%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS096+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 70 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 1161 ( 144 equ)
% Maximal formula atoms : 64 ( 16 avg)
% Number of connectives : 2101 (1053 ~; 838 |; 148 &)
% ( 56 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 43 ( 43 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-4 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 337 ( 310 !; 18 ?; 337 :)
% Comments :
%------------------------------------------------------------------------------
tff(cd_type,type,
cd: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(i2003_11_14_17_20_18265_type,type,
i2003_11_14_17_20_18265: $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cc_type,type,
cc: $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(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( 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] :
( ~ cd(Y)
| ~ rr(X,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] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) )
<=> ! [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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) )
<=> ! [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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) )
<=> ! [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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,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) )
<=> ~ ( ~ cd(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cd(Y) )
<=> ~ ~ ( ~ cd(Y)
| ~ rr(X,Y) ) )),
rewrite(( ~ ~ ( ~ cd(Y)
| ~ rr(X,Y) )
<=> ( ~ cd(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cd(Y) )
<=> ( ~ cd(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cd(Y) )
<=> ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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] :
( ~ cd(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) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(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) ) ) )
<=> ( 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] :
( ~ cd(Y)
| ~ rr(X,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)
| ~ ( ~ 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] :
( ~ cd(Y)
| ~ rr(X,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)
| ~ ( ~ 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] :
( ~ cd(Y)
| ~ rr(X,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)
| ~ ( ~ 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] :
( ~ cd(Y)
| ~ rr(X,Y) ) ) )
<=> ~ ( ~ ( 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] :
( ~ cd(Y)
| ~ rr(X,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_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_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] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
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] :
( ~ ( 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_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] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,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(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] :
( ~ ( 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)],[8]) ).
tff(10,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(11,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(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(quant_intro,[status(thm)],[11]) ).
tff(13,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/sandbox/benchmark/theBenchmark.p',axiom_2) ).
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 ) ) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,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)],[14,10]) ).
tff(16,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)],[15]) ).
tff(17,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)],[16,9]) ).
tff(18,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,5]) ).
tff(20,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ) ) )
<=> ( ~ ! [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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) ) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) ) ) ) ) ),
inference(quant_inst,[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) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(X,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(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ) ),
inference(unit_resolution,[status(thm)],[25,19]) ).
tff(27,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y0_3(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y1_2(i2003_11_14_17_20_18265))
| ( tptp_fun_Y0_3(i2003_11_14_17_20_18265) = tptp_fun_Y1_2(i2003_11_14_17_20_18265) ) )
| ! [Y: $i] :
( ~ cc(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) )
| ! [Y: $i] :
( ~ cd(Y)
| ~ rr(i2003_11_14_17_20_18265,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(28,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( cUnsatisfiable(i2003_11_14_17_20_18265)
<=> cUnsatisfiable(i2003_11_14_17_20_18265) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
cUnsatisfiable(i2003_11_14_17_20_18265),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(31,plain,
cUnsatisfiable(i2003_11_14_17_20_18265),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(33,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) )
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ),
inference(unit_resolution,[status(thm)],[33,28]) ).
tff(35,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265)) ),
inference(tautology,[status(thm)],[]) ).
tff(38,plain,
rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265)),
inference(unit_resolution,[status(thm)],[37,34]) ).
tff(39,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) ) ),
inference(tautology,[status(thm)],[]) ).
tff(40,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) ),
inference(unit_resolution,[status(thm)],[39,34]) ).
tff(41,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) ) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) )
<=> ( ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) ) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ( tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
tptp_fun_Y_1(i2003_11_14_17_20_18265) = tptp_fun_Y_0(i2003_11_14_17_20_18265),
inference(unit_resolution,[status(thm)],[46,40,38,36]) ).
tff(48,plain,
( cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
<=> cd(tptp_fun_Y_0(i2003_11_14_17_20_18265)) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( cd(tptp_fun_Y_0(i2003_11_14_17_20_18265))
<=> cd(tptp_fun_Y_1(i2003_11_14_17_20_18265)) ),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_18265))
<=> ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265)) ),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| cc(tptp_fun_Y_0(i2003_11_14_17_20_18265)) ),
inference(tautology,[status(thm)],[]) ).
tff(52,plain,
cc(tptp_fun_Y_0(i2003_11_14_17_20_18265)),
inference(unit_resolution,[status(thm)],[51,34]) ).
tff(53,plain,
^ [X: $i] :
refl(( ( ~ cc(X)
| ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
^ [X: $i] :
rewrite(( ( cc(X)
=> ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i] :
( cc(X)
=> ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [X: $i] :
( cc(X)
=> ~ cd(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(59,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[61,54]) ).
tff(63,plain,
( ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_18265)) )
<=> ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_18265)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_18265)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_18265)) ),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
~ cd(tptp_fun_Y_0(i2003_11_14_17_20_18265)),
inference(unit_resolution,[status(thm)],[65,62,52]) ).
tff(67,plain,
~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265)),
inference(modus_ponens,[status(thm)],[66,50]) ).
tff(68,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_20_18265,Y0)
| ~ rr(i2003_11_14_17_20_18265,Y1) )
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_1(i2003_11_14_17_20_18265))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_18265))
| ~ rr(i2003_11_14_17_20_18265,tptp_fun_Y_0(i2003_11_14_17_20_18265))
| cd(tptp_fun_Y_1(i2003_11_14_17_20_18265)) ),
inference(tautology,[status(thm)],[]) ).
tff(69,plain,
cd(tptp_fun_Y_1(i2003_11_14_17_20_18265)),
inference(unit_resolution,[status(thm)],[68,34]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KRS096+1 : TPTP v9.0.0. Released v3.1.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:11:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------