%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS095+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:22 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 22
% Syntax : Number of formulae : 52 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 957 ( 274 equ)
% Maximal formula atoms : 56 ( 18 avg)
% Number of connectives : 1738 ( 847 ~; 735 |; 117 &)
% ( 36 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 328 ( 304 !; 18 ?; 328 :)
% Comments :
%------------------------------------------------------------------------------
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_1_type,type,
tptp_fun_Y0_1: $i > $i ).
tff(i2003_11_14_17_20_14253_type,type,
i2003_11_14_17_20_14253: $i ).
tff(tptp_fun_Y1_0_type,type,
tptp_fun_Y1_0: $i > $i ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y1_2_type,type,
tptp_fun_Y1_2: $i > $i ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
<=> ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) ) )
<=> ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y0: $i,Y1: $i] :
( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) )
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y0_1(X))
& rr(X,tptp_fun_Y1_0(X))
& ( tptp_fun_Y0_1(X) != tptp_fun_Y1_0(X) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
~ ( rr(X,Y0)
& rr(X,Y1)
& ( Y0 != Y1 ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) )
| ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y0_1(X))
| ~ rr(X,tptp_fun_Y1_0(X))
| ( tptp_fun_Y0_1(X) = tptp_fun_Y1_0(X) )
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_3(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_2(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_14253) = tptp_fun_Y1_2(i2003_11_14_17_20_14253) ) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_20_14253)
<=> cUnsatisfiable(i2003_11_14_17_20_14253) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_20_14253),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_20_14253),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_14253)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) )
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ),
inference(tautology,[status(thm)],[]) ).
tff(39,plain,
rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253)) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253)),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) != tptp_fun_Y1_0(i2003_11_14_17_20_14253) ) ),
inference(tautology,[status(thm)],[]) ).
tff(43,plain,
tptp_fun_Y0_1(i2003_11_14_17_20_14253) != tptp_fun_Y1_0(i2003_11_14_17_20_14253),
inference(unit_resolution,[status(thm)],[42,37]) ).
tff(44,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ) ),
inference(tautology,[status(thm)],[]) ).
tff(45,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) ),
inference(unit_resolution,[status(thm)],[44,37]) ).
tff(46,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253)) )
<=> ( ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_14253,Y0)
| ~ rr(i2003_11_14_17_20_14253,Y1) )
| ( tptp_fun_Y0_1(i2003_11_14_17_20_14253) = tptp_fun_Y1_0(i2003_11_14_17_20_14253) )
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y1_0(i2003_11_14_17_20_14253))
| ~ rr(i2003_11_14_17_20_14253,tptp_fun_Y0_1(i2003_11_14_17_20_14253)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
$false,
inference(unit_resolution,[status(thm)],[51,45,43,41,39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS095+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 19:10:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------