TSTP Solution File: RNG123+4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG123+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 8.56s 5.66s
% Output : Proof 8.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 36
% Syntax : Number of formulae : 68 ( 15 unt; 15 typ; 0 def)
% Number of atoms : 367 ( 14 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 521 ( 218 ~; 165 |; 72 &)
% ( 32 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 9 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 176 ( 152 !; 19 ?; 176 :)
% 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(aElement0_type,type,
aElement0: $i > $o ).
tff(xI_type,type,
xI: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(xr_type,type,
xr: $i ).
tff(1,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
<=> aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( aElementOf0(smndt0(sdtasdt0(xq,xu)),xI)
<=> aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = smndt0(sdtasdt0(xq,xu)) ) )
& aElementOf0(smndt0(sdtasdt0(xq,xu)),xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2690) ).
tff(4,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),xI),
inference(modus_ponens,[status(thm)],[4,2]) ).
tff(6,plain,
aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(transitivity,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) )
<=> ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )),
( ( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
rewrite(
( ( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
( ( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) )
& ( xI = sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2174) ).
tff(20,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,xI)
<=> ? [W1: $i,W2: $i] :
( aElementOf0(W1,slsdtgt0(xa))
& aElementOf0(W2,slsdtgt0(xb))
& ( sdtpldt0(W1,W2) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[19]) ).
tff(21,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) )
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xb))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xb,W1) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[20]) ).
tff(22,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI)
& ! [W0: $i] :
( aElementOf0(W0,slsdtgt0(xa))
<=> ? [W1: $i] :
( aElement0(W1)
& ( sdtasdt0(xa,W1) = W0 ) ) ) ),
inference(and_elim,[status(thm)],[21]) ).
tff(23,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) )
& aIdeal0(xI) ),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
( aSet0(xI)
& ! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) ) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
! [W0: $i] :
( aElementOf0(W0,xI)
=> ( ! [W1: $i] :
( aElementOf0(W1,xI)
=> aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( aElement0(W1)
=> aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xI)
| ( ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| aElementOf0(sdtpldt0(W0,W1),xI) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),xI) ) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(modus_ponens,[status(thm)],[27,15]) ).
tff(29,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ( ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
& ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(modus_ponens,[status(thm)],[29,13]) ).
tff(31,plain,
! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(modus_ponens,[status(thm)],[30,11]) ).
tff(32,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(34,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(W0,W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,W0),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) )
| ~ aElementOf0(smndt0(sdtasdt0(xq,xu)),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| ~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(unit_resolution,[status(thm)],[34,31,6]) ).
tff(36,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| aElementOf0(sdtasdt0(W1,smndt0(sdtasdt0(xq,xu))),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(tautology,[status(thm)],]) ).
tff(37,plain,
! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ aElementOf0(xr,xI)
<=> ~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ~ aElementOf0(xr,xI)
<=> ~ aElementOf0(xr,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
~ ( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xr ) )
| aElementOf0(xr,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(41,plain,
~ aElementOf0(xr,xI),
inference(or_elim,[status(thm)],[40]) ).
tff(42,plain,
~ aElementOf0(xr,xI),
inference(modus_ponens,[status(thm)],[41,39]) ).
tff(43,plain,
~ aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( aElementOf0(xb,xI)
<=> aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( aElementOf0(xb,xI)
<=> aElementOf0(xb,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
( ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xb ) )
& ? [W0: $i,W1: $i] :
( aElementOf0(W0,slsdtgt0(xa))
& aElementOf0(W1,slsdtgt0(xb))
& ( sdtpldt0(W0,W1) = xb ) )
& aElementOf0(xb,xI) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2699) ).
tff(47,plain,
aElementOf0(xb,xI),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
aElementOf0(xb,xI),
inference(modus_ponens,[status(thm)],[47,45]) ).
tff(49,plain,
aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),W1),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) )
| ~ aElementOf0(xb,sdtpldt1(slsdtgt0(xa),slsdtgt0(xb)))
| aElementOf0(sdtpldt0(smndt0(sdtasdt0(xq,xu)),xb),sdtpldt1(slsdtgt0(xa),slsdtgt0(xb))) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,49,43,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG123+4 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.31 % Computer : n021.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Fri Sep 2 22:43:44 EDT 2022
% 0.09/0.31 % CPUTime :
% 0.09/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.31 Usage: tptp [options] [-file:]file
% 0.09/0.31 -h, -? prints this message.
% 0.09/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.31 -m, -model generate model.
% 0.09/0.31 -p, -proof generate proof.
% 0.09/0.31 -c, -core generate unsat core of named formulas.
% 0.09/0.31 -st, -statistics display statistics.
% 0.09/0.31 -t:timeout set timeout (in second).
% 0.09/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.31 -<param>:<value> configuration parameter and value.
% 0.09/0.31 -o:<output-file> file to place output in.
% 8.56/5.66 % SZS status Theorem
% 8.56/5.66 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------