TSTP Solution File: RNG123+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG123+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 03:18:32 EDT 2022
% Result : Theorem 95.98s 60.67s
% Output : Proof 95.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 53
% Syntax : Number of formulae : 100 ( 27 unt; 21 typ; 0 def)
% Number of atoms : 783 ( 13 equ)
% Maximal formula atoms : 28 ( 9 avg)
% Number of connectives : 1537 ( 847 ~; 572 |; 65 &)
% ( 44 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 14 >; 5 *; 0 +; 0 <<)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 229 ( 223 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtpldt1_type,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(slsdtgt0_type,type,
slsdtgt0: $i > $i ).
tff(xb_type,type,
xb: $i ).
tff(xa_type,type,
xa: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $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(xr_type,type,
xr: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xI_type,type,
xI: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(tptp_fun_W1_8_type,type,
tptp_fun_W1_8: $i > $i ).
tff(tptp_fun_W2_10_type,type,
tptp_fun_W2_10: $i > $i ).
tff(tptp_fun_W2_9_type,type,
tptp_fun_W2_9: $i > $i ).
tff(1,plain,
( ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) )
<=> ( xb = sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) )
<=> ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aElement0(xq)
& aElement0(xr)
& ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) )
& ( ( xr = sz00 )
| iLess0(sbrdtbr0(xr),sbrdtbr0(xu)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2666) ).
tff(4,plain,
( aElement0(xq)
& aElement0(xr)
& ( xb = sdtpldt0(sdtasdt0(xq,xu),xr) ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),xr),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
xb = sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)) = xb,
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))) = sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
<=> aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
<=> aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
<=> ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
( ~ aElementOf0(xr,xI)
<=> ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ~ aElementOf0(xr,xI)
<=> ~ aElementOf0(xr,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ aElementOf0(xr,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(16,plain,
~ aElementOf0(xr,xI),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,plain,
~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[17,12]) ).
tff(19,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
^ [W0: $i] :
refl(
( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[24,22]) ).
tff(26,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )),
rewrite(
( ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
<=> ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )),
( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ( ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
rewrite(
( ( ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [W0: $i] :
rewrite(
( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( ~ ~ aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( ~ ~ aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(31,plain,
^ [W0: $i] :
rewrite(
( ( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,axiom,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
tff(34,plain,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( ~ ~ aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[36,29]) ).
tff(38,plain,
! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[37,27]) ).
tff(39,plain,
! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,25]) ).
tff(40,plain,
! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[39,20]) ).
tff(41,plain,
( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aElementOf0(tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),tptp_fun_W2_9(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ( ~ aElement0(tptp_fun_W2_10(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) )
| ~ ( ~ aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
~ ( ~ ( aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aElementOf0(tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),tptp_fun_W2_9(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ( ~ aElement0(tptp_fun_W2_10(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) )
| ~ ( ~ aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ ( aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aElementOf0(tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),tptp_fun_W2_9(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ( ~ aElement0(tptp_fun_W2_10(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),tptp_fun_W1_8(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) )
| ~ ( ~ aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) )
| ~ aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(44,plain,
( ~ aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[43,42]) ).
tff(45,plain,
( aIdeal0(xI)
<=> aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( aIdeal0(xI)
<=> aIdeal0(xI) ),
inference(rewrite,[status(thm)],]) ).
tff(47,axiom,
( aIdeal0(xI)
& ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
tff(48,plain,
aIdeal0(xI),
inference(and_elim,[status(thm)],[47]) ).
tff(49,plain,
aIdeal0(xI),
inference(modus_ponens,[status(thm)],[48,46]) ).
tff(50,plain,
aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[49,45]) ).
tff(51,plain,
( ~ ( ~ aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) )
| ~ aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
( ~ ( ~ aIdeal0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) )
| ~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
~ ( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(unit_resolution,[status(thm)],[52,44]) ).
tff(54,plain,
( ~ aSet0(sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(55,plain,
! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
<=> aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
<=> aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(rewrite,[status(thm)],]) ).
tff(58,axiom,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
tff(59,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[59,56]) ).
tff(61,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W1,W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(unit_resolution,[status(thm)],[63,60,55]) ).
tff(65,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(tautology,[status(thm)],]) ).
tff(66,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( aElementOf0(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
<=> aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(68,plain,
( aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
<=> aElementOf0(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(symmetry,[status(thm)],[67]) ).
tff(69,plain,
( aElementOf0(xb,xI)
<=> aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( aElementOf0(xb,xI)
<=> aElementOf0(xb,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
aElementOf0(xb,xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).
tff(72,plain,
aElementOf0(xb,xI),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[72,69]) ).
tff(74,plain,
aElementOf0(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[73,68]) ).
tff(75,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ aElementOf0(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ aElementOf0(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ aElementOf0(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(quant_inst,[status(thm)],]) ).
tff(77,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W2),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ aElementOf0(sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),sdtpldt0(sdtasdt0(xq,xu),sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(unit_resolution,[status(thm)],[77,74,66]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : RNG123+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Sep 2 22:43:35 EDT 2022
% 0.13/0.34 % 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.
% 95.98/60.67 % SZS status Theorem
% 95.98/60.67 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------