%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS109+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:24 AM UTC 2025
% Result : Unsatisfiable 0.13s 0.41s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 90
% Syntax : Number of formulae : 223 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 2038 ( 43 equ)
% Maximal formula atoms : 40 ( 9 avg)
% Number of connectives : 3739 (2011 ~;1393 |; 132 &)
% ( 191 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 87 ( 87 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 641 ( 571 !; 31 ?; 641 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(i2003_11_14_17_21_08508_type,type,
i2003_11_14_17_21_08508: $i ).
tff(cp_type,type,
cp: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(rinvS_type,type,
rinvS: ( $i * $i ) > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(tptp_fun_Y_5_type,type,
tptp_fun_Y_5: $i > $i ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(ca_Vx3_type,type,
ca_Vx3: $i > $o ).
tff(rinvF_type,type,
rinvF: ( $i * $i ) > $o ).
tff(ca_Ax2_type,type,
ca_Ax2: $i > $o ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(cpxcomp_type,type,
cpxcomp: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y0_2_type,type,
tptp_fun_Y0_2: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) )
<=> ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )),
( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
rewrite(( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px1(X,tptp_fun_Y_1(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_1(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px1(X,Y)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) )),
rewrite(( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(16,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_1(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_1(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y_1(i2003_11_14_17_21_08508)) )
| ~ ( ~ cp(i2003_11_14_17_21_08508)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
~ ( ~ ( cp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y_1(i2003_11_14_17_21_08508)) )
| ~ ( ~ cp(i2003_11_14_17_21_08508)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( cp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y_1(i2003_11_14_17_21_08508)) )
| ~ ( ~ cp(i2003_11_14_17_21_08508)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) )
| ~ cp(i2003_11_14_17_21_08508)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(26,plain,
( ~ cp(i2003_11_14_17_21_08508)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X)) ) )
<=> ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) ) )),
rewrite(( ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) )
<=> ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) )),
rewrite(( ( ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) )),
( ( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) )
<=> ! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(36,plain,
! [X: $i] :
( ca_Vx3(X)
<=> ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] :
( ( ~ ca_Vx3(X)
| ( rs(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X)) ) )
& ( ca_Vx3(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_08508,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_08508,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_08508,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_08508,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_08508,Y)
| ~ cp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_08508,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_08508,Y)
| ~ cp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_08508,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_08508,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx3(X)
| ~ ( ~ rs(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X)) ) )
| ~ ( ca_Vx3(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_08508,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
~ ( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_08508,Y) ) ) ),
inference(unit_resolution,[status(thm)],[45,39]) ).
tff(47,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ca_Vx3(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_08508,Y) ) )
| ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(48,plain,
( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(unit_resolution,[status(thm)],[47,46]) ).
tff(49,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(52,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(transitivity,[status(thm)],[54,52]) ).
tff(56,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
rewrite(( ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
<=> ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) )),
rewrite(( ( ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
^ [X: $i] :
rewrite(( ( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
^ [X: $i] :
rewrite(( ( ca_Ax2(X)
<=> ( ! [Y: $i] :
( rinvS(X,Y)
=> cp(Y) )
& ! [Y: $i] :
( rinvF(X,Y)
=> ca_Vx3(Y) ) ) )
<=> ( ca_Ax2(X)
<=> ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( ! [Y: $i] :
( rinvS(X,Y)
=> cp(Y) )
& ! [Y: $i] :
( rinvF(X,Y)
=> ca_Vx3(Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [X: $i] :
( ca_Ax2(X)
<=> ( ! [Y: $i] :
( rinvS(X,Y)
=> cp(Y) )
& ! [Y: $i] :
( rinvF(X,Y)
=> ca_Vx3(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(64,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ),
inference(skolemize,[status(sab)],[65]) ).
tff(67,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
& ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
& ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[66,59]) ).
tff(68,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[67,57]) ).
tff(69,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) )
| ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) ) ),
inference(modus_ponens,[status(thm)],[68,55]) ).
tff(70,plain,
! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[69,50]) ).
tff(71,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) )
<=> ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax2(X)
| ~ ( cp(tptp_fun_Y_3(X))
| ~ rinvS(X,tptp_fun_Y_3(X)) )
| ~ ( ca_Vx3(tptp_fun_Y_4(X))
| ~ rinvF(X,tptp_fun_Y_4(X)) ) )
| ~ ( ~ ca_Ax2(X)
| ~ ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) )
| ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(X,Y) ) ) ) )
| ~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ ( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ) ),
inference(unit_resolution,[status(thm)],[76,70]) ).
tff(78,plain,
( ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ca_Vx3(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_08508))) )
| ~ ( cp(tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),tptp_fun_Y_3(tptp_fun_Y_0(i2003_11_14_17_21_08508))) ) )
| ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(79,plain,
( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(81,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) )
<=> ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(86,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cpxcomp(X)
& ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cpxcomp(X)
& ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(90,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cpxcomp(X)
& ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(91,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cpxcomp(X)
& ? [Y: $i] :
( rf(X,Y)
& ca_Ax2(Y) ) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( cpxcomp(X)
& rf(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X)) ) )
& ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
~ ( rf(X,Y)
& ca_Ax2(Y) ) ) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ),
inference(modus_ponens,[status(thm)],[93,86]) ).
tff(95,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) ),
inference(modus_ponens,[status(thm)],[94,84]) ).
tff(96,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_08508,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_08508,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ cpxcomp(i2003_11_14_17_21_08508) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_08508,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_08508,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ cpxcomp(i2003_11_14_17_21_08508) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_08508,Y)
| ~ ca_Ax2(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_08508,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[97]) ).
tff(99,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ cpxcomp(i2003_11_14_17_21_08508) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_08508,Y)
| ~ ca_Ax2(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_08508,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ cpxcomp(i2003_11_14_17_21_08508) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_21_08508,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_08508,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_08508,Y) ) ) ),
inference(unit_resolution,[status(thm)],[101,95]) ).
tff(103,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rf(i2003_11_14_17_21_08508,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) ),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
( cUnsatisfiable(i2003_11_14_17_21_08508)
<=> cUnsatisfiable(i2003_11_14_17_21_08508) ),
inference(rewrite,[status(thm)],[]) ).
tff(106,axiom,
cUnsatisfiable(i2003_11_14_17_21_08508),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
tff(107,plain,
cUnsatisfiable(i2003_11_14_17_21_08508),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(109,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_08508)
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) )
| ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) ),
inference(unit_resolution,[status(thm)],[108,107]) ).
tff(110,plain,
~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ),
inference(unit_resolution,[status(thm)],[109,104]) ).
tff(111,plain,
( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508)) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508)),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(114,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) )
| ~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ) ),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
~ ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ),
inference(unit_resolution,[status(thm)],[114,79]) ).
tff(116,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(117,plain,
! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ),
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvF(X,Y)
<=> rf(Y,X) )
<=> ( rinvF(X,Y)
<=> rf(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(119,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)],[118]) ).
tff(120,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(121,axiom,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(122,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
| ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ),
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ),
inference(tautology,[status(thm)],[]) ).
tff(128,plain,
rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)),
inference(unit_resolution,[status(thm)],[127,110]) ).
tff(129,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) )
| rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ),
inference(tautology,[status(thm)],[]) ).
tff(130,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) )
| rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(unit_resolution,[status(thm)],[130,126]) ).
tff(132,plain,
( ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ca_Vx3(i2003_11_14_17_21_08508)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) )
<=> ( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ca_Vx3(i2003_11_14_17_21_08508)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ca_Vx3(i2003_11_14_17_21_08508)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ca_Vx3(i2003_11_14_17_21_08508)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
ca_Vx3(i2003_11_14_17_21_08508),
inference(unit_resolution,[status(thm)],[134,131,117]) ).
tff(136,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(137,plain,
( ~ ( ~ ca_Vx3(i2003_11_14_17_21_08508)
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) )
| ~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
~ ( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ),
inference(unit_resolution,[status(thm)],[137,48]) ).
tff(139,plain,
( ~ cp(tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ),
inference(tautology,[status(thm)],[]) ).
tff(140,plain,
rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rs(X,Y)
| rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rs(X,Y)
=> rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(145,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_14) ).
tff(147,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(152,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(153,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)),
inference(unit_resolution,[status(thm)],[153,150,140]) ).
tff(155,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(156,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)],[155]) ).
tff(157,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(158,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)],[157]) ).
tff(159,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(160,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(161,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)],[160]) ).
tff(162,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(163,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[163,159]) ).
tff(165,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(modus_ponens,[status(thm)],[165,158]) ).
tff(167,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(modus_ponens,[status(thm)],[166,156]) ).
tff(168,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ( ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) )
<=> ( ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(170,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(transitivity,[status(thm)],[170,168]) ).
tff(172,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(173,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ( tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508) )
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ),
inference(modus_ponens,[status(thm)],[172,171]) ).
tff(174,plain,
tptp_fun_Y_0(i2003_11_14_17_21_08508) = tptp_fun_Y_5(i2003_11_14_17_21_08508),
inference(unit_resolution,[status(thm)],[173,167,128,154]) ).
tff(175,plain,
( rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(monotonicity,[status(thm)],[174]) ).
tff(176,plain,
( rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(symmetry,[status(thm)],[175]) ).
tff(177,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvS(X,Y)
<=> rs(Y,X) )
<=> ( rinvS(X,Y)
<=> rs(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(178,plain,
( ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ) ),
inference(quant_intro,[status(thm)],[177]) ).
tff(179,plain,
( ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,axiom,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(181,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(skolemize,[status(sab)],[181]) ).
tff(183,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[182,178]) ).
tff(184,plain,
( ~ ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
| ( rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(185,plain,
( rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ),
inference(unit_resolution,[status(thm)],[184,183]) ).
tff(186,plain,
( ~ ( rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) )
| rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
| ~ rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) ),
inference(tautology,[status(thm)],[]) ).
tff(187,plain,
( ~ ( rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508)
<=> rs(i2003_11_14_17_21_08508,tptp_fun_Y_5(i2003_11_14_17_21_08508)) )
| rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(unit_resolution,[status(thm)],[186,140]) ).
tff(188,plain,
rinvS(tptp_fun_Y_5(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(unit_resolution,[status(thm)],[187,185]) ).
tff(189,plain,
rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508),
inference(modus_ponens,[status(thm)],[188,176]) ).
tff(190,plain,
( ~ ! [Y: $i] :
( ca_Vx3(Y)
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(191,plain,
! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) ),
inference(unit_resolution,[status(thm)],[190,115]) ).
tff(192,plain,
( ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| cp(i2003_11_14_17_21_08508)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) )
<=> ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| cp(i2003_11_14_17_21_08508)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(193,plain,
( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| cp(i2003_11_14_17_21_08508)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(quant_inst,[status(thm)],[]) ).
tff(194,plain,
( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),Y) )
| cp(i2003_11_14_17_21_08508)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(modus_ponens,[status(thm)],[193,192]) ).
tff(195,plain,
( cp(i2003_11_14_17_21_08508)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_08508),i2003_11_14_17_21_08508) ),
inference(unit_resolution,[status(thm)],[194,191]) ).
tff(196,plain,
cp(i2003_11_14_17_21_08508),
inference(unit_resolution,[status(thm)],[195,189]) ).
tff(197,plain,
( ~ ( ~ cp(i2003_11_14_17_21_08508)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) )
| ~ cp(i2003_11_14_17_21_08508)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(198,plain,
( ~ ( ~ cp(i2003_11_14_17_21_08508)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) )
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y) ),
inference(unit_resolution,[status(thm)],[197,196]) ).
tff(199,plain,
! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y),
inference(unit_resolution,[status(thm)],[198,26]) ).
tff(200,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(201,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[200]) ).
tff(202,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(203,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[202]) ).
tff(204,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[203,201]) ).
tff(205,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(206,plain,
( ! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[205]) ).
tff(207,plain,
( ! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(208,axiom,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(209,plain,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[208,207]) ).
tff(210,plain,
! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[209]) ).
tff(211,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[210,206]) ).
tff(212,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[211,204]) ).
tff(213,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_2(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) )
| ~ ( cpxcomp(i2003_11_14_17_21_08508)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(214,plain,
~ ( ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) )
| ~ ( cpxcomp(i2003_11_14_17_21_08508)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y0) ) ),
inference(unit_resolution,[status(thm)],[213,212]) ).
tff(215,plain,
( ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) )
| ~ ( cpxcomp(i2003_11_14_17_21_08508)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y0) )
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) ),
inference(tautology,[status(thm)],[]) ).
tff(216,plain,
( ~ cpxcomp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) ),
inference(unit_resolution,[status(thm)],[215,214]) ).
tff(217,plain,
( ~ cpxcomp(i2003_11_14_17_21_08508)
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_08508))
| ~ rf(i2003_11_14_17_21_08508,tptp_fun_Y_0(i2003_11_14_17_21_08508))
| cpxcomp(i2003_11_14_17_21_08508) ),
inference(tautology,[status(thm)],[]) ).
tff(218,plain,
cpxcomp(i2003_11_14_17_21_08508),
inference(unit_resolution,[status(thm)],[217,110]) ).
tff(219,plain,
( ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) )
| ~ cpxcomp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) ),
inference(tautology,[status(thm)],[]) ).
tff(220,plain,
( ~ ( ~ cpxcomp(i2003_11_14_17_21_08508)
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) )
| ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) ),
inference(unit_resolution,[status(thm)],[219,218]) ).
tff(221,plain,
ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)),
inference(unit_resolution,[status(thm)],[220,216]) ).
tff(222,plain,
( ~ ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_08508,Y)
| ~ ra_Px1(i2003_11_14_17_21_08508,tptp_fun_Y0_2(i2003_11_14_17_21_08508)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(223,plain,
$false,
inference(unit_resolution,[status(thm)],[222,221,199]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KRS109+1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n015.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Jun 19 19:11:25 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.13/0.41 % SZS status Unsatisfiable
% 0.13/0.41 % SZS output start Proof
% See solution above
% 0.22/0.45 % E exiting
%------------------------------------------------------------------------------