TSTP Solution File: KRS071+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS071+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:36 EDT 2022
% Result : Unsatisfiable 0.17s 0.37s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 73
% Syntax : Number of formulae : 153 ( 31 unt; 14 typ; 0 def)
% Number of atoms : 2241 ( 493 equ)
% Maximal formula atoms : 52 ( 16 avg)
% Number of connectives : 3435 (1432 ~;1611 |; 264 &)
% ( 107 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 99 ( 99 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 13 >; 1 *; 0 +; 0 <<)
% Number of predicates : 17 ( 15 usr; 1 prp; 0-5 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-1 aty)
% Number of variables : 554 ( 502 !; 27 ?; 554 :)
% Comments :
%------------------------------------------------------------------------------
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(i2003_11_14_17_18_39380_type,type,
i2003_11_14_17_18_39380: $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(cp1_type,type,
cp1: $i > $o ).
tff(cp5_type,type,
cp5: $i > $o ).
tff(cp4_type,type,
cp4: $i > $o ).
tff(cp3_type,type,
cp3: $i > $o ).
tff(cp2_type,type,
cp2: $i > $o ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y2_3_type,type,
tptp_fun_Y2_3: $i > $i ).
tff(tptp_fun_Y1_4_type,type,
tptp_fun_Y1_4: $i > $i ).
tff(tptp_fun_Y0_5_type,type,
tptp_fun_Y0_5: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) ) )),
trans(
monotonicity(
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)
& 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) ) )),
rewrite(
( ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) )
<=> ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) )
=> ( ( Y0 = Y1 )
| ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) )
=> ( ( Y0 = Y1 )
| ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) )
=> ( ( Y0 = Y1 )
| ( Y0 = Y2 )
| ( Y1 = Y2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cp1(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp2(Y) )
& ? [Y: $i] :
( rr(X,Y)
& cp3(Y) )
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cp1(tptp_fun_Y_0(X))
& rr(X,tptp_fun_Y_1(X))
& cp2(tptp_fun_Y_1(X))
& rr(X,tptp_fun_Y_2(X))
& cp3(tptp_fun_Y_2(X))
& ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ ( rr(X,Y0)
& rr(X,Y1)
& rr(X,Y2) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cp1(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp2(Y) )
| ! [Y: $i] :
~ ( rr(X,Y)
& cp3(Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ ( rr(X,tptp_fun_Y0_5(X))
& rr(X,tptp_fun_Y1_4(X))
& rr(X,tptp_fun_Y2_3(X)) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) )
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cp1(tptp_fun_Y_0(X))
| ~ rr(X,tptp_fun_Y_1(X))
| ~ cp2(tptp_fun_Y_1(X))
| ~ rr(X,tptp_fun_Y_2(X))
| ~ cp3(tptp_fun_Y_2(X))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(X,Y0)
| ~ rr(X,Y1)
| ~ rr(X,Y2) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ( tptp_fun_Y1_4(X) = tptp_fun_Y2_3(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y1_4(X) )
| ( tptp_fun_Y0_5(X) = tptp_fun_Y2_3(X) )
| ~ rr(X,tptp_fun_Y0_5(X))
| ~ rr(X,tptp_fun_Y1_4(X))
| ~ rr(X,tptp_fun_Y2_3(X)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ( tptp_fun_Y1_4(i2003_11_14_17_18_39380) = tptp_fun_Y2_3(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y0_5(i2003_11_14_17_18_39380) = tptp_fun_Y1_4(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y0_5(i2003_11_14_17_18_39380) = tptp_fun_Y2_3(i2003_11_14_17_18_39380) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y0_5(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y1_4(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y2_3(i2003_11_14_17_18_39380)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ( tptp_fun_Y1_4(i2003_11_14_17_18_39380) = tptp_fun_Y2_3(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y0_5(i2003_11_14_17_18_39380) = tptp_fun_Y1_4(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y0_5(i2003_11_14_17_18_39380) = tptp_fun_Y2_3(i2003_11_14_17_18_39380) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y0_5(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y1_4(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y2_3(i2003_11_14_17_18_39380)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) ) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ( tptp_fun_Y1_4(i2003_11_14_17_18_39380) = tptp_fun_Y2_3(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y0_5(i2003_11_14_17_18_39380) = tptp_fun_Y1_4(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y0_5(i2003_11_14_17_18_39380) = tptp_fun_Y2_3(i2003_11_14_17_18_39380) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y0_5(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y1_4(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y2_3(i2003_11_14_17_18_39380)) )
| ! [Y: $i] :
( ~ cp1(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) )
| ! [Y: $i] :
( ~ cp2(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) )
| ! [Y: $i] :
( ~ cp3(Y)
| ~ rr(i2003_11_14_17_18_39380,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(26,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( cUnsatisfiable(i2003_11_14_17_18_39380)
<=> cUnsatisfiable(i2003_11_14_17_18_39380) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
cUnsatisfiable(i2003_11_14_17_18_39380),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
tff(29,plain,
cUnsatisfiable(i2003_11_14_17_18_39380),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(31,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_39380)
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) )
| ~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
~ ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ),
inference(unit_resolution,[status(thm)],[31,26]) ).
tff(33,plain,
( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(34,plain,
cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
( cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(36,plain,
( cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,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(38,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)],[37]) ).
tff(39,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(40,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ~ ( cp4(X)
| cp2(X)
| cp3(X)
| cp5(X) )
<=> ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )),
( ( cp1(X)
=> ~ ( cp4(X)
| cp2(X)
| cp3(X)
| cp5(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)
=> ~ ( cp4(X)
| cp2(X)
| cp3(X)
| cp5(X) ) )
<=> ( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X: $i] :
( cp1(X)
=> ~ ( cp4(X)
| cp2(X)
| cp3(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [X: $i] :
( cp1(X)
=> ~ ( cp4(X)
| cp2(X)
| cp3(X)
| cp5(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(43,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ( cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ( cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ( cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ( cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
~ cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[49,46,36]) ).
tff(51,plain,
( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[51,32]) ).
tff(53,plain,
^ [A: $i,B: $i] :
refl(
( ( cp1(B)
| ( A != B )
| ~ cp1(A) )
<=> ( cp1(B)
| ( A != B )
| ~ cp1(A) ) )),
inference(bind,[status(th)],]) ).
tff(54,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)],[53]) ).
tff(55,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(56,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)],[55]) ).
tff(57,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(58,plain,
^ [A: $i,B: $i] :
rewrite(
( ( ( ( A = B )
& cp1(A) )
=> cp1(B) )
<=> ( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(59,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)],[58]) ).
tff(60,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& cp1(A) )
=> cp1(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp1_substitution_1) ).
tff(61,plain,
! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [A: $i,B: $i] :
( cp1(B)
| ~ ( ( A = B )
& cp1(A) ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) ),
inference(modus_ponens,[status(thm)],[64,54]) ).
tff(66,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) )
<=> ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380),
inference(unit_resolution,[status(thm)],[71,65,52,50]) ).
tff(73,plain,
( cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(74,plain,
( cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ),
inference(unit_resolution,[status(thm)],[73,34]) ).
tff(75,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(76,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)],[75]) ).
tff(77,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(78,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ~ ( cp4(X)
| cp3(X)
| cp5(X) )
<=> ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )),
( ( cp2(X)
=> ~ ( cp4(X)
| cp3(X)
| cp5(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)
| cp3(X)
| cp5(X) ) )
<=> ( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X: $i] :
( cp2(X)
=> ~ ( cp4(X)
| cp3(X)
| cp5(X) ) )
<=> ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i] :
( cp2(X)
=> ~ ( cp4(X)
| cp3(X)
| cp5(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
tff(81,plain,
! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
( ( ~ ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ( cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ( cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ( cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [X: $i] :
( ~ cp2(X)
| ~ ( cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ( cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_2(i2003_11_14_17_18_39380)) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
~ cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[87,84,74]) ).
tff(89,plain,
( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(90,plain,
cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[89,32]) ).
tff(91,plain,
^ [A: $i,B: $i] :
refl(
( ( cp2(B)
| ( A != B )
| ~ cp2(A) )
<=> ( cp2(B)
| ( A != B )
| ~ cp2(A) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
<=> ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
^ [A: $i,B: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ( A = B )
& cp2(A) )
<=> ~ ( ( A != B )
| ~ cp2(A) ) )),
( ~ ( ( A = B )
& cp2(A) )
<=> ~ ~ ( ( A != B )
| ~ cp2(A) ) )),
rewrite(
( ~ ~ ( ( A != B )
| ~ cp2(A) )
<=> ( ( A != B )
| ~ cp2(A) ) )),
( ~ ( ( A = B )
& cp2(A) )
<=> ( ( A != B )
| ~ cp2(A) ) )),
( ( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) )
<=> ( cp2(B)
| ( A != B )
| ~ cp2(A) ) )),
rewrite(
( ( cp2(B)
| ( A != B )
| ~ cp2(A) )
<=> ( cp2(B)
| ( A != B )
| ~ cp2(A) ) )),
( ( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) )
<=> ( cp2(B)
| ( A != B )
| ~ cp2(A) ) )),
inference(bind,[status(th)],]) ).
tff(94,plain,
( ! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) )
<=> ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) ) ),
inference(quant_intro,[status(thm)],[93]) ).
tff(95,plain,
( ! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) )
<=> ! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(96,plain,
^ [A: $i,B: $i] :
rewrite(
( ( ( ( A = B )
& cp2(A) )
=> cp2(B) )
<=> ( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ) )),
inference(bind,[status(th)],]) ).
tff(97,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
& cp2(A) )
=> cp2(B) )
<=> ! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,axiom,
! [A: $i,B: $i] :
( ( ( A = B )
& cp2(A) )
=> cp2(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cp2_substitution_1) ).
tff(99,plain,
! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
! [A: $i,B: $i] :
( cp2(B)
| ~ ( ( A = B )
& cp2(A) ) ),
inference(skolemize,[status(sab)],[100]) ).
tff(102,plain,
! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) ),
inference(modus_ponens,[status(thm)],[101,94]) ).
tff(103,plain,
! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) ),
inference(modus_ponens,[status(thm)],[102,92]) ).
tff(104,plain,
( ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ( cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380)) )
<=> ( ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(106,plain,
( ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(monotonicity,[status(thm)],[105]) ).
tff(107,plain,
( ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(transitivity,[status(thm)],[106,104]) ).
tff(108,plain,
( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380)) ),
inference(quant_inst,[status(thm)],]) ).
tff(109,plain,
( ~ ! [A: $i,B: $i] :
( cp2(B)
| ( A != B )
| ~ cp2(A) )
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp2(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
tptp_fun_Y_1(i2003_11_14_17_18_39380) != tptp_fun_Y_2(i2003_11_14_17_18_39380),
inference(unit_resolution,[status(thm)],[109,103,90,88]) ).
tff(111,plain,
( cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(112,plain,
( cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_1(i2003_11_14_17_18_39380)) ),
inference(unit_resolution,[status(thm)],[111,90]) ).
tff(113,plain,
( ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ ( cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_1(i2003_11_14_17_18_39380)) ) )
<=> ( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ ( cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_1(i2003_11_14_17_18_39380)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(114,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ ( cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_1(i2003_11_14_17_18_39380)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
( ~ ! [X: $i] :
( ~ cp1(X)
| ~ ( cp2(X)
| cp3(X)
| cp4(X)
| cp5(X) ) )
| ~ cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ ( cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp3(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp4(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| cp5(tptp_fun_Y_1(i2003_11_14_17_18_39380)) ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
~ cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[115,46,112]) ).
tff(117,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) ) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(118,plain,
( ( cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) )
<=> ( ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) ) ) ),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) )
<=> ( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) ) ) ),
inference(transitivity,[status(thm)],[119,117]) ).
tff(121,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380)) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
( ~ ! [A: $i,B: $i] :
( cp1(B)
| ( A != B )
| ~ cp1(A) )
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| cp1(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380) ) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
tptp_fun_Y_0(i2003_11_14_17_18_39380) != tptp_fun_Y_1(i2003_11_14_17_18_39380),
inference(unit_resolution,[status(thm)],[122,65,52,116]) ).
tff(124,plain,
( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ) ),
inference(tautology,[status(thm)],]) ).
tff(125,plain,
! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) ),
inference(unit_resolution,[status(thm)],[124,32]) ).
tff(126,plain,
( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(127,plain,
rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[126,32]) ).
tff(128,plain,
( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(129,plain,
rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[128,32]) ).
tff(130,plain,
( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ cp1(tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ cp2(tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ cp3(tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380)) ),
inference(tautology,[status(thm)],]) ).
tff(131,plain,
rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380)),
inference(unit_resolution,[status(thm)],[130,32]) ).
tff(132,plain,
( ( ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) ) )
<=> ( ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(133,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380)) )
<=> ( ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(134,plain,
( ( ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380)) )
<=> ( ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(monotonicity,[status(thm)],[133]) ).
tff(135,plain,
( ( ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380)) )
<=> ( ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ) ),
inference(transitivity,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380)) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
( ~ ! [Y0: $i,Y1: $i,Y2: $i] :
( ( Y1 = Y2 )
| ( Y0 = Y1 )
| ( Y0 = Y2 )
| ~ rr(i2003_11_14_17_18_39380,Y0)
| ~ rr(i2003_11_14_17_18_39380,Y1)
| ~ rr(i2003_11_14_17_18_39380,Y2) )
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_0(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_1(i2003_11_14_17_18_39380))
| ~ rr(i2003_11_14_17_18_39380,tptp_fun_Y_2(i2003_11_14_17_18_39380))
| ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ( tptp_fun_Y_1(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_1(i2003_11_14_17_18_39380) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_39380) = tptp_fun_Y_2(i2003_11_14_17_18_39380) ) ),
inference(unit_resolution,[status(thm)],[137,131,129,127,125]) ).
tff(139,plain,
$false,
inference(unit_resolution,[status(thm)],[138,123,110,72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.11 % Problem : KRS071+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.31 % Computer : n002.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Thu Sep 1 09:41:45 EDT 2022
% 0.12/0.31 % CPUTime :
% 0.12/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.32 Usage: tptp [options] [-file:]file
% 0.12/0.32 -h, -? prints this message.
% 0.12/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.32 -m, -model generate model.
% 0.12/0.32 -p, -proof generate proof.
% 0.12/0.32 -c, -core generate unsat core of named formulas.
% 0.12/0.32 -st, -statistics display statistics.
% 0.12/0.32 -t:timeout set timeout (in second).
% 0.12/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.32 -<param>:<value> configuration parameter and value.
% 0.12/0.32 -o:<output-file> file to place output in.
% 0.17/0.37 % SZS status Unsatisfiable
% 0.17/0.37 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------