ( 438 ~; 309 |; 153 &)
% ( 51 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 9 >; 5 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 231 ( 177 !; 46 ?; 231 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(xb_type,type,
xb: $i ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xu_type,type,
xu: $i ).
tff(xq_type,type,
xq: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slsdtgt0_type,type,
slsdtgt0: $i > $i ).
tff(xa_type,type,
xa: $i ).
tff(sdtpldt1_type,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(xI_type,type,
xI: $i ).
tff(xr_type,type,
xr: $i ).
tff(sz00_type,type,
sz00: $i ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(1,plain,
( aElementOf0(xr,xI)
<=> aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aElementOf0(xr,xI)
<=> aElementOf0(xr,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xr ) )
& aElementOf0(xr,xI) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2729) ).
tff(4,plain,
aElementOf0(xr,xI),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aElementOf0(xr,xI),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) )
| ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(tautology,[status(thm)],]) ).
tff(8,plain,
( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ),
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
( ( xr != sz00 )
<=> ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
( ( xr != sz00 )
<=> ( xr != sz00 ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
xr != sz00,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2673) ).
tff(12,plain,
xr != sz00,
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) != sz00,
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
<=> iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( iLess0(sbrdtbr0(xr),sbrdtbr0(xu))
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,plain,
( ( $false
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) )
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ( xr = sz00 )
<=> $false ),
inference(iff_false,[status(thm)],[11]) ).
tff(18,plain,
( ( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) )
<=> ( $false
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
inference(monotonicity,[status(thm)],[17]) ).
tff(19,plain,
( ( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) )
<=> iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(transitivity,[status(thm)],[18,16]) ).
tff(20,axiom,
( aElement0(xq)
& aElement0(xr)
& ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) )
& ( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2666) ).
tff(21,plain,
( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ),
inference(and_elim,[status(thm)],[20]) ).
tff(22,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(modus_ponens,[status(thm)],[21,19]) ).
tff(23,plain,
iLess0(sbrdtbr0(xr),sbrdtbr0(xu)),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu)),
inference(modus_ponens,[status(thm)],[23,14]) ).
tff(25,plain,
^ [W0: $i] :
refl(
( ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
^ [W0: $i] :
rewrite(
( ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(28,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(transitivity,[status(thm)],[28,26]) ).
tff(30,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i,W2: $i] :
trans(
monotonicity(
rewrite(
( ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
<=> ~ ( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )),
( ~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
<=> ~ ~ ( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) )
<=> ( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )),
( ~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
<=> ( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ))),
( ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
<=> ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )),
( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
<=> ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )),
rewrite(
( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
<=> ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )),
( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
<=> ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )),
( ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
rewrite(
( ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
( ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [W0: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
<=> ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )),
rewrite(
( ~ ( ( W0 != sz00 ) )
<=> ( W0 = sz00 ) )),
( ( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
| ~ ( ( W0 != sz00 ) ) )
<=> ( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
| ( W0 = sz00 ) ) )),
rewrite(
( ( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
| ( W0 = sz00 ) )
<=> ( ( W0 = sz00 )
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ) )),
( ( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
| ~ ( ( W0 != sz00 ) ) )
<=> ( ( W0 = sz00 )
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ) )),
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
| ~ ( ( W0 != sz00 ) ) )
<=> ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( W0 = sz00 )
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ) )),
rewrite(
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( W0 = sz00 )
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ) )),
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
| ~ ( ( W0 != sz00 ) ) )
<=> ( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
| ~ ( ( W0 != sz00 ) ) )
<=> ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [W0: $i] :
rewrite(
( ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) )
<=> ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) )
<=> ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) )
<=> ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
| aElementOf0(W0,xI) )
& ( W0 != sz00 ) )
<=> ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) )),
( ( ( ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
| aElementOf0(W0,xI) )
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
<=> ( ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) )),
rewrite(
( ( ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
<=> ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ) )),
( ( ( ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
| aElementOf0(W0,xI) )
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
<=> ( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [W0: $i] :
( ( ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
| aElementOf0(W0,xI) )
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) )
<=> ! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xu ) )
& aElementOf0(xu,xI)
& ( xu != sz00 )
& ! [W0: $i] :
( ( ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
| aElementOf0(W0,xI) )
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2273) ).
tff(40,plain,
! [W0: $i] :
( ( ( ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) )
| aElementOf0(W0,xI) )
& ( W0 != sz00 ) )
=> ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu)) ),
inference(and_elim,[status(thm)],[39]) ).
tff(41,plain,
! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[40,38]) ).
tff(42,plain,
! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,xI)
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[41,36]) ).
tff(43,plain,
! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( W0 != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
! [W0: $i] :
( ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
| ~ ( ( W0 != sz00 ) ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
& ! [W1: $i,W2: $i] :
~ ( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[44,33]) ).
tff(46,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(modus_ponens,[status(thm)],[45,31]) ).
tff(47,plain,
! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(modus_ponens,[status(thm)],[46,29]) ).
tff(48,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
( ( ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) )
<=> ( ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) )
<=> ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ( ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ( ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ( ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
<=> ( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) ) ),
inference(transitivity,[status(thm)],[53,48]) ).
tff(55,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( ~ ! [W0: $i] :
( ( W0 = sz00 )
| ~ iLess0(sbrdtbr0(W0),sbrdtbr0(xu))
| ~ ( aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ( sdtpldt0(W1,W2) != W0 )
| ~ aElementOf0(W1,slsdtgt0(xa)) ) ) )
| ( sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) = sz00 )
| ~ iLess0(sbrdtbr0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sbrdtbr0(xu))
| ~ ( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i,W2: $i] :
( ~ aElementOf0(W2,slsdtgt0(xb))
| ~ aElementOf0(W1,slsdtgt0(xa))
| ( sdtpldt0(W1,W2) != sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb) ) ) ) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,47,24,13,8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : RNG124+4 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 22:11:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------