TSTP Solution File: KRS082+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS082+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:39 EDT 2022
% Result : Unsatisfiable 0.13s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 79
% Syntax : Number of formulae : 160 ( 28 unt; 19 typ; 0 def)
% Number of atoms : 2160 ( 0 equ)
% Maximal formula atoms : 68 ( 15 avg)
% Number of connectives : 3528 (1602 ~;1222 |; 471 &)
% ( 142 <=>; 91 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 93 ( 93 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 18 >; 6 *; 0 +; 0 <<)
% Number of predicates : 18 ( 17 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-1 aty)
% Number of variables : 924 ( 735 !; 163 ?; 924 :)
% Comments :
%------------------------------------------------------------------------------
tff(rinvS_type,type,
rinvS: ( $i * $i ) > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_19_28752_type,type,
i2003_11_14_17_19_28752: $i ).
tff(ca_type,type,
ca: $i > $o ).
tff(rinvP_type,type,
rinvP: ( $i * $i ) > $o ).
tff(tptp_fun_Z_1_type,type,
tptp_fun_Z_1: $i > $i ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(tptp_fun_W_2_type,type,
tptp_fun_W_2: $i > $i ).
tff(cc_type,type,
cc: $i > $o ).
tff(tptp_fun_W_7_type,type,
tptp_fun_W_7: $i > $i ).
tff(tptp_fun_Z_6_type,type,
tptp_fun_Z_6: $i > $i ).
tff(tptp_fun_Y_5_type,type,
tptp_fun_Y_5: $i > $i ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(rp_type,type,
rp: ( $i * $i ) > $o ).
tff(tptp_fun_Z_4_type,type,
tptp_fun_Z_4: $i > $i ).
tff(tptp_fun_W_3_type,type,
tptp_fun_W_3: $i > $i ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(1,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ~ ( ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) )
| ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) )
| ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
<=> ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) )),
rewrite(
( ( cc(X)
| ( rinvR(X,tptp_fun_Y_5(X))
& rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )),
( ( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( rinvR(X,tptp_fun_Y_5(X))
& rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )
<=> ( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )),
rewrite(
( ( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) )
<=> ~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )),
( ( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( rinvR(X,tptp_fun_Y_5(X))
& rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )
<=> ~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( rinvR(X,tptp_fun_Y_5(X))
& rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( ~ ~ rinvR(X,tptp_fun_Y_5(X))
& ~ ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )
<=> ( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( rinvR(X,tptp_fun_Y_5(X))
& rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( ~ ~ rinvR(X,tptp_fun_Y_5(X))
& ~ ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) )
<=> ! [X: $i] :
( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( rinvR(X,tptp_fun_Y_5(X))
& rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cc(X)
<=> ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
<=> ! [X: $i] :
( cc(X)
<=> ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [X: $i] :
rewrite(
( ( cc(X)
<=> ! [Y: $i] :
( rinvR(X,Y)
=> ! [Z: $i] :
( rinvP(Y,Z)
=> ! [W: $i] :
( rinvS(Z,W)
=> ~ ca(W) ) ) ) )
<=> ( cc(X)
<=> ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [X: $i] :
( cc(X)
<=> ! [Y: $i] :
( rinvR(X,Y)
=> ! [Z: $i] :
( rinvP(Y,Z)
=> ! [W: $i] :
( rinvS(Z,W)
=> ~ ca(W) ) ) ) )
<=> ! [X: $i] :
( cc(X)
<=> ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cc(X)
<=> ! [Y: $i] :
( rinvR(X,Y)
=> ! [Z: $i] :
( rinvP(Y,Z)
=> ! [W: $i] :
( rinvS(Z,W)
=> ~ ca(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(16,plain,
! [X: $i] :
( cc(X)
<=> ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cc(X)
<=> ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( ~ ~ rinvR(X,tptp_fun_Y_5(X))
& ~ ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
& ( cc(X)
| ( rinvR(X,tptp_fun_Y_5(X))
& rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
& ~ ( ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) )
| ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ~ ! [X: $i] :
~ ( ~ ( cc(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_5(X))
| ~ rinvP(tptp_fun_Y_5(X),tptp_fun_Z_6(X))
| ~ ca(tptp_fun_W_7(X))
| ~ rinvS(tptp_fun_Z_6(X),tptp_fun_W_7(X)) ) )
| ~ ( ~ cc(X)
| ! [Y: $i] :
( ~ rinvR(X,Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) )
| ~ ( ~ ( cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
~ ( ~ ( cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(26,plain,
( ~ cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( cUnsatisfiable(i2003_11_14_17_19_28752)
<=> cUnsatisfiable(i2003_11_14_17_19_28752) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
cUnsatisfiable(i2003_11_14_17_19_28752),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(29,plain,
cUnsatisfiable(i2003_11_14_17_19_28752),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
^ [X: $i] :
rewrite(
( ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(X),Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) )
<=> ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(X),Z) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [X: $i] :
refl(
( ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) )
<=> ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [X: $i] :
rewrite(
( ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) )
<=> ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) )
<=> ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ) ),
inference(transitivity,[status(thm)],[35,33]) ).
tff(37,plain,
^ [X: $i] :
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cowlThing(tptp_fun_Z_1(X))
& ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rr(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rp(Z,tptp_fun_W_3(Z))
& cowlThing(tptp_fun_W_3(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
& cowlThing(tptp_fun_Z_4(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $i] :
( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cowlThing(tptp_fun_Z_1(X))
& ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rr(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rp(Z,tptp_fun_W_3(Z))
& cowlThing(tptp_fun_W_3(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
& cowlThing(tptp_fun_Z_4(X)) ) )
<=> ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
^ [X: $i] :
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cowlThing(tptp_fun_Z_1(X))
& ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rr(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rp(Z,tptp_fun_W_3(Z))
& cowlThing(tptp_fun_W_3(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
& cowlThing(tptp_fun_Z_4(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cowlThing(tptp_fun_Z_1(X))
& ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rr(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rp(Z,tptp_fun_W_3(Z))
& cowlThing(tptp_fun_W_3(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
& cowlThing(tptp_fun_Z_4(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(40,plain,
( ! [X: $i] :
( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cowlThing(tptp_fun_Z_1(X))
& ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rr(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rp(Z,tptp_fun_W_3(Z))
& cowlThing(tptp_fun_W_3(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
& cowlThing(tptp_fun_Z_4(X)) ) )
<=> ! [X: $i] :
( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cowlThing(tptp_fun_Z_1(X))
& ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rr(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rp(Z,tptp_fun_W_3(Z))
& cowlThing(tptp_fun_W_3(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
& cowlThing(tptp_fun_Z_4(X)) ) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [X: $i] :
( ~ cUnsatisfiable(X)
| ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) )
<=> ! [X: $i] :
( ~ cUnsatisfiable(X)
| ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
^ [X: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) ) ) )),
quant_intro(
proof_bind(
^ [Z: $i] :
rewrite(
( ( rr(Y,Z)
=> cc(Z) )
<=> ( cc(Z)
| ~ rr(Y,Z) ) ))),
( ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
<=> ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) ) ) )),
rewrite(
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) ) ) )),
quant_intro(
proof_bind(
^ [Z: $i] :
rewrite(
( ( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
<=> ( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) ) ))),
( ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
<=> ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) ) ) )),
rewrite(
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) ) ) )),
quant_intro(
proof_bind(
^ [Z: $i] :
rewrite(
( ( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
<=> ( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) ) ))),
( ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
<=> ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) ) ) )),
rewrite(
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) ) ) )),
quant_intro(
proof_bind(
^ [Z: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W: $i] :
rewrite(
( ( rr(Z,W)
=> cc(W) )
<=> ( cc(W)
| ~ rr(Z,W) ) ))),
( ! [W: $i] :
( rr(Z,W)
=> cc(W) )
<=> ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )),
( ( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
<=> ( rp(Y,Z)
=> ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) ) )),
rewrite(
( ( rp(Y,Z)
=> ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
<=> ( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) ) )),
( ( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
<=> ( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) ) ))),
( ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
<=> ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) ) ) )),
rewrite(
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) )),
rewrite(
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) )),
( ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) )
<=> ( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ))),
( ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) )
<=> ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) )),
( ( cUnsatisfiable(X)
=> ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) )
<=> ( cUnsatisfiable(X)
=> ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
=> ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ) )),
( ( cUnsatisfiable(X)
=> ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(43,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
=> ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) )
<=> ! [X: $i] :
( ~ cUnsatisfiable(X)
| ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,axiom,
! [X: $i] :
( cUnsatisfiable(X)
=> ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( rr(Y,Z)
=> cc(Z) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( rp(Y,Z)
=> ! [W: $i] :
( rr(Z,W)
=> cc(W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(45,plain,
! [X: $i] :
( ~ cUnsatisfiable(X)
| ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
! [X: $i] :
( ~ cUnsatisfiable(X)
| ? [Y: $i] :
( rs(X,Y)
& ? [Z: $i] :
( rp(Y,Z)
& cowlThing(Z) )
& ! [Z: $i] :
( cc(Z)
| ~ rr(Y,Z) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rr(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ? [W: $i] :
( rp(Z,W)
& cowlThing(W) ) )
& ! [Z: $i] :
( ~ rp(Y,Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& ? [Z: $i] :
( rr(Y,Z)
& cowlThing(Z) ) ) ),
inference(modus_ponens,[status(thm)],[45,41]) ).
tff(47,plain,
! [X: $i] :
( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cowlThing(tptp_fun_Z_1(X))
& ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rr(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rp(Z,tptp_fun_W_3(Z))
& cowlThing(tptp_fun_W_3(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
& cowlThing(tptp_fun_Z_4(X)) ) ),
inference(skolemize,[status(sab)],[46]) ).
tff(48,plain,
! [X: $i] :
( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
& cowlThing(tptp_fun_Z_1(X))
& ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rr(Z,tptp_fun_W_2(Z))
& cowlThing(tptp_fun_W_2(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ( rp(Z,tptp_fun_W_3(Z))
& cowlThing(tptp_fun_W_3(Z)) ) )
& ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
& rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
& cowlThing(tptp_fun_Z_4(X)) ) ),
inference(modus_ponens,[status(thm)],[47,40]) ).
tff(49,plain,
! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ! [W: $i] :
( cc(W)
| ~ rr(Z,W) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ),
inference(modus_ponens,[status(thm)],[48,38]) ).
tff(50,plain,
! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ ! [Z: $i,W: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| cc(W)
| ~ rr(Z,W) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X)) ) ),
inference(modus_ponens,[status(thm)],[49,36]) ).
tff(51,plain,
! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(X),Z) ) ) ),
inference(modus_ponens,[status(thm)],[50,31]) ).
tff(52,plain,
( ( ~ ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(X),Z) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_28752)
| ~ ( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) ) ) )
<=> ( ~ ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(X),Z) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_28752)
| ~ ( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(X),Z) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_28752)
| ~ ( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [X: $i] :
( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ rp(tptp_fun_Y_0(X),tptp_fun_Z_1(X))
| ~ cowlThing(tptp_fun_Z_1(X))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(X),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(X),tptp_fun_Z_4(X))
| ~ cowlThing(tptp_fun_Z_4(X))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(X),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(X),Z) ) ) )
| ~ cUnsatisfiable(i2003_11_14_17_19_28752)
| ~ ( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) ) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
~ ( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) ) ),
inference(unit_resolution,[status(thm)],[54,51,29]) ).
tff(56,plain,
( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(57,plain,
! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)),
inference(unit_resolution,[status(thm)],[58,55]) ).
tff(60,plain,
( ( ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ( ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) )
<=> ( ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ( ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ( ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
( ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ( ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ ( ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(unit_resolution,[status(thm)],[62,59,57]) ).
tff(64,plain,
( ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(tautology,[status(thm)],]) ).
tff(65,plain,
rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))),
inference(unit_resolution,[status(thm)],[64,63]) ).
tff(66,plain,
( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) ) ),
inference(tautology,[status(thm)],]) ).
tff(67,plain,
! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) ),
inference(unit_resolution,[status(thm)],[66,55]) ).
tff(68,plain,
( ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) )
<=> ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) )
<=> ( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) )
<=> ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) )
<=> ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))),
inference(unit_resolution,[status(thm)],[73,59,67,65]) ).
tff(75,plain,
( ~ ( ~ cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ~ cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(76,plain,
( ~ ( ~ cc(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) )
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ),
inference(unit_resolution,[status(thm)],[75,74]) ).
tff(77,plain,
! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ),
inference(unit_resolution,[status(thm)],[76,26]) ).
tff(78,plain,
^ [X: $i,Y: $i] :
refl(
( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(82,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
<=> rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
<=> rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ ( rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
<=> rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) )
| rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
( ~ ( rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
<=> rr(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752))) )
| rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752)) ),
inference(unit_resolution,[status(thm)],[87,65]) ).
tff(89,plain,
rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752)),
inference(unit_resolution,[status(thm)],[88,86]) ).
tff(90,plain,
( ( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) )
| ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) )
<=> ( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) )
| ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) )
| ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(92,plain,
( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) )
| ~ rinvR(tptp_fun_W_2(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ),
inference(modus_ponens,[status(thm)],[91,90]) ).
tff(93,plain,
! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ),
inference(unit_resolution,[status(thm)],[92,89,77]) ).
tff(94,plain,
^ [X: $i,Y: $i] :
refl(
( ( rinvP(X,Y)
<=> rp(Y,X) )
<=> ( rinvP(X,Y)
<=> rp(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,axiom,
! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(98,plain,
! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ),
inference(modus_ponens,[status(thm)],[97,96]) ).
tff(99,plain,
! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ),
inference(modus_ponens,[status(thm)],[99,95]) ).
tff(101,plain,
( ~ ! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) )
| ( rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
<=> rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
<=> rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) ),
inference(unit_resolution,[status(thm)],[101,100]) ).
tff(103,plain,
( ~ ( rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
<=> rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) )
| rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) ),
inference(tautology,[status(thm)],]) ).
tff(104,plain,
( ~ ( rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
<=> rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752)) )
| rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752)) ),
inference(unit_resolution,[status(thm)],[103,59]) ).
tff(105,plain,
rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752)),
inference(unit_resolution,[status(thm)],[104,102]) ).
tff(106,plain,
( ( ~ ! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) )
| ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) ) )
<=> ( ~ ! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) )
| ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(107,plain,
( ~ ! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) )
| ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
( ~ ! [Z: $i] :
( ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) )
| ~ rinvP(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) ),
inference(unit_resolution,[status(thm)],[108,105,93]) ).
tff(110,plain,
^ [X: $i,Y: $i] :
refl(
( ( rinvS(X,Y)
<=> rs(Y,X) )
<=> ( rinvS(X,Y)
<=> rs(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(111,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)],[110]) ).
tff(112,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(113,axiom,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(114,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(skolemize,[status(sab)],[114]) ).
tff(116,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[115,111]) ).
tff(117,plain,
( ~ ! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) )
| ( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752)
<=> rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752)
<=> rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ),
inference(unit_resolution,[status(thm)],[117,116]) ).
tff(119,plain,
( ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rr(Z,tptp_fun_W_2(Z))
| ~ cowlThing(tptp_fun_W_2(Z)) ) )
| ~ ! [Z: $i] :
( ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z)
| ~ ( ~ rp(Z,tptp_fun_W_3(Z))
| ~ cowlThing(tptp_fun_W_3(Z)) ) )
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ),
inference(tautology,[status(thm)],]) ).
tff(120,plain,
rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)),
inference(unit_resolution,[status(thm)],[119,55]) ).
tff(121,plain,
( ~ ( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752)
<=> rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752)
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ),
inference(tautology,[status(thm)],]) ).
tff(122,plain,
( ~ ( rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752)
<=> rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) )
| rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752) ),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752),
inference(unit_resolution,[status(thm)],[122,118]) ).
tff(124,plain,
^ [X: $i] :
refl(
( ( ca(X)
| ~ cUnsatisfiable(X) )
<=> ( ca(X)
| ~ cUnsatisfiable(X) ) )),
inference(bind,[status(th)],]) ).
tff(125,plain,
( ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) )
<=> ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
( ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) )
<=> ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(127,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
=> ca(X) )
<=> ( ca(X)
| ~ cUnsatisfiable(X) ) )),
inference(bind,[status(th)],]) ).
tff(128,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
=> ca(X) )
<=> ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[127]) ).
tff(129,axiom,
! [X: $i] :
( cUnsatisfiable(X)
=> ca(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(130,plain,
! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[130,126]) ).
tff(132,plain,
! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(skolemize,[status(sab)],[131]) ).
tff(133,plain,
! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[132,125]) ).
tff(134,plain,
( ( ~ ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) )
| ca(i2003_11_14_17_19_28752)
| ~ cUnsatisfiable(i2003_11_14_17_19_28752) )
<=> ( ~ ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) )
| ca(i2003_11_14_17_19_28752)
| ~ cUnsatisfiable(i2003_11_14_17_19_28752) ) ),
inference(rewrite,[status(thm)],]) ).
tff(135,plain,
( ~ ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) )
| ca(i2003_11_14_17_19_28752)
| ~ cUnsatisfiable(i2003_11_14_17_19_28752) ),
inference(quant_inst,[status(thm)],]) ).
tff(136,plain,
( ~ ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) )
| ca(i2003_11_14_17_19_28752)
| ~ cUnsatisfiable(i2003_11_14_17_19_28752) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
ca(i2003_11_14_17_19_28752),
inference(unit_resolution,[status(thm)],[136,133,29]) ).
tff(138,plain,
( ( ~ ! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) )
| ~ ca(i2003_11_14_17_19_28752)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752) )
<=> ( ~ ! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) )
| ~ ca(i2003_11_14_17_19_28752)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ~ ! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) )
| ~ ca(i2003_11_14_17_19_28752)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) )
| ~ ca(i2003_11_14_17_19_28752)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
$false,
inference(unit_resolution,[status(thm)],[140,137,123,109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : KRS082+1 : TPTP v8.1.0. Released v3.1.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Sep 1 09:27:34 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.13/0.39 % SZS status Unsatisfiable
% 0.13/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------