TSTP Solution File: KRS070+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS070+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n009.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 17:44:35 EDT 2022
% Result : Unsatisfiable 0.18s 0.38s
% Output : Proof 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 61
% Syntax : Number of formulae : 132 ( 27 unt; 10 typ; 0 def)
% Number of atoms : 1587 ( 93 equ)
% Maximal formula atoms : 64 ( 13 avg)
% Number of connectives : 2823 (1434 ~;1071 |; 211 &)
% ( 95 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 76 ( 76 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 9 >; 3 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 453 ( 395 !; 27 ?; 453 :)
% Comments :
%------------------------------------------------------------------------------
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(i2003_11_14_17_18_32242_type,type,
i2003_11_14_17_18_32242: $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(cc2_type,type,
cc2: $i > $o ).
tff(rrx3_type,type,
rrx3: ( $i * $i ) > $o ).
tff(cc1_type,type,
cc1: $i > $o ).
tff(rrx4_type,type,
rrx4: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(rrx_type,type,
rrx: ( $i * $i ) > $o ).
tff(1,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) ) )),
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rrx4(X,Y)
& cc2(Y) )
<=> ~ ( ~ rrx4(X,Y)
| ~ cc2(Y) ) )),
( ~ ( rrx4(X,Y)
& cc2(Y) )
<=> ~ ~ ( ~ rrx4(X,Y)
| ~ cc2(Y) ) )),
rewrite(
( ~ ~ ( ~ rrx4(X,Y)
| ~ cc2(Y) )
<=> ( ~ rrx4(X,Y)
| ~ cc2(Y) ) )),
( ~ ( rrx4(X,Y)
& cc2(Y) )
<=> ( ~ rrx4(X,Y)
| ~ cc2(Y) ) ))),
( ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
<=> ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) )),
rewrite(
( ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
<=> ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rrx3(X,Y)
& cc1(Y) )
<=> ~ ( ~ rrx3(X,Y)
| ~ cc1(Y) ) )),
( ~ ( rrx3(X,Y)
& cc1(Y) )
<=> ~ ~ ( ~ rrx3(X,Y)
| ~ cc1(Y) ) )),
rewrite(
( ~ ~ ( ~ rrx3(X,Y)
| ~ cc1(Y) )
<=> ( ~ rrx3(X,Y)
| ~ cc1(Y) ) )),
( ~ ( rrx3(X,Y)
& cc1(Y) )
<=> ( ~ rrx3(X,Y)
| ~ cc1(Y) ) ))),
( ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) )
<=> ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ rrx4(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc1(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ rrx4(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc1(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ rrx4(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc1(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ rrx4(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc1(Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_18_32242)
<=> cUnsatisfiable(i2003_11_14_17_18_32242) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_18_32242),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_18_32242),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ),
inference(tautology,[status(thm)],]) ).
tff(39,plain,
! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(tautology,[status(thm)],]) ).
tff(41,plain,
cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(tautology,[status(thm)],]) ).
tff(43,plain,
rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[42,37]) ).
tff(44,plain,
( ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[49,43,41,39]) ).
tff(51,plain,
( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[51,37]) ).
tff(53,plain,
^ [A: $i,B: $i] :
refl(
( ( cc2(B)
| ( A != B )
| ~ cc2(A) )
<=> ( cc2(B)
| ( A != B )
| ~ cc2(A) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
<=> ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [A: $i,B: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( A = B )
& cc2(A) )
<=> ~ ( ( A != B )
| ~ cc2(A) ) )),
( ~ ( ( A = B )
& cc2(A) )
<=> ~ ~ ( ( A != B )
| ~ cc2(A) ) )),
rewrite(
( ~ ~ ( ( A != B )
| ~ cc2(A) )
<=> ( ( A != B )
| ~ cc2(A) ) )),
( ~ ( ( A = B )
& cc2(A) )
<=> ( ( A != B )
| ~ cc2(A) ) )),
( ( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) )
<=> ( cc2(B)
| ( A != B )
| ~ cc2(A) ) )),
rewrite(
( ( cc2(B)
| ( A != B )
| ~ cc2(A) )
<=> ( cc2(B)
| ( A != B )
| ~ cc2(A) ) )),
( ( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) )
<=> ( cc2(B)
| ( A != B )
| ~ cc2(A) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [A: $i,B: $i] :
( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) )
<=> ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [A: $i,B: $i] :
( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) )
<=> ! [A: $i,B: $i] :
( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
^ [A: $i,B: $i] :
rewrite(
( ( ( ( A = B )
& cc2(A) )
=> cc2(B) )
<=> ( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
& cc2(A) )
=> cc2(B) )
<=> ! [A: $i,B: $i] :
( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& cc2(A) )
=> cc2(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_substitution_1) ).
tff(61,plain,
! [A: $i,B: $i] :
( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [A: $i,B: $i] :
( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [A: $i,B: $i] :
( cc2(B)
| ~ ( ( A = B )
& cc2(A) ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) ),
inference(modus_ponens,[status(thm)],[64,54]) ).
tff(66,plain,
( ( ~ ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)) )
<=> ( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) ) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) ) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [A: $i,B: $i] :
( cc2(B)
| ( A != B )
| ~ cc2(A) )
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
tptp_fun_Y_0(i2003_11_14_17_18_32242) != tptp_fun_Y_1(i2003_11_14_17_18_32242),
inference(unit_resolution,[status(thm)],[71,65,52,50]) ).
tff(73,plain,
( ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(tautology,[status(thm)],]) ).
tff(74,plain,
rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[73,37]) ).
tff(75,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rrx4(X,Y)
| rrx(X,Y) )
<=> ( ~ rrx4(X,Y)
| rrx(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rrx4(X,Y)
=> rrx(X,Y) )
<=> ( ~ rrx4(X,Y)
| rrx(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X: $i,Y: $i] :
( rrx4(X,Y)
=> rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i,Y: $i] :
( rrx4(X,Y)
=> rrx(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
tff(81,plain,
! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[87,84,74]) ).
tff(89,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rrx3(X,Y)
| rrx(X,Y) )
<=> ( ~ rrx3(X,Y)
| rrx(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rrx3(X,Y)
=> rrx(X,Y) )
<=> ( ~ rrx3(X,Y)
| rrx(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(93,plain,
( ! [X: $i,Y: $i] :
( rrx3(X,Y)
=> rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,axiom,
! [X: $i,Y: $i] :
( rrx3(X,Y)
=> rrx(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
tff(95,plain,
! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[95,91]) ).
tff(97,plain,
! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(skolemize,[status(sab)],[96]) ).
tff(98,plain,
! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[97,90]) ).
tff(99,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[101,98,43]) ).
tff(103,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
( ( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
<=> ( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(104,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[103]) ).
tff(105,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( rrx(X,Y)
& rrx(X,Z) )
<=> ~ ( ~ rrx(X,Z)
| ~ rrx(X,Y) ) )),
( ~ ( rrx(X,Y)
& rrx(X,Z) )
<=> ~ ~ ( ~ rrx(X,Z)
| ~ rrx(X,Y) ) )),
rewrite(
( ~ ~ ( ~ rrx(X,Z)
| ~ rrx(X,Y) )
<=> ( ~ rrx(X,Z)
| ~ rrx(X,Y) ) )),
( ~ ( rrx(X,Y)
& rrx(X,Z) )
<=> ( ~ rrx(X,Z)
| ~ rrx(X,Y) ) )),
( ( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) )
<=> ( ~ rrx(X,Z)
| ~ rrx(X,Y)
| ( Y = Z ) ) )),
rewrite(
( ( ~ rrx(X,Z)
| ~ rrx(X,Y)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) ) )),
( ( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(106,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[105]) ).
tff(107,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(108,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ( ( rrx(X,Y)
& rrx(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rrx(X,Y)
& rrx(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rrx(X,Y)
& rrx(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(111,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[112]) ).
tff(114,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[113,106]) ).
tff(115,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[114,104]) ).
tff(116,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ( ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) )
<=> ( ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(monotonicity,[status(thm)],[117]) ).
tff(119,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(transitivity,[status(thm)],[118,116]) ).
tff(120,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Z)
| ~ rrx(X,Y) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
$false,
inference(unit_resolution,[status(thm)],[121,115,102,88,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : KRS070+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n009.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Sep 1 09:26:35 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.18/0.38 % SZS status Unsatisfiable
% 0.18/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------