%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : COM017+4 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 Jun 21 05:00:59 AM UTC 2025
% Result : Theorem 0.23s 0.44s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 32
% Syntax : Number of formulae : 84 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 2781 ( 288 equ)
% Maximal formula atoms : 80 ( 33 avg)
% Number of connectives : 4196 (1671 ~;1667 |; 763 &)
% ( 82 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 172 ( 172 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 17 usr; 1 prp; 0-6 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 321 ( 178 !; 127 ?; 321 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtmndtplgtdt0_type,type,
sdtmndtplgtdt0: ( $i * $i * $i ) > $o ).
tff(tptp_fun_W3_12_type,type,
tptp_fun_W3_12: ( $i * $i ) > $i ).
tff(xu_type,type,
xu: $i ).
tff(xv_type,type,
xv: $i ).
tff(xR_type,type,
xR: $i ).
tff(aReductOfIn0_type,type,
aReductOfIn0: ( $i * $i * $i ) > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtmndtasgtdt0_type,type,
sdtmndtasgtdt0: ( $i * $i * $i ) > $o ).
tff(tptp_fun_W4_14_type,type,
tptp_fun_W4_14: ( $i * $i ) > $i ).
tff(tptp_fun_W4_13_type,type,
tptp_fun_W4_13: ( $i * $i ) > $i ).
tff(xa_type,type,
xa: $i ).
tff(xc_type,type,
xc: $i ).
tff(xb_type,type,
xb: $i ).
tff(isLocallyConfluent0_type,type,
isLocallyConfluent0: $i > $o ).
tff(iLess0_type,type,
iLess0: ( $i * $i ) > $o ).
tff(isTerminating0_type,type,
isTerminating0: $i > $o ).
tff(1,plain,
( aReductOfIn0(xv,xa,xR)
<=> aReductOfIn0(xv,xa,xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& ( ( xv = xc )
| ( ( aReductOfIn0(xc,xv,xR)
| ? [W0: $i] :
( aElement0(W0)
& aReductOfIn0(W0,xv,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) )
& sdtmndtplgtdt0(xv,xR,xc) ) )
& sdtmndtasgtdt0(xv,xR,xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__779) ).
tff(3,plain,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR)
& ( ( xv = xc )
| ( ( aReductOfIn0(xc,xv,xR)
| ? [W0: $i] :
( aElement0(W0)
& aReductOfIn0(W0,xv,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) )
& sdtmndtplgtdt0(xv,xR,xc) ) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
( aElement0(xv)
& aReductOfIn0(xv,xa,xR) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
aReductOfIn0(xv,xa,xR),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
aReductOfIn0(xv,xa,xR),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aElement0(xv)
<=> aElement0(xv) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
aElement0(xv),
inference(and_elim,[status(thm)],[4]) ).
tff(9,plain,
aElement0(xv),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
( aReductOfIn0(xu,xa,xR)
<=> aReductOfIn0(xu,xa,xR) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& ( ( xu = xb )
| ( ( aReductOfIn0(xb,xu,xR)
| ? [W0: $i] :
( aElement0(W0)
& aReductOfIn0(W0,xu,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtplgtdt0(xu,xR,xb) ) )
& sdtmndtasgtdt0(xu,xR,xb) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__755) ).
tff(12,plain,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& ( ( xu = xb )
| ( ( aReductOfIn0(xb,xu,xR)
| ? [W0: $i] :
( aElement0(W0)
& aReductOfIn0(W0,xu,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtplgtdt0(xu,xR,xb) ) ) ),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR) ),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
aReductOfIn0(xu,xa,xR),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
aReductOfIn0(xu,xa,xR),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( aElement0(xu)
<=> aElement0(xu) ),
inference(rewrite,[status(thm)],[]) ).
tff(17,plain,
aElement0(xu),
inference(and_elim,[status(thm)],[13]) ).
tff(18,plain,
aElement0(xu),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
( aElement0(xa)
<=> aElement0(xa) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__731) ).
tff(21,plain,
( aElement0(xa)
& aElement0(xb) ),
inference(and_elim,[status(thm)],[20]) ).
tff(22,plain,
aElement0(xa),
inference(and_elim,[status(thm)],[21]) ).
tff(23,plain,
aElement0(xa),
inference(modus_ponens,[status(thm)],[22,19]) ).
tff(24,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
<=> ~ ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR) ) )),
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
<=> ~ ~ ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR) ) )),
rewrite(( ~ ~ ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR) ) )),
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR) ) )),
trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) )
<=> ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )),
( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) ) )),
rewrite(( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) ) )),
( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) ) )),
( ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) )
<=> ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )),
rewrite(( ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) )
<=> ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )),
( ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) )
<=> ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )),
( ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
rewrite(( ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
( ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) )
<=> ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )),
( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) ) )),
rewrite(( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) ) )),
( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) ) )),
( ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) )
<=> ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )),
rewrite(( ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) )
<=> ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )),
( ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) )
<=> ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )),
( ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
rewrite(( ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
( ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
( ( aElement0(tptp_fun_W3_12(W2,W1))
& ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
& ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) )
<=> ( aElement0(tptp_fun_W3_12(W2,W1))
& ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
& ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )),
rewrite(( ( aElement0(tptp_fun_W3_12(W2,W1))
& ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
& ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) )
<=> ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )),
( ( aElement0(tptp_fun_W3_12(W2,W1))
& ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
& ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) )
<=> ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ( aElement0(tptp_fun_W3_12(W2,W1))
& ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
& ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
rewrite(( ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ( aElement0(tptp_fun_W3_12(W2,W1))
& ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
& ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ( aElement0(tptp_fun_W3_12(W2,W1))
& ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
& ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2) ) )),
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR) ) )),
rewrite(( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR) ) )),
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR) ) )),
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) ) )),
rewrite(( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) ) )),
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
<=> ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) ) )),
quant_intro(proof_bind(^ [W3: $i] :
trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) ) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) ) ) )),
( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3) ) )),
rewrite(( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3) ) )),
( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3) ) )),
rewrite(( ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
<=> ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) ) )),
( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) ) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) ) ) )),
rewrite(( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) ) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) ) ) )),
( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) ) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) ) ) )),
( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )),
rewrite(( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )),
( ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) )
<=> ( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ))),
( ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) )
<=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )),
( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
<=> ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ) )),
rewrite(( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ) )),
( ( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
& isLocallyConfluent0(xR)
& ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( aReductOfIn0(W1,W0,xR)
| ? [W2: $i] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1) )
=> iLess0(W1,W0) ) )
& isTerminating0(xR) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__656_01) ).
tff(32,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
& isLocallyConfluent0(xR)
& ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( aReductOfIn0(W1,W0,xR)
| ? [W2: $i] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1) )
=> iLess0(W1,W0) ) ) ),
inference(and_elim,[status(thm)],[31]) ).
tff(33,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
& isLocallyConfluent0(xR) ),
inference(and_elim,[status(thm)],[32]) ).
tff(34,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ? [W3: $i] :
( aElement0(W3)
& ( ( W1 = W3 )
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( ( W2 = W3 )
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4: $i] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) ),
inference(modus_ponens,[status(thm)],[35,28]) ).
tff(37,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
| ( aElement0(tptp_fun_W3_12(W2,W1))
& ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ( aElement0(tptp_fun_W4_13(W2,W1))
& aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
& sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
& ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ( ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ( aElement0(tptp_fun_W4_14(W2,W1))
& aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
& sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
& sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ),
inference(modus_ponens,[status(thm)],[37,27]) ).
tff(39,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) ),
inference(modus_ponens,[status(thm)],[38,25]) ).
tff(40,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) )
| ~ aReductOfIn0(xv,xa,xR) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) )
| ~ aReductOfIn0(xv,xa,xR) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) ) )
<=> ( ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) )
| ~ aReductOfIn0(xv,xa,xR) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ( ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) )
<=> ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
<=> ( ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
<=> ( ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) )
| ~ aReductOfIn0(xv,xa,xR) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) )
| ~ aReductOfIn0(xv,xa,xR) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) )
| ~ aReductOfIn0(xv,xa,xR) ) ),
inference(transitivity,[status(thm)],[45,40]) ).
tff(47,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ aElement0(xv)
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aReductOfIn0(xv,xa,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ~ aElement0(W2)
| ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ~ ( ~ aElement0(tptp_fun_W3_12(W2,W1))
| ~ ( ( W1 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W1,xR)
| ~ ( ~ aElement0(tptp_fun_W4_13(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_13(W2,W1),W1,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W1,xR,tptp_fun_W3_12(W2,W1))
| ~ ( ( W2 = tptp_fun_W3_12(W2,W1) )
| ~ ( ~ ( aReductOfIn0(tptp_fun_W3_12(W2,W1),W2,xR)
| ~ ( ~ aElement0(tptp_fun_W4_14(W2,W1))
| ~ aReductOfIn0(tptp_fun_W4_14(W2,W1),W2,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(W2,W1),xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtplgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ sdtmndtasgtdt0(W2,xR,tptp_fun_W3_12(W2,W1)) ) )
| ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aElement0(xv)
| ~ aReductOfIn0(xu,xa,xR)
| ~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) )
| ~ aReductOfIn0(xv,xa,xR) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) ) ),
inference(unit_resolution,[status(thm)],[48,39,23,18,15,9,6]) ).
tff(50,plain,
( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) )
| sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) )
| ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu)) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
( sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) )
| sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)) ),
inference(tautology,[status(thm)],[]) ).
tff(55,plain,
sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)),
inference(unit_resolution,[status(thm)],[54,49]) ).
tff(56,plain,
( sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) )
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu)) ),
inference(tautology,[status(thm)],[]) ).
tff(57,plain,
( sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_13(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_13(xv,xu),xu,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_13(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR) ) ) )
| ~ ( ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ( ~ sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ~ ( ~ ( ~ aElement0(tptp_fun_W4_14(xv,xu))
| ~ aReductOfIn0(tptp_fun_W4_14(xv,xu),xv,xR)
| ~ sdtmndtplgtdt0(tptp_fun_W4_14(xv,xu),xR,tptp_fun_W3_12(xv,xu)) )
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR) ) ) )
| aElement0(tptp_fun_W3_12(xv,xu)) ),
inference(tautology,[status(thm)],[]) ).
tff(59,plain,
aElement0(tptp_fun_W3_12(xv,xu)),
inference(unit_resolution,[status(thm)],[58,49]) ).
tff(60,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
<=> ( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
<=> ( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ) ),
inference(transitivity,[status(thm)],[63,61]) ).
tff(65,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ( ~ aReductOfIn0(W0,xu,xR)
& ~ sdtmndtasgtdt0(xu,xR,W0)
& ~ sdtmndtplgtdt0(xu,xR,W0)
& ( xu != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
| ( ~ aReductOfIn0(W0,xv,xR)
& ~ sdtmndtasgtdt0(xv,xR,W0)
& ~ sdtmndtplgtdt0(xv,xR,W0)
& ( xv != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) )
<=> ( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(66,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ( ~ aReductOfIn0(W0,xu,xR)
& ~ sdtmndtasgtdt0(xu,xR,W0)
& ~ sdtmndtplgtdt0(xu,xR,W0)
& ( xu != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
| ( ~ aReductOfIn0(W0,xv,xR)
& ~ sdtmndtasgtdt0(xv,xR,W0)
& ~ sdtmndtplgtdt0(xv,xR,W0)
& ( xv != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
& ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
& ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& ( ( xu = W0 )
| aReductOfIn0(W0,xu,xR)
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xu,xR,W0)
| sdtmndtasgtdt0(xu,xR,W0) )
& ( ( xv = W0 )
| aReductOfIn0(W0,xv,xR)
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xv,xR,W0)
| sdtmndtasgtdt0(xv,xR,W0) ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
& ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,axiom,
~ ? [W0: $i] :
( aElement0(W0)
& ( ( xu = W0 )
| aReductOfIn0(W0,xu,xR)
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xu,xR,W0)
| sdtmndtasgtdt0(xu,xR,W0) )
& ( ( xv = W0 )
| aReductOfIn0(W0,xv,xR)
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xv,xR,W0)
| sdtmndtasgtdt0(xv,xR,W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(70,plain,
~ ? [W0: $i] :
( aElement0(W0)
& ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
& ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ ? [W0: $i] :
( aElement0(W0)
& ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
& ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ),
inference(modus_ponens,[status(thm)],[70,67]) ).
tff(72,plain,
~ ? [W0: $i] :
( aElement0(W0)
& ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
& ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ),
inference(modus_ponens,[status(thm)],[71,67]) ).
tff(73,plain,
~ ? [W0: $i] :
( aElement0(W0)
& ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
& ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ),
inference(modus_ponens,[status(thm)],[72,67]) ).
tff(74,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aElement0(W0),~ aElement0(W0))),
nnf_neg(refl($oeq(~ aReductOfIn0(W0,xu,xR),~ aReductOfIn0(W0,xu,xR))),refl($oeq(~ sdtmndtasgtdt0(xu,xR,W0),~ sdtmndtasgtdt0(xu,xR,W0))),refl($oeq(~ sdtmndtplgtdt0(xu,xR,W0),~ sdtmndtplgtdt0(xu,xR,W0))),refl($oeq(xu != W0,xu != W0)),
nnf_neg(proof_bind(^ [W1: $i] :
refl($oeq(~ ( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ),
~ ( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) )))),
$oeq(~ ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ),
! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ))),
$oeq(~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ),
( ~ aReductOfIn0(W0,xu,xR)
& ~ sdtmndtasgtdt0(xu,xR,W0)
& ~ sdtmndtplgtdt0(xu,xR,W0)
& ( xu != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ))),
nnf_neg(refl($oeq(~ aReductOfIn0(W0,xv,xR),~ aReductOfIn0(W0,xv,xR))),refl($oeq(~ sdtmndtasgtdt0(xv,xR,W0),~ sdtmndtasgtdt0(xv,xR,W0))),refl($oeq(~ sdtmndtplgtdt0(xv,xR,W0),~ sdtmndtplgtdt0(xv,xR,W0))),refl($oeq(xv != W0,xv != W0)),
nnf_neg(proof_bind(^ [W1: $i] :
refl($oeq(~ ( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ),
~ ( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) )))),
$oeq(~ ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ),
! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ))),
$oeq(~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ),
( ~ aReductOfIn0(W0,xv,xR)
& ~ sdtmndtasgtdt0(xv,xR,W0)
& ~ sdtmndtplgtdt0(xv,xR,W0)
& ( xv != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ))),
$oeq(~ ( aElement0(W0)
& ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
& ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ? [W1: $i] :
( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ),
( ~ aElement0(W0)
| ( ~ aReductOfIn0(W0,xu,xR)
& ~ sdtmndtasgtdt0(xu,xR,W0)
& ~ sdtmndtplgtdt0(xu,xR,W0)
& ( xu != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
| ( ~ aReductOfIn0(W0,xv,xR)
& ~ sdtmndtasgtdt0(xv,xR,W0)
& ~ sdtmndtplgtdt0(xv,xR,W0)
& ( xv != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(75,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ( ~ aReductOfIn0(W0,xu,xR)
& ~ sdtmndtasgtdt0(xu,xR,W0)
& ~ sdtmndtplgtdt0(xu,xR,W0)
& ( xu != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xu,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) )
| ( ~ aReductOfIn0(W0,xv,xR)
& ~ sdtmndtasgtdt0(xv,xR,W0)
& ~ sdtmndtplgtdt0(xv,xR,W0)
& ( xv != W0 )
& ! [W1: $i] :
~ ( aElement0(W1)
& aReductOfIn0(W1,xv,xR)
& sdtmndtplgtdt0(W1,xR,W0) ) ) ),
inference(nnf-neg,[status(sab)],[73,74]) ).
tff(76,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ),
inference(modus_ponens,[status(thm)],[75,66]) ).
tff(77,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) ),
inference(modus_ponens,[status(thm)],[76,64]) ).
tff(78,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,plain,
( ( ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) )
<=> ( ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) ) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) ) ),
inference(transitivity,[status(thm)],[80,78]) ).
tff(82,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ ( aReductOfIn0(W0,xu,xR)
| sdtmndtasgtdt0(xu,xR,W0)
| sdtmndtplgtdt0(xu,xR,W0)
| ( xu = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ~ ( aReductOfIn0(W0,xv,xR)
| sdtmndtasgtdt0(xv,xR,W0)
| sdtmndtplgtdt0(xv,xR,W0)
| ( xv = W0 )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) ) )
| ~ aElement0(tptp_fun_W3_12(xv,xu))
| ~ ( sdtmndtasgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xu,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xu,xR)
| ( xu = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xu,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) )
| ~ ( sdtmndtasgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| sdtmndtplgtdt0(xv,xR,tptp_fun_W3_12(xv,xu))
| aReductOfIn0(tptp_fun_W3_12(xv,xu),xv,xR)
| ( xv = tptp_fun_W3_12(xv,xu) )
| ~ ! [W1: $i] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xv,xR)
| ~ sdtmndtplgtdt0(W1,xR,tptp_fun_W3_12(xv,xu)) ) ) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
$false,
inference(unit_resolution,[status(thm)],[83,77,59,57,53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : COM017+4 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n012.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 12:20:41 EDT 2025
% 0.14/0.37 % CPUTime :
% 0.23/0.44 % SZS status Theorem
% 0.23/0.44 % SZS output start Proof
% See solution above
% 0.23/0.51 % E exiting
%------------------------------------------------------------------------------