TSTP Solution File: KRS097+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS097+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 17:44:43 EDT 2022
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 40
% Syntax : Number of formulae : 86 ( 18 unt; 10 typ; 0 def)
% Number of atoms : 1408 ( 154 equ)
% Maximal formula atoms : 72 ( 18 avg)
% Number of connectives : 2586 (1304 ~;1011 |; 207 &)
% ( 64 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 50 ( 50 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 9 >; 1 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 431 ( 376 !; 45 ?; 431 :)
% Comments :
%------------------------------------------------------------------------------
tff(cd_type,type,
cd: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(i2003_11_14_17_20_21603_type,type,
i2003_11_14_17_20_21603: $i ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cc_type,type,
cc: $i > $o ).
tff(tptp_fun_Y0_0_type,type,
tptp_fun_Y0_0: $i > $i ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y1_3_type,type,
tptp_fun_Y1_3: $i > $i ).
tff(tptp_fun_Y0_4_type,type,
tptp_fun_Y0_4: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) ) )),
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cd(Y) )
<=> ~ ( ~ rr(X,Y)
| ~ cd(Y) ) )),
( ~ ( rr(X,Y)
& cd(Y) )
<=> ~ ~ ( ~ rr(X,Y)
| ~ cd(Y) ) )),
rewrite(
( ~ ~ ( ~ rr(X,Y)
| ~ cd(Y) )
<=> ( ~ rr(X,Y)
| ~ cd(Y) ) )),
( ~ ( rr(X,Y)
& cd(Y) )
<=> ( ~ rr(X,Y)
| ~ cd(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
<=> ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) )),
rewrite(
( ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
<=> ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cc(Y) )
<=> ~ ( ~ rr(X,Y)
| ~ cc(Y) ) )),
( ~ ( rr(X,Y)
& cc(Y) )
<=> ~ ~ ( ~ rr(X,Y)
| ~ cc(Y) ) )),
rewrite(
( ~ ~ ( ~ rr(X,Y)
| ~ cc(Y) )
<=> ( ~ rr(X,Y)
| ~ cc(Y) ) )),
( ~ ( rr(X,Y)
& cc(Y) )
<=> ( ~ rr(X,Y)
| ~ cc(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
<=> ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i] : rr(X,Y0)
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ~ ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& cc(Y) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& rr(X,tptp_fun_Y_2(X))
& cc(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ( rr(X,tptp_fun_Y0_4(X))
& rr(X,tptp_fun_Y1_3(X))
& ( tptp_fun_Y0_4(X) != tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) )
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_21603,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_21603,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_21603,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_21603,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_21603,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_21603,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_21603,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_21603,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_4(X))
| ~ rr(X,tptp_fun_Y1_3(X))
| ( tptp_fun_Y0_4(X) = tptp_fun_Y1_3(X) ) )
| ! [Y0: $i] : ~ rr(X,Y0)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cc(Y) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cc(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y1)
| ~ rr(X,Y0) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_4(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y1_3(i2003_11_14_17_20_21603))
| ( tptp_fun_Y0_4(i2003_11_14_17_20_21603) = tptp_fun_Y1_3(i2003_11_14_17_20_21603) ) )
| ! [Y0: $i] : ~ rr(i2003_11_14_17_20_21603,Y0)
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_21603,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_20_21603)
<=> cUnsatisfiable(i2003_11_14_17_20_21603) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_20_21603),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_20_21603),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_21603)
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) )
| ~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ) ),
inference(tautology,[status(thm)],]) ).
tff(39,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) ),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603)) ),
inference(tautology,[status(thm)],]) ).
tff(41,plain,
rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603)),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603)) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603)),
inference(unit_resolution,[status(thm)],[42,37]) ).
tff(44,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) ) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603)) )
<=> ( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) ) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ( tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
tptp_fun_Y_1(i2003_11_14_17_20_21603) = tptp_fun_Y_2(i2003_11_14_17_20_21603),
inference(unit_resolution,[status(thm)],[49,43,41,39]) ).
tff(51,plain,
( cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
<=> cd(tptp_fun_Y_2(i2003_11_14_17_20_21603)) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( cd(tptp_fun_Y_2(i2003_11_14_17_20_21603))
<=> cd(tptp_fun_Y_1(i2003_11_14_17_20_21603)) ),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
( ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603))
<=> ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603)) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| cc(tptp_fun_Y_2(i2003_11_14_17_20_21603)) ),
inference(tautology,[status(thm)],]) ).
tff(55,plain,
cc(tptp_fun_Y_2(i2003_11_14_17_20_21603)),
inference(unit_resolution,[status(thm)],[54,37]) ).
tff(56,plain,
^ [X: $i] :
refl(
( ( ~ cd(X)
| ~ cc(X) )
<=> ( ~ cd(X)
| ~ cc(X) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
<=> ! [X: $i] :
( ~ cd(X)
| ~ cc(X) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( cd(X)
& cc(X) )
<=> ~ ( ~ cd(X)
| ~ cc(X) ) )),
( ~ ( cd(X)
& cc(X) )
<=> ~ ~ ( ~ cd(X)
| ~ cc(X) ) )),
rewrite(
( ~ ~ ( ~ cd(X)
| ~ cc(X) )
<=> ( ~ cd(X)
| ~ cc(X) ) )),
( ~ ( cd(X)
& cc(X) )
<=> ( ~ cd(X)
| ~ cc(X) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X: $i] :
~ ( cd(X)
& cc(X) )
<=> ! [X: $i] :
( ~ cd(X)
| ~ cc(X) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X: $i] :
~ ( cd(X)
& cc(X) )
<=> ! [X: $i] :
~ ( cd(X)
& cc(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,axiom,
! [X: $i] :
~ ( cd(X)
& cc(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(62,plain,
! [X: $i] :
~ ( cd(X)
& cc(X) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X: $i] :
~ ( cd(X)
& cc(X) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [X: $i] :
( ~ cd(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [X: $i] :
( ~ cd(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603)) )
<=> ( ~ ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603)) )
<=> ( ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603)) )
<=> ( ~ ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603)) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603)) )
<=> ( ~ ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603)) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X: $i] :
( ~ cd(X)
| ~ cc(X) )
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
~ cd(tptp_fun_Y_2(i2003_11_14_17_20_21603)),
inference(unit_resolution,[status(thm)],[71,65,55]) ).
tff(73,plain,
~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603)),
inference(modus_ponens,[status(thm)],[72,53]) ).
tff(74,plain,
( ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y0_0(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_21603))
| ~ rr(i2003_11_14_17_20_21603,tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ cc(tptp_fun_Y_2(i2003_11_14_17_20_21603))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_21603,Y1)
| ~ rr(i2003_11_14_17_20_21603,Y0) )
| cd(tptp_fun_Y_1(i2003_11_14_17_20_21603)) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
cd(tptp_fun_Y_1(i2003_11_14_17_20_21603)),
inference(unit_resolution,[status(thm)],[74,37]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS097+1 : TPTP v8.1.0. Released v3.1.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 09:55:49 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------