%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS092+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:13:21 AM UTC 2025
% Result : Unsatisfiable 0.15s 0.40s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 27
% Syntax : Number of formulae : 63 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 904 ( 0 equ)
% Maximal formula atoms : 48 ( 14 avg)
% Number of connectives : 1905 (1097 ~; 660 |; 95 &)
% ( 47 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 33 ( 33 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 201 ( 183 !; 9 ?; 201 :)
% Comments :
%------------------------------------------------------------------------------
tff(cc_type,type,
cc: $i > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_20_04172_type,type,
i2003_11_14_17_20_04172: $i ).
tff(cd_type,type,
cd: $i > $o ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(1,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rr(X,Y)
& cowlThing(Y) )
<=> ~ ( ~ rr(X,Y)
| ~ cowlThing(Y) ) )),
( ~ ( rr(X,Y)
& cowlThing(Y) )
<=> ~ ~ ( ~ rr(X,Y)
| ~ cowlThing(Y) ) )),
rewrite(( ~ ~ ( ~ rr(X,Y)
| ~ cowlThing(Y) )
<=> ( ~ rr(X,Y)
| ~ cowlThing(Y) ) )),
( ~ ( rr(X,Y)
& cowlThing(Y) )
<=> ( ~ rr(X,Y)
| ~ cowlThing(Y) ) ))),
( ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
<=> ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) )),
rewrite(( ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) )
<=> ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ( cd(Y)
& cc(Y) ) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ( cd(Y)
& cc(Y) ) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( rr(X,Y)
=> ( cd(Y)
& cc(Y) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(16,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& cowlThing(Y) )
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& cowlThing(tptp_fun_Y_0(X))
& ! [Y: $i] :
( ~ rr(X,Y)
| ( cd(Y)
& cc(Y) ) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ( cd(tptp_fun_Y_1(X))
& cc(tptp_fun_Y_1(X)) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) )
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rr(i2003_11_14_17_20_04172,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rr(i2003_11_14_17_20_04172,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ cowlThing(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rr(i2003_11_14_17_20_04172,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ cowlThing(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rr(i2003_11_14_17_20_04172,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ cowlThing(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rr(i2003_11_14_17_20_04172,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ cowlThing(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ cowlThing(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( ~ rr(X,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_1(X))
| ~ ( ~ cd(tptp_fun_Y_1(X))
| ~ cc(tptp_fun_Y_1(X)) ) )
| ! [Y: $i] :
( ~ rr(X,Y)
| ~ cowlThing(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rr(i2003_11_14_17_20_04172,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rr(i2003_11_14_17_20_04172,Y) ) ) ),
inference(unit_resolution,[status(thm)],[28,22]) ).
tff(30,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ ( ~ cc(tptp_fun_Y_1(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_1(i2003_11_14_17_20_04172)) ) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rr(i2003_11_14_17_20_04172,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(31,plain,
( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) ),
inference(unit_resolution,[status(thm)],[30,29]) ).
tff(32,plain,
( cUnsatisfiable(i2003_11_14_17_20_04172)
<=> cUnsatisfiable(i2003_11_14_17_20_04172) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
cUnsatisfiable(i2003_11_14_17_20_04172),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
tff(34,plain,
cUnsatisfiable(i2003_11_14_17_20_04172),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_20_04172)
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
| ~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
~ ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ),
inference(unit_resolution,[status(thm)],[36,31]) ).
tff(38,plain,
( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)) ),
inference(tautology,[status(thm)],[]) ).
tff(39,plain,
rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172)),
inference(unit_resolution,[status(thm)],[38,37]) ).
tff(40,plain,
( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ cowlThing(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(41,plain,
! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) ),
inference(unit_resolution,[status(thm)],[40,37]) ).
tff(42,plain,
( ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) )
<=> ( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Y: $i] :
( ~ rr(i2003_11_14_17_20_04172,Y)
| ~ ( ~ cd(Y)
| ~ cc(Y) ) )
| ~ rr(i2003_11_14_17_20_04172,tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
~ ( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ),
inference(unit_resolution,[status(thm)],[44,41,39]) ).
tff(46,plain,
( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| cc(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ),
inference(tautology,[status(thm)],[]) ).
tff(47,plain,
cc(tptp_fun_Y_0(i2003_11_14_17_20_04172)),
inference(unit_resolution,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| cd(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ),
inference(tautology,[status(thm)],[]) ).
tff(49,plain,
cd(tptp_fun_Y_0(i2003_11_14_17_20_04172)),
inference(unit_resolution,[status(thm)],[48,45]) ).
tff(50,plain,
^ [X: $i] :
refl(( ( ~ cc(X)
| ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
( ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
^ [X: $i] :
rewrite(( ( cc(X)
=> ~ cd(X) )
<=> ( ~ cc(X)
| ~ cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [X: $i] :
( cc(X)
=> ~ cd(X) )
<=> ! [X: $i] :
( ~ cc(X)
| ~ cd(X) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,axiom,
! [X: $i] :
( cc(X)
=> ~ cd(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(56,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[56,52]) ).
tff(58,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [X: $i] :
( ~ cc(X)
| ~ cd(X) ),
inference(modus_ponens,[status(thm)],[58,51]) ).
tff(60,plain,
( ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172)) )
<=> ( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
( ~ ! [X: $i] :
( ~ cc(X)
| ~ cd(X) )
| ~ cc(tptp_fun_Y_0(i2003_11_14_17_20_04172))
| ~ cd(tptp_fun_Y_0(i2003_11_14_17_20_04172)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
$false,
inference(unit_resolution,[status(thm)],[62,59,49,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : KRS092+1 : TPTP v9.0.0. Released v3.1.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n016.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Jun 19 19:11:17 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.15/0.40 % SZS status Unsatisfiable
% 0.15/0.40 % SZS output start Proof
% See solution above
% 0.23/0.41 % E exiting
%------------------------------------------------------------------------------