%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS101+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:23 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 34
% Syntax : Number of formulae : 79 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 1812 ( 302 equ)
% Maximal formula atoms : 96 ( 22 avg)
% Number of connectives : 3194 (1488 ~;1459 |; 186 &)
% ( 49 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 27 ( 27 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-1 aty)
% Number of variables : 616 ( 580 !; 27 ?; 616 :)
% Comments :
%------------------------------------------------------------------------------
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_20_36582_type,type,
i2003_11_14_17_20_36582: $i ).
tff(cc_type,type,
cc: $i > $o ).
tff(cd_type,type,
cd: $i > $o ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(tptp_fun_Z0_2_type,type,
tptp_fun_Z0_2: $i > $i ).
tff(tptp_fun_Z1_1_type,type,
tptp_fun_Z1_1: $i > $i ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Z1_5_type,type,
tptp_fun_Z1_5: $i > $i ).
tff(tptp_fun_Z0_6_type,type,
tptp_fun_Z0_6: $i > $i ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
rewrite(( ( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
<=> ( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ))),
( ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
<=> ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) )),
rewrite(( ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) )
<=> ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) ) )),
( ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) ) )
<=> ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )),
( ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( rr(X,Y)
=> cd(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ( ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) )
| cc(Y) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ( rs(Y,Z0)
& rs(Y,Z1) )
=> ( Z0 = Z1 ) ) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( rr(X,Y)
=> cd(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ( ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) )
| cc(Y) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ( rs(Y,Z0)
& rs(Y,Z1) )
=> ( Z0 = Z1 ) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( rr(X,Y)
=> cd(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ( ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) )
| cc(Y) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ( rs(Y,Z0)
& rs(Y,Z1) )
=> ( Z0 = Z1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ~ ? [Z0: $i,Z1: $i] :
( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& ~ ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) )
& ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
~ ( rs(Y,Z0)
& rs(Y,Z1)
& ( Z0 != Z1 ) ) )
& rr(X,tptp_fun_Y_0(X))
& ~ ( ~ ( rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
& rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X)) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ~ ( rs(Y,Z0)
& rs(Y,Z1) )
| ( Z0 = Z1 ) ) )
| ( ~ cc(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_4(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
& rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
& ( tptp_fun_Z0_6(X) != tptp_fun_Z1_5(X) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z0_2(X))
| ~ rs(tptp_fun_Y_0(X),tptp_fun_Z1_1(X))
| ( tptp_fun_Z0_2(X) = tptp_fun_Z1_1(X) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ! [Y: $i] :
( cd(Y)
| ~ rr(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cc(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z0_6(X))
| ~ rs(tptp_fun_Y_4(X),tptp_fun_Z1_5(X))
| ( tptp_fun_Z0_6(X) = tptp_fun_Z1_5(X) ) )
| ~ ( cd(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_3(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_20_36582)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ~ ( cd(tptp_fun_Y_3(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_3(i2003_11_14_17_20_36582)) )
| ~ ( cc(tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_4(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z0_6(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_4(i2003_11_14_17_20_36582),tptp_fun_Z1_5(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_6(i2003_11_14_17_20_36582) = tptp_fun_Z1_5(i2003_11_14_17_20_36582) ) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_20_36582)
<=> cUnsatisfiable(i2003_11_14_17_20_36582) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_20_36582),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_20_36582),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_36582)
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) )
| ~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ),
inference(tautology,[status(thm)],[]) ).
tff(39,plain,
rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) ),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
( ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| cd(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) )
<=> ( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| cd(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| cd(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| cd(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
cd(tptp_fun_Y_0(i2003_11_14_17_20_36582)),
inference(unit_resolution,[status(thm)],[44,41,39]) ).
tff(46,plain,
^ [X: $i] :
refl(( ( ~ cc(X)
| ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [X: $i] :
rewrite(( ( cc(X)
=> ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [X: $i] :
( cc(X)
=> ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [X: $i] :
( cc(X)
=> ~ cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(52,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_36582)) )
<=> ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_36582)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_36582)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(58,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_36582)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
~ cc(tptp_fun_Y_0(i2003_11_14_17_20_36582)),
inference(unit_resolution,[status(thm)],[58,55,45]) ).
tff(60,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(61,plain,
! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) ),
inference(unit_resolution,[status(thm)],[60,37]) ).
tff(62,plain,
( ( ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) ) )
<=> ( ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
( cc(tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) ) ),
inference(unit_resolution,[status(thm)],[64,61,39]) ).
tff(66,plain,
! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) ),
inference(unit_resolution,[status(thm)],[65,59]) ).
tff(67,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582)) ),
inference(tautology,[status(thm)],[]) ).
tff(68,plain,
rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582)),
inference(unit_resolution,[status(thm)],[67,37]) ).
tff(69,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582)) ),
inference(tautology,[status(thm)],[]) ).
tff(70,plain,
rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582)),
inference(unit_resolution,[status(thm)],[69,37]) ).
tff(71,plain,
( ~ ! [Y: $i] :
( cd(Y)
| ~ rr(i2003_11_14_17_20_36582,Y) )
| ~ ! [Y: $i] :
( cc(Y)
| ~ rr(i2003_11_14_17_20_36582,Y)
| ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(Y,Z0)
| ~ rs(Y,Z1) ) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rr(i2003_11_14_17_20_36582,tptp_fun_Y_0(i2003_11_14_17_20_36582))
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) != tptp_fun_Z1_1(i2003_11_14_17_20_36582) ) ),
inference(tautology,[status(thm)],[]) ).
tff(72,plain,
tptp_fun_Z0_2(i2003_11_14_17_20_36582) != tptp_fun_Z1_1(i2003_11_14_17_20_36582),
inference(unit_resolution,[status(thm)],[71,37]) ).
tff(73,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582)) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
( ( ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582)) )
<=> ( ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582)) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582)) ) ),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
( ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582)) )
<=> ( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582)) ) ),
inference(transitivity,[status(thm)],[75,73]) ).
tff(77,plain,
( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
( ~ ! [Z0: $i,Z1: $i] :
( ( Z0 = Z1 )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z0)
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),Z1) )
| ( tptp_fun_Z0_2(i2003_11_14_17_20_36582) = tptp_fun_Z1_1(i2003_11_14_17_20_36582) )
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z1_1(i2003_11_14_17_20_36582))
| ~ rs(tptp_fun_Y_0(i2003_11_14_17_20_36582),tptp_fun_Z0_2(i2003_11_14_17_20_36582)) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
$false,
inference(unit_resolution,[status(thm)],[78,72,70,68,66]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KRS101+1 : TPTP v9.0.0. Released v3.1.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n014.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:11:24 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------