%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS098+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:13:22 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 68
% Syntax : Number of formulae : 171 ( 42 unt; 0 typ; 0 def)
% Number of atoms : 3615 ( 614 equ)
% Maximal formula atoms : 176 ( 21 avg)
% Number of connectives : 6455 (3081 ~;2794 |; 452 &)
% ( 104 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 70 ( 70 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-5 aty)
% Number of functors : 11 ( 11 usr; 1 con; 0-1 aty)
% Number of variables : 1321 (1217 !; 72 ?;1321 :)
% Comments :
%------------------------------------------------------------------------------
tff(cd_type,type,
cd: $i > $o ).
tff(tptp_fun_Z_3_type,type,
tptp_fun_Z_3: $i > $i ).
tff(i2003_11_14_17_20_25524_type,type,
i2003_11_14_17_20_25524: $i ).
tff(tptp_fun_Z_1_type,type,
tptp_fun_Z_1: $i > $i ).
tff(rtt_type,type,
rtt: ( $i * $i ) > $o ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(rr1_type,type,
rr1: ( $i * $i ) > $o ).
tff(rr2_type,type,
rr2: ( $i * $i ) > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rr3_type,type,
rr3: ( $i * $i ) > $o ).
tff(rt3_type,type,
rt3: ( $i * $i ) > $o ).
tff(ce_type,type,
ce: $i > $o ).
tff(rt2_type,type,
rt2: ( $i * $i ) > $o ).
tff(rt1_type,type,
rt1: ( $i * $i ) > $o ).
tff(tptp_fun_Z_5_type,type,
tptp_fun_Z_5: $i > $i ).
tff(cc_type,type,
cc: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y1_8_type,type,
tptp_fun_Y1_8: $i > $i ).
tff(tptp_fun_Y0_9_type,type,
tptp_fun_Y0_9: $i > $i ).
tff(tptp_fun_Z1_6_type,type,
tptp_fun_Z1_6: $i > $i ).
tff(tptp_fun_Z0_7_type,type,
tptp_fun_Z0_7: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [Z: $i] :
trans(monotonicity(rewrite(( ( rt3(Y,Z)
& ce(Z) )
<=> ~ ( ~ rt3(Y,Z)
| ~ ce(Z) ) )),
( ~ ( rt3(Y,Z)
& ce(Z) )
<=> ~ ~ ( ~ rt3(Y,Z)
| ~ ce(Z) ) )),
rewrite(( ~ ~ ( ~ rt3(Y,Z)
| ~ ce(Z) )
<=> ( ~ rt3(Y,Z)
| ~ ce(Z) ) )),
( ~ ( rt3(Y,Z)
& ce(Z) )
<=> ( ~ rt3(Y,Z)
| ~ ce(Z) ) ))),
( ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
<=> ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )),
rewrite(( ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
<=> ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )),
( ( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
<=> ( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) ) )),
rewrite(( ( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
<=> ( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) ) )),
( ( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
<=> ( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) ) ))),
( ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
<=> ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) ) )),
quant_intro(proof_bind(^ [Y: $i] :
rewrite(( ( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
<=> ( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) ) ))),
( ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
<=> ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) ) )),
rewrite(( ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
<=> ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) )),
quant_intro(proof_bind(^ [Y: $i] :
rewrite(( ( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) )
<=> ( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ))),
( ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) )
<=> ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ( rtt(Y,Z0)
& rtt(Y,Z1) )
=> ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr3(X,Y)
& ? [Z: $i] :
( rt3(Y,Z)
& ce(Z) )
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) ) )
& ? [Y: $i] :
( rr2(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt2(Y,Z)
& cd(Z) ) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr1(X,Y)
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(Y,Z0)
& rtt(Y,Z1) )
| ( Z0 = Z1 ) )
& ? [Z: $i] :
( rt1(Y,Z)
& cc(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr3(X,tptp_fun_Y_0(X))
& rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& ce(tptp_fun_Z_1(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_0(X),Z0)
& rtt(tptp_fun_Y_0(X),Z1) )
| ( Z0 = Z1 ) )
& rr2(X,tptp_fun_Y_2(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_2(X),Z0)
& rtt(tptp_fun_Y_2(X),Z1) )
| ( Z0 = Z1 ) )
& rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
& cd(tptp_fun_Z_3(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr1(X,tptp_fun_Y_4(X))
& ! [Z0: $i,Z1: $i] :
( ~ ( rtt(tptp_fun_Y_4(X),Z0)
& rtt(tptp_fun_Y_4(X),Z1) )
| ( Z0 = Z1 ) )
& rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
& cc(tptp_fun_Z_5(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
~ ( rt3(Y,Z)
& ce(Z) )
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt2(Y,Z)
& cd(Z) ) )
| ( rr(X,tptp_fun_Y0_9(X))
& rr(X,tptp_fun_Y1_8(X))
& ( tptp_fun_Y0_9(X) != tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ ( rtt(Y,tptp_fun_Z0_7(Y))
& rtt(Y,tptp_fun_Z1_6(Y)) )
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
~ ( rt1(Y,Z)
& cc(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) ) )
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr2(X,tptp_fun_Y_2(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr3(X,tptp_fun_Y_0(X))
| ~ rt3(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ ce(tptp_fun_Z_1(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(X),Z0)
| ~ rtt(tptp_fun_Y_2(X),Z1) )
| ~ rt2(tptp_fun_Y_2(X),tptp_fun_Z_3(X))
| ~ cd(tptp_fun_Z_3(X))
| ~ rr1(X,tptp_fun_Y_4(X))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(X),Z0)
| ~ rtt(tptp_fun_Y_4(X),Z1) )
| ~ rt1(tptp_fun_Y_4(X),tptp_fun_Z_5(X))
| ~ cc(tptp_fun_Z_5(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_9(X))
| ~ rr(X,tptp_fun_Y1_8(X))
| ( tptp_fun_Y0_9(X) = tptp_fun_Y1_8(X) ) )
| ! [Y: $i] :
( ~ rr2(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_20_25524)
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr2(i2003_11_14_17_20_25524,Y)
| ~ ( ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y))
| ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) ) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ~ ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y0_9(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y1_8(i2003_11_14_17_20_25524))
| ( tptp_fun_Y0_9(i2003_11_14_17_20_25524) = tptp_fun_Y1_8(i2003_11_14_17_20_25524) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_20_25524)
<=> cUnsatisfiable(i2003_11_14_17_20_25524) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_20_25524),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_20_25524),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) )
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],[]) ).
tff(39,plain,
rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rr1(X,Y)
| rr(X,Y) )
<=> ( ~ rr1(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rr1(X,Y)
=> rr(X,Y) )
<=> ( ~ rr1(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [X: $i,Y: $i] :
( rr1(X,Y)
=> rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [X: $i,Y: $i] :
( rr1(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(46,plain,
! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[52,49,39]) ).
tff(54,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],[]) ).
tff(55,plain,
rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[54,37]) ).
tff(56,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rr2(X,Y)
| rr(X,Y) )
<=> ( ~ rr2(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rr2(X,Y)
=> rr(X,Y) )
<=> ( ~ rr2(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [X: $i,Y: $i] :
( rr2(X,Y)
=> rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [X: $i,Y: $i] :
( rr2(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(62,plain,
! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[68,65,55]) ).
tff(70,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) ) ),
inference(tautology,[status(thm)],[]) ).
tff(71,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) ),
inference(unit_resolution,[status(thm)],[70,37]) ).
tff(72,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) )
<=> ( ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ) ),
inference(transitivity,[status(thm)],[74,72]) ).
tff(76,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524),
inference(unit_resolution,[status(thm)],[77,71,69,53]) ).
tff(79,plain,
tptp_fun_Y_4(i2003_11_14_17_20_25524) = tptp_fun_Y_2(i2003_11_14_17_20_25524),
inference(symmetry,[status(thm)],[78]) ).
tff(80,plain,
( rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
<=> rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
<=> rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(symmetry,[status(thm)],[80]) ).
tff(82,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],[]) ).
tff(83,plain,
rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[82,37]) ).
tff(84,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rt2(X,Y)
| rtt(X,Y) )
<=> ( ~ rt2(X,Y)
| rtt(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rt2(X,Y)
=> rtt(X,Y) )
<=> ( ~ rt2(X,Y)
| rtt(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [X: $i,Y: $i] :
( rt2(X,Y)
=> rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [X: $i,Y: $i] :
( rt2(X,Y)
=> rtt(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(90,plain,
! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) )
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) )
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) )
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) )
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[95,94]) ).
tff(97,plain,
rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[96,93,83]) ).
tff(98,plain,
rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)),
inference(modus_ponens,[status(thm)],[97,81]) ).
tff(99,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],[]) ).
tff(100,plain,
rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[99,37]) ).
tff(101,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rr3(X,Y)
| rr(X,Y) )
<=> ( ~ rr3(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(102,plain,
( ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,plain,
( ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rr3(X,Y)
=> rr(X,Y) )
<=> ( ~ rr3(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(105,plain,
( ! [X: $i,Y: $i] :
( rr3(X,Y)
=> rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[104]) ).
tff(106,axiom,
! [X: $i,Y: $i] :
( rr3(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
tff(107,plain,
! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[107,103]) ).
tff(109,plain,
! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[108]) ).
tff(110,plain,
! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[109,102]) ).
tff(111,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) )
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) )
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(112,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) )
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) )
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[113,110,100]) ).
tff(115,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_0(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_0(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(116,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_0(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(117,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ( tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_0(i2003_11_14_17_20_25524) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
tptp_fun_Y_2(i2003_11_14_17_20_25524) = tptp_fun_Y_0(i2003_11_14_17_20_25524),
inference(unit_resolution,[status(thm)],[117,71,69,114]) ).
tff(119,plain,
tptp_fun_Y_4(i2003_11_14_17_20_25524) = tptp_fun_Y_0(i2003_11_14_17_20_25524),
inference(transitivity,[status(thm)],[79,118]) ).
tff(120,plain,
( rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
<=> rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
<=> rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(symmetry,[status(thm)],[120]) ).
tff(122,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],[]) ).
tff(123,plain,
rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[122,37]) ).
tff(124,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rt3(X,Y)
| rtt(X,Y) )
<=> ( ~ rt3(X,Y)
| rtt(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(125,plain,
( ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rt3(X,Y)
=> rtt(X,Y) )
<=> ( ~ rt3(X,Y)
| rtt(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(128,plain,
( ! [X: $i,Y: $i] :
( rt3(X,Y)
=> rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,axiom,
! [X: $i,Y: $i] :
( rt3(X,Y)
=> rtt(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_13) ).
tff(130,plain,
! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) )
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) )
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) )
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(136,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rt3(X,Y)
| rtt(X,Y) )
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[136,133,123]) ).
tff(138,plain,
rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)),
inference(modus_ponens,[status(thm)],[137,121]) ).
tff(139,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) ) ),
inference(tautology,[status(thm)],[]) ).
tff(140,plain,
! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) ),
inference(unit_resolution,[status(thm)],[139,37]) ).
tff(141,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(142,plain,
( ( ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) )
<=> ( ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(143,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ) ),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ) ),
inference(transitivity,[status(thm)],[143,141]) ).
tff(145,plain,
( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(146,plain,
( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[145,144]) ).
tff(147,plain,
( ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(unit_resolution,[status(thm)],[146,140]) ).
tff(148,plain,
tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_1(i2003_11_14_17_20_25524),
inference(unit_resolution,[status(thm)],[147,138,98]) ).
tff(149,plain,
( cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
<=> cd(tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( cd(tptp_fun_Z_1(i2003_11_14_17_20_25524))
<=> cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(symmetry,[status(thm)],[149]) ).
tff(151,plain,
( ~ cd(tptp_fun_Z_1(i2003_11_14_17_20_25524))
<=> ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(monotonicity,[status(thm)],[150]) ).
tff(152,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| ce(tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],[]) ).
tff(153,plain,
ce(tptp_fun_Z_1(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[152,37]) ).
tff(154,plain,
^ [X: $i] :
refl(( ( ~ cd(X)
| ~ ce(X) )
<=> ( ~ cd(X)
| ~ ce(X) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [X: $i] :
( ~ cd(X)
| ~ ce(X) )
<=> ! [X: $i] :
( ~ cd(X)
| ~ ce(X) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ce(X)
& cd(X) )
<=> ~ ( ~ cd(X)
| ~ ce(X) ) )),
( ~ ( ce(X)
& cd(X) )
<=> ~ ~ ( ~ cd(X)
| ~ ce(X) ) )),
rewrite(( ~ ~ ( ~ cd(X)
| ~ ce(X) )
<=> ( ~ cd(X)
| ~ ce(X) ) )),
( ~ ( ce(X)
& cd(X) )
<=> ( ~ cd(X)
| ~ ce(X) ) )),
inference(bind,[status(th)],[]) ).
tff(157,plain,
( ! [X: $i] :
~ ( ce(X)
& cd(X) )
<=> ! [X: $i] :
( ~ cd(X)
| ~ ce(X) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [X: $i] :
~ ( ce(X)
& cd(X) )
<=> ! [X: $i] :
~ ( ce(X)
& cd(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,axiom,
! [X: $i] :
~ ( ce(X)
& cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(160,plain,
! [X: $i] :
~ ( ce(X)
& cd(X) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [X: $i] :
~ ( ce(X)
& cd(X) ),
inference(skolemize,[status(sab)],[160]) ).
tff(162,plain,
! [X: $i] :
( ~ cd(X)
| ~ ce(X) ),
inference(modus_ponens,[status(thm)],[161,157]) ).
tff(163,plain,
! [X: $i] :
( ~ cd(X)
| ~ ce(X) ),
inference(modus_ponens,[status(thm)],[162,155]) ).
tff(164,plain,
( ( ~ ! [X: $i] :
( ~ cd(X)
| ~ ce(X) )
| ~ cd(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [X: $i] :
( ~ cd(X)
| ~ ce(X) )
| ~ cd(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(165,plain,
( ~ ! [X: $i] :
( ~ cd(X)
| ~ ce(X) )
| ~ cd(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(166,plain,
( ~ ! [X: $i] :
( ~ cd(X)
| ~ ce(X) )
| ~ cd(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[165,164]) ).
tff(167,plain,
~ cd(tptp_fun_Z_1(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[166,163,153]) ).
tff(168,plain,
~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)),
inference(modus_ponens,[status(thm)],[167,151]) ).
tff(169,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y0)
| ~ rr(i2003_11_14_17_20_25524,Y1) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),Z1) )
| ~ rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rt2(tptp_fun_Y_2(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_2(i2003_11_14_17_20_25524),Z1) )
| ~ ce(tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rt3(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_1(i2003_11_14_17_20_25524))
| ~ rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524))
| ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ~ rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524))
| cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],[]) ).
tff(170,plain,
cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[169,37]) ).
tff(171,plain,
$false,
inference(unit_resolution,[status(thm)],[170,168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS098+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:15:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.20/0.46 % E exiting
%------------------------------------------------------------------------------