TSTP Solution File: KRS111+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS111+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:44:48 EDT 2022
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 79
% Syntax : Number of formulae : 177 ( 40 unt; 14 typ; 0 def)
% Number of atoms : 1637 ( 88 equ)
% Maximal formula atoms : 56 ( 10 avg)
% Number of connectives : 2730 (1359 ~;1037 |; 195 &)
% ( 127 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 103 ( 103 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 13 >; 4 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 561 ( 485 !; 35 ?; 561 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_4_type,type,
tptp_fun_Y0_4: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_21_15425_type,type,
i2003_11_14_17_21_15425: $i ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(rf1_type,type,
rf1: ( $i * $i ) > $o ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(cp_type,type,
cp: $i > $o ).
tff(rf_type,type,
rf: ( $i * $i ) > $o ).
tff(cowlThing_type,type,
cowlThing: $i > $o ).
tff(cpxcomp_type,type,
cpxcomp: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) ) )),
trans(
monotonicity(
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rf1(X,Y)
& cpxcomp(Y) )
<=> ~ ( ~ cpxcomp(Y)
| ~ rf1(X,Y) ) )),
( ~ ( rf1(X,Y)
& cpxcomp(Y) )
<=> ~ ~ ( ~ cpxcomp(Y)
| ~ rf1(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
<=> ( ~ cpxcomp(Y)
| ~ rf1(X,Y) ) )),
( ~ ( rf1(X,Y)
& cpxcomp(Y) )
<=> ( ~ cpxcomp(Y)
| ~ rf1(X,Y) ) ))),
( ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
<=> ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rs(X,Y)
& cowlThing(Y) )
<=> ~ ( ~ rs(X,Y)
| ~ cowlThing(Y) ) )),
( ~ ( rs(X,Y)
& cowlThing(Y) )
<=> ~ ~ ( ~ rs(X,Y)
| ~ cowlThing(Y) ) )),
rewrite(
( ~ ~ ( ~ rs(X,Y)
| ~ cowlThing(Y) )
<=> ( ~ rs(X,Y)
| ~ cowlThing(Y) ) )),
( ~ ( rs(X,Y)
& cowlThing(Y) )
<=> ( ~ rs(X,Y)
| ~ cowlThing(Y) ) ))),
( ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
<=> ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) ) )),
quant_intro(
proof_bind(
^ [Y: $i] :
trans(
monotonicity(
rewrite(
( ( rf(X,Y)
& cp(Y) )
<=> ~ ( ~ cp(Y)
| ~ rf(X,Y) ) )),
( ~ ( rf(X,Y)
& cp(Y) )
<=> ~ ~ ( ~ cp(Y)
| ~ rf(X,Y) ) )),
rewrite(
( ~ ~ ( ~ cp(Y)
| ~ rf(X,Y) )
<=> ( ~ cp(Y)
| ~ rf(X,Y) ) )),
( ~ ( rf(X,Y)
& cp(Y) )
<=> ( ~ cp(Y)
| ~ rf(X,Y) ) ))),
( ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) )
<=> ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(11,plain,
^ [X: $i] :
rewrite(
( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(14,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rf1(X,Y)
& cpxcomp(Y) )
& ? [Y: $i] :
( rs(X,Y)
& cowlThing(Y) )
& ? [Y: $i] :
( rf(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rf1(X,tptp_fun_Y_0(X))
& cpxcomp(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& cowlThing(tptp_fun_Y_1(X))
& rf(X,tptp_fun_Y_2(X))
& cp(tptp_fun_Y_2(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rf1(X,Y)
& cpxcomp(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& cowlThing(Y) )
| ! [Y: $i] :
~ ( rf(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[16,9]) ).
tff(18,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[17,7]) ).
tff(19,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[18,5]) ).
tff(20,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_15425,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_15425,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_15425,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_15425,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_15425,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_15425,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_15425,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_15425,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_15425,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rf1(X,tptp_fun_Y_0(X))
| ~ cpxcomp(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ cowlThing(tptp_fun_Y_1(X))
| ~ rf(X,tptp_fun_Y_2(X))
| ~ cp(tptp_fun_Y_2(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ cowlThing(Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(X,Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_15425,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_15425,Y) ) ) ),
inference(unit_resolution,[status(thm)],[25,19]) ).
tff(27,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_15425)
| ! [Y: $i] :
( ~ cpxcomp(Y)
| ~ rf1(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cp(Y)
| ~ rf(i2003_11_14_17_21_15425,Y) )
| ! [Y: $i] :
( ~ cowlThing(Y)
| ~ rs(i2003_11_14_17_21_15425,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) ),
inference(tautology,[status(thm)],]) ).
tff(28,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) ),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
( cUnsatisfiable(i2003_11_14_17_21_15425)
<=> cUnsatisfiable(i2003_11_14_17_21_15425) ),
inference(rewrite,[status(thm)],]) ).
tff(30,axiom,
cUnsatisfiable(i2003_11_14_17_21_15425),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
tff(31,plain,
cUnsatisfiable(i2003_11_14_17_21_15425),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) ),
inference(tautology,[status(thm)],]) ).
tff(33,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_15425)
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) )
| ~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ) ),
inference(unit_resolution,[status(thm)],[32,31]) ).
tff(34,plain,
~ ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ),
inference(unit_resolution,[status(thm)],[33,28]) ).
tff(35,plain,
( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(tautology,[status(thm)],]) ).
tff(36,plain,
rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rs(X,Y)
| rf1(X,Y) )
<=> ( ~ rs(X,Y)
| rf1(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rs(X,Y)
=> rf1(X,Y) )
<=> ( ~ rs(X,Y)
| rf1(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(41,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf1(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_13) ).
tff(43,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf1(X,Y) )
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)),
inference(unit_resolution,[status(thm)],[49,46,36]) ).
tff(51,plain,
( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425)) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425)),
inference(unit_resolution,[status(thm)],[51,34]) ).
tff(53,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
( ( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
<=> ( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( rf1(X,Y)
& rf1(X,Z) )
<=> ~ ( ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
( ~ ( rf1(X,Y)
& rf1(X,Z) )
<=> ~ ~ ( ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
rewrite(
( ~ ~ ( ~ rf1(X,Z)
| ~ rf1(X,Y) )
<=> ( ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
( ~ ( rf1(X,Y)
& rf1(X,Z) )
<=> ( ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
( ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf1(X,Z)
| ~ rf1(X,Y)
| ( Y = Z ) ) )),
rewrite(
( ( ~ rf1(X,Z)
| ~ rf1(X,Y)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
( ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf1(X,Y)
& rf1(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(61,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf1(X,Y)
& rf1(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) ),
inference(modus_ponens,[status(thm)],[64,54]) ).
tff(66,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(transitivity,[status(thm)],[68,66]) ).
tff(70,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf1(X,Z)
| ~ rf1(X,Y) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425) )
| ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425),
inference(unit_resolution,[status(thm)],[71,65,52,50]) ).
tff(73,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ rs(X,Y)
| rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
( ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(76,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( rs(X,Y)
=> rf(X,Y) )
<=> ( ~ rs(X,Y)
| rf(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,axiom,
! [X: $i,Y: $i] :
( rs(X,Y)
=> rf(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
tff(79,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[79,75]) ).
tff(81,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) ),
inference(modus_ponens,[status(thm)],[81,74]) ).
tff(83,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(84,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
( ~ ! [X: $i,Y: $i] :
( ~ rs(X,Y)
| rf(X,Y) )
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)),
inference(unit_resolution,[status(thm)],[85,82,36]) ).
tff(87,plain,
( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425)) ),
inference(tautology,[status(thm)],]) ).
tff(88,plain,
rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425)),
inference(unit_resolution,[status(thm)],[87,34]) ).
tff(89,plain,
^ [X: $i,Y: $i,Z: $i] :
refl(
( ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( rf(X,Y)
& rf(X,Z) )
<=> ~ ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ~ ~ ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
rewrite(
( ~ ~ ( ~ rf(X,Z)
| ~ rf(X,Y) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ~ ( rf(X,Y)
& rf(X,Z) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ~ rf(X,Z)
| ~ rf(X,Y)
| ( Y = Z ) ) )),
rewrite(
( ( ~ rf(X,Z)
| ~ rf(X,Y)
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
( ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( rf(X,Y)
& rf(X,Z) )
=> ( Y = Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
tff(97,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( rf(X,Y)
& rf(X,Z) )
| ( Y = Z ) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) ),
inference(modus_ponens,[status(thm)],[100,90]) ).
tff(102,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ) ),
inference(transitivity,[status(thm)],[104,102]) ).
tff(106,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(quant_inst,[status(thm)],]) ).
tff(107,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( ( Y = Z )
| ~ rf(X,Z)
| ~ rf(X,Y) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ( tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425) )
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425)) ),
inference(modus_ponens,[status(thm)],[106,105]) ).
tff(108,plain,
tptp_fun_Y_1(i2003_11_14_17_21_15425) = tptp_fun_Y_2(i2003_11_14_17_21_15425),
inference(unit_resolution,[status(thm)],[107,101,88,86]) ).
tff(109,plain,
tptp_fun_Y_2(i2003_11_14_17_21_15425) = tptp_fun_Y_1(i2003_11_14_17_21_15425),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
tptp_fun_Y_2(i2003_11_14_17_21_15425) = tptp_fun_Y_0(i2003_11_14_17_21_15425),
inference(transitivity,[status(thm)],[109,72]) ).
tff(111,plain,
( ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425)))
<=> ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) ),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
( ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425)))
<=> ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) ),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[116,114]) ).
tff(118,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
tff(122,plain,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[123,119]) ).
tff(125,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[124,117]) ).
tff(126,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_4(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),Y0) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
~ ( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),Y0) ) ),
inference(unit_resolution,[status(thm)],[126,125]) ).
tff(128,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),Y0) )
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) ),
inference(tautology,[status(thm)],]) ).
tff(129,plain,
( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) ),
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425)) ),
inference(tautology,[status(thm)],]) ).
tff(131,plain,
cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425)),
inference(unit_resolution,[status(thm)],[130,34]) ).
tff(132,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) )
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) ),
inference(tautology,[status(thm)],]) ).
tff(133,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) )
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) ),
inference(unit_resolution,[status(thm)],[132,131]) ).
tff(134,plain,
ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))),
inference(unit_resolution,[status(thm)],[133,129]) ).
tff(135,plain,
ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))),
inference(modus_ponens,[status(thm)],[134,112]) ).
tff(136,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(137,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(139,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(141,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) ),
inference(quant_intro,[status(thm)],[140]) ).
tff(142,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) ),
inference(transitivity,[status(thm)],[141,139]) ).
tff(143,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
<=> ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )),
( ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
rewrite(
( ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
( ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(144,plain,
( ! [X: $i] :
( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ) ),
inference(quant_intro,[status(thm)],[143]) ).
tff(145,plain,
( ! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,axiom,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(147,plain,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [X: $i] :
( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ),
inference(skolemize,[status(sab)],[147]) ).
tff(149,plain,
! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ),
inference(modus_ponens,[status(thm)],[148,144]) ).
tff(150,plain,
! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) ) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[150,137]) ).
tff(152,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_3(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),tptp_fun_Y_3(tptp_fun_Y_2(i2003_11_14_17_21_15425))) )
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
~ ( ~ ( cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),tptp_fun_Y_3(tptp_fun_Y_2(i2003_11_14_17_21_15425))) )
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) ) ),
inference(unit_resolution,[status(thm)],[152,151]) ).
tff(154,plain,
( ~ ( cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),tptp_fun_Y_3(tptp_fun_Y_2(i2003_11_14_17_21_15425))) )
| ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) )
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) ),
inference(tautology,[status(thm)],]) ).
tff(155,plain,
( ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) ),
inference(unit_resolution,[status(thm)],[154,153]) ).
tff(156,plain,
( ~ rf1(i2003_11_14_17_21_15425,tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_15425))
| ~ rs(i2003_11_14_17_21_15425,tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ cowlThing(tptp_fun_Y_1(i2003_11_14_17_21_15425))
| ~ rf(i2003_11_14_17_21_15425,tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)) ),
inference(tautology,[status(thm)],]) ).
tff(157,plain,
cp(tptp_fun_Y_2(i2003_11_14_17_21_15425)),
inference(unit_resolution,[status(thm)],[156,34]) ).
tff(158,plain,
( ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) )
| ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) ),
inference(tautology,[status(thm)],]) ).
tff(159,plain,
( ~ ( ~ cp(tptp_fun_Y_2(i2003_11_14_17_21_15425))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y) ),
inference(unit_resolution,[status(thm)],[158,157]) ).
tff(160,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y),
inference(unit_resolution,[status(thm)],[159,155]) ).
tff(161,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),Y)
| ~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))) ),
inference(quant_inst,[status(thm)],]) ).
tff(162,plain,
~ ra_Px1(tptp_fun_Y_2(i2003_11_14_17_21_15425),tptp_fun_Y0_4(tptp_fun_Y_0(i2003_11_14_17_21_15425))),
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
$false,
inference(unit_resolution,[status(thm)],[162,135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS111+1 : TPTP v8.1.0. Released v3.1.0.
% 0.12/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 09:30:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.20/0.34 Usage: tptp [options] [-file:]file
% 0.20/0.34 -h, -? prints this message.
% 0.20/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.20/0.34 -m, -model generate model.
% 0.20/0.34 -p, -proof generate proof.
% 0.20/0.34 -c, -core generate unsat core of named formulas.
% 0.20/0.34 -st, -statistics display statistics.
% 0.20/0.34 -t:timeout set timeout (in second).
% 0.20/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.20/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.20/0.34 -<param>:<value> configuration parameter and value.
% 0.20/0.34 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------