TSTP Solution File: KRS098+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS098+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n024.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 Sep 17 17:44:44 EDT 2022
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 96
% Syntax : Number of formulae : 201 ( 44 unt; 23 typ; 0 def)
% Number of atoms : 3024 ( 525 equ)
% Maximal formula atoms : 88 ( 16 avg)
% Number of connectives : 5150 (2389 ~;2155 |; 468 &)
% ( 111 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 85 ( 85 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 30 ( 22 >; 8 *; 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 : 1132 (1022 !; 72 ?;1132 :)
% Comments :
%------------------------------------------------------------------------------
tff(rtt_type,type,
rtt: ( $i * $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_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(rr2_type,type,
rr2: ( $i * $i ) > $o ).
tff(cc_type,type,
cc: $i > $o ).
tff(tptp_fun_Z_5_type,type,
tptp_fun_Z_5: $i > $i ).
tff(rt1_type,type,
rt1: ( $i * $i ) > $o ).
tff(rr1_type,type,
rr1: ( $i * $i ) > $o ).
tff(cd_type,type,
cd: $i > $o ).
tff(rt2_type,type,
rt2: ( $i * $i ) > $o ).
tff(ce_type,type,
ce: $i > $o ).
tff(tptp_fun_Z_1_type,type,
tptp_fun_Z_1: $i > $i ).
tff(rt3_type,type,
rt3: ( $i * $i ) > $o ).
tff(rr3_type,type,
rr3: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
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(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(1,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( 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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,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)) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( 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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,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)) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ 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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ) ),
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)
| ~ ( ~ 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_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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) ) )
<=> ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) ) ) )),
rewrite(
( ( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) ) )
<=> ( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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) ) ) ) )
<=> ( ( ~ 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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ) )),
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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [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) ) ) ) )
<=> ~ ( ~ ( ~ 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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ) )),
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)
| ~ ( ~ 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_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ) ),
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)
| ~ ( ~ 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_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) )
| ~ 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] :
( ~ rr3(X,Y)
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) )
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(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) ) )
| ! [Y: $i] :
( ~ rr2(X,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)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( 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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,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)) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,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] :
( ( Z0 = Z1 )
| ~ rtt(tptp_fun_Y_0(X),Z0)
| ~ rtt(tptp_fun_Y_0(X),Z1) )
| ~ rr2(X,tptp_fun_Y_2(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,Y1)
| ~ rr(X,Y0) ) ) )
| ~ ( 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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(X,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(X,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)) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) )
| ~ ( 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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,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)) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) )
| ~ ( 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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,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)) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) )
| ~ ( 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)
| ~ ( ( tptp_fun_Z0_7(Y) = tptp_fun_Z1_6(Y) )
| ~ rtt(Y,tptp_fun_Z0_7(Y))
| ~ rtt(Y,tptp_fun_Z1_6(Y)) )
| ! [Z: $i] :
( ~ rt2(Y,Z)
| ~ cd(Z) ) )
| ! [Y: $i] :
( ~ rr1(i2003_11_14_17_20_25524,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)) )
| ! [Z: $i] :
( ~ rt1(Y,Z)
| ~ cc(Z) ) )
| ! [Y: $i] :
( ~ rr3(i2003_11_14_17_20_25524,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)) )
| ! [Z: $i] :
( ~ rt3(Y,Z)
| ~ ce(Z) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(26,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( cUnsatisfiable(i2003_11_14_17_20_25524)
<=> cUnsatisfiable(i2003_11_14_17_20_25524) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
cUnsatisfiable(i2003_11_14_17_20_25524),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(29,plain,
cUnsatisfiable(i2003_11_14_17_20_25524),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_25524)
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) )
| ~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
~ ( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ),
inference(unit_resolution,[status(thm)],[31,26]) ).
tff(33,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],]) ).
tff(34,plain,
rr2(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rr2(X,Y)
| rr(X,Y) )
<=> ( ~ rr2(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(36,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)],[35]) ).
tff(37,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(38,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rr2(X,Y)
=> rr(X,Y) )
<=> ( ~ rr2(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(39,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)],[38]) ).
tff(40,axiom,
! [X: $i,Y: $i] :
( rr2(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(41,plain,
! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [X: $i,Y: $i] :
( ~ rr2(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,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(46,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(47,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)],[46,45]) ).
tff(48,plain,
rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[47,44,34]) ).
tff(49,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],]) ).
tff(50,plain,
rr1(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[49,32]) ).
tff(51,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rr1(X,Y)
| rr(X,Y) )
<=> ( ~ rr1(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(52,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)],[51]) ).
tff(53,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(54,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rr1(X,Y)
=> rr(X,Y) )
<=> ( ~ rr1(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(55,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)],[54]) ).
tff(56,axiom,
! [X: $i,Y: $i] :
( rr1(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(57,plain,
! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [X: $i,Y: $i] :
( ~ rr1(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[59,52]) ).
tff(61,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(62,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(63,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)],[62,61]) ).
tff(64,plain,
rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[63,60,50]) ).
tff(65,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ) ),
inference(tautology,[status(thm)],]) ).
tff(66,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) ),
inference(unit_resolution,[status(thm)],[65,32]) ).
tff(67,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ( 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))
| ~ rr(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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ( 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))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ( 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))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],]) ).
tff(69,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ( 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))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_2(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,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)],[69,66,64,48]) ).
tff(71,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)],[70]) ).
tff(72,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],]) ).
tff(73,plain,
rr3(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[72,32]) ).
tff(74,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rr3(X,Y)
| rr(X,Y) )
<=> ( ~ rr3(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(75,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)],[74]) ).
tff(76,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(77,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rr3(X,Y)
=> rr(X,Y) )
<=> ( ~ rr3(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(78,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)],[77]) ).
tff(79,axiom,
! [X: $i,Y: $i] :
( rr3(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_12) ).
tff(80,plain,
! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [X: $i,Y: $i] :
( ~ rr3(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[82,75]) ).
tff(84,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(85,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(86,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)],[85,84]) ).
tff(87,plain,
rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[86,83,73]) ).
tff(88,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_0(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_0(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_0(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_0(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(89,plain,
( ( ( tptp_fun_Y_0(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))
| ~ rr(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_4(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_0(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_0(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ( tptp_fun_Y_0(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))
| ~ 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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_0(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_0(i2003_11_14_17_20_25524)) ) ),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ( tptp_fun_Y_0(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))
| ~ 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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_0(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_0(i2003_11_14_17_20_25524)) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ( tptp_fun_Y_0(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))
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_0(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_25524,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ~ rr(i2003_11_14_17_20_25524,tptp_fun_Y_4(i2003_11_14_17_20_25524))
| ( tptp_fun_Y_0(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_0(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
tptp_fun_Y_0(i2003_11_14_17_20_25524) = tptp_fun_Y_4(i2003_11_14_17_20_25524),
inference(unit_resolution,[status(thm)],[93,66,64,87]) ).
tff(95,plain,
tptp_fun_Y_0(i2003_11_14_17_20_25524) = tptp_fun_Y_2(i2003_11_14_17_20_25524),
inference(transitivity,[status(thm)],[94,71]) ).
tff(96,plain,
( rtt(tptp_fun_Y_0(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)],[95]) ).
tff(97,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_0(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| 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(99,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)],[98,32]) ).
tff(100,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rt2(X,Y)
| rtt(X,Y) )
<=> ( ~ rt2(X,Y)
| rtt(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(101,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)],[100]) ).
tff(102,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(103,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rt2(X,Y)
=> rtt(X,Y) )
<=> ( ~ rt2(X,Y)
| rtt(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(104,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)],[103]) ).
tff(105,axiom,
! [X: $i,Y: $i] :
( rt2(X,Y)
=> rtt(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(106,plain,
! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ),
inference(skolemize,[status(sab)],[107]) ).
tff(109,plain,
! [X: $i,Y: $i] :
( ~ rt2(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,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(111,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(112,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)],[111,110]) ).
tff(113,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)],[112,109,99]) ).
tff(114,plain,
rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524)),
inference(modus_ponens,[status(thm)],[113,97]) ).
tff(115,plain,
( rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
<=> rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(monotonicity,[status(thm)],[94]) ).
tff(116,plain,
( rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
<=> rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],]) ).
tff(118,plain,
rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[117,32]) ).
tff(119,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rt1(X,Y)
| rtt(X,Y) )
<=> ( ~ rt1(X,Y)
| rtt(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(120,plain,
( ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) ) ),
inference(quant_intro,[status(thm)],[119]) ).
tff(121,plain,
( ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(122,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rt1(X,Y)
=> rtt(X,Y) )
<=> ( ~ rt1(X,Y)
| rtt(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [X: $i,Y: $i] :
( rt1(X,Y)
=> rtt(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,axiom,
! [X: $i,Y: $i] :
( rt1(X,Y)
=> rtt(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
tff(125,plain,
! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[124,123]) ).
tff(126,plain,
! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[125,121]) ).
tff(127,plain,
! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) ),
inference(modus_ponens,[status(thm)],[127,120]) ).
tff(129,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) )
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) )
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(130,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) )
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],]) ).
tff(131,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rt1(X,Y)
| rtt(X,Y) )
| ~ rt1(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524))
| rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
rtt(tptp_fun_Y_4(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[131,128,118]) ).
tff(133,plain,
rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)),
inference(modus_ponens,[status(thm)],[132,116]) ).
tff(134,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| cc(tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],]) ).
tff(135,plain,
cc(tptp_fun_Z_5(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[134,32]) ).
tff(136,plain,
^ [X: $i] :
refl(
( ( ~ cc(X)
| ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( cc(X)
& cd(X) )
<=> ~ ( ~ cc(X)
| ~ cd(X) ) )),
( ~ ( cc(X)
& cd(X) )
<=> ~ ~ ( ~ cc(X)
| ~ cd(X) ) )),
rewrite(
( ~ ~ ( ~ cc(X)
| ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
( ~ ( cc(X)
& cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],]) ).
tff(139,plain,
( ! [X: $i] :
~ ( cc(X)
& cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
( ! [X: $i] :
~ ( cc(X)
& cd(X) )
<=> ! [X: $i] :
~ ( cc(X)
& cd(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,axiom,
! [X: $i] :
~ ( cc(X)
& cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(142,plain,
! [X: $i] :
~ ( cc(X)
& cd(X) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
! [X: $i] :
~ ( cc(X)
& cd(X) ),
inference(skolemize,[status(sab)],[142]) ).
tff(144,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[143,139]) ).
tff(145,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[144,137]) ).
tff(146,plain,
( ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_5(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_5(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],]) ).
tff(148,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ~ cd(tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[147,146]) ).
tff(149,plain,
~ cd(tptp_fun_Z_5(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[148,145,135]) ).
tff(150,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(tautology,[status(thm)],]) ).
tff(151,plain,
cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)),
inference(unit_resolution,[status(thm)],[150,32]) ).
tff(152,plain,
^ [A: $i,B: $i] :
refl(
( ( cd(B)
| ( A != B )
| ~ cd(A) )
<=> ( cd(B)
| ( A != B )
| ~ cd(A) ) )),
inference(bind,[status(th)],]) ).
tff(153,plain,
( ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
<=> ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,plain,
^ [A: $i,B: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( A = B )
& cd(A) )
<=> ~ ( ( A != B )
| ~ cd(A) ) )),
( ~ ( ( A = B )
& cd(A) )
<=> ~ ~ ( ( A != B )
| ~ cd(A) ) )),
rewrite(
( ~ ~ ( ( A != B )
| ~ cd(A) )
<=> ( ( A != B )
| ~ cd(A) ) )),
( ~ ( ( A = B )
& cd(A) )
<=> ( ( A != B )
| ~ cd(A) ) )),
( ( cd(B)
| ~ ( ( A = B )
& cd(A) ) )
<=> ( cd(B)
| ( A != B )
| ~ cd(A) ) )),
rewrite(
( ( cd(B)
| ( A != B )
| ~ cd(A) )
<=> ( cd(B)
| ( A != B )
| ~ cd(A) ) )),
( ( cd(B)
| ~ ( ( A = B )
& cd(A) ) )
<=> ( cd(B)
| ( A != B )
| ~ cd(A) ) )),
inference(bind,[status(th)],]) ).
tff(155,plain,
( ! [A: $i,B: $i] :
( cd(B)
| ~ ( ( A = B )
& cd(A) ) )
<=> ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
( ! [A: $i,B: $i] :
( cd(B)
| ~ ( ( A = B )
& cd(A) ) )
<=> ! [A: $i,B: $i] :
( cd(B)
| ~ ( ( A = B )
& cd(A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
^ [A: $i,B: $i] :
rewrite(
( ( ( ( A = B )
& cd(A) )
=> cd(B) )
<=> ( cd(B)
| ~ ( ( A = B )
& cd(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(158,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
& cd(A) )
=> cd(B) )
<=> ! [A: $i,B: $i] :
( cd(B)
| ~ ( ( A = B )
& cd(A) ) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& cd(A) )
=> cd(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cd_substitution_1) ).
tff(160,plain,
! [A: $i,B: $i] :
( cd(B)
| ~ ( ( A = B )
& cd(A) ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [A: $i,B: $i] :
( cd(B)
| ~ ( ( A = B )
& cd(A) ) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
! [A: $i,B: $i] :
( cd(B)
| ~ ( ( A = B )
& cd(A) ) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) ),
inference(modus_ponens,[status(thm)],[162,155]) ).
tff(164,plain,
! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) ),
inference(modus_ponens,[status(thm)],[163,153]) ).
tff(165,plain,
( ( ~ ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(166,plain,
( ( cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)) )
<=> ( ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(167,plain,
( ( ~ ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) ) ) ),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( ( ~ ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)) )
<=> ( ~ ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) ) ) ),
inference(transitivity,[status(thm)],[167,165]) ).
tff(169,plain,
( ~ ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],]) ).
tff(170,plain,
( ~ ! [A: $i,B: $i] :
( cd(B)
| ( A != B )
| ~ cd(A) )
| ~ cd(tptp_fun_Z_3(i2003_11_14_17_20_25524))
| cd(tptp_fun_Z_5(i2003_11_14_17_20_25524))
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524) ) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
tptp_fun_Z_3(i2003_11_14_17_20_25524) != tptp_fun_Z_5(i2003_11_14_17_20_25524),
inference(unit_resolution,[status(thm)],[170,164,151,149]) ).
tff(172,plain,
( ~ 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_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_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,Y1)
| ~ rr(i2003_11_14_17_20_25524,Y0) )
| ! [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) ) ),
inference(tautology,[status(thm)],]) ).
tff(173,plain,
! [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) ),
inference(unit_resolution,[status(thm)],[172,32]) ).
tff(174,plain,
( ( ~ ! [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) )
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_5(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_0(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_0(i2003_11_14_17_20_25524),Z0)
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),Z1) )
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_5(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(175,plain,
( ~ ! [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) )
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_5(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(quant_inst,[status(thm)],]) ).
tff(176,plain,
( ~ ! [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) )
| ( tptp_fun_Z_3(i2003_11_14_17_20_25524) = tptp_fun_Z_5(i2003_11_14_17_20_25524) )
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(modus_ponens,[status(thm)],[175,174]) ).
tff(177,plain,
( ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_3(i2003_11_14_17_20_25524))
| ~ rtt(tptp_fun_Y_0(i2003_11_14_17_20_25524),tptp_fun_Z_5(i2003_11_14_17_20_25524)) ),
inference(unit_resolution,[status(thm)],[176,173,171]) ).
tff(178,plain,
$false,
inference(unit_resolution,[status(thm)],[177,133,114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS098+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.33 % Computer : n024.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Thu Sep 1 09:35:49 EDT 2022
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.33 Usage: tptp [options] [-file:]file
% 0.14/0.33 -h, -? prints this message.
% 0.14/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.33 -m, -model generate model.
% 0.14/0.33 -p, -proof generate proof.
% 0.14/0.33 -c, -core generate unsat core of named formulas.
% 0.14/0.33 -st, -statistics display statistics.
% 0.14/0.33 -t:timeout set timeout (in second).
% 0.14/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.33 -<param>:<value> configuration parameter and value.
% 0.14/0.33 -o:<output-file> file to place output in.
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------