TSTP Solution File: KRS114+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KRS114+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 17:44:49 EDT 2022
% Result : Unsatisfiable 0.06s 0.28s
% Output : Proof 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 95
% Syntax : Number of formulae : 206 ( 40 unt; 20 typ; 0 def)
% Number of atoms : 1822 ( 114 equ)
% Maximal formula atoms : 40 ( 9 avg)
% Number of connectives : 3247 (1669 ~;1232 |; 186 &)
% ( 154 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 58 ( 58 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 19 >; 4 *; 0 +; 0 <<)
% Number of predicates : 18 ( 16 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-1 aty)
% Number of variables : 564 ( 514 !; 25 ?; 564 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(i2003_11_14_17_21_262_type,type,
i2003_11_14_17_21_262: $i ).
tff(cp_type,type,
cp: $i > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(tptp_fun_Y_6_type,type,
tptp_fun_Y_6: $i > $i ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(rinvR_type,type,
rinvR: ( $i * $i ) > $o ).
tff(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(ca_Ax3_type,type,
ca_Ax3: $i > $o ).
tff(ca_Ax4_type,type,
ca_Ax4: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(ca_Vx5_type,type,
ca_Vx5: $i > $o ).
tff(tptp_fun_Y1_7_type,type,
tptp_fun_Y1_7: $i > $i ).
tff(tptp_fun_Y0_8_type,type,
tptp_fun_Y0_8: $i > $i ).
tff(tptp_fun_Y_9_type,type,
tptp_fun_Y_9: $i > $i ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
tff(cpxcomp_type,type,
cpxcomp: $i > $o ).
tff(cqxcomp_type,type,
cqxcomp: $i > $o ).
tff(1,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,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_2(X)) ) )
<=> ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
rewrite(
( ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
( ( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [X: $i] :
( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,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(11,axiom,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(12,plain,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X: $i] :
( ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
& ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ),
inference(skolemize,[status(sab)],[12]) ).
tff(14,plain,
! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i] :
~ ( ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) )
| ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) ) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[15,2]) ).
tff(17,plain,
( ~ ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ~ cp(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_262))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
~ ( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_262))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) ) ),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ~ ( cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y_2(tptp_fun_Y_1(i2003_11_14_17_21_262))) )
| ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) ),
inference(tautology,[status(thm)],]) ).
tff(20,plain,
( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) ),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
^ [X: $i,Y: $i] :
refl(
( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
<=> ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
tff(25,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) )
| ( rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
<=> rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
( rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
<=> rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)) ),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) ),
inference(transitivity,[status(thm)],[33,31]) ).
tff(35,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) ) )),
rewrite(
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) )),
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(36,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[35]) ).
tff(37,plain,
^ [X: $i] :
rewrite(
( ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ca_Ax4(Y) )
& ? [Y: $i] :
( rs(X,Y)
& ca_Ax3(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ca_Ax4(Y) )
& ? [Y: $i] :
( rs(X,Y)
& ca_Ax3(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ca_Ax4(Y) )
& ? [Y: $i] :
( rs(X,Y)
& ca_Ax3(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(41,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rr(X,Y)
& ca_Ax4(Y) )
& ? [Y: $i] :
( rs(X,Y)
& ca_Ax3(Y) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rr(X,tptp_fun_Y_0(X))
& ca_Ax4(tptp_fun_Y_0(X))
& rs(X,tptp_fun_Y_1(X))
& ca_Ax3(tptp_fun_Y_1(X)) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rr(X,Y)
& ca_Ax4(Y) )
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax3(Y) ) ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) ),
inference(modus_ponens,[status(thm)],[44,34]) ).
tff(46,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ ca_Ax3(Y)
| ~ rs(i2003_11_14_17_21_262,Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ ca_Ax3(Y)
| ~ rs(i2003_11_14_17_21_262,Y) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(47,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_262,Y)
| ~ ca_Ax3(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ ca_Ax3(Y)
| ~ rs(i2003_11_14_17_21_262,Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_262,Y)
| ~ ca_Ax3(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ ca_Ax3(Y)
| ~ rs(i2003_11_14_17_21_262,Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_262,Y)
| ~ ca_Ax3(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ ca_Ax3(Y)
| ~ rs(i2003_11_14_17_21_262,Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_262,Y)
| ~ ca_Ax3(Y) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(51,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rr(X,tptp_fun_Y_0(X))
| ~ ca_Ax4(tptp_fun_Y_0(X))
| ~ rs(X,tptp_fun_Y_1(X))
| ~ ca_Ax3(tptp_fun_Y_1(X)) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(X,Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ ca_Ax3(Y)
| ~ rs(i2003_11_14_17_21_262,Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ ca_Ax3(Y)
| ~ rs(i2003_11_14_17_21_262,Y) ) ) ),
inference(unit_resolution,[status(thm)],[51,45]) ).
tff(53,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_262)
| ! [Y: $i] :
( ~ ca_Ax4(Y)
| ~ rr(i2003_11_14_17_21_262,Y) )
| ! [Y: $i] :
( ~ ca_Ax3(Y)
| ~ rs(i2003_11_14_17_21_262,Y) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ),
inference(tautology,[status(thm)],]) ).
tff(54,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( cUnsatisfiable(i2003_11_14_17_21_262)
<=> cUnsatisfiable(i2003_11_14_17_21_262) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
cUnsatisfiable(i2003_11_14_17_21_262),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(57,plain,
cUnsatisfiable(i2003_11_14_17_21_262),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_262)
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
~ ( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(unit_resolution,[status(thm)],[59,54]) ).
tff(61,plain,
( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
| rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)) ),
inference(tautology,[status(thm)],]) ).
tff(62,plain,
rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
( ~ ( rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
<=> rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)) )
| rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)) ),
inference(tautology,[status(thm)],]) ).
tff(64,plain,
( ~ ( rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
<=> rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)) )
| rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262) ),
inference(unit_resolution,[status(thm)],[63,62]) ).
tff(65,plain,
rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262),
inference(unit_resolution,[status(thm)],[64,29]) ).
tff(66,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )
<=> ~ ( ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) )
| ~ ( ~ ca_Ax4(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(67,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) )
| ~ ( ~ ca_Ax4(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[66]) ).
tff(68,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(69,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[68]) ).
tff(70,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(71,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[70]) ).
tff(72,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) ),
inference(transitivity,[status(thm)],[71,69]) ).
tff(73,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
<=> ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) ) )),
rewrite(
( ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) )
<=> ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )),
( ( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) )
<=> ( ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) )),
rewrite(
( ( ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) )),
( ( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(74,plain,
( ! [X: $i] :
( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[73]) ).
tff(75,plain,
^ [X: $i] :
rewrite(
( ( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) )
<=> ( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(76,plain,
( ! [X: $i] :
( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[75]) ).
tff(77,plain,
( ! [X: $i] :
( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) )
<=> ! [X: $i] :
( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(78,plain,
^ [X: $i] :
rewrite(
( ( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rinvR(X,Y0)
& rinvR(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) )
<=> ( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X: $i] :
( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rinvR(X,Y0)
& rinvR(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) )
<=> ! [X: $i] :
( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,axiom,
! [X: $i] :
( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ( rinvR(X,Y0)
& rinvR(X,Y1) )
=> ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(81,plain,
! [X: $i] :
( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [X: $i] :
( ca_Ax4(X)
<=> ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& ? [Y: $i] :
( rinvR(X,Y)
& ca_Vx5(Y) ) ) ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
! [X: $i] :
( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i] :
( ( ~ ca_Ax4(X)
| ( ! [Y0: $i,Y1: $i] :
( ~ ( rinvR(X,Y0)
& rinvR(X,Y1) )
| ( Y0 = Y1 ) )
& rinvR(X,tptp_fun_Y_6(X))
& ca_Vx5(tptp_fun_Y_6(X)) ) )
& ( ca_Ax4(X)
| ~ ( ~ ( rinvR(X,tptp_fun_Y0_8(X))
& rinvR(X,tptp_fun_Y1_7(X)) )
| ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) ) )
| ! [Y: $i] :
~ ( rinvR(X,Y)
& ca_Vx5(Y) ) ) ),
inference(modus_ponens,[status(thm)],[83,76]) ).
tff(85,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[84,74]) ).
tff(86,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) )
| ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X)) ) )
| ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[85,72]) ).
tff(87,plain,
! [X: $i] :
~ ( ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) )
| ~ ( ~ ca_Ax4(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) ) ) ) ),
inference(modus_ponens,[status(thm)],[86,67]) ).
tff(88,plain,
( ~ ! [X: $i] :
~ ( ~ ( ca_Ax4(X)
| ~ ( ( tptp_fun_Y0_8(X) = tptp_fun_Y1_7(X) )
| ~ rinvR(X,tptp_fun_Y0_8(X))
| ~ rinvR(X,tptp_fun_Y1_7(X)) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(X,Y) ) )
| ~ ( ~ ca_Ax4(X)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y1)
| ~ rinvR(X,Y0) ) ) ) )
| ~ ( ~ ( ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ( tptp_fun_Y0_8(tptp_fun_Y_0(i2003_11_14_17_21_262)) = tptp_fun_Y1_7(tptp_fun_Y_0(i2003_11_14_17_21_262)) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y0_8(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y1_7(tptp_fun_Y_0(i2003_11_14_17_21_262))) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y) ) )
| ~ ( ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
~ ( ~ ( ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ( tptp_fun_Y0_8(tptp_fun_Y_0(i2003_11_14_17_21_262)) = tptp_fun_Y1_7(tptp_fun_Y_0(i2003_11_14_17_21_262)) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y0_8(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y1_7(tptp_fun_Y_0(i2003_11_14_17_21_262))) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y) ) )
| ~ ( ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) ) ),
inference(unit_resolution,[status(thm)],[88,87]) ).
tff(90,plain,
( ~ ( ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ( tptp_fun_Y0_8(tptp_fun_Y_0(i2003_11_14_17_21_262)) = tptp_fun_Y1_7(tptp_fun_Y_0(i2003_11_14_17_21_262)) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y0_8(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y1_7(tptp_fun_Y_0(i2003_11_14_17_21_262))) )
| ! [Y: $i] :
( ~ ca_Vx5(Y)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y) ) )
| ~ ( ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) )
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(91,plain,
( ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) ),
inference(unit_resolution,[status(thm)],[90,89]) ).
tff(92,plain,
( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262)) ),
inference(tautology,[status(thm)],]) ).
tff(93,plain,
ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[92,60]) ).
tff(94,plain,
( ~ ( ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) )
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(95,plain,
( ~ ( ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) )
| ~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ) ),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
~ ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ),
inference(unit_resolution,[status(thm)],[95,91]) ).
tff(97,plain,
( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ) ),
inference(tautology,[status(thm)],]) ).
tff(98,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) ),
inference(unit_resolution,[status(thm)],[97,96]) ).
tff(99,plain,
( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))) ),
inference(tautology,[status(thm)],]) ).
tff(100,plain,
rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))),
inference(unit_resolution,[status(thm)],[99,96]) ).
tff(101,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ( ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))) )
<=> ( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262) ) ),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))) )
<=> ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262) ) ),
inference(transitivity,[status(thm)],[103,101]) ).
tff(105,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ( tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262,
inference(unit_resolution,[status(thm)],[106,100,98,65]) ).
tff(108,plain,
( rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_1(i2003_11_14_17_21_262))
<=> rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(monotonicity,[status(thm)],[107]) ).
tff(109,plain,
( rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
<=> rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
| rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(tautology,[status(thm)],]) ).
tff(111,plain,
rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[110,60]) ).
tff(112,plain,
rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(modus_ponens,[status(thm)],[111,109]) ).
tff(113,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(116,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) ),
inference(transitivity,[status(thm)],[116,114]) ).
tff(118,plain,
^ [X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
<=> ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) ) )),
( ( ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
& ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ( ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
& ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) )),
rewrite(
( ( ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
& ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) )),
( ( ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
& ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(119,plain,
( ! [X: $i] :
( ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
& ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,plain,
( ! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
<=> ! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(121,plain,
^ [X: $i] :
rewrite(
( ( ca_Vx5(X)
<=> ! [Y: $i] :
( rs(X,Y)
=> cp(Y) ) )
<=> ( ca_Vx5(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(122,plain,
( ! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( rs(X,Y)
=> cp(Y) ) )
<=> ! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,axiom,
! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( rs(X,Y)
=> cp(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(124,plain,
! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) ),
inference(modus_ponens,[status(thm)],[123,122]) ).
tff(125,plain,
! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) ),
inference(modus_ponens,[status(thm)],[124,120]) ).
tff(126,plain,
! [X: $i] :
( ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
& ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ),
inference(skolemize,[status(sab)],[125]) ).
tff(127,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ),
inference(modus_ponens,[status(thm)],[126,119]) ).
tff(128,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) ),
inference(modus_ponens,[status(thm)],[127,117]) ).
tff(129,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Vx5(X)
| ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) )
| ~ ( ca_Vx5(X)
| ~ ( cp(tptp_fun_Y_9(X))
| ~ rs(X,tptp_fun_Y_9(X)) ) ) )
| ~ ( ~ ( ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) )
| ~ ( ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ( cp(tptp_fun_Y_9(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))))
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_9(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
~ ( ~ ( ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) )
| ~ ( ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ( cp(tptp_fun_Y_9(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))))
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_9(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))) ) ) ),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
( ~ ( ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) )
| ~ ( ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ( cp(tptp_fun_Y_9(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))))
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_9(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))) ) )
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) ),
inference(tautology,[status(thm)],]) ).
tff(132,plain,
( ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) ),
inference(unit_resolution,[status(thm)],[131,130]) ).
tff(133,plain,
( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0) )
| ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))) ),
inference(tautology,[status(thm)],]) ).
tff(134,plain,
ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))),
inference(unit_resolution,[status(thm)],[133,96]) ).
tff(135,plain,
( ~ ( ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) )
| ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) ),
inference(tautology,[status(thm)],]) ).
tff(136,plain,
( ~ ( ~ ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)))
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) )
| ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ) ),
inference(unit_resolution,[status(thm)],[135,134]) ).
tff(137,plain,
! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) ),
inference(unit_resolution,[status(thm)],[136,132]) ).
tff(138,plain,
( ( ~ ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) )
| cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_1(i2003_11_14_17_21_262)) )
<=> ( ~ ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) )
| cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(139,plain,
( ~ ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) )
| cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [Y: $i] :
( cp(Y)
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),Y) )
| cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
( cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ rs(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)),tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(unit_resolution,[status(thm)],[140,137]) ).
tff(142,plain,
cp(tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[141,112]) ).
tff(143,plain,
( ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) )
| ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) ),
inference(tautology,[status(thm)],]) ).
tff(144,plain,
( ~ ( ~ cp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y) ),
inference(unit_resolution,[status(thm)],[143,142]) ).
tff(145,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y),
inference(unit_resolution,[status(thm)],[144,20]) ).
tff(146,plain,
^ [X: $i] :
refl(
( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(147,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[146]) ).
tff(148,plain,
^ [X: $i] :
rewrite(
( ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(149,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[148]) ).
tff(150,plain,
( ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[149,147]) ).
tff(151,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_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],]) ).
tff(152,plain,
( ! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[151]) ).
tff(153,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(154,axiom,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(155,plain,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[154,153]) ).
tff(156,plain,
! [X: $i] :
( ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
& ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[155]) ).
tff(157,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[156,152]) ).
tff(158,plain,
! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[157,150]) ).
tff(159,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cpxcomp(X)
| ra_Px1(X,tptp_fun_Y0_3(X)) )
| ~ ( cpxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) )
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y0) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(160,plain,
~ ( ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) )
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y0) ) ),
inference(unit_resolution,[status(thm)],[159,158]) ).
tff(161,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) )
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y0) )
| ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) ),
inference(tautology,[status(thm)],]) ).
tff(162,plain,
( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) ),
inference(unit_resolution,[status(thm)],[161,160]) ).
tff(163,plain,
^ [X: $i] :
refl(
( ( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) )
<=> ( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(164,plain,
( ! [X: $i] :
( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) )
<=> ! [X: $i] :
( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[163]) ).
tff(165,plain,
^ [X: $i] :
rewrite(
( ( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) )
<=> ( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) ) )),
inference(bind,[status(th)],]) ).
tff(166,plain,
( ! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) )
<=> ! [X: $i] :
( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[165]) ).
tff(167,plain,
( ! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) )
<=> ! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(168,axiom,
! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(169,plain,
! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[168,167]) ).
tff(170,plain,
! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) ),
inference(skolemize,[status(sab)],[169]) ).
tff(171,plain,
! [X: $i] :
( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[170,166]) ).
tff(172,plain,
! [X: $i] :
( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[171,164]) ).
tff(173,plain,
( ~ ! [X: $i] :
( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) )
| ( ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
<=> ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ cqxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(174,plain,
( ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
<=> ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ cqxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ),
inference(unit_resolution,[status(thm)],[173,172]) ).
tff(175,plain,
( ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(tautology,[status(thm)],]) ).
tff(176,plain,
ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[175,60]) ).
tff(177,plain,
( ~ ( ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
<=> ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ cqxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ cqxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ),
inference(tautology,[status(thm)],]) ).
tff(178,plain,
( ~ ( ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262))
<=> ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ cqxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) )
| ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ cqxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)) ) ),
inference(unit_resolution,[status(thm)],[177,176]) ).
tff(179,plain,
~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ cqxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(unit_resolution,[status(thm)],[178,174]) ).
tff(180,plain,
( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ~ cqxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(tautology,[status(thm)],]) ).
tff(181,plain,
cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[180,179]) ).
tff(182,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) )
| ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) ),
inference(tautology,[status(thm)],]) ).
tff(183,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262))
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) )
| ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) ),
inference(unit_resolution,[status(thm)],[182,181]) ).
tff(184,plain,
ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))),
inference(unit_resolution,[status(thm)],[183,162]) ).
tff(185,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y)
| ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),tptp_fun_Y0_3(tptp_fun_Y_1(i2003_11_14_17_21_262))) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
$false,
inference(unit_resolution,[status(thm)],[185,184,145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.06 % Problem : KRS114+1 : TPTP v8.1.0. Released v3.1.0.
% 0.06/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.25 % Computer : n013.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Thu Sep 1 09:31:01 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.06/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.26 Usage: tptp [options] [-file:]file
% 0.06/0.26 -h, -? prints this message.
% 0.06/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.26 -m, -model generate model.
% 0.06/0.26 -p, -proof generate proof.
% 0.06/0.26 -c, -core generate unsat core of named formulas.
% 0.06/0.26 -st, -statistics display statistics.
% 0.06/0.26 -t:timeout set timeout (in second).
% 0.06/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.26 -<param>:<value> configuration parameter and value.
% 0.06/0.26 -o:<output-file> file to place output in.
% 0.06/0.28 % SZS status Unsatisfiable
% 0.06/0.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------