%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS127+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:13:27 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 49
% Syntax : Number of formulae : 123 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 1579 ( 154 equ)
% Maximal formula atoms : 64 ( 12 avg)
% Number of connectives : 2801 (1420 ~;1099 |; 165 &)
% ( 111 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 75 ( 75 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 506 ( 446 !; 41 ?; 506 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_5_type,type,
tptp_fun_Y0_5: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_22_27794_type,type,
i2003_11_14_17_22_27794: $i ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cc_type,type,
cc: $i > $o ).
tff(cd_type,type,
cd: $i > $o ).
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(cdxcomp_type,type,
cdxcomp: $i > $o ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rr(X,Y)
& cc(Y) )
<=> ~ ( ~ cc(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cc(Y) )
<=> ~ ~ ( ~ cc(Y)
| ~ rr(X,Y) ) )),
rewrite(( ~ ~ ( ~ cc(Y)
| ~ rr(X,Y) )
<=> ( ~ cc(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cc(Y) )
<=> ( ~ cc(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
<=> ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) ) )),
quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rr(X,Y)
& cd(Y) )
<=> ~ ( ~ rr(X,Y)
| ~ cd(Y) ) )),
( ~ ( rr(X,Y)
& cd(Y) )
<=> ~ ~ ( ~ rr(X,Y)
| ~ cd(Y) ) )),
rewrite(( ~ ~ ( ~ rr(X,Y)
| ~ cd(Y) )
<=> ( ~ rr(X,Y)
| ~ cd(Y) ) )),
( ~ ( rr(X,Y)
& cd(Y) )
<=> ( ~ rr(X,Y)
| ~ cd(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
<=> ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) )),
rewrite(( ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(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) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) )
| ~ ( ~ 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)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [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)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [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)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cc(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cd(Y) )
& ! [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_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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_Y_0(X))
& cc(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cd(tptp_fun_Y_1(X))
& ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cc(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
| ~ ( ~ ( 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(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ~ ( ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X))
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y0)
| ~ rr(i2003_11_14_17_22_27794,Y1) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_22_27794,Y)
| ~ cd(Y) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y0)
| ~ rr(i2003_11_14_17_22_27794,Y1) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_22_27794,Y)
| ~ cd(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y0)
| ~ rr(i2003_11_14_17_22_27794,Y1) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_22_27794,Y)
| ~ cd(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y0)
| ~ rr(i2003_11_14_17_22_27794,Y1) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_22_27794,Y)
| ~ cd(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cc(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cd(tptp_fun_Y_1(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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cd(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y0_3(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y1_2(i2003_11_14_17_22_27794))
| ( tptp_fun_Y0_3(i2003_11_14_17_22_27794) = tptp_fun_Y1_2(i2003_11_14_17_22_27794) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_22_27794,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_22_27794)
<=> cUnsatisfiable(i2003_11_14_17_22_27794) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_22_27794),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_22_27794),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_22_27794)
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) )
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(39,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) ),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794)) ),
inference(tautology,[status(thm)],[]) ).
tff(43,plain,
rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[42,37]) ).
tff(44,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) ) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794)) )
<=> ( ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) ) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) ) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ( tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
tptp_fun_Y_1(i2003_11_14_17_22_27794) = tptp_fun_Y_0(i2003_11_14_17_22_27794),
inference(unit_resolution,[status(thm)],[49,43,41,39]) ).
tff(51,plain,
( ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794)))
<=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794)))
<=> ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) ),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[56,54]) ).
tff(58,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(59,plain,
( ! [X: $i] :
( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,axiom,
! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
tff(62,plain,
! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X: $i] :
( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_5(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) )
| ~ ( cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
~ ( ~ ( ~ cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) )
| ~ ( cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),Y0) ) ),
inference(unit_resolution,[status(thm)],[66,65]) ).
tff(68,plain,
( ~ ( ~ cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) )
| ~ ( cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),Y0) )
| ~ cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) ),
inference(tautology,[status(thm)],[]) ).
tff(69,plain,
( ~ cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) ),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(tautology,[status(thm)],[]) ).
tff(71,plain,
cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[70,37]) ).
tff(72,plain,
^ [X: $i] :
refl(( ( cdxcomp(X)
| ~ cc(X) )
<=> ( cdxcomp(X)
| ~ cc(X) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [X: $i] :
rewrite(( ( cc(X)
=> cdxcomp(X) )
<=> ( cdxcomp(X)
| ~ cc(X) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i] :
( cc(X)
=> cdxcomp(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [X: $i] :
( cc(X)
=> cdxcomp(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(78,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
( ( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) )
<=> ( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794)) ),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[84,81,71]) ).
tff(86,plain,
( ~ ( ~ cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) )
| ~ cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
( ~ ( ~ cdxcomp(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) )
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) ),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
ra_Px1(tptp_fun_Y_0(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))),
inference(unit_resolution,[status(thm)],[87,69]) ).
tff(89,plain,
ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))),
inference(modus_ponens,[status(thm)],[88,52]) ).
tff(90,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(91,plain,
( ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[90]) ).
tff(92,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(transitivity,[status(thm)],[95,93]) ).
tff(97,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) )
<=> ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )),
( ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
rewrite(( ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
( ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [X: $i] :
( ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px1(X,tptp_fun_Y_4(X))
| cd(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_4(X))
| cd(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
( ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px1(X,Y)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )),
( ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) )),
rewrite(( ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) )),
( ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) )),
( ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(103,plain,
( ! [X: $i] :
( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) ),
inference(quant_intro,[status(thm)],[102]) ).
tff(104,axiom,
! [X: $i] :
( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
tff(105,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_4(X))
| cd(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(skolemize,[status(sab)],[106]) ).
tff(108,plain,
! [X: $i] :
( ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(modus_ponens,[status(thm)],[107,100]) ).
tff(109,plain,
! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(modus_ponens,[status(thm)],[108,98]) ).
tff(110,plain,
! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(modus_ponens,[status(thm)],[109,96]) ).
tff(111,plain,
! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[110,91]) ).
tff(112,plain,
( ~ ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_4(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y_4(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
~ ( ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y_4(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ) ),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
( ~ ( cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y_4(tptp_fun_Y_1(i2003_11_14_17_22_27794))) )
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(115,plain,
( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ rr(i2003_11_14_17_22_27794,tptp_fun_Y_0(i2003_11_14_17_22_27794))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_22_27794,Y1)
| ~ rr(i2003_11_14_17_22_27794,Y0) )
| cd(tptp_fun_Y_1(i2003_11_14_17_22_27794)) ),
inference(tautology,[status(thm)],[]) ).
tff(117,plain,
cd(tptp_fun_Y_1(i2003_11_14_17_22_27794)),
inference(unit_resolution,[status(thm)],[116,37]) ).
tff(118,plain,
( ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(119,plain,
( ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_22_27794))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y) ),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y),
inference(unit_resolution,[status(thm)],[119,115]) ).
tff(121,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),Y)
| ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_22_27794),tptp_fun_Y0_5(tptp_fun_Y_0(i2003_11_14_17_22_27794))),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
$false,
inference(unit_resolution,[status(thm)],[122,89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS127+1 : TPTP v9.0.0. Released v3.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n002.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 19:13:01 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.41 % E exiting
%------------------------------------------------------------------------------