%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS118+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 05:13:25 AM UTC 2025
% Result : Unsatisfiable 0.18s 0.37s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 97
% Syntax : Number of formulae : 241 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 2406 ( 44 equ)
% Maximal formula atoms : 48 ( 9 avg)
% Number of connectives : 4451 (2388 ~;1663 |; 185 &)
% ( 206 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 102 ( 102 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 19 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 664 ( 584 !; 40 ?; 664 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_21_4056_type,type,
i2003_11_14_17_21_4056: $i ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(ccxcomp_type,type,
ccxcomp: $i > $o ).
tff(cc_type,type,
cc: $i > $o ).
tff(cd_type,type,
cd: $i > $o ).
tff(rinvF_type,type,
rinvF: ( $i * $i ) > $o ).
tff(ca_Vx3_type,type,
ca_Vx3: $i > $o ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
<=> ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) ) )),
rewrite(( ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) ) )
<=> ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )),
( ( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) ) ) )
<=> ( ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) )),
rewrite(( ( ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) )),
( ( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [X: $i] :
rewrite(( ( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) )
| ~ cc(X) ) )
<=> ( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) )
| ~ cc(X) ) )
<=> ! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [X: $i] :
( cd(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ccxcomp(Y) )
& cc(X) ) )
<=> ! [X: $i] :
( cd(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ccxcomp(Y) )
& cc(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,axiom,
! [X: $i] :
( cd(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ccxcomp(Y) )
& cc(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(12,plain,
! [X: $i] :
( cd(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ccxcomp(Y) )
& cc(X) ) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) )
| ~ cc(X) ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i] :
( ( ~ cd(X)
| ( rf(X,tptp_fun_Y_4(X))
& ccxcomp(tptp_fun_Y_4(X))
& cc(X) ) )
& ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ccxcomp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,5]) ).
tff(17,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y)
| ~ ccxcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y)
| ~ ccxcomp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y)
| ~ ccxcomp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y)
| ~ ccxcomp(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ ( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y) ) ) ),
inference(unit_resolution,[status(thm)],[22,16]) ).
tff(24,plain,
( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),Y) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(25,plain,
( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) ),
inference(unit_resolution,[status(thm)],[24,23]) ).
tff(26,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Vx3(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X)) ) )
<=> ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) ) )),
rewrite(( ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) ) )
<=> ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) ) ) )
<=> ( ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) )),
rewrite(( ( ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) ) )
<=> ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(35,plain,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) ) ) ),
inference(skolemize,[status(sab)],[35]) ).
tff(37,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ cd(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ cd(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ cd(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ ( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ),
inference(unit_resolution,[status(thm)],[44,38]) ).
tff(46,plain,
( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) )
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(47,plain,
( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) ),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(49,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)],[48]) ).
tff(50,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(51,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(52,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvF(X,Y)
<=> rf(Y,X) )
<=> ( rinvF(X,Y)
<=> rf(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(58,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)],[57]) ).
tff(59,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(60,axiom,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(61,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(skolemize,[status(sab)],[61]) ).
tff(63,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
| ( rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
<=> rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
<=> rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) ) )),
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) ) )),
( ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) )
<=> ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ccxcomp(X) ) )),
rewrite(( ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ccxcomp(X) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )),
( ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( rinvR(X,Y)
=> ca_Vx3(Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) )
<=> ( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( rinvR(X,Y)
=> ca_Vx3(Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( rinvR(X,Y)
=> ca_Vx3(Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(81,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& ? [Y: $i] :
( rinvF(X,Y)
& cd(Y) )
& ccxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
& rinvF(X,tptp_fun_Y_0(X))
& cd(tptp_fun_Y_0(X))
& ccxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
~ ( rinvF(X,Y)
& cd(Y) )
| ~ ccxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) )
| ~ ccxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) )
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[85,72]) ).
tff(87,plain,
! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[86,67]) ).
tff(88,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_21_4056,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_21_4056,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(89,plain,
( ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ! [Y: $i] :
( ~ rinvF(i2003_11_14_17_21_4056,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_21_4056,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ! [Y: $i] :
( ~ rinvF(i2003_11_14_17_21_4056,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_21_4056,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ! [Y: $i] :
( ~ rinvF(i2003_11_14_17_21_4056,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_21_4056,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ) ) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ! [Y: $i] :
( ~ rinvF(i2003_11_14_17_21_4056,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(93,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ca_Vx3(tptp_fun_Y_1(X))
| ~ rinvR(X,tptp_fun_Y_1(X)) )
| ~ ccxcomp(X)
| ! [Y: $i] :
( ~ rinvF(X,Y)
| ~ cd(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rinvF(X,tptp_fun_Y_0(X))
| ~ cd(tptp_fun_Y_0(X))
| ~ ccxcomp(X)
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(X,Y) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_21_4056,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ) ) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_21_4056,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ) ),
inference(unit_resolution,[status(thm)],[93,87]) ).
tff(95,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ ( ca_Vx3(tptp_fun_Y_1(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_1(i2003_11_14_17_21_4056)) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rinvF(i2003_11_14_17_21_4056,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(96,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ),
inference(unit_resolution,[status(thm)],[95,94]) ).
tff(97,plain,
( cUnsatisfiable(i2003_11_14_17_21_4056)
<=> cUnsatisfiable(i2003_11_14_17_21_4056) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,axiom,
cUnsatisfiable(i2003_11_14_17_21_4056),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(99,plain,
cUnsatisfiable(i2003_11_14_17_21_4056),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(101,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_4056)
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) )
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ),
inference(unit_resolution,[status(thm)],[100,99]) ).
tff(102,plain,
~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(unit_resolution,[status(thm)],[101,96]) ).
tff(103,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
( ~ ( rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
<=> rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) )
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(tautology,[status(thm)],[]) ).
tff(106,plain,
( ~ ( rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
<=> rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) )
| rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(unit_resolution,[status(thm)],[105,104]) ).
tff(107,plain,
rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056),
inference(unit_resolution,[status(thm)],[106,65]) ).
tff(108,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rf(X,Y)
| rr(X,Y) )
<=> ( ~ rf(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(109,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)],[108]) ).
tff(110,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(111,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rf(X,Y)
=> rr(X,Y) )
<=> ( ~ rf(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(112,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)],[111]) ).
tff(113,axiom,
! [X: $i,Y: $i] :
( rf(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
tff(114,plain,
! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056)
| rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056)
| rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056)
| rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(quant_inst,[status(thm)],[]) ).
tff(120,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rf(X,Y)
| rr(X,Y) )
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056)
| rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(modus_ponens,[status(thm)],[119,118]) ).
tff(121,plain,
rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056),
inference(unit_resolution,[status(thm)],[120,117,107]) ).
tff(122,plain,
( ~ ( rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) )
| rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) ),
inference(tautology,[status(thm)],[]) ).
tff(123,plain,
( ~ ( rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
<=> rr(tptp_fun_Y_0(i2003_11_14_17_21_4056),i2003_11_14_17_21_4056) )
| rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(unit_resolution,[status(thm)],[122,121]) ).
tff(124,plain,
rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)),
inference(unit_resolution,[status(thm)],[123,56]) ).
tff(125,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(126,plain,
! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) ),
inference(unit_resolution,[status(thm)],[125,102]) ).
tff(127,plain,
( ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) )
<=> ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(129,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvR(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(modus_ponens,[status(thm)],[128,127]) ).
tff(130,plain,
ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056)),
inference(unit_resolution,[status(thm)],[129,126,124]) ).
tff(131,plain,
( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(132,plain,
( ~ ( ~ ca_Vx3(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) ),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ),
inference(unit_resolution,[status(thm)],[132,47]) ).
tff(134,plain,
( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ),
inference(tautology,[status(thm)],[]) ).
tff(135,plain,
cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),
inference(unit_resolution,[status(thm)],[134,133]) ).
tff(136,plain,
( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(137,plain,
( ~ ( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) )
| ~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
~ ( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ),
inference(unit_resolution,[status(thm)],[137,25]) ).
tff(139,plain,
( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ),
inference(tautology,[status(thm)],[]) ).
tff(140,plain,
rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
| ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
<=> rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
<=> rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(unit_resolution,[status(thm)],[141,63]) ).
tff(143,plain,
( ~ cd(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ),
inference(tautology,[status(thm)],[]) ).
tff(144,plain,
rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),
inference(unit_resolution,[status(thm)],[143,133]) ).
tff(145,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
<=> rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056)) )
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(tautology,[status(thm)],[]) ).
tff(146,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
<=> rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056)) )
| rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(unit_resolution,[status(thm)],[145,144]) ).
tff(147,plain,
rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056)),
inference(unit_resolution,[status(thm)],[146,142]) ).
tff(148,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(( ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(149,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rf(X,Y)
& rf(X,Z) )
<=> ~ ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ~ ~ ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
rewrite(( ~ ~ ( ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y)
| ( Y = Z ) ) )),
rewrite(( ( ~ rf(X,Z)
| ~ rf(X,Y)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(151,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,Z)
| ~ rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[150]) ).
tff(152,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(153,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(154,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)],[153]) ).
tff(155,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(156,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[155,154]) ).
tff(157,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[156,152]) ).
tff(158,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[157]) ).
tff(159,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(modus_ponens,[status(thm)],[158,151]) ).
tff(160,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(modus_ponens,[status(thm)],[159,149]) ).
tff(161,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) ) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
( ( ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) )
<=> ( ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(163,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) ) ) ),
inference(monotonicity,[status(thm)],[162]) ).
tff(164,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) ) ) ),
inference(transitivity,[status(thm)],[163,161]) ).
tff(165,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ( tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056) ) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))) = tptp_fun_Y_0(i2003_11_14_17_21_4056),
inference(unit_resolution,[status(thm)],[166,160,147,140]) ).
tff(168,plain,
tptp_fun_Y_0(i2003_11_14_17_21_4056) = tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),
inference(symmetry,[status(thm)],[167]) ).
tff(169,plain,
( ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))))
<=> ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))))
<=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) ),
inference(symmetry,[status(thm)],[169]) ).
tff(171,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(172,plain,
( ! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[171]) ).
tff(173,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(174,plain,
( ! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[173]) ).
tff(175,plain,
( ! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[174,172]) ).
tff(176,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(( ( ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(177,plain,
( ! [X: $i] :
( ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[176]) ).
tff(178,plain,
( ! [X: $i] :
( ccxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( ccxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(179,axiom,
! [X: $i] :
( ccxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(180,plain,
! [X: $i] :
( ccxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
! [X: $i] :
( ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[180]) ).
tff(182,plain,
! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[181,177]) ).
tff(183,plain,
! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[182,175]) ).
tff(184,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ccxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( ccxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) )
| ~ ( ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
~ ( ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) )
| ~ ( ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),Y0) ) ),
inference(unit_resolution,[status(thm)],[184,183]) ).
tff(186,plain,
( ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) )
| ~ ( ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),Y0) )
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) ),
inference(tautology,[status(thm)],[]) ).
tff(187,plain,
( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) ),
inference(unit_resolution,[status(thm)],[186,185]) ).
tff(188,plain,
( ~ cc(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)),tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))) ),
inference(tautology,[status(thm)],[]) ).
tff(189,plain,
ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056)))),
inference(unit_resolution,[status(thm)],[188,138]) ).
tff(190,plain,
( ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) )
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) ),
inference(tautology,[status(thm)],[]) ).
tff(191,plain,
( ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) )
| ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) ),
inference(unit_resolution,[status(thm)],[190,189]) ).
tff(192,plain,
ra_Px1(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))),
inference(unit_resolution,[status(thm)],[191,187]) ).
tff(193,plain,
ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))),
inference(modus_ponens,[status(thm)],[192,170]) ).
tff(194,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cc(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(195,plain,
( ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cc(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(197,plain,
( ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) ),
inference(quant_intro,[status(thm)],[196]) ).
tff(198,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(199,plain,
( ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) ),
inference(quant_intro,[status(thm)],[198]) ).
tff(200,plain,
( ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) ),
inference(transitivity,[status(thm)],[199,197]) ).
tff(201,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) )
<=> ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )),
( ( ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ( ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) )),
rewrite(( ( ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) )),
( ( ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(202,plain,
( ! [X: $i] :
( ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) ),
inference(quant_intro,[status(thm)],[201]) ).
tff(203,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px1(X,tptp_fun_Y_2(X))
| cc(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ( ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(204,plain,
( ! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_2(X))
| cc(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) )
<=> ! [X: $i] :
( ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ) ),
inference(quant_intro,[status(thm)],[203]) ).
tff(205,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(206,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px1(X,Y)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )),
( ( cc(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ( cc(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) )),
rewrite(( ( cc(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) ) )),
( ( cc(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) ) )),
( ( cc(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) ) )),
inference(bind,[status(th)],[]) ).
tff(207,plain,
( ! [X: $i] :
( cc(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) ) ),
inference(quant_intro,[status(thm)],[206]) ).
tff(208,axiom,
! [X: $i] :
( cc(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(209,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cc(X) ),
inference(modus_ponens,[status(thm)],[209,205]) ).
tff(211,plain,
! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_2(X))
| cc(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(skolemize,[status(sab)],[210]) ).
tff(212,plain,
! [X: $i] :
( ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(modus_ponens,[status(thm)],[211,204]) ).
tff(213,plain,
! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(modus_ponens,[status(thm)],[212,202]) ).
tff(214,plain,
! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cc(X) ) ),
inference(modus_ponens,[status(thm)],[213,200]) ).
tff(215,plain,
! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cc(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[214,195]) ).
tff(216,plain,
( ~ ! [X: $i] :
~ ( ~ ( cc(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cc(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_2(tptp_fun_Y_0(i2003_11_14_17_21_4056))) )
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(217,plain,
~ ( ~ ( cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_2(tptp_fun_Y_0(i2003_11_14_17_21_4056))) )
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ),
inference(unit_resolution,[status(thm)],[216,215]) ).
tff(218,plain,
( ~ ( cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_2(tptp_fun_Y_0(i2003_11_14_17_21_4056))) )
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(219,plain,
( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ),
inference(unit_resolution,[status(thm)],[218,217]) ).
tff(220,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(221,plain,
( ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ ccxcomp(Y) ) ) )
<=> ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(222,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ ccxcomp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[221]) ).
tff(223,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ ccxcomp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[222,220]) ).
tff(224,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056)) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ ccxcomp(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(225,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd(X)
| ~ ( ~ ccxcomp(tptp_fun_Y_4(X))
| ~ rf(X,tptp_fun_Y_4(X))
| ~ cc(X) ) )
| ~ ( cd(X)
| ~ cc(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ccxcomp(Y) ) ) )
| ~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[224,223]) ).
tff(226,plain,
~ ( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) ) ),
inference(unit_resolution,[status(thm)],[225,16]) ).
tff(227,plain,
( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] :
( ~ ccxcomp(Y)
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(228,plain,
( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) ),
inference(unit_resolution,[status(thm)],[227,226]) ).
tff(229,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvR(i2003_11_14_17_21_4056,Y) )
| ~ ccxcomp(i2003_11_14_17_21_4056)
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rinvF(i2003_11_14_17_21_4056,tptp_fun_Y_0(i2003_11_14_17_21_4056))
| cd(tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(tautology,[status(thm)],[]) ).
tff(230,plain,
cd(tptp_fun_Y_0(i2003_11_14_17_21_4056)),
inference(unit_resolution,[status(thm)],[229,102]) ).
tff(231,plain,
( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(232,plain,
( ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) )
| ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ) ),
inference(unit_resolution,[status(thm)],[231,230]) ).
tff(233,plain,
~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056))) ),
inference(unit_resolution,[status(thm)],[232,228]) ).
tff(234,plain,
( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ~ rf(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| ~ ccxcomp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_4056)))
| cc(tptp_fun_Y_0(i2003_11_14_17_21_4056)) ),
inference(tautology,[status(thm)],[]) ).
tff(235,plain,
cc(tptp_fun_Y_0(i2003_11_14_17_21_4056)),
inference(unit_resolution,[status(thm)],[234,233]) ).
tff(236,plain,
( ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(237,plain,
( ~ ( ~ cc(tptp_fun_Y_0(i2003_11_14_17_21_4056))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y) ),
inference(unit_resolution,[status(thm)],[236,235]) ).
tff(238,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y),
inference(unit_resolution,[status(thm)],[237,219]) ).
tff(239,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),Y)
| ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(240,plain,
~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_4056),tptp_fun_Y0_3(tptp_fun_Y_4(tptp_fun_Y_0(tptp_fun_Y_0(i2003_11_14_17_21_4056))))),
inference(unit_resolution,[status(thm)],[239,238]) ).
tff(241,plain,
$false,
inference(unit_resolution,[status(thm)],[240,193]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : KRS118+1 : TPTP v9.0.0. Released v3.1.0.
% 0.00/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n006.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 19:11:05 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.18/0.37 % SZS status Unsatisfiable
% 0.18/0.37 % SZS output start Proof
% See solution above
% 0.18/0.42 % E exiting
%------------------------------------------------------------------------------