%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS084+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:13:20 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 75
% Syntax : Number of formulae : 190 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 2272 ( 66 equ)
% Maximal formula atoms : 56 ( 11 avg)
% Number of connectives : 4260 (2254 ~;1650 |; 199 &)
% ( 148 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 76 ( 76 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 599 ( 549 !; 22 ?; 599 :)
% Comments :
%------------------------------------------------------------------------------
tff(cc_type,type,
cc: $i > $o ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(tptp_fun_Z_1_type,type,
tptp_fun_Z_1: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_19_35232_type,type,
i2003_11_14_17_19_35232: $i ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(cd_type,type,
cd: $i > $o ).
tff(rinvF_type,type,
rinvF: ( $i * $i ) > $o ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
<=> ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) ) )),
rewrite(( ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) ) )
<=> ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )),
( ( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) ) ) )
<=> ( ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) )),
rewrite(( ( ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) )),
( ( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) ) ) )
<=> ~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [X: $i] :
rewrite(( ( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) )
| ~ cc(X) ) )
<=> ( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) )
| ~ cc(X) ) )
<=> ! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [X: $i] :
( cd(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ~ cc(Y) )
& cc(X) ) )
<=> ! [X: $i] :
( cd(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ~ cc(Y) )
& cc(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [X: $i] :
( cd(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ~ cc(Y) )
& cc(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(12,plain,
! [X: $i] :
( cd(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ~ cc(Y) )
& cc(X) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) )
| ~ cc(X) ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_3(X))
& ~ cc(tptp_fun_Y_3(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ~ cc(Y) ) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) )
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) )
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) ) )
<=> ~ ( ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) )
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) )
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) )
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) )
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ ( ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) )
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ) ),
inference(unit_resolution,[status(thm)],[22,16]) ).
tff(24,plain,
( ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),Y) ) )
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(25,plain,
( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rinvF(X,Y)
& cd(Y) )
<=> ~ ( ~ rinvF(X,Y)
| ~ cd(Y) ) )),
( ~ ( rinvF(X,Y)
& cd(Y) )
<=> ~ ~ ( ~ rinvF(X,Y)
| ~ cd(Y) ) )),
rewrite(( ~ ~ ( ~ rinvF(X,Y)
| ~ cd(Y) )
<=> ( ~ rinvF(X,Y)
| ~ cd(Y) ) )),
( ~ ( rinvF(X,Y)
& cd(Y) )
<=> ( ~ rinvF(X,Y)
| ~ cd(Y) ) ))),
( ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
<=> ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Z: $i] :
trans(monotonicity(rewrite(( ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) )
<=> ~ ( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) )),
( ~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) )
<=> ~ ~ ( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) )),
rewrite(( ~ ~ ( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) )
<=> ( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) )),
( ~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) )
<=> ( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ))),
( ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) )
<=> ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) )),
( ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) )
<=> ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )),
rewrite(( ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) )
<=> ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )),
( ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) )
<=> ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )),
( ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) ) )
<=> ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
<=> ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) ) )),
( ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) ) )
<=> ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) )
& ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) )
& ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) )
| cc(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) )
| cc(X) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( rinvR(X,Y)
=> ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( rinvR(X,Y)
=> ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( rinvR(X,Y)
=> ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(39,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ? [Z: $i] :
( rinvF(Y,Z)
& cd(Z) ) )
& ~ cc(X) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) )
| cc(X) ) ),
inference(skolemize,[status(sab)],[40]) ).
tff(42,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rinvR(X,Y)
| ( rinvF(Y,tptp_fun_Z_1(Y))
& cd(tptp_fun_Z_1(Y)) ) )
& ~ cc(X) ) )
& ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ( rinvR(X,tptp_fun_Y_2(X))
& ! [Z: $i] :
~ ( rinvF(tptp_fun_Y_2(X),Z)
& cd(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[41,34]) ).
tff(43,plain,
! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[42,32]) ).
tff(44,plain,
! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[43,30]) ).
tff(45,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_19_35232,Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_19_35232,Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ rinvF(i2003_11_14_17_19_35232,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( cc(i2003_11_14_17_19_35232)
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_19_35232,Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ rinvF(i2003_11_14_17_19_35232,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( cc(i2003_11_14_17_19_35232)
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_19_35232,Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ) ) ) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ rinvF(i2003_11_14_17_19_35232,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( cc(i2003_11_14_17_19_35232)
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_19_35232,Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ) ) ) ),
inference(transitivity,[status(thm)],[47,45]) ).
tff(49,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ rinvF(i2003_11_14_17_19_35232,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( cc(i2003_11_14_17_19_35232)
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_19_35232,Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ) ) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_19_35232,Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ) ),
inference(unit_resolution,[status(thm)],[50,44]) ).
tff(52,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_19_35232)
| cc(i2003_11_14_17_19_35232)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_19_35232,Y) )
| ~ ( ~ rinvR(i2003_11_14_17_19_35232,tptp_fun_Y_2(i2003_11_14_17_19_35232))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(i2003_11_14_17_19_35232),Z) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
( cUnsatisfiable(i2003_11_14_17_19_35232)
<=> cUnsatisfiable(i2003_11_14_17_19_35232) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
cUnsatisfiable(i2003_11_14_17_19_35232),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(56,plain,
cUnsatisfiable(i2003_11_14_17_19_35232),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ),
inference(tautology,[status(thm)],[]) ).
tff(58,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) )
| ~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
~ ( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232) ),
inference(unit_resolution,[status(thm)],[58,53]) ).
tff(60,plain,
( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232)
| cd(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ),
inference(tautology,[status(thm)],[]) ).
tff(61,plain,
cd(tptp_fun_Y_0(i2003_11_14_17_19_35232)),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) )
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(unit_resolution,[status(thm)],[63,25]) ).
tff(65,plain,
( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(tautology,[status(thm)],[]) ).
tff(66,plain,
rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvF(X,Y)
<=> rf(Y,X) )
<=> ( rinvF(X,Y)
<=> rf(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
( ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(71,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
| ( rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
<=> rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(75,plain,
( rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
<=> rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
( ~ ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_19_35232,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(i2003_11_14_17_19_35232)
| rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232)) ),
inference(tautology,[status(thm)],[]) ).
tff(77,plain,
rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232)),
inference(unit_resolution,[status(thm)],[76,59]) ).
tff(78,plain,
( ~ ( rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
<=> rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232) )
| ~ rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
| rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232) ),
inference(tautology,[status(thm)],[]) ).
tff(79,plain,
( ~ ( rinvF(i2003_11_14_17_19_35232,tptp_fun_Y_0(i2003_11_14_17_19_35232))
<=> rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232) )
| rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232) ),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
inference(unit_resolution,[status(thm)],[79,75]) ).
tff(81,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(( ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(82,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rf(X,Y)
& rf(X,Z) )
<=> ~ ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ~ ~ ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
rewrite(( ~ ~ ( ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z)
| ( Y = Z ) ) )),
rewrite(( ( ~ rf(X,Y)
| ~ rf(X,Z)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(87,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(89,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[89,85]) ).
tff(91,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[90]) ).
tff(92,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[92,82]) ).
tff(94,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) )
<=> ( ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ( i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
i2003_11_14_17_19_35232 = tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),
inference(unit_resolution,[status(thm)],[99,93,80,66]) ).
tff(101,plain,
tptp_fun_Y_0(i2003_11_14_17_19_35232) = tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_0(i2003_11_14_17_19_35232),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
| ( rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
<=> rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(104,plain,
( rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
<=> rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ),
inference(unit_resolution,[status(thm)],[103,73]) ).
tff(105,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(106,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(109,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[109]) ).
tff(111,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[110,106]) ).
tff(112,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
<=> rr(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
<=> rr(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
( rr(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(115,plain,
( rr(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
<=> rr(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rf(X,Y)
| rr(X,Y) )
<=> ( ~ rf(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(117,plain,
( ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[116]) ).
tff(118,plain,
( ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rf(X,Y)
=> rr(X,Y) )
<=> ( ~ rf(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(120,plain,
( ! [X: $i,Y: $i] :
( rf(X,Y)
=> rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,axiom,
! [X: $i,Y: $i] :
( rf(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(122,plain,
! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[122,118]) ).
tff(124,plain,
! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[123]) ).
tff(125,plain,
! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| rr(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| rr(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| rr(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| rr(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(modus_ponens,[status(thm)],[127,126]) ).
tff(129,plain,
rr(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),
inference(unit_resolution,[status(thm)],[128,125,66]) ).
tff(130,plain,
rr(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),
inference(modus_ponens,[status(thm)],[129,115]) ).
tff(131,plain,
( ~ ( rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
<=> rr(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) )
| rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rr(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(tautology,[status(thm)],[]) ).
tff(132,plain,
rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),
inference(unit_resolution,[status(thm)],[131,130,113]) ).
tff(133,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ~ ( ~ ( cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[135,133]) ).
tff(137,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(138,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| cc(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ~ rinvR(X,tptp_fun_Y_2(X))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_2(X),Z)
| ~ cd(Z) ) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( cc(X)
| ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[137,136]) ).
tff(139,plain,
~ ( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z) ) ) ) ),
inference(unit_resolution,[status(thm)],[138,44]) ).
tff(140,plain,
( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y) )
| ~ ( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ! [Z: $i] :
( ~ cd(Z)
| ~ rinvF(tptp_fun_Y_2(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),Z) ) ) )
| ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(141,plain,
( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) ),
inference(unit_resolution,[status(thm)],[140,139]) ).
tff(142,plain,
( cUnsatisfiable(i2003_11_14_17_19_35232)
<=> cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(143,plain,
cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),
inference(modus_ponens,[status(thm)],[56,142]) ).
tff(144,plain,
( ~ ( ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) )
| ~ cUnsatisfiable(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(145,plain,
~ ( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ),
inference(unit_resolution,[status(thm)],[144,143,141]) ).
tff(146,plain,
( cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rinvF(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(147,plain,
! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) ),
inference(unit_resolution,[status(thm)],[146,145]) ).
tff(148,plain,
( ( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ( ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) )
<=> ( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ( ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(149,plain,
( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ( ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),Y)
| ~ ( ~ rinvF(Y,tptp_fun_Z_1(Y))
| ~ cd(tptp_fun_Z_1(Y)) ) )
| ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ( ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
( ~ rinvR(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ ( ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ),
inference(unit_resolution,[status(thm)],[150,147]) ).
tff(152,plain,
~ ( ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ),
inference(unit_resolution,[status(thm)],[151,132]) ).
tff(153,plain,
( ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ),
inference(tautology,[status(thm)],[]) ).
tff(154,plain,
rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
( ~ ( rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
<=> rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) )
| ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ),
inference(tautology,[status(thm)],[]) ).
tff(156,plain,
( ~ ( rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
<=> rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) )
| rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))) ),
inference(unit_resolution,[status(thm)],[155,154]) ).
tff(157,plain,
rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),
inference(unit_resolution,[status(thm)],[156,104]) ).
tff(158,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) )
| ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) )
| ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,plain,
( ~ ( ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) )
| ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) ) )
<=> ~ ( ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) )
| ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(160,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) )
| ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) )
| ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) )
| ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) )
| ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ) ) ) ),
inference(transitivity,[status(thm)],[160,158]) ).
tff(162,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) )
| ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ cc(X)
| ~ rf(X,tptp_fun_Y_3(X))
| cc(tptp_fun_Y_3(X)) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( cc(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) )
| ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ) ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
~ ( ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) )
| ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ) ),
inference(unit_resolution,[status(thm)],[163,16]) ).
tff(165,plain,
( ~ ( cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ! [Y: $i] :
( cc(Y)
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),Y) ) )
| ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) )
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(166,plain,
( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ),
inference(unit_resolution,[status(thm)],[165,164]) ).
tff(167,plain,
( ~ rinvF(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ),
inference(tautology,[status(thm)],[]) ).
tff(168,plain,
cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))),
inference(unit_resolution,[status(thm)],[167,152]) ).
tff(169,plain,
( ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) )
| ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(170,plain,
( ~ ( ~ cd(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) )
| ~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ) ),
inference(unit_resolution,[status(thm)],[169,168]) ).
tff(171,plain,
~ ( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ),
inference(unit_resolution,[status(thm)],[170,166]) ).
tff(172,plain,
( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ),
inference(tautology,[status(thm)],[]) ).
tff(173,plain,
rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))),
inference(unit_resolution,[status(thm)],[172,171]) ).
tff(174,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(175,plain,
( ( ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) )
<=> ( ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(176,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ) ),
inference(monotonicity,[status(thm)],[175]) ).
tff(177,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ) ),
inference(transitivity,[status(thm)],[176,174]) ).
tff(178,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(179,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))
| ( tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) ) ),
inference(modus_ponens,[status(thm)],[178,177]) ).
tff(180,plain,
tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))) = tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))),
inference(unit_resolution,[status(thm)],[179,93,173,157]) ).
tff(181,plain,
tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) = tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))),
inference(symmetry,[status(thm)],[180]) ).
tff(182,plain,
tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))) = tptp_fun_Y_0(i2003_11_14_17_19_35232),
inference(transitivity,[status(thm)],[181,102]) ).
tff(183,plain,
( cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
<=> cc(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ),
inference(monotonicity,[status(thm)],[182]) ).
tff(184,plain,
( cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
<=> cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ),
inference(symmetry,[status(thm)],[183]) ).
tff(185,plain,
( ~ cc(tptp_fun_Y_0(i2003_11_14_17_19_35232))
| cc(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_19_35232),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))
| cc(tptp_fun_Y_0(i2003_11_14_17_19_35232)) ),
inference(tautology,[status(thm)],[]) ).
tff(186,plain,
cc(tptp_fun_Y_0(i2003_11_14_17_19_35232)),
inference(unit_resolution,[status(thm)],[185,64]) ).
tff(187,plain,
cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))),
inference(modus_ponens,[status(thm)],[186,184]) ).
tff(188,plain,
( ~ cc(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))
| cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ rf(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))),tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232))))))
| ~ cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))) ),
inference(tautology,[status(thm)],[]) ).
tff(189,plain,
~ cc(tptp_fun_Y_3(tptp_fun_Z_1(tptp_fun_Y_0(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_19_35232)))))),
inference(unit_resolution,[status(thm)],[188,171]) ).
tff(190,plain,
$false,
inference(unit_resolution,[status(thm)],[189,187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KRS084+1 : TPTP v9.0.0. Released v3.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n006.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:10:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------