%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS070+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:18 AM UTC 2025
% Result : Unsatisfiable 0.14s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 42
% Syntax : Number of formulae : 104 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 1413 ( 33 equ)
% Maximal formula atoms : 64 ( 13 avg)
% Number of connectives : 2567 (1319 ~; 966 |; 195 &)
% ( 78 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 61 ( 61 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-4 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 391 ( 339 !; 27 ?; 391 :)
% Comments :
%------------------------------------------------------------------------------
tff(cc2_type,type,
cc2: $i > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_18_32242_type,type,
i2003_11_14_17_18_32242: $i ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(rrx_type,type,
rrx: ( $i * $i ) > $o ).
tff(rrx3_type,type,
rrx3: ( $i * $i ) > $o ).
tff(cc1_type,type,
cc1: $i > $o ).
tff(rrx4_type,type,
rrx4: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rrx4(X,Y)
& cc2(Y) )
<=> ~ ( ~ rrx4(X,Y)
| ~ cc2(Y) ) )),
( ~ ( rrx4(X,Y)
& cc2(Y) )
<=> ~ ~ ( ~ rrx4(X,Y)
| ~ cc2(Y) ) )),
rewrite(( ~ ~ ( ~ rrx4(X,Y)
| ~ cc2(Y) )
<=> ( ~ rrx4(X,Y)
| ~ cc2(Y) ) )),
( ~ ( rrx4(X,Y)
& cc2(Y) )
<=> ( ~ rrx4(X,Y)
| ~ cc2(Y) ) ))),
( ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
<=> ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) )),
rewrite(( ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
<=> ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) )),
quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rrx3(X,Y)
& cc1(Y) )
<=> ~ ( ~ rrx3(X,Y)
| ~ cc1(Y) ) )),
( ~ ( rrx3(X,Y)
& cc1(Y) )
<=> ~ ~ ( ~ rrx3(X,Y)
| ~ cc1(Y) ) )),
rewrite(( ~ ~ ( ~ rrx3(X,Y)
| ~ cc1(Y) )
<=> ( ~ rrx3(X,Y)
| ~ cc1(Y) ) )),
( ~ ( rrx3(X,Y)
& cc1(Y) )
<=> ( ~ rrx3(X,Y)
| ~ cc1(Y) ) ))),
( ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) )
<=> ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rrx4(X,Y)
& cc2(Y) )
& ~ ? [Y: $i] :
( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& ? [Y: $i] :
( rrx3(X,Y)
& cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rrx4(X,tptp_fun_Y_0(X))
& cc2(tptp_fun_Y_0(X))
& ! [Y: $i] :
~ ( rrx3(X,Y)
& cc2(Y)
& cc1(Y) )
& rrx3(X,tptp_fun_Y_1(X))
& cc1(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rrx4(X,Y)
& cc2(Y) )
| ( rrx3(X,tptp_fun_Y_2(X))
& cc2(tptp_fun_Y_2(X))
& cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
~ ( rrx3(X,Y)
& cc1(Y) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) )
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) )
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ rrx3(i2003_11_14_17_18_32242,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(i2003_11_14_17_18_32242,Y)
| ~ cc2(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rrx4(X,tptp_fun_Y_0(X))
| ~ cc2(tptp_fun_Y_0(X))
| ~ rrx3(X,tptp_fun_Y_1(X))
| ~ cc1(tptp_fun_Y_1(X))
| ~ ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc2(Y)
| ~ cc1(Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rrx3(X,tptp_fun_Y_2(X))
| ~ cc2(tptp_fun_Y_2(X))
| ~ cc1(tptp_fun_Y_2(X)) )
| ! [Y: $i] :
( ~ rrx3(X,Y)
| ~ cc1(Y) )
| ! [Y: $i] :
( ~ rrx4(X,Y)
| ~ cc2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_2(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_2(i2003_11_14_17_18_32242)) )
| ! [Y: $i] :
( ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ rrx4(i2003_11_14_17_18_32242,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_18_32242)
<=> cUnsatisfiable(i2003_11_14_17_18_32242) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_18_32242),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_18_32242),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_32242)
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) )
| ~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(tautology,[status(thm)],[]) ).
tff(39,plain,
rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rrx3(X,Y)
| rrx(X,Y) )
<=> ( ~ rrx3(X,Y)
| rrx(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rrx3(X,Y)
=> rrx(X,Y) )
<=> ( ~ rrx3(X,Y)
| rrx(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [X: $i,Y: $i] :
( rrx3(X,Y)
=> rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [X: $i,Y: $i] :
( rrx3(X,Y)
=> rrx(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
tff(46,plain,
! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rrx3(X,Y)
| rrx(X,Y) )
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[52,49,39]) ).
tff(54,plain,
( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(tautology,[status(thm)],[]) ).
tff(55,plain,
rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[54,37]) ).
tff(56,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rrx4(X,Y)
| rrx(X,Y) )
<=> ( ~ rrx4(X,Y)
| rrx(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rrx4(X,Y)
=> rrx(X,Y) )
<=> ( ~ rrx4(X,Y)
| rrx(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [X: $i,Y: $i] :
( rrx4(X,Y)
=> rrx(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [X: $i,Y: $i] :
( rrx4(X,Y)
=> rrx(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_16) ).
tff(62,plain,
! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rrx4(X,Y)
| rrx(X,Y) )
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[68,65,55]) ).
tff(70,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(( ( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) )
<=> ( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(71,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rrx(X,Y)
& rrx(X,Z) )
<=> ~ ( ~ rrx(X,Y)
| ~ rrx(X,Z) ) )),
( ~ ( rrx(X,Y)
& rrx(X,Z) )
<=> ~ ~ ( ~ rrx(X,Y)
| ~ rrx(X,Z) ) )),
rewrite(( ~ ~ ( ~ rrx(X,Y)
| ~ rrx(X,Z) )
<=> ( ~ rrx(X,Y)
| ~ rrx(X,Z) ) )),
( ~ ( rrx(X,Y)
& rrx(X,Z) )
<=> ( ~ rrx(X,Y)
| ~ rrx(X,Z) ) )),
( ( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) )
<=> ( ~ rrx(X,Y)
| ~ rrx(X,Z)
| ( Y = Z ) ) )),
rewrite(( ( ~ rrx(X,Y)
| ~ rrx(X,Z)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) ) )),
( ( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(73,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rrx(X,Y)
& rrx(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rrx(X,Y)
& rrx(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rrx(X,Y)
& rrx(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(78,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[78,74]) ).
tff(80,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rrx(X,Y)
& rrx(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[79]) ).
tff(81,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) ),
inference(modus_ponens,[status(thm)],[80,73]) ).
tff(82,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) ),
inference(modus_ponens,[status(thm)],[81,71]) ).
tff(83,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(85,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rrx(X,Y)
| ~ rrx(X,Z) )
| ( tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242) )
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
tptp_fun_Y_0(i2003_11_14_17_18_32242) = tptp_fun_Y_1(i2003_11_14_17_18_32242),
inference(unit_resolution,[status(thm)],[85,82,69,53]) ).
tff(87,plain,
( cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
<=> cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
<=> cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
<=> ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(91,plain,
! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) ),
inference(unit_resolution,[status(thm)],[90,37]) ).
tff(92,plain,
( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(tautology,[status(thm)],[]) ).
tff(93,plain,
cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[92,37]) ).
tff(94,plain,
( ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(95,plain,
( ( ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
( ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) )
<=> ( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ) ),
inference(transitivity,[status(thm)],[96,94]) ).
tff(98,plain,
( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(99,plain,
( ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
~ cc2(tptp_fun_Y_1(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[99,93,39,91]) ).
tff(101,plain,
~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)),
inference(modus_ponens,[status(thm)],[100,89]) ).
tff(102,plain,
( ~ cc1(tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ rrx3(i2003_11_14_17_18_32242,tptp_fun_Y_1(i2003_11_14_17_18_32242))
| ~ cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ rrx4(i2003_11_14_17_18_32242,tptp_fun_Y_0(i2003_11_14_17_18_32242))
| ~ ! [Y: $i] :
( ~ cc2(Y)
| ~ cc1(Y)
| ~ rrx3(i2003_11_14_17_18_32242,Y) )
| cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)) ),
inference(tautology,[status(thm)],[]) ).
tff(103,plain,
cc2(tptp_fun_Y_0(i2003_11_14_17_18_32242)),
inference(unit_resolution,[status(thm)],[102,37]) ).
tff(104,plain,
$false,
inference(unit_resolution,[status(thm)],[103,101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KRS070+1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n003.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Jun 19 19:10:54 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40 % SZS output start Proof
% See solution above
% 0.22/0.43 % E exiting
%------------------------------------------------------------------------------