TSTP Solution File: LAT382+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT382+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:33:39 EDT 2022
% Result : Theorem 0.19s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 56
% Syntax : Number of formulae : 133 ( 31 unt; 11 typ; 0 def)
% Number of atoms : 1125 ( 52 equ)
% Maximal formula atoms : 22 ( 9 avg)
% Number of connectives : 1600 ( 670 ~; 603 |; 168 &)
% ( 80 <=>; 79 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 73 ( 73 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 7 >; 6 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 235 ( 217 !; 0 ?; 235 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xu_type,type,
xu: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xT_type,type,
xT: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xS_type,type,
xS: $i ).
tff(aLowerBoundOfIn0_type,type,
aLowerBoundOfIn0: ( $i * $i * $i ) > $o ).
tff(aInfimumOfIn0_type,type,
aInfimumOfIn0: ( $i * $i * $i ) > $o ).
tff(xv_type,type,
xv: $i ).
tff(tptp_fun_W1_6_type,type,
tptp_fun_W1_6: $i > $i ).
tff(1,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
aSet0(xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__773) ).
tff(3,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[7,5]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(10,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(13,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ),
inference(unit_resolution,[status(thm)],[19,16,3]) ).
tff(21,plain,
( aElementOf0(xu,xT)
<=> aElementOf0(xu,xT) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xv,W0) )
& aLowerBoundOfIn0(xv,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xv) )
& aInfimumOfIn0(xv,xS,xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__792) ).
tff(23,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xv,W0) )
& aLowerBoundOfIn0(xv,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xv) ) ),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xv,W0) )
& aLowerBoundOfIn0(xv,xS,xT) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xv,W0) ) ),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT)
& aElementOf0(xv,xT) ),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
& aInfimumOfIn0(xu,xS,xT)
& aElementOf0(xv,xT) ),
inference(and_elim,[status(thm)],[26]) ).
tff(28,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
& aInfimumOfIn0(xu,xS,xT) ),
inference(and_elim,[status(thm)],[27]) ).
tff(29,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT)
& ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) ) ),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) )
& aLowerBoundOfIn0(xu,xS,xT) ),
inference(and_elim,[status(thm)],[29]) ).
tff(31,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT)
& ! [W0: $i] :
( aElementOf0(W0,xS)
=> sdtlseqdt0(xu,W0) ) ),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
( aElementOf0(xu,xT)
& aElementOf0(xu,xT) ),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
aElementOf0(xu,xT),
inference(and_elim,[status(thm)],[32]) ).
tff(34,plain,
aElementOf0(xu,xT),
inference(modus_ponens,[status(thm)],[33,21]) ).
tff(35,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xu)
| ~ aElementOf0(xu,xT) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xu)
| ~ aElementOf0(xu,xT) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xu)
| ~ aElementOf0(xu,xT) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xu)
| ~ aElementOf0(xu,xT) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
aElement0(xu),
inference(unit_resolution,[status(thm)],[37,34,20]) ).
tff(39,plain,
( aElementOf0(xv,xT)
<=> aElementOf0(xv,xT) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
aElementOf0(xv,xT),
inference(and_elim,[status(thm)],[27]) ).
tff(41,plain,
aElementOf0(xv,xT),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xv)
| ~ aElementOf0(xv,xT) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xv)
| ~ aElementOf0(xv,xT) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xv)
| ~ aElementOf0(xv,xT) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(xv)
| ~ aElementOf0(xv,xT) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
aElement0(xv),
inference(unit_resolution,[status(thm)],[44,41,20]) ).
tff(46,plain,
( aLowerBoundOfIn0(xv,xS,xT)
<=> aLowerBoundOfIn0(xv,xS,xT) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(and_elim,[status(thm)],[24]) ).
tff(48,plain,
aLowerBoundOfIn0(xv,xS,xT),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT)
| ~ aLowerBoundOfIn0(xv,xS,xT) ),
inference(tautology,[status(thm)],]) ).
tff(50,plain,
( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) ),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
^ [W0: $i] :
refl(
( ( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) )
<=> ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )),
( ( sdtlseqdt0(W0,xu)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) )),
rewrite(
( ( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) )),
( ( sdtlseqdt0(W0,xu)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [W0: $i] :
rewrite(
( ( ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) )
<=> ( sdtlseqdt0(W0,xu)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [W0: $i] :
( ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) )
<=> ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) )
<=> ! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
<=> ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )),
( ( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
<=> ( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) ) )),
rewrite(
( ( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
<=> ( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) ) )),
( ( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
<=> ( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) )
<=> ! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xu) ),
inference(and_elim,[status(thm)],[29]) ).
tff(61,plain,
! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [W0: $i] :
( ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xu) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ),
inference(modus_ponens,[status(thm)],[64,54]) ).
tff(66,plain,
! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ),
inference(modus_ponens,[status(thm)],[65,52]) ).
tff(67,plain,
( ( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) )
| sdtlseqdt0(xv,xu) )
<=> ( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) )
| sdtlseqdt0(xv,xu) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( sdtlseqdt0(xv,xu)
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) ) )
<=> ( ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) )
| sdtlseqdt0(xv,xu) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| sdtlseqdt0(xv,xu)
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) ) )
<=> ( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) )
| sdtlseqdt0(xv,xu) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| sdtlseqdt0(xv,xu)
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) ) )
<=> ( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) )
| sdtlseqdt0(xv,xu) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| sdtlseqdt0(xv,xu)
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xu)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| ~ ( ~ ( ~ aElementOf0(xv,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xv),xS)
| sdtlseqdt0(xv,tptp_fun_W1_6(xv)) ) )
| aLowerBoundOfIn0(xv,xS,xT) )
| sdtlseqdt0(xv,xu) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
sdtlseqdt0(xv,xu),
inference(unit_resolution,[status(thm)],[72,66,50]) ).
tff(74,plain,
( aLowerBoundOfIn0(xu,xS,xT)
<=> aLowerBoundOfIn0(xu,xS,xT) ),
inference(rewrite,[status(thm)],]) ).
tff(75,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(and_elim,[status(thm)],[30]) ).
tff(76,plain,
aLowerBoundOfIn0(xu,xS,xT),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
( ~ ( ~ aElementOf0(xu,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xu),xS)
| sdtlseqdt0(xu,tptp_fun_W1_6(xu)) ) )
| aLowerBoundOfIn0(xu,xS,xT)
| ~ aLowerBoundOfIn0(xu,xS,xT) ),
inference(tautology,[status(thm)],]) ).
tff(78,plain,
( ~ ( ~ aElementOf0(xu,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xu),xS)
| sdtlseqdt0(xu,tptp_fun_W1_6(xu)) ) )
| aLowerBoundOfIn0(xu,xS,xT) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
^ [W0: $i] :
refl(
( ( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) )),
inference(bind,[status(th)],]) ).
tff(80,plain,
( ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) )
<=> ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )),
( ( sdtlseqdt0(W0,xv)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) )),
rewrite(
( ( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) )),
( ( sdtlseqdt0(W0,xv)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) )
<=> ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [W0: $i] :
rewrite(
( ( ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) )
<=> ( sdtlseqdt0(W0,xv)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [W0: $i] :
( ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) )
<=> ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) )
<=> ! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
<=> ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )),
( ( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xv) )
<=> ( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xv) ) )),
rewrite(
( ( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xv) )
<=> ( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) ) )),
( ( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xv) )
<=> ( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xv) )
<=> ! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
! [W0: $i] :
( ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( aElementOf0(W1,xS)
=> sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
=> sdtlseqdt0(W0,xv) ),
inference(and_elim,[status(thm)],[23]) ).
tff(89,plain,
! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [W0: $i] :
( ~ ( ( aElementOf0(W0,xT)
& ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| sdtlseqdt0(W0,W1) ) )
| aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [W0: $i] :
( ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) )
| sdtlseqdt0(W0,xv) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ( ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
& ~ aLowerBoundOfIn0(W0,xS,xT) ) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ),
inference(modus_ponens,[status(thm)],[92,82]) ).
tff(94,plain,
! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) ),
inference(modus_ponens,[status(thm)],[93,80]) ).
tff(95,plain,
( ( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| sdtlseqdt0(xu,xv)
| ~ ( ~ ( ~ aElementOf0(xu,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xu),xS)
| sdtlseqdt0(xu,tptp_fun_W1_6(xu)) ) )
| aLowerBoundOfIn0(xu,xS,xT) ) )
<=> ( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| sdtlseqdt0(xu,xv)
| ~ ( ~ ( ~ aElementOf0(xu,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xu),xS)
| sdtlseqdt0(xu,tptp_fun_W1_6(xu)) ) )
| aLowerBoundOfIn0(xu,xS,xT) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| sdtlseqdt0(xu,xv)
| ~ ( ~ ( ~ aElementOf0(xu,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xu),xS)
| sdtlseqdt0(xu,tptp_fun_W1_6(xu)) ) )
| aLowerBoundOfIn0(xu,xS,xT) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [W0: $i] :
( sdtlseqdt0(W0,xv)
| ~ ( ~ ( ~ aElementOf0(W0,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(W0),xS)
| sdtlseqdt0(W0,tptp_fun_W1_6(W0)) ) )
| aLowerBoundOfIn0(W0,xS,xT) ) )
| sdtlseqdt0(xu,xv)
| ~ ( ~ ( ~ aElementOf0(xu,xT)
| ~ ( ~ aElementOf0(tptp_fun_W1_6(xu),xS)
| sdtlseqdt0(xu,tptp_fun_W1_6(xu)) ) )
| aLowerBoundOfIn0(xu,xS,xT) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
sdtlseqdt0(xu,xv),
inference(unit_resolution,[status(thm)],[97,94,78]) ).
tff(99,plain,
( ( xu != xv )
<=> ( xu != xv ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
xu != xv,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(101,plain,
xu != xv,
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
<=> ( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(103,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
rewrite(
( ~ ~ ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0) ) )),
trans(
monotonicity(
rewrite(
( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(
( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(
( ( ( W0 = W1 )
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) )),
( ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],]) ).
tff(105,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )),
( ( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( aElement0(W0)
& aElement0(W1) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) ) )),
rewrite(
( ( ( aElement0(W0)
& aElement0(W1) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
( ( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
inference(bind,[status(th)],]) ).
tff(108,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mASymm) ).
tff(110,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(skolemize,[status(sab)],[111]) ).
tff(113,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[112,105]) ).
tff(114,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[113,103]) ).
tff(115,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ) ),
inference(rewrite,[status(thm)],]) ).
tff(116,plain,
( ( ( xu = xv )
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) )
<=> ( ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ) ),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ) ),
inference(transitivity,[status(thm)],[117,115]) ).
tff(119,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xv)
| ~ sdtlseqdt0(xu,xv)
| ~ sdtlseqdt0(xv,xu)
| ~ aElement0(xu) ),
inference(quant_inst,[status(thm)],]) ).
tff(120,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ aElement0(W1)
| ~ sdtlseqdt0(W0,W1)
| ~ sdtlseqdt0(W1,W0)
| ~ aElement0(W0) )
| ( xu = xv )
| ~ aElement0(xu)
| ~ sdtlseqdt0(xv,xu)
| ~ sdtlseqdt0(xu,xv)
| ~ aElement0(xv) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
( ~ aElement0(xu)
| ~ aElement0(xv) ),
inference(unit_resolution,[status(thm)],[120,114,101,98,73]) ).
tff(122,plain,
$false,
inference(unit_resolution,[status(thm)],[121,45,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT382+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.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 : Thu Sep 1 16:42:16 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.
% 0.19/0.40 % SZS status Theorem
% 0.19/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------