TSTP Solution File: KRS080+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS080+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:38 EDT 2022
% Result : Unsatisfiable 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 108
% Syntax : Number of formulae : 226 ( 44 unt; 20 typ; 0 def)
% Number of atoms : 5329 (1158 equ)
% Maximal formula atoms : 224 ( 25 avg)
% Number of connectives : 8504 (3541 ~;4148 |; 625 &)
% ( 163 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 42 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 160 ( 160 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 19 >; 1 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-9 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-1 aty)
% Number of variables : 1130 (1030 !; 63 ?;1130 :)
% Comments :
%------------------------------------------------------------------------------
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(i2003_11_14_17_19_21224_type,type,
i2003_11_14_17_19_21224: $i ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(cp4_type,type,
cp4: $i > $o ).
tff(cp5_type,type,
cp5: $i > $o ).
tff(cp3_type,type,
cp3: $i > $o ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cp_type,type,
cp: $i > $o ).
tff(tptp_fun_Y_6_type,type,
tptp_fun_Y_6: $i > $i ).
tff(cp2_type,type,
cp2: $i > $o ).
tff(tptp_fun_Y_5_type,type,
tptp_fun_Y_5: $i > $i ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(cp1_type,type,
cp1: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y3_7_type,type,
tptp_fun_Y3_7: $i > $i ).
tff(tptp_fun_Y2_8_type,type,
tptp_fun_Y2_8: $i > $i ).
tff(tptp_fun_Y1_9_type,type,
tptp_fun_Y1_9: $i > $i ).
tff(tptp_fun_Y0_10_type,type,
tptp_fun_Y0_10: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) ) )),
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cp(Y)
& cp1(Y) )
<=> ~ ( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
( ~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
<=> ~ ~ ( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
rewrite(
( ~ ~ ( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
<=> ( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
( ~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
<=> ( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
<=> ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cp1(Y) )
<=> ~ ( ~ cp1(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp1(Y) )
<=> ~ ~ ( ~ cp1(Y)
| ~ rr(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cp1(Y)
| ~ rr(X,Y) )
<=> ( ~ cp1(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp1(Y) )
<=> ( ~ cp1(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
<=> ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cp4(Y) )
<=> ~ ( ~ cp4(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp4(Y) )
<=> ~ ~ ( ~ cp4(Y)
| ~ rr(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cp4(Y)
| ~ rr(X,Y) )
<=> ( ~ cp4(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp4(Y) )
<=> ( ~ cp4(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
<=> ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) ) )),
rewrite(
( ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
<=> ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cp2(Y) )
<=> ~ ( ~ cp2(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp2(Y) )
<=> ~ ~ ( ~ cp2(Y)
| ~ rr(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cp2(Y)
| ~ rr(X,Y) )
<=> ( ~ cp2(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp2(Y) )
<=> ( ~ cp2(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
<=> ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cp3(Y) )
<=> ~ ( ~ cp3(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp3(Y) )
<=> ~ ~ ( ~ cp3(Y)
| ~ rr(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cp3(Y)
| ~ rr(X,Y) )
<=> ( ~ cp3(Y)
| ~ rr(X,Y) ) )),
( ~ ( rr(X,Y)
& cp3(Y) )
<=> ( ~ cp3(Y)
| ~ rr(X,Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
<=> ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cp(Y)
& cp3(Y) )
<=> ~ ( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
( ~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
<=> ~ ~ ( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
rewrite(
( ~ ~ ( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
<=> ( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
( ~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
<=> ( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
<=> ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rr(X,Y)
& cp2(Y)
& cp(Y) )
<=> ~ ( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
( ~ ( rr(X,Y)
& cp2(Y)
& cp(Y) )
<=> ~ ~ ( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
rewrite(
( ~ ~ ( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
<=> ( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
( ~ ( rr(X,Y)
& cp2(Y)
& cp(Y) )
<=> ( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) )
<=> ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) )
=> ( ( Y0 = Y1 )
| ( Y0 = Y2 )
| ( Y0 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y2 = Y3 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) )
=> ( ( Y0 = Y1 )
| ( Y0 = Y2 )
| ( Y0 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y2 = Y3 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) )
=> ( ( Y0 = Y1 )
| ( Y0 = Y2 )
| ( Y0 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y2 = Y3 ) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp4(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp(Y)
& cp3(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp(tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp1(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp4(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2)
& rr(X,Y3) ) )
& rr(X,tptp_fun_Y_3(X))
& cp2(tptp_fun_Y_3(X))
& rr(X,tptp_fun_Y_4(X))
& cp3(tptp_fun_Y_4(X))
& rr(X,tptp_fun_Y_5(X))
& cp(tptp_fun_Y_5(X))
& cp3(tptp_fun_Y_5(X))
& rr(X,tptp_fun_Y_6(X))
& cp2(tptp_fun_Y_6(X))
& cp(tptp_fun_Y_6(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp4(Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ ( rr(X,tptp_fun_Y0_10(X))
& rr(X,tptp_fun_Y1_9(X))
& rr(X,tptp_fun_Y2_8(X))
& rr(X,tptp_fun_Y3_7(X)) ) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp(Y)
& cp3(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) )
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp(tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp1(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp4(tptp_fun_Y_2(X))
| ~ rr(X,tptp_fun_Y_3(X))
| ~ cp2(tptp_fun_Y_3(X))
| ~ rr(X,tptp_fun_Y_4(X))
| ~ cp3(tptp_fun_Y_4(X))
| ~ rr(X,tptp_fun_Y_5(X))
| ~ cp(tptp_fun_Y_5(X))
| ~ cp3(tptp_fun_Y_5(X))
| ~ rr(X,tptp_fun_Y_6(X))
| ~ cp2(tptp_fun_Y_6(X))
| ~ cp(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2)
| ~ rr(X,Y3) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y2_8(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y1_9(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y3_7(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y2_8(X) )
| ( tptp_fun_Y0_10(X) = tptp_fun_Y1_9(X) )
| ~ rr(X,tptp_fun_Y0_10(X))
| ~ rr(X,tptp_fun_Y1_9(X))
| ~ rr(X,tptp_fun_Y2_8(X))
| ~ rr(X,tptp_fun_Y3_7(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y)
| ~ cp(Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ( tptp_fun_Y2_8(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y1_9(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y3_7(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y2_8(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y0_10(i2003_11_14_17_19_21224) = tptp_fun_Y1_9(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y0_10(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y1_9(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y2_8(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y3_7(i2003_11_14_17_19_21224)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp4(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ cp(Y)
| ~ rr(i2003_11_14_17_19_21224,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_19_21224)
<=> cUnsatisfiable(i2003_11_14_17_19_21224) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_19_21224),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_19_21224),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_21224)
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) )
| ~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(39,plain,
cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
^ [X: $i] :
refl(
( ( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) )
<=> ( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
^ [X: $i] :
rewrite(
( ( cp3(X)
=> ~ ( cp4(X)
| cp5(X) ) )
<=> ( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(44,plain,
( ! [X: $i] :
( cp3(X)
=> ~ ( cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [X: $i] :
( cp3(X)
=> ~ ( cp4(X)
| cp5(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(46,plain,
! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ ( cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ ( cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ ( cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [X: $i] :
( ~ cp3(X)
| ~ ( cp4(X)
| cp5(X) ) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ ( cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
~ ( cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ),
inference(unit_resolution,[status(thm)],[52,49,39]) ).
tff(54,plain,
( cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(55,plain,
~ cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(57,plain,
cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[56,37]) ).
tff(58,plain,
^ [A: $i,B: $i] :
refl(
( ( cp4(B)
| ( A != B )
| ~ cp4(A) )
<=> ( cp4(B)
| ( A != B )
| ~ cp4(A) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
<=> ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
^ [A: $i,B: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( A = B )
& cp4(A) )
<=> ~ ( ( A != B )
| ~ cp4(A) ) )),
( ~ ( ( A = B )
& cp4(A) )
<=> ~ ~ ( ( A != B )
| ~ cp4(A) ) )),
rewrite(
( ~ ~ ( ( A != B )
| ~ cp4(A) )
<=> ( ( A != B )
| ~ cp4(A) ) )),
( ~ ( ( A = B )
& cp4(A) )
<=> ( ( A != B )
| ~ cp4(A) ) )),
( ( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) )
<=> ( cp4(B)
| ( A != B )
| ~ cp4(A) ) )),
rewrite(
( ( cp4(B)
| ( A != B )
| ~ cp4(A) )
<=> ( cp4(B)
| ( A != B )
| ~ cp4(A) ) )),
( ( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) )
<=> ( cp4(B)
| ( A != B )
| ~ cp4(A) ) )),
inference(bind,[status(th)],]) ).
tff(61,plain,
( ! [A: $i,B: $i] :
( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) )
<=> ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,plain,
( ! [A: $i,B: $i] :
( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) )
<=> ! [A: $i,B: $i] :
( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
^ [A: $i,B: $i] :
rewrite(
( ( ( ( A = B )
& cp4(A) )
=> cp4(B) )
<=> ( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
& cp4(A) )
=> cp4(B) )
<=> ! [A: $i,B: $i] :
( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& cp4(A) )
=> cp4(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp4_substitution_1) ).
tff(66,plain,
! [A: $i,B: $i] :
( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
! [A: $i,B: $i] :
( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) ),
inference(modus_ponens,[status(thm)],[66,62]) ).
tff(68,plain,
! [A: $i,B: $i] :
( cp4(B)
| ~ ( ( A = B )
& cp4(A) ) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) ),
inference(modus_ponens,[status(thm)],[68,61]) ).
tff(70,plain,
! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) ),
inference(modus_ponens,[status(thm)],[69,59]) ).
tff(71,plain,
( ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) )
<=> ( ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224),
inference(unit_resolution,[status(thm)],[76,70,57,55]) ).
tff(78,plain,
( cp2(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(79,plain,
( cp2(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ),
inference(unit_resolution,[status(thm)],[78,39]) ).
tff(80,plain,
^ [X: $i] :
refl(
( ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(81,plain,
( ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[80]) ).
tff(82,plain,
( ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ~ ( cp2(X)
| cp4(X)
| cp5(X)
| cp3(X) )
<=> ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )),
( ( cp1(X)
=> ~ ( cp2(X)
| cp4(X)
| cp5(X)
| cp3(X) ) )
<=> ( cp1(X)
=> ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
rewrite(
( ( cp1(X)
=> ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
( ( cp1(X)
=> ~ ( cp2(X)
| cp4(X)
| cp5(X)
| cp3(X) ) )
<=> ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [X: $i] :
( cp1(X)
=> ~ ( cp2(X)
| cp4(X)
| cp5(X)
| cp3(X) ) )
<=> ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,axiom,
! [X: $i] :
( cp1(X)
=> ~ ( cp2(X)
| cp4(X)
| cp5(X)
| cp3(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(86,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[86,82]) ).
tff(88,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(skolemize,[status(sab)],[87]) ).
tff(89,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[88,81]) ).
tff(90,plain,
( ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
~ cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[92,89,79]) ).
tff(94,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(95,plain,
cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[94,37]) ).
tff(96,plain,
^ [A: $i,B: $i] :
refl(
( ( cp1(B)
| ( A != B )
| ~ cp1(A) )
<=> ( cp1(B)
| ( A != B )
| ~ cp1(A) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
<=> ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
^ [A: $i,B: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( A = B )
& cp1(A) )
<=> ~ ( ( A != B )
| ~ cp1(A) ) )),
( ~ ( ( A = B )
& cp1(A) )
<=> ~ ~ ( ( A != B )
| ~ cp1(A) ) )),
rewrite(
( ~ ~ ( ( A != B )
| ~ cp1(A) )
<=> ( ( A != B )
| ~ cp1(A) ) )),
( ~ ( ( A = B )
& cp1(A) )
<=> ( ( A != B )
| ~ cp1(A) ) )),
( ( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) )
<=> ( cp1(B)
| ( A != B )
| ~ cp1(A) ) )),
rewrite(
( ( cp1(B)
| ( A != B )
| ~ cp1(A) )
<=> ( cp1(B)
| ( A != B )
| ~ cp1(A) ) )),
( ( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) )
<=> ( cp1(B)
| ( A != B )
| ~ cp1(A) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) )
<=> ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) )
<=> ! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
^ [A: $i,B: $i] :
rewrite(
( ( ( ( A = B )
& cp1(A) )
=> cp1(B) )
<=> ( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
& cp1(A) )
=> cp1(B) )
<=> ! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& cp1(A) )
=> cp1(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp1_substitution_1) ).
tff(104,plain,
! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) ),
inference(modus_ponens,[status(thm)],[107,97]) ).
tff(109,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(111,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(transitivity,[status(thm)],[111,109]) ).
tff(113,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_4(i2003_11_14_17_19_21224),
inference(unit_resolution,[status(thm)],[114,108,95,93]) ).
tff(116,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(117,plain,
cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[116,37]) ).
tff(118,plain,
^ [X: $i] :
refl(
( ( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ~ ( cp4(X)
| cp5(X)
| cp3(X) )
<=> ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )),
( ( cp2(X)
=> ~ ( cp4(X)
| cp5(X)
| cp3(X) ) )
<=> ( cp2(X)
=> ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) )),
rewrite(
( ( cp2(X)
=> ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
<=> ( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) )),
( ( cp2(X)
=> ~ ( cp4(X)
| cp5(X)
| cp3(X) ) )
<=> ( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [X: $i] :
( cp2(X)
=> ~ ( cp4(X)
| cp5(X)
| cp3(X) ) )
<=> ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,axiom,
! [X: $i] :
( cp2(X)
=> ~ ( cp4(X)
| cp5(X)
| cp3(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(124,plain,
! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[126,119]) ).
tff(128,plain,
( ( ~ ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ( cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ( cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(129,plain,
( ~ ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ( cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
( ~ ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ( cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
~ ( cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ),
inference(unit_resolution,[status(thm)],[130,127,117]) ).
tff(132,plain,
( cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(133,plain,
~ cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[132,131]) ).
tff(134,plain,
^ [A: $i,B: $i] :
refl(
( ( cp3(B)
| ( A != B )
| ~ cp3(A) )
<=> ( cp3(B)
| ( A != B )
| ~ cp3(A) ) )),
inference(bind,[status(th)],]) ).
tff(135,plain,
( ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
<=> ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) ) ),
inference(quant_intro,[status(thm)],[134]) ).
tff(136,plain,
^ [A: $i,B: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( A = B )
& cp3(A) )
<=> ~ ( ( A != B )
| ~ cp3(A) ) )),
( ~ ( ( A = B )
& cp3(A) )
<=> ~ ~ ( ( A != B )
| ~ cp3(A) ) )),
rewrite(
( ~ ~ ( ( A != B )
| ~ cp3(A) )
<=> ( ( A != B )
| ~ cp3(A) ) )),
( ~ ( ( A = B )
& cp3(A) )
<=> ( ( A != B )
| ~ cp3(A) ) )),
( ( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) )
<=> ( cp3(B)
| ( A != B )
| ~ cp3(A) ) )),
rewrite(
( ( cp3(B)
| ( A != B )
| ~ cp3(A) )
<=> ( cp3(B)
| ( A != B )
| ~ cp3(A) ) )),
( ( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) )
<=> ( cp3(B)
| ( A != B )
| ~ cp3(A) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [A: $i,B: $i] :
( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) )
<=> ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
( ! [A: $i,B: $i] :
( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) )
<=> ! [A: $i,B: $i] :
( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
^ [A: $i,B: $i] :
rewrite(
( ( ( ( A = B )
& cp3(A) )
=> cp3(B) )
<=> ( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(140,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
& cp3(A) )
=> cp3(B) )
<=> ! [A: $i,B: $i] :
( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) ) ),
inference(quant_intro,[status(thm)],[139]) ).
tff(141,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& cp3(A) )
=> cp3(B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cp3_substitution_1) ).
tff(142,plain,
! [A: $i,B: $i] :
( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) ),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
! [A: $i,B: $i] :
( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) ),
inference(modus_ponens,[status(thm)],[142,138]) ).
tff(144,plain,
! [A: $i,B: $i] :
( cp3(B)
| ~ ( ( A = B )
& cp3(A) ) ),
inference(skolemize,[status(sab)],[143]) ).
tff(145,plain,
! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) ),
inference(modus_ponens,[status(thm)],[144,137]) ).
tff(146,plain,
! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) ),
inference(modus_ponens,[status(thm)],[145,135]) ).
tff(147,plain,
( ( ~ ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(148,plain,
( ( cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224)) )
<=> ( ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(149,plain,
( ( ~ ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(monotonicity,[status(thm)],[148]) ).
tff(150,plain,
( ( ~ ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(transitivity,[status(thm)],[149,147]) ).
tff(151,plain,
( ~ ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224)) ),
inference(quant_inst,[status(thm)],]) ).
tff(152,plain,
( ~ ! [A: $i,B: $i] :
( cp3(B)
| ( A != B )
| ~ cp3(A) )
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ),
inference(modus_ponens,[status(thm)],[151,150]) ).
tff(153,plain,
tptp_fun_Y_4(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224),
inference(unit_resolution,[status(thm)],[152,146,39,133]) ).
tff(154,plain,
( cp2(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(155,plain,
( cp2(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ),
inference(unit_resolution,[status(thm)],[154,57]) ).
tff(156,plain,
( ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(157,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ) ),
inference(modus_ponens,[status(thm)],[157,156]) ).
tff(159,plain,
~ cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[158,89,155]) ).
tff(160,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(161,plain,
( ( cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(162,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) ) ) ),
inference(monotonicity,[status(thm)],[161]) ).
tff(163,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) ) ) ),
inference(transitivity,[status(thm)],[162,160]) ).
tff(164,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) ),
inference(quant_inst,[status(thm)],]) ).
tff(165,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224) ) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_2(i2003_11_14_17_19_21224),
inference(unit_resolution,[status(thm)],[165,108,95,159]) ).
tff(167,plain,
( cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(168,plain,
~ cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[167,131]) ).
tff(169,plain,
( ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(170,plain,
( ( cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) )
<=> ( ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(171,plain,
( ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
( ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(transitivity,[status(thm)],[171,169]) ).
tff(173,plain,
( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224)) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
( ~ ! [A: $i,B: $i] :
( cp4(B)
| ( A != B )
| ~ cp4(A) )
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ),
inference(modus_ponens,[status(thm)],[173,172]) ).
tff(175,plain,
tptp_fun_Y_2(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224),
inference(unit_resolution,[status(thm)],[174,70,57,168]) ).
tff(176,plain,
( cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(177,plain,
( cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ),
inference(unit_resolution,[status(thm)],[176,117]) ).
tff(178,plain,
( ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(179,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(180,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ( cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp3(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp4(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| cp5(tptp_fun_Y_6(i2003_11_14_17_19_21224)) ) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
~ cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[180,89,177]) ).
tff(182,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(183,plain,
( ( cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(184,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ) ),
inference(transitivity,[status(thm)],[184,182]) ).
tff(186,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224)) ),
inference(quant_inst,[status(thm)],]) ).
tff(187,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| cp1(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224) ) ),
inference(modus_ponens,[status(thm)],[186,185]) ).
tff(188,plain,
tptp_fun_Y_0(i2003_11_14_17_19_21224) != tptp_fun_Y_6(i2003_11_14_17_19_21224),
inference(unit_resolution,[status(thm)],[187,108,95,181]) ).
tff(189,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ) ),
inference(tautology,[status(thm)],]) ).
tff(190,plain,
! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) ),
inference(unit_resolution,[status(thm)],[189,37]) ).
tff(191,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(192,plain,
rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[191,37]) ).
tff(193,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(194,plain,
rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[193,37]) ).
tff(195,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(196,plain,
rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[195,37]) ).
tff(197,plain,
( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ cp4(tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_3(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ cp3(tptp_fun_Y_5(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp2(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ cp(tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224)) ),
inference(tautology,[status(thm)],]) ).
tff(198,plain,
rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224)),
inference(unit_resolution,[status(thm)],[197,37]) ).
tff(199,plain,
( ( ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) ) )
<=> ( ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(200,plain,
( ( ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224)) )
<=> ( ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(201,plain,
( ( ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(monotonicity,[status(thm)],[200]) ).
tff(202,plain,
( ( ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224)) )
<=> ( ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ) ),
inference(transitivity,[status(thm)],[201,199]) ).
tff(203,plain,
( ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224)) ),
inference(quant_inst,[status(thm)],]) ).
tff(204,plain,
( ~ ! [Y0: $i,Y1: $i,Y2: $i,Y3: $i] :
( ( Y2 = Y3 )
| ( Y1 = Y2 )
| ( Y1 = Y3 )
| ( Y0 = Y3 )
| ( Y0 = Y2 )
| ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_21224,Y0)
| ~ rr(i2003_11_14_17_19_21224,Y1)
| ~ rr(i2003_11_14_17_19_21224,Y2)
| ~ rr(i2003_11_14_17_19_21224,Y3) )
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_0(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_2(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_4(i2003_11_14_17_19_21224))
| ~ rr(i2003_11_14_17_19_21224,tptp_fun_Y_6(i2003_11_14_17_19_21224))
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ),
inference(modus_ponens,[status(thm)],[203,202]) ).
tff(205,plain,
( ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_2(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_4(i2003_11_14_17_19_21224) = tptp_fun_Y_6(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_0(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) )
| ( tptp_fun_Y_2(i2003_11_14_17_19_21224) = tptp_fun_Y_4(i2003_11_14_17_19_21224) ) ),
inference(unit_resolution,[status(thm)],[204,198,196,194,192,190]) ).
tff(206,plain,
$false,
inference(unit_resolution,[status(thm)],[205,188,175,166,153,115,77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS080+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n007.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 09:15:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.19/0.43 % SZS status Unsatisfiable
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------