%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS073+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.23s 0.42s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 47
% Syntax : Number of formulae : 115 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 1275 ( 43 equ)
% Maximal formula atoms : 64 ( 11 avg)
% Number of connectives : 2323 (1195 ~; 899 |; 123 &)
% ( 94 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 32 ( 32 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-1 aty)
% Number of variables : 445 ( 405 !; 18 ?; 445 :)
% Comments :
%------------------------------------------------------------------------------
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(tptp_fun_W_1_type,type,
tptp_fun_W_1: $i > $i ).
tff(i2003_11_14_17_18_54369_type,type,
i2003_11_14_17_18_54369: $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(cp_type,type,
cp: $i > $o ).
tff(rinvF_type,type,
rinvF: ( $i * $i ) > $o ).
tff(rinvS_type,type,
rinvS: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Z_3_type,type,
tptp_fun_Z_3: $i > $i ).
tff(tptp_fun_Z_2_type,type,
tptp_fun_Z_2: $i > $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvF(X,Y)
<=> rf(Y,X) )
<=> ( rinvF(X,Y)
<=> rf(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
tff(5,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i] :
( rinvF(X,Y)
<=> rf(Y,X) )
| ( rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
<=> rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
<=> rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) ) )
<=> ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) )
| cp(X) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(18,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) )
| cp(X) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) )
& ! [Z: $i] :
( ~ rinvF(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) )
& ! [Z: $i] :
( ~ rinvF(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) )
& ! [Z: $i] :
( rinvF(Y,Z)
=> ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) )
& ! [Z: $i] :
( ~ rinvF(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) )
& ! [Z: $i] :
( rinvF(Y,Z)
=> ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) )
& ! [Z: $i] :
( ~ rinvF(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( rinvS(Y,Z)
=> cp(Z) )
& ! [Z: $i] :
( rinvF(Y,Z)
=> ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(23,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) )
& ! [Z: $i] :
( ~ rinvF(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf(X,Y)
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(Y,Z) )
& ! [Z: $i] :
( ~ rinvF(Y,Z)
| ? [W: $i] :
( rs(Z,W)
& cp(W) ) ) )
& ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) )
| cp(X) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf(X,tptp_fun_Y_0(X))
& ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ( rs(Z,tptp_fun_W_1(Z))
& cp(tptp_fun_W_1(Z)) ) )
& ~ cp(X) ) )
& ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ( rinvF(Y,tptp_fun_Z_3(Y))
& ! [W: $i] :
~ ( rs(tptp_fun_Z_3(Y),W)
& cp(W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,18]) ).
tff(27,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,14]) ).
tff(29,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[30]) ).
tff(32,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( cp(X)
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(X),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rf(X,tptp_fun_Y_0(X))
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(X),Z) ) ) )
| ~ ( cUnsatisfiable(X)
| cp(X)
| ! [Y: $i] :
( ~ rf(X,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[34,28]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_18_54369)
| cp(i2003_11_14_17_18_54369)
| ! [Y: $i] :
( ~ rf(i2003_11_14_17_18_54369,Y)
| ~ ( cp(tptp_fun_Z_2(Y))
| ~ rinvS(Y,tptp_fun_Z_2(Y)) )
| ~ ( ~ rinvF(Y,tptp_fun_Z_3(Y))
| ~ ! [W: $i] :
( ~ cp(W)
| ~ rs(tptp_fun_Z_3(Y),W) ) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(37,plain,
( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) ),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( cUnsatisfiable(i2003_11_14_17_18_54369)
<=> cUnsatisfiable(i2003_11_14_17_18_54369) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
cUnsatisfiable(i2003_11_14_17_18_54369),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
tff(40,plain,
cUnsatisfiable(i2003_11_14_17_18_54369),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(42,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_18_54369)
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) )
| ~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
~ ( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ),
inference(unit_resolution,[status(thm)],[42,37]) ).
tff(44,plain,
( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ),
inference(tautology,[status(thm)],[]) ).
tff(45,plain,
rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
<=> rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) )
| rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ),
inference(tautology,[status(thm)],[]) ).
tff(47,plain,
( ~ ( rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
<=> rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) )
| rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) ),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369),
inference(unit_resolution,[status(thm)],[47,9]) ).
tff(49,plain,
( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(50,plain,
! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) ),
inference(unit_resolution,[status(thm)],[49,43]) ).
tff(51,plain,
( ( ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
| ~ ( ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ cp(tptp_fun_W_1(i2003_11_14_17_18_54369)) ) )
<=> ( ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
| ~ ( ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ cp(tptp_fun_W_1(i2003_11_14_17_18_54369)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
| ~ ( ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ cp(tptp_fun_W_1(i2003_11_14_17_18_54369)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(53,plain,
( ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
| ~ ( ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ cp(tptp_fun_W_1(i2003_11_14_17_18_54369)) ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
~ ( ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ cp(tptp_fun_W_1(i2003_11_14_17_18_54369)) ),
inference(unit_resolution,[status(thm)],[53,50,48]) ).
tff(55,plain,
( ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ cp(tptp_fun_W_1(i2003_11_14_17_18_54369))
| rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ),
inference(tautology,[status(thm)],[]) ).
tff(56,plain,
rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ rs(X,Y)
| rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(60,plain,
^ [X: $i,Y: $i] :
rewrite(( ( rs(X,Y)
=> rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(61,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[60]) ).
tff(62,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
tff(63,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[63,59]) ).
tff(65,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)),
inference(unit_resolution,[status(thm)],[69,66,56]) ).
tff(71,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(( ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(72,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rf(X,Y)
& rf(X,Z) )
<=> ~ ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ~ ~ ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
rewrite(( ~ ~ ( ~ rf(X,Y)
| ~ rf(X,Z) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf(X,Y)
| ~ rf(X,Z)
| ( Y = Z ) ) )),
rewrite(( ( ~ rf(X,Y)
| ~ rf(X,Z)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(74,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(79,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) ),
inference(modus_ponens,[status(thm)],[82,72]) ).
tff(84,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
( ( ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) )
<=> ( ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(86,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ) ),
inference(monotonicity,[status(thm)],[85]) ).
tff(87,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ) ),
inference(transitivity,[status(thm)],[86,84]) ).
tff(88,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(89,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Y)
| ~ rf(X,Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ( tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
tptp_fun_W_1(i2003_11_14_17_18_54369) = tptp_fun_Y_0(i2003_11_14_17_18_54369),
inference(unit_resolution,[status(thm)],[89,83,45,70]) ).
tff(91,plain,
( rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369))
<=> rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ),
inference(monotonicity,[status(thm)],[90]) ).
tff(92,plain,
( rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
<=> rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
( ~ rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
<=> ~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)) ),
inference(monotonicity,[status(thm)],[92]) ).
tff(94,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvS(X,Y)
<=> rs(Y,X) )
<=> ( rinvS(X,Y)
<=> rs(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(95,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)],[94]) ).
tff(96,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(97,axiom,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
tff(98,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
| ( rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
<=> rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
( rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
<=> rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) ) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) ),
inference(unit_resolution,[status(thm)],[103,43]) ).
tff(105,plain,
( cp(i2003_11_14_17_18_54369)
| ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| ~ rf(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369))
| ~ ! [Z: $i] :
( ~ rinvF(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z)
| ~ ( ~ rs(Z,tptp_fun_W_1(Z))
| ~ cp(tptp_fun_W_1(Z)) ) )
| ~ cp(i2003_11_14_17_18_54369) ),
inference(tautology,[status(thm)],[]) ).
tff(106,plain,
~ cp(i2003_11_14_17_18_54369),
inference(unit_resolution,[status(thm)],[105,43]) ).
tff(107,plain,
( ( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| cp(i2003_11_14_17_18_54369)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) )
<=> ( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| cp(i2003_11_14_17_18_54369)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| cp(i2003_11_14_17_18_54369)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) ),
inference(quant_inst,[status(thm)],[]) ).
tff(109,plain,
( ~ ! [Z: $i] :
( cp(Z)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),Z) )
| cp(i2003_11_14_17_18_54369)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369) ),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
~ rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369),
inference(unit_resolution,[status(thm)],[109,106,104]) ).
tff(111,plain,
( ~ ( rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
<=> rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
| ~ rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ),
inference(tautology,[status(thm)],[]) ).
tff(112,plain,
( ~ ( rinvS(tptp_fun_Y_0(i2003_11_14_17_18_54369),i2003_11_14_17_18_54369)
<=> rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) )
| ~ rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)) ),
inference(unit_resolution,[status(thm)],[111,110]) ).
tff(113,plain,
~ rs(i2003_11_14_17_18_54369,tptp_fun_Y_0(i2003_11_14_17_18_54369)),
inference(unit_resolution,[status(thm)],[112,102]) ).
tff(114,plain,
~ rs(i2003_11_14_17_18_54369,tptp_fun_W_1(i2003_11_14_17_18_54369)),
inference(modus_ponens,[status(thm)],[113,93]) ).
tff(115,plain,
$false,
inference(unit_resolution,[status(thm)],[56,114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : KRS073+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n012.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Jun 19 19:09:56 EDT 2025
% 0.13/0.36 % CPUTime :
% 0.23/0.42 % SZS status Unsatisfiable
% 0.23/0.42 % SZS output start Proof
% See solution above
% 0.23/0.45 % E exiting
%------------------------------------------------------------------------------