%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS108+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 05:13:24 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 76
% Syntax : Number of formulae : 189 ( 40 unt; 0 typ; 0 def)
% Number of atoms : 2001 ( 143 equ)
% Maximal formula atoms : 48 ( 10 avg)
% Number of connectives : 3543 (1820 ~;1294 |; 206 &)
% ( 217 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 89 ( 89 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 541 ( 479 !; 36 ?; 541 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px5_type,type,
ra_Px5: ( $i * $i ) > $o ).
tff(i2003_11_14_17_21_04740_type,type,
i2003_11_14_17_21_04740: $i ).
tff(cp2xcomp_type,type,
cp2xcomp: $i > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(cp4xcomp_type,type,
cp4xcomp: $i > $o ).
tff(cp3xcomp_type,type,
cp3xcomp: $i > $o ).
tff(cp5xcomp_type,type,
cp5xcomp: $i > $o ).
tff(ca_Cx1_type,type,
ca_Cx1: $i > $o ).
tff(tptp_fun_Y_9_type,type,
tptp_fun_Y_9: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cp1_type,type,
cp1: $i > $o ).
tff(ca_Ax14_type,type,
ca_Ax14: $i > $o ).
tff(tptp_fun_Y1_10_type,type,
tptp_fun_Y1_10: $i > $i ).
tff(tptp_fun_Y0_11_type,type,
tptp_fun_Y0_11: $i > $i ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(cp2_type,type,
cp2: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y0_1_type,type,
tptp_fun_Y0_1: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp2xcomp(X)
| ! [Y: $i] : ~ ra_Px5(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp2xcomp(X)
| ! [Y: $i] : ~ ra_Px5(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) )
<=> ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )),
( ( ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ( ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) )),
rewrite(( ( ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) )),
( ( ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px5(X,tptp_fun_Y_2(X))
| cp2xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ( ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ra_Px5(X,tptp_fun_Y_2(X))
| cp2xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) )
<=> ! [X: $i] :
( ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px5(X,Y)
<=> ~ ? [Y: $i] : ra_Px5(X,Y) )),
( ( cp2xcomp(X)
<=> ~ ? [Y: $i] : ra_Px5(X,Y) )
<=> ( cp2xcomp(X)
<=> ~ ? [Y: $i] : ra_Px5(X,Y) ) )),
rewrite(( ( cp2xcomp(X)
<=> ~ ? [Y: $i] : ra_Px5(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) ) )),
( ( cp2xcomp(X)
<=> ~ ? [Y: $i] : ra_Px5(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) )
<=> ~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) ) )),
( ( cp2xcomp(X)
<=> ~ ? [Y: $i] : ra_Px5(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cp2xcomp(X)
<=> ~ ? [Y: $i] : ra_Px5(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cp2xcomp(X)
<=> ~ ? [Y: $i] : ra_Px5(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(16,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px5(X,Y)
<=> cp2xcomp(X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ra_Px5(X,tptp_fun_Y_2(X))
| cp2xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px5(X,Y)
| ~ cp2xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp2xcomp(X)
| ! [Y: $i] : ~ ra_Px5(X,Y) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp2xcomp(X)
| ra_Px5(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp2xcomp(X)
| ! [Y: $i] : ~ ra_Px5(X,Y) ) )
| ~ ( ~ ( cp2xcomp(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y_2(i2003_11_14_17_21_04740)) )
| ~ ( ~ cp2xcomp(i2003_11_14_17_21_04740)
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
~ ( ~ ( cp2xcomp(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y_2(i2003_11_14_17_21_04740)) )
| ~ ( ~ cp2xcomp(i2003_11_14_17_21_04740)
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( cp2xcomp(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y_2(i2003_11_14_17_21_04740)) )
| ~ ( ~ cp2xcomp(i2003_11_14_17_21_04740)
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) )
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(26,plain,
( ~ cp2xcomp(i2003_11_14_17_21_04740)
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [X: $i] :
refl(( ~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
<=> ~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
<=> ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) )
<=> ~ ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) ) )),
( ( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) )
<=> ( ca_Cx1(X)
<=> ~ ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) ) ) )),
rewrite(( ( ca_Cx1(X)
<=> ~ ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) ) )
<=> ~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ) )),
( ( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) )
<=> ~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ) )),
rewrite(( ~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
<=> ~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ) )),
( ( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) )
<=> ~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) )
<=> ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) )
<=> ! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [X: $i] :
rewrite(( ( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) )
<=> ( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) )
<=> ! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
tff(35,plain,
! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [X: $i] :
( ca_Cx1(X)
<=> ( cp2xcomp(X)
& cp5xcomp(X)
& cp3xcomp(X)
& cp4xcomp(X) ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) ),
inference(modus_ponens,[status(thm)],[38,28]) ).
tff(40,plain,
( ( ~ ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
| ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) )
<=> ( ~ ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
| ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) )
<=> ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) )
<=> ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) )
<=> ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) )
<=> ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ( ~ ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
| ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) )
<=> ( ~ ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
| ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
| ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) )
<=> ( ~ ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
| ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ) ),
inference(transitivity,[status(thm)],[45,40]) ).
tff(47,plain,
( ~ ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
| ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [X: $i] :
~ ( ( ~ cp5xcomp(X)
| ~ cp2xcomp(X)
| ~ cp3xcomp(X)
| ~ cp4xcomp(X) )
<=> ca_Cx1(X) )
| ~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) ),
inference(unit_resolution,[status(thm)],[48,39]) ).
tff(50,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
<=> ~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
<=> ~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
<=> ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rr(X,Y)
& cp1(Y) )
<=> ~ ( ~ cp1(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp1(Y) )
<=> ~ ~ ( ~ cp1(Y)
| ~ rr(X,Y) ) )),
rewrite(( ~ ~ ( ~ cp1(Y)
| ~ rr(X,Y) )
<=> ( ~ cp1(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp1(Y) )
<=> ( ~ cp1(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
<=> ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )),
rewrite(( ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
<=> ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) )),
( ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) )
<=> ( ca_Ax14(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) )),
rewrite(( ( ca_Ax14(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) )
<=> ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) ) )),
( ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) )
<=> ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) ) )),
( ( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) )
<=> ( ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
& ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) ) ) )),
rewrite(( ( ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) )
& ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) ) )
<=> ~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) )),
( ( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) )
<=> ~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [X: $i] :
( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [X: $i] :
rewrite(( ( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) )
<=> ( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X: $i] :
( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [X: $i] :
( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
<=> ! [X: $i] :
( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
^ [X: $i] :
rewrite(( ( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) )
<=> ( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [X: $i] :
( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) )
<=> ! [X: $i] :
( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [X: $i] :
( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_15) ).
tff(63,plain,
! [X: $i] :
( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X: $i] :
( ca_Ax14(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [X: $i] :
( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X: $i] :
( ( ~ ca_Ax14(X)
| ( rr(X,tptp_fun_Y_9(X))
& cp1(tptp_fun_Y_9(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( ca_Ax14(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_11(X))
& rr(X,tptp_fun_Y1_10(X)) )
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) ) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,plain,
! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ),
inference(modus_ponens,[status(thm)],[67,54]) ).
tff(69,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,plain,
( ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) ) ) ) )
<=> ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ) ) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y0_11(X))
| ~ rr(X,tptp_fun_Y1_10(X))
| ( tptp_fun_Y0_11(X) = tptp_fun_Y1_10(X) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ ca_Ax14(X)
| ~ ( ~ rr(X,tptp_fun_Y_9(X))
| ~ cp1(tptp_fun_Y_9(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ) ) ),
inference(modus_ponens,[status(thm)],[73,72]) ).
tff(75,plain,
~ ( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ) ),
inference(unit_resolution,[status(thm)],[74,68]) ).
tff(76,plain,
( ~ ( ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y0_11(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = tptp_fun_Y1_10(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y) ) )
| ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) )
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(77,plain,
( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ),
inference(unit_resolution,[status(thm)],[76,75]) ).
tff(78,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) ),
inference(transitivity,[status(thm)],[81,79]) ).
tff(83,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) ) )
<=> ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(84,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) )
| ~ cp2(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) )
| ~ cp2(X) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ca_Ax14(Y) )
& cp2(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ca_Ax14(Y) )
& cp2(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ca_Ax14(Y) )
& cp2(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(89,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rinvR(X,Y)
& ca_Ax14(Y) )
& cp2(X) ) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) )
| ~ cp2(X) ) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rinvR(X,tptp_fun_Y_0(X))
& ca_Ax14(tptp_fun_Y_0(X))
& cp2(X) ) )
& ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Ax14(Y) ) ) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ),
inference(modus_ponens,[status(thm)],[91,84]) ).
tff(93,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) ),
inference(modus_ponens,[status(thm)],[92,82]) ).
tff(94,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ ca_Ax14(Y)
| ~ rinvR(i2003_11_14_17_21_04740,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ ca_Ax14(Y)
| ~ rinvR(i2003_11_14_17_21_04740,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_21_04740,Y)
| ~ ca_Ax14(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ ca_Ax14(Y)
| ~ rinvR(i2003_11_14_17_21_04740,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_21_04740,Y)
| ~ ca_Ax14(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ ca_Ax14(Y)
| ~ rinvR(i2003_11_14_17_21_04740,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_21_04740,Y)
| ~ ca_Ax14(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ ca_Ax14(Y)
| ~ rinvR(i2003_11_14_17_21_04740,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ rinvR(i2003_11_14_17_21_04740,Y)
| ~ ca_Ax14(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ cp2(X)
| ~ rinvR(X,tptp_fun_Y_0(X))
| ~ ca_Ax14(tptp_fun_Y_0(X)) ) )
| ~ ( cUnsatisfiable(X)
| ~ cp2(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ~ ca_Ax14(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ ca_Ax14(Y)
| ~ rinvR(i2003_11_14_17_21_04740,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ ca_Ax14(Y)
| ~ rinvR(i2003_11_14_17_21_04740,Y) ) ) ),
inference(unit_resolution,[status(thm)],[99,93]) ).
tff(101,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ cp2(i2003_11_14_17_21_04740)
| ! [Y: $i] :
( ~ ca_Ax14(Y)
| ~ rinvR(i2003_11_14_17_21_04740,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(102,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) ),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
( cUnsatisfiable(i2003_11_14_17_21_04740)
<=> cUnsatisfiable(i2003_11_14_17_21_04740) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,axiom,
cUnsatisfiable(i2003_11_14_17_21_04740),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_26) ).
tff(105,plain,
cUnsatisfiable(i2003_11_14_17_21_04740),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(107,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_04740)
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) )
| ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ) ),
inference(unit_resolution,[status(thm)],[106,105]) ).
tff(108,plain,
~ ( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ),
inference(unit_resolution,[status(thm)],[107,102]) ).
tff(109,plain,
( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740)) ),
inference(tautology,[status(thm)],[]) ).
tff(110,plain,
ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740)),
inference(unit_resolution,[status(thm)],[109,108]) ).
tff(111,plain,
( ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) )
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
( ~ ( ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) )
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ),
inference(unit_resolution,[status(thm)],[112,77]) ).
tff(114,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ),
inference(tautology,[status(thm)],[]) ).
tff(115,plain,
rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(117,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) ),
inference(unit_resolution,[status(thm)],[116,113]) ).
tff(118,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(119,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)],[118]) ).
tff(120,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(121,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_25) ).
tff(122,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740) ),
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
| rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)) ),
inference(tautology,[status(thm)],[]) ).
tff(128,plain,
rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740)),
inference(unit_resolution,[status(thm)],[127,108]) ).
tff(129,plain,
( ~ ( rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740) )
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
| rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740) ),
inference(tautology,[status(thm)],[]) ).
tff(130,plain,
( ~ ( rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740) )
| rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740) ),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740),
inference(unit_resolution,[status(thm)],[130,126]) ).
tff(132,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 ) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ( ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) )
<=> ( ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(134,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 ) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 ) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),i2003_11_14_17_21_04740)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ( tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740 ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)) = i2003_11_14_17_21_04740,
inference(unit_resolution,[status(thm)],[137,131,117,115]) ).
tff(139,plain,
i2003_11_14_17_21_04740 = tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ca_Cx1(i2003_11_14_17_21_04740)
<=> ca_Cx1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ca_Cx1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
<=> ca_Cx1(i2003_11_14_17_21_04740) ),
inference(symmetry,[status(thm)],[140]) ).
tff(142,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y1)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),Y0) )
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_04740),tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ),
inference(tautology,[status(thm)],[]) ).
tff(143,plain,
cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))),
inference(unit_resolution,[status(thm)],[142,113]) ).
tff(144,plain,
^ [X: $i] :
refl(( ( ca_Cx1(X)
| ~ cp1(X) )
<=> ( ca_Cx1(X)
| ~ cp1(X) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) )
<=> ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,plain,
( ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) )
<=> ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(147,plain,
^ [X: $i] :
rewrite(( ( cp1(X)
=> ca_Cx1(X) )
<=> ( ca_Cx1(X)
| ~ cp1(X) ) )),
inference(bind,[status(th)],[]) ).
tff(148,plain,
( ! [X: $i] :
( cp1(X)
=> ca_Cx1(X) )
<=> ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) ) ),
inference(quant_intro,[status(thm)],[147]) ).
tff(149,axiom,
! [X: $i] :
( cp1(X)
=> ca_Cx1(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(150,plain,
! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) ),
inference(modus_ponens,[status(thm)],[149,148]) ).
tff(151,plain,
! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) ),
inference(skolemize,[status(sab)],[151]) ).
tff(153,plain,
! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) ),
inference(modus_ponens,[status(thm)],[152,145]) ).
tff(154,plain,
( ( ~ ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) )
| ca_Cx1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) )
<=> ( ~ ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) )
| ca_Cx1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(155,plain,
( ~ ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) )
| ca_Cx1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(156,plain,
( ~ ! [X: $i] :
( ca_Cx1(X)
| ~ cp1(X) )
| ca_Cx1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740)))
| ~ cp1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
ca_Cx1(tptp_fun_Y_9(tptp_fun_Y_0(i2003_11_14_17_21_04740))),
inference(unit_resolution,[status(thm)],[156,153,143]) ).
tff(158,plain,
ca_Cx1(i2003_11_14_17_21_04740),
inference(modus_ponens,[status(thm)],[157,141]) ).
tff(159,plain,
( ( ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
<=> ca_Cx1(i2003_11_14_17_21_04740) )
| ~ ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) )
| ~ ca_Cx1(i2003_11_14_17_21_04740) ),
inference(tautology,[status(thm)],[]) ).
tff(160,plain,
~ ( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740) ),
inference(unit_resolution,[status(thm)],[159,158,49]) ).
tff(161,plain,
( ~ cp5xcomp(i2003_11_14_17_21_04740)
| ~ cp3xcomp(i2003_11_14_17_21_04740)
| ~ cp4xcomp(i2003_11_14_17_21_04740)
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| cp2xcomp(i2003_11_14_17_21_04740) ),
inference(tautology,[status(thm)],[]) ).
tff(162,plain,
cp2xcomp(i2003_11_14_17_21_04740),
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
( ~ ( ~ cp2xcomp(i2003_11_14_17_21_04740)
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) )
| ~ cp2xcomp(i2003_11_14_17_21_04740)
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(164,plain,
( ~ ( ~ cp2xcomp(i2003_11_14_17_21_04740)
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) )
| ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y) ),
inference(unit_resolution,[status(thm)],[163,162]) ).
tff(165,plain,
! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y),
inference(unit_resolution,[status(thm)],[164,26]) ).
tff(166,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(167,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[166]) ).
tff(168,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(169,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[168]) ).
tff(170,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[169,167]) ).
tff(171,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) )
<=> ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )),
( ( ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
& ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ( ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
& ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) )),
rewrite(( ( ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
& ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) )),
( ( ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
& ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(172,plain,
( ! [X: $i] :
( ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
& ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,plain,
( ! [X: $i] :
( cp2(X)
<=> ? [Y0: $i] : ra_Px5(X,Y0) )
<=> ! [X: $i] :
( cp2(X)
<=> ? [Y0: $i] : ra_Px5(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(174,axiom,
! [X: $i] :
( cp2(X)
<=> ? [Y0: $i] : ra_Px5(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
tff(175,plain,
! [X: $i] :
( cp2(X)
<=> ? [Y0: $i] : ra_Px5(X,Y0) ),
inference(modus_ponens,[status(thm)],[174,173]) ).
tff(176,plain,
! [X: $i] :
( ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
& ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ),
inference(skolemize,[status(sab)],[175]) ).
tff(177,plain,
! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[176,172]) ).
tff(178,plain,
! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[177,170]) ).
tff(179,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cp2(X)
| ra_Px5(X,tptp_fun_Y0_1(X)) )
| ~ ( cp2(X)
| ! [Y0: $i] : ~ ra_Px5(X,Y0) ) )
| ~ ( ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) )
| ~ ( cp2(i2003_11_14_17_21_04740)
| ! [Y0: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(180,plain,
~ ( ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) )
| ~ ( cp2(i2003_11_14_17_21_04740)
| ! [Y0: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y0) ) ),
inference(unit_resolution,[status(thm)],[179,178]) ).
tff(181,plain,
( ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) )
| ~ ( cp2(i2003_11_14_17_21_04740)
| ! [Y0: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y0) )
| ~ cp2(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) ),
inference(tautology,[status(thm)],[]) ).
tff(182,plain,
( ~ cp2(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) ),
inference(unit_resolution,[status(thm)],[181,180]) ).
tff(183,plain,
( ~ cp2(i2003_11_14_17_21_04740)
| ~ ca_Ax14(tptp_fun_Y_0(i2003_11_14_17_21_04740))
| ~ rinvR(i2003_11_14_17_21_04740,tptp_fun_Y_0(i2003_11_14_17_21_04740))
| cp2(i2003_11_14_17_21_04740) ),
inference(tautology,[status(thm)],[]) ).
tff(184,plain,
cp2(i2003_11_14_17_21_04740),
inference(unit_resolution,[status(thm)],[183,108]) ).
tff(185,plain,
( ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) )
| ~ cp2(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) ),
inference(tautology,[status(thm)],[]) ).
tff(186,plain,
( ~ ( ~ cp2(i2003_11_14_17_21_04740)
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) )
| ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) ),
inference(unit_resolution,[status(thm)],[185,184]) ).
tff(187,plain,
ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)),
inference(unit_resolution,[status(thm)],[186,182]) ).
tff(188,plain,
( ~ ! [Y: $i] : ~ ra_Px5(i2003_11_14_17_21_04740,Y)
| ~ ra_Px5(i2003_11_14_17_21_04740,tptp_fun_Y0_1(i2003_11_14_17_21_04740)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
$false,
inference(unit_resolution,[status(thm)],[188,187,165]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS108+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n014.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 19:11:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
% 0.19/0.43 % E exiting
%------------------------------------------------------------------------------