%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS077+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:19 AM UTC 2025
% Result : Unsatisfiable 0.11s 0.36s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 36
% Syntax : Number of formulae : 89 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 1532 ( 154 equ)
% Maximal formula atoms : 80 ( 17 avg)
% Number of connectives : 2694 (1285 ~;1176 |; 152 &)
% ( 72 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 34 ( 34 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 475 ( 444 !; 18 ?; 475 :)
% Comments :
%------------------------------------------------------------------------------
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(i2003_11_14_17_19_09372_type,type,
i2003_11_14_17_19_09372: $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cp_type,type,
cp: $i > $o ).
tff(rinvS_type,type,
rinvS: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y1_2_type,type,
tptp_fun_Y1_2: $i > $i ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(tptp_fun_Z_4_type,type,
tptp_fun_Z_4: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) ) )),
trans(monotonicity(rewrite(( ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
<=> ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) ) )),
quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rs(X,Y)
& cp(Y) )
<=> ~ ( ~ cp(Y)
| ~ rs(X,Y) ) )),
( ~ ( rs(X,Y)
& cp(Y) )
<=> ~ ~ ( ~ cp(Y)
| ~ rs(X,Y) ) )),
rewrite(( ~ ~ ( ~ cp(Y)
| ~ rs(X,Y) )
<=> ( ~ cp(Y)
| ~ rs(X,Y) ) )),
( ~ ( rs(X,Y)
& cp(Y) )
<=> ( ~ cp(Y)
| ~ rs(X,Y) ) ))),
( ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) )
<=> ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) )),
( ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) ) )
<=> ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )),
( ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| cp(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| cp(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rr(X,Y0)
& rr(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rr(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) ) )
& ~ cp(X)
& ? [Y: $i] :
( rs(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| cp(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rr(X,Y0)
& rr(X,Y1) )
| ( Y0 = Y1 ) )
& rr(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ~ cp(X)
& rs(X,tptp_fun_Y_1(X))
& cp(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ~ ( ~ ( rr(X,tptp_fun_Y0_3(X))
& rr(X,tptp_fun_Y1_2(X)) )
| ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ rr(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| cp(i2003_11_14_17_19_09372)
| ~ ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| cp(i2003_11_14_17_19_09372)
| ~ ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y0)
| ~ rr(i2003_11_14_17_19_09372,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| cp(i2003_11_14_17_19_09372)
| ~ ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y0)
| ~ rr(i2003_11_14_17_19_09372,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| cp(i2003_11_14_17_19_09372)
| ~ ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y0)
| ~ rr(i2003_11_14_17_19_09372,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| cp(i2003_11_14_17_19_09372)
| ~ ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y0)
| ~ rr(i2003_11_14_17_19_09372,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| cp(i2003_11_14_17_19_09372)
| ~ ( ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ rr(X,tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cp(tptp_fun_Y_1(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(X,Y0)
| ~ rr(X,Y1) )
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ~ ( ( tptp_fun_Y0_3(X) = tptp_fun_Y1_2(X) )
| ~ rr(X,tptp_fun_Y0_3(X))
| ~ rr(X,tptp_fun_Y1_2(X)) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(X,Y) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| cp(i2003_11_14_17_19_09372)
| ~ ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| cp(i2003_11_14_17_19_09372)
| ~ ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) ) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_19_09372)
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_19_09372,Y)
| ~ ( cp(tptp_fun_Z_4(Y))
| ~ rinvS(Y,tptp_fun_Z_4(Y)) ) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rs(i2003_11_14_17_19_09372,Y) )
| cp(i2003_11_14_17_19_09372)
| ~ ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y1_2(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y0_3(i2003_11_14_17_19_09372))
| ( tptp_fun_Y0_3(i2003_11_14_17_19_09372) = tptp_fun_Y1_2(i2003_11_14_17_19_09372) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_19_09372)
<=> cUnsatisfiable(i2003_11_14_17_19_09372) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_19_09372),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_19_09372),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) )
| ~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(tautology,[status(thm)],[]) ).
tff(39,plain,
rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rs(X,Y)
| rr(X,Y) )
<=> ( ~ rs(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rs(X,Y)
=> rr(X,Y) )
<=> ( ~ rs(X,Y)
| rr(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(44,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rr(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ) ),
inference(quant_intro,[status(thm)],[43]) ).
tff(45,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rr(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(46,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[46,42]) ).
tff(48,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(skolemize,[status(sab)],[47]) ).
tff(49,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) ),
inference(modus_ponens,[status(thm)],[48,41]) ).
tff(50,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rr(X,Y) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)),
inference(unit_resolution,[status(thm)],[52,49,39]) ).
tff(54,plain,
( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ) ),
inference(tautology,[status(thm)],[]) ).
tff(55,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) ),
inference(unit_resolution,[status(thm)],[54,37]) ).
tff(56,plain,
( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) ),
inference(tautology,[status(thm)],[]) ).
tff(57,plain,
rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)),
inference(unit_resolution,[status(thm)],[56,37]) ).
tff(58,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(63,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ( tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372) )
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
tptp_fun_Y_1(i2003_11_14_17_19_09372) = tptp_fun_Y_0(i2003_11_14_17_19_09372),
inference(unit_resolution,[status(thm)],[63,57,55,53]) ).
tff(65,plain,
( rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
<=> ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)) ),
inference(monotonicity,[status(thm)],[66]) ).
tff(68,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvS(X,Y)
<=> rs(Y,X) )
<=> ( rinvS(X,Y)
<=> rs(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(69,plain,
( ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
( ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,axiom,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(72,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(skolemize,[status(sab)],[72]) ).
tff(74,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[73,69]) ).
tff(75,plain,
( ~ ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
| ( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ) ),
inference(tautology,[status(thm)],[]) ).
tff(78,plain,
! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) ),
inference(unit_resolution,[status(thm)],[77,37]) ).
tff(79,plain,
( cp(i2003_11_14_17_19_09372)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372))
| ~ rr(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rr(i2003_11_14_17_19_09372,Y1)
| ~ rr(i2003_11_14_17_19_09372,Y0) )
| ~ cp(i2003_11_14_17_19_09372) ),
inference(tautology,[status(thm)],[]) ).
tff(80,plain,
~ cp(i2003_11_14_17_19_09372),
inference(unit_resolution,[status(thm)],[79,37]) ).
tff(81,plain,
( ( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| cp(i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )
<=> ( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| cp(i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| cp(i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(quant_inst,[status(thm)],[]) ).
tff(83,plain,
( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),Z) )
| cp(i2003_11_14_17_19_09372)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
inference(modus_ponens,[status(thm)],[82,81]) ).
tff(84,plain,
~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
inference(unit_resolution,[status(thm)],[83,80,78]) ).
tff(85,plain,
( ~ ( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) ),
inference(tautology,[status(thm)],[]) ).
tff(86,plain,
( ~ ( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
<=> rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) )
| ~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_0(i2003_11_14_17_19_09372)),
inference(unit_resolution,[status(thm)],[86,76]) ).
tff(88,plain,
~ rs(i2003_11_14_17_19_09372,tptp_fun_Y_1(i2003_11_14_17_19_09372)),
inference(modus_ponens,[status(thm)],[87,67]) ).
tff(89,plain,
$false,
inference(unit_resolution,[status(thm)],[39,88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KRS077+1 : TPTP v9.0.0. Released v3.1.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n011.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:11:12 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.11/0.39 % E exiting
%------------------------------------------------------------------------------