%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS082+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n006.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 05:13:20 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 75
% Syntax : Number of formulae : 176 ( 32 unt; 0 typ; 0 def)
% Number of atoms : 2687 ( 0 equ)
% Maximal formula atoms : 68 ( 15 avg)
% Number of connectives : 4591 (2187 ~;1657 |; 487 &)
% ( 166 <=>; 94 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 107 ( 107 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 1116 ( 921 !; 163 ?;1116 :)
% 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_W_3_type,type,
tptp_fun_W_3: $i > $i ).
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_Z_6_type,type,
tptp_fun_Z_6: $i > $i ).
tff(tptp_fun_Y_5_type,type,
tptp_fun_Y_5: $i > $i ).
tff(tptp_fun_W_7_type,type,
tptp_fun_W_7: $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(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(tptp_fun_Z_4_type,type,
tptp_fun_Z_4: $i > $i ).
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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) )
<=> ( ~ ! [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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) )
<=> ( ~ ! [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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) )
<=> ( ~ ! [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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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(28,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),Y)
| ! [Z: $i] :
( ~ rinvP(Y,Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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)],[28,22]) ).
tff(30,plain,
( ~ ( cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ ( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvS(tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ ca(tptp_fun_W_7(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))))
| ~ rinvP(tptp_fun_Y_5(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),tptp_fun_Z_6(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))) ) )
| ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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(31,plain,
( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_19_28752)
<=> cUnsatisfiable(i2003_11_14_17_19_28752) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_19_28752),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_19_28752),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,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(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,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)],[35]) ).
tff(37,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(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,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)],[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,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(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,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)],[39]) ).
tff(41,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)],[40,38]) ).
tff(42,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(43,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)],[42]) ).
tff(44,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(45,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)],[44]) ).
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) ) ) )
<=> ! [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(47,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(48,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)],[47]) ).
tff(49,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(50,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)],[49,48]) ).
tff(51,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)],[50,46]) ).
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] :
( 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)],[51]) ).
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] :
( 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)],[52,45]) ).
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] :
( 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)],[53,43]) ).
tff(55,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)],[54,41]) ).
tff(56,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)],[55,36]) ).
tff(57,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)
| ~ ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ) )
<=> ( ~ ! [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)
| ~ ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ 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) ) ) )
<=> ( ~ cUnsatisfiable(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) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,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)
| ~ ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ) ) ),
inference(monotonicity,[status(thm)],[58]) ).
tff(60,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)
| ~ ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ) ) ),
inference(transitivity,[status(thm)],[59,57]) ).
tff(61,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(62,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)
| ~ ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
~ ( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)) ),
inference(unit_resolution,[status(thm)],[62,56,34]) ).
tff(64,plain,
( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ 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)) ),
inference(tautology,[status(thm)],[]) ).
tff(65,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)],[64,63]) ).
tff(66,plain,
( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752))
| ! [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)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(67,plain,
! [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)) ) ),
inference(unit_resolution,[status(thm)],[66,63]) ).
tff(68,plain,
( ( ~ ! [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)) ) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ( ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) )
<=> ( ~ ! [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)) ) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ( ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ~ ! [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)) ) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ( ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(70,plain,
( ~ ! [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)) ) )
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_1(i2003_11_14_17_19_28752))
| ~ ( ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
~ ( ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(unit_resolution,[status(thm)],[70,67,65]) ).
tff(72,plain,
( ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ cowlThing(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(tautology,[status(thm)],[]) ).
tff(73,plain,
rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
( ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( rp(X,Y)
& rp(Y,Z) )
<=> ~ ( ~ rp(Y,Z)
| ~ rp(X,Y) ) )),
( ~ ( rp(X,Y)
& rp(Y,Z) )
<=> ~ ~ ( ~ rp(Y,Z)
| ~ rp(X,Y) ) )),
rewrite(( ~ ~ ( ~ rp(Y,Z)
| ~ rp(X,Y) )
<=> ( ~ rp(Y,Z)
| ~ rp(X,Y) ) )),
( ~ ( rp(X,Y)
& rp(Y,Z) )
<=> ( ~ rp(Y,Z)
| ~ rp(X,Y) ) )),
( ( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) )
<=> ( ~ rp(Y,Z)
| ~ rp(X,Y)
| rp(X,Z) ) )),
rewrite(( ( ~ rp(Y,Z)
| ~ rp(X,Y)
| rp(X,Z) )
<=> ( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) ) )),
( ( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) )
<=> ( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(76,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(78,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(( ( ( rp(X,Y)
& rp(Y,Z) )
=> rp(X,Z) )
<=> ( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(79,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rp(X,Y)
& rp(Y,Z) )
=> rp(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rp(X,Y)
& rp(Y,Z) )
=> rp(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(81,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rp(X,Y)
& rp(Y,Z) )
| rp(X,Z) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
| ~ 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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
| ~ 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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
( ( rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(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))
| rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(88,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
| rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(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)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
| ~ 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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
| rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(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)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
| ~ 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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(transitivity,[status(thm)],[88,86]) ).
tff(90,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
| rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(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(91,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( rp(X,Z)
| ~ rp(Y,Z)
| ~ rp(X,Y) )
| ~ 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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rp(tptp_fun_Z_1(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),
inference(unit_resolution,[status(thm)],[91,85,65,73]) ).
tff(93,plain,
( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(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)) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(94,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)],[93,63]) ).
tff(95,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ ( ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ ( ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ ( ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ ( ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
~ ( ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ),
inference(unit_resolution,[status(thm)],[97,94,92]) ).
tff(99,plain,
( ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ cowlThing(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ),
inference(tautology,[status(thm)],[]) ).
tff(100,plain,
rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),
inference(unit_resolution,[status(thm)],[99,98]) ).
tff(101,plain,
( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(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) ) ),
inference(tautology,[status(thm)],[]) ).
tff(102,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)],[101,63]) ).
tff(103,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(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) )
| cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(104,plain,
( ( cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) )
<=> ( cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(105,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(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) )
| cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) ),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(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) )
| cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) ),
inference(transitivity,[status(thm)],[105,103]) ).
tff(107,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))),
inference(unit_resolution,[status(thm)],[108,102,92,100]) ).
tff(110,plain,
( ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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(111,plain,
( ~ ( ~ cc(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))))
| ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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_W_3(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)],[110,109]) ).
tff(112,plain,
! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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)],[111,31]) ).
tff(113,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(114,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)],[113]) ).
tff(115,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(116,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_6) ).
tff(117,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[117]) ).
tff(119,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[118,114]) ).
tff(120,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
<=> rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(121,plain,
( rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
<=> rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ),
inference(unit_resolution,[status(thm)],[120,119]) ).
tff(122,plain,
( ~ ( rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
<=> rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) )
| rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ~ rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) ),
inference(tautology,[status(thm)],[]) ).
tff(123,plain,
( ~ ( rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
<=> rr(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))) )
| rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(unit_resolution,[status(thm)],[122,100]) ).
tff(124,plain,
rinvR(tptp_fun_W_2(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),
inference(unit_resolution,[status(thm)],[123,121]) ).
tff(125,plain,
( ( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Z: $i] :
( ~ rinvP(tptp_fun_W_3(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_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Z: $i] :
( ~ rinvP(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Z: $i] :
( ~ rinvP(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
( ~ ! [Y: $i] :
( ~ rinvR(tptp_fun_W_2(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))),tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)))
| ! [Z: $i] :
( ~ rinvP(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [Z: $i] :
( ~ rinvP(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) ),
inference(unit_resolution,[status(thm)],[127,124,112]) ).
tff(129,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvP(X,Y)
<=> rp(Y,X) )
<=> ( rinvP(X,Y)
<=> rp(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(130,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)],[129]) ).
tff(131,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(132,axiom,
! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_5) ).
tff(133,plain,
! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
( ~ ! [X: $i,Y: $i] :
( rinvP(X,Y)
<=> rp(Y,X) )
| ( rinvP(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
( rinvP(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ ( rinvP(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) )
| rinvP(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) ),
inference(tautology,[status(thm)],[]) ).
tff(139,plain,
( ~ ( rinvP(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752))) )
| rinvP(tptp_fun_W_3(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)],[138,92]) ).
tff(140,plain,
rinvP(tptp_fun_W_3(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)],[139,137]) ).
tff(141,plain,
( ( ~ ! [Z: $i] :
( ~ rinvP(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) )
| ~ rinvP(tptp_fun_W_3(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_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) )
| ~ rinvP(tptp_fun_W_3(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(142,plain,
( ~ ! [Z: $i] :
( ~ rinvP(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) )
| ~ rinvP(tptp_fun_W_3(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(143,plain,
( ~ ! [Z: $i] :
( ~ rinvP(tptp_fun_W_3(tptp_fun_Z_1(i2003_11_14_17_19_28752)),Z)
| ! [W: $i] :
( ~ ca(W)
| ~ rinvS(Z,W) ) )
| ~ rinvP(tptp_fun_W_3(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)],[142,141]) ).
tff(144,plain,
! [W: $i] :
( ~ ca(W)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),W) ),
inference(unit_resolution,[status(thm)],[143,140,128]) ).
tff(145,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvS(X,Y)
<=> rs(Y,X) )
<=> ( rinvS(X,Y)
<=> rs(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(146,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)],[145]) ).
tff(147,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(148,axiom,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(149,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(skolemize,[status(sab)],[149]) ).
tff(151,plain,
! [X: $i,Y: $i] :
( rinvS(X,Y)
<=> rs(Y,X) ),
inference(modus_ponens,[status(thm)],[150,146]) ).
tff(152,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(153,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)],[152,151]) ).
tff(154,plain,
( ~ ! [Z: $i,W: $i] :
( cc(W)
| ~ rr(Z,W)
| ~ rp(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ ! [Z: $i] :
( cc(Z)
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),Z) )
| ~ cowlThing(tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ rr(tptp_fun_Y_0(i2003_11_14_17_19_28752),tptp_fun_Z_4(i2003_11_14_17_19_28752))
| ~ ! [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)) ) )
| ~ ! [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)) ) )
| ~ cowlThing(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))
| ~ rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(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(155,plain,
rs(i2003_11_14_17_19_28752,tptp_fun_Y_0(i2003_11_14_17_19_28752)),
inference(unit_resolution,[status(thm)],[154,63]) ).
tff(156,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(157,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)],[156,155]) ).
tff(158,plain,
rinvS(tptp_fun_Y_0(i2003_11_14_17_19_28752),i2003_11_14_17_19_28752),
inference(unit_resolution,[status(thm)],[157,153]) ).
tff(159,plain,
^ [X: $i] :
refl(( ( ca(X)
| ~ cUnsatisfiable(X) )
<=> ( ca(X)
| ~ cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) )
<=> ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,plain,
( ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) )
<=> ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(162,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
=> ca(X) )
<=> ( ca(X)
| ~ cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(163,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
=> ca(X) )
<=> ! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[162]) ).
tff(164,axiom,
! [X: $i] :
( cUnsatisfiable(X)
=> ca(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(165,plain,
! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[164,163]) ).
tff(166,plain,
! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(skolemize,[status(sab)],[166]) ).
tff(168,plain,
! [X: $i] :
( ca(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[167,160]) ).
tff(169,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(170,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(171,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)],[170,169]) ).
tff(172,plain,
ca(i2003_11_14_17_19_28752),
inference(unit_resolution,[status(thm)],[171,168,34]) ).
tff(173,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(174,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(175,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)],[174,173]) ).
tff(176,plain,
$false,
inference(unit_resolution,[status(thm)],[175,172,158,144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KRS082+1 : TPTP v9.0.0. Released v3.1.0.
% 0.10/0.11 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n006.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:10:20 EDT 2025
% 0.11/0.32 % CPUTime :
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41 % SZS output start Proof
% See solution above
% 0.19/0.46 % E exiting
%------------------------------------------------------------------------------