%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS113+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 0.17s 0.36s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 65
% Syntax : Number of formulae : 163 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 1973 ( 155 equ)
% Maximal formula atoms : 72 ( 12 avg)
% Number of connectives : 3453 (1729 ~;1373 |; 190 &)
% ( 152 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 86 ( 86 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 613 ( 545 !; 41 ?; 613 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(i2003_11_14_17_21_22376_type,type,
i2003_11_14_17_21_22376: $i ).
tff(cp_type,type,
cp: $i > $o ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $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_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(ca_Vx2_type,type,
ca_Vx2: $i > $o ).
tff(cpxcomp_type,type,
cpxcomp: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y1_2_type,type,
tptp_fun_Y1_2: $i > $i ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(tptp_fun_Y_6_type,type,
tptp_fun_Y_6: $i > $i ).
tff(tptp_fun_Y0_5_type,type,
tptp_fun_Y0_5: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
rewrite(( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_4(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_4(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_4(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_4(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_4(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_4(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_4(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_4(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y_4(i2003_11_14_17_21_22376)) )
| ~ ( ~ cp(i2003_11_14_17_21_22376)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
~ ( ~ ( cp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y_4(i2003_11_14_17_21_22376)) )
| ~ ( ~ cp(i2003_11_14_17_21_22376)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( cp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y_4(i2003_11_14_17_21_22376)) )
| ~ ( ~ cp(i2003_11_14_17_21_22376)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) )
| ~ cp(i2003_11_14_17_21_22376)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(26,plain,
( ~ cp(i2003_11_14_17_21_22376)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(32,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) ),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) ) )),
trans(monotonicity(rewrite(( ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
<=> ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) )),
quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rr(X,Y)
& ca_Vx2(Y) )
<=> ~ ( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& ca_Vx2(Y) )
<=> ~ ~ ( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )),
rewrite(( ~ ~ ( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
<=> ( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& ca_Vx2(Y) )
<=> ( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
<=> ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )),
quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rs(X,Y)
& cp(Y) )
<=> ~ ( ~ rs(X,Y)
| ~ cp(Y) ) )),
( ~ ( rs(X,Y)
& cp(Y) )
<=> ~ ~ ( ~ rs(X,Y)
| ~ cp(Y) ) )),
rewrite(( ~ ~ ( ~ rs(X,Y)
| ~ cp(Y) )
<=> ( ~ rs(X,Y)
| ~ cp(Y) ) )),
( ~ ( rs(X,Y)
& cp(Y) )
<=> ( ~ rs(X,Y)
| ~ cp(Y) ) ))),
( ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
<=> ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) ) )),
( ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) )
<=> ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ~ cpxcomp(X) ) )),
rewrite(( ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ~ cpxcomp(X) )
<=> ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )),
( ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) )
<=> ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(37,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[36]) ).
tff(38,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) )
<=> ( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(42,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ca_Vx2(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) )
& cpxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ca_Vx2(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X))
& cpxcomp(X) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Vx2(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
| ~ cpxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[44,37]) ).
tff(46,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[45,35]) ).
tff(47,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) )
| ~ cpxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[46,33]) ).
tff(48,plain,
! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,28]) ).
tff(49,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) )
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) )
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
( ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_22376,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) )
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_22376,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) )
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_22376,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) )
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ) ) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_22376,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ~ cpxcomp(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(X,Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Vx2(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ cpxcomp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) )
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) )
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ) ),
inference(unit_resolution,[status(thm)],[54,48]) ).
tff(56,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ! [Y: $i] :
( ~ ca_Vx2(Y)
| ~ rr(i2003_11_14_17_21_22376,Y) )
| ~ ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y0_3(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y1_2(i2003_11_14_17_21_22376))
| ( tptp_fun_Y0_3(i2003_11_14_17_21_22376) = tptp_fun_Y1_2(i2003_11_14_17_21_22376) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_21_22376,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(57,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( cUnsatisfiable(i2003_11_14_17_21_22376)
<=> cUnsatisfiable(i2003_11_14_17_21_22376) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,axiom,
cUnsatisfiable(i2003_11_14_17_21_22376),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(60,plain,
cUnsatisfiable(i2003_11_14_17_21_22376),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(62,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_22376)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) )
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ) ),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ),
inference(unit_resolution,[status(thm)],[62,57]) ).
tff(64,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ),
inference(tautology,[status(thm)],[]) ).
tff(65,plain,
rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rs(X,Y)
| rr(X,Y) )
<=> ( ~ rs(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(67,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rs(X,Y)
=> rr(X,Y) )
<=> ( ~ rs(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(70,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(72,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)),
inference(unit_resolution,[status(thm)],[78,75,65]) ).
tff(80,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)),
inference(unit_resolution,[status(thm)],[80,63]) ).
tff(82,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) ) ),
inference(tautology,[status(thm)],[]) ).
tff(83,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) ),
inference(unit_resolution,[status(thm)],[82,63]) ).
tff(84,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) )
<=> ( ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ( tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376) )
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
tptp_fun_Y_1(i2003_11_14_17_21_22376) = tptp_fun_Y_0(i2003_11_14_17_21_22376),
inference(unit_resolution,[status(thm)],[89,83,81,79]) ).
tff(91,plain,
tptp_fun_Y_0(i2003_11_14_17_21_22376) = tptp_fun_Y_1(i2003_11_14_17_21_22376),
inference(symmetry,[status(thm)],[90]) ).
tff(92,plain,
( rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376)
<=> rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376)
<=> rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376) ),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvS(X,Y)
<=> rs(Y,X) )
<=> ( rinvS(X,Y)
<=> rs(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(95,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)],[94]) ).
tff(96,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(97,axiom,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(98,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
| ( rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376)
<=> rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376)
<=> rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
( ~ ( rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376)
<=> rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) )
| rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376)
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
( ~ ( rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376)
<=> rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376)) )
| rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376) ),
inference(unit_resolution,[status(thm)],[103,65]) ).
tff(105,plain,
rinvS(tptp_fun_Y_1(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376),
inference(unit_resolution,[status(thm)],[104,102]) ).
tff(106,plain,
rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376),
inference(modus_ponens,[status(thm)],[105,93]) ).
tff(107,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(108,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[107]) ).
tff(109,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(110,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
<=> ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) ) )),
( ( ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
& ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ( ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
& ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) )),
rewrite(( ( ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
& ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) )),
( ( ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
& ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(113,plain,
( ! [X: $i] :
( ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
& ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [X: $i] :
( ca_Vx2(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
<=> ! [X: $i] :
( ca_Vx2(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(115,plain,
^ [X: $i] :
rewrite(( ( ca_Vx2(X)
<=> ! [Y: $i] :
( rinvS(X,Y)
=> cp(Y) ) )
<=> ( ca_Vx2(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [X: $i] :
( ca_Vx2(X)
<=> ! [Y: $i] :
( rinvS(X,Y)
=> cp(Y) ) )
<=> ! [X: $i] :
( ca_Vx2(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,axiom,
! [X: $i] :
( ca_Vx2(X)
<=> ! [Y: $i] :
( rinvS(X,Y)
=> cp(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(118,plain,
! [X: $i] :
( ca_Vx2(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [X: $i] :
( ca_Vx2(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
! [X: $i] :
( ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
& ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ),
inference(skolemize,[status(sab)],[119]) ).
tff(121,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ),
inference(modus_ponens,[status(thm)],[120,113]) ).
tff(122,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) ),
inference(modus_ponens,[status(thm)],[121,111]) ).
tff(123,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx2(X)
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(X,Y) ) )
| ~ ( ca_Vx2(X)
| ~ ( cp(tptp_fun_Y_6(X))
| ~ rinvS(X,tptp_fun_Y_6(X)) ) ) )
| ~ ( ~ ( ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) )
| ~ ( ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ ( cp(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_22376)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_22376))) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(124,plain,
~ ( ~ ( ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) )
| ~ ( ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ ( cp(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_22376)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_22376))) ) ) ),
inference(unit_resolution,[status(thm)],[123,122]) ).
tff(125,plain,
( ~ ( ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) )
| ~ ( ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ ( cp(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_22376)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_22376))) ) )
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(126,plain,
( ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) ),
inference(unit_resolution,[status(thm)],[125,124]) ).
tff(127,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376)) ),
inference(tautology,[status(thm)],[]) ).
tff(128,plain,
ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376)),
inference(unit_resolution,[status(thm)],[127,63]) ).
tff(129,plain,
( ~ ( ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) )
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(130,plain,
( ~ ( ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) )
| ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ) ),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) ),
inference(unit_resolution,[status(thm)],[130,126]) ).
tff(132,plain,
( ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) )
| cp(i2003_11_14_17_21_22376)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376) )
<=> ( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) )
| cp(i2003_11_14_17_21_22376)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) )
| cp(i2003_11_14_17_21_22376)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376) ),
inference(quant_inst,[status(thm)],[]) ).
tff(134,plain,
( ~ ! [Y: $i] :
( cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),Y) )
| cp(i2003_11_14_17_21_22376)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376) ),
inference(modus_ponens,[status(thm)],[133,132]) ).
tff(135,plain,
( cp(i2003_11_14_17_21_22376)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_22376),i2003_11_14_17_21_22376) ),
inference(unit_resolution,[status(thm)],[134,131]) ).
tff(136,plain,
cp(i2003_11_14_17_21_22376),
inference(unit_resolution,[status(thm)],[135,106]) ).
tff(137,plain,
( ~ ( ~ cp(i2003_11_14_17_21_22376)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) )
| ~ cp(i2003_11_14_17_21_22376)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(138,plain,
( ~ ( ~ cp(i2003_11_14_17_21_22376)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) )
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y) ),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y),
inference(unit_resolution,[status(thm)],[138,26]) ).
tff(140,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(141,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(143,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[142]) ).
tff(144,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,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_5(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(146,plain,
( ! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[145]) ).
tff(147,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(148,axiom,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(149,plain,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[151,144]) ).
tff(153,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cpxcomp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) )
| ~ ( cpxcomp(i2003_11_14_17_21_22376)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(154,plain,
~ ( ~ ( ~ cpxcomp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) )
| ~ ( cpxcomp(i2003_11_14_17_21_22376)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y0) ) ),
inference(unit_resolution,[status(thm)],[153,152]) ).
tff(155,plain,
( ~ ( ~ cpxcomp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) )
| ~ ( cpxcomp(i2003_11_14_17_21_22376)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y0) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) ),
inference(tautology,[status(thm)],[]) ).
tff(156,plain,
( ~ cpxcomp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) ),
inference(unit_resolution,[status(thm)],[155,154]) ).
tff(157,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_21_22376,Y0)
| ~ rr(i2003_11_14_17_21_22376,Y1) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ rs(i2003_11_14_17_21_22376,tptp_fun_Y_1(i2003_11_14_17_21_22376))
| ~ ca_Vx2(tptp_fun_Y_0(i2003_11_14_17_21_22376))
| ~ rr(i2003_11_14_17_21_22376,tptp_fun_Y_0(i2003_11_14_17_21_22376))
| cpxcomp(i2003_11_14_17_21_22376) ),
inference(tautology,[status(thm)],[]) ).
tff(158,plain,
cpxcomp(i2003_11_14_17_21_22376),
inference(unit_resolution,[status(thm)],[157,63]) ).
tff(159,plain,
( ~ ( ~ cpxcomp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) )
| ~ cpxcomp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) ),
inference(tautology,[status(thm)],[]) ).
tff(160,plain,
( ~ ( ~ cpxcomp(i2003_11_14_17_21_22376)
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) )
| ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) ),
inference(unit_resolution,[status(thm)],[159,158]) ).
tff(161,plain,
ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)),
inference(unit_resolution,[status(thm)],[160,156]) ).
tff(162,plain,
( ~ ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_21_22376,Y)
| ~ ra_Px1(i2003_11_14_17_21_22376,tptp_fun_Y0_5(i2003_11_14_17_21_22376)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(163,plain,
$false,
inference(unit_resolution,[status(thm)],[162,161,139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KRS113+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.11 % Command : run_E %s %d THM
% 0.11/0.31 % Computer : n002.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Thu Jun 19 19:13:01 EDT 2025
% 0.11/0.31 % CPUTime :
% 0.17/0.36 % SZS status Unsatisfiable
% 0.17/0.36 % SZS output start Proof
% See solution above
% 0.17/0.39 % E exiting
%------------------------------------------------------------------------------