%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS114+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:13:25 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 79
% Syntax : Number of formulae : 198 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 2103 ( 147 equ)
% Maximal formula atoms : 48 ( 10 avg)
% Number of connectives : 3783 (1958 ~;1432 |; 194 &)
% ( 193 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 80 ( 80 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 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 : 647 ( 580 !; 40 ?; 647 :)
% 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(ca_Vx5_type,type,
ca_Vx5: $i > $o ).
tff(ca_Ax4_type,type,
ca_Ax4: $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(rr_type,type,
rr: ( $i * $i ) > $o ).
tff(ca_Ax3_type,type,
ca_Ax3: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
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)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(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)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(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)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) )
<=> ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )),
( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
rewrite(( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
( ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px1(X,tptp_fun_Y_2(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_2(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) )
<=> ! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px1(X,Y)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) )),
rewrite(( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
( ( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [X: $i] :
( cp(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(16,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cp(X) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_2(X))
| cp(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [X: $i] :
( ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [X: $i] :
~ ( ~ ( cp(X)
| ra_Px1(X,tptp_fun_Y_2(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cp(X) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,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)],[21,2]) ).
tff(23,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(24,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)],[23,22]) ).
tff(25,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(26,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)],[25,24]) ).
tff(27,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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)
| ~ ( ~ 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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)
| ~ ( ~ 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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,Y0)
| ~ rinvR(X,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(30,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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,Y0)
| ~ rinvR(X,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)],[29]) ).
tff(31,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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,Y0)
| ~ rinvR(X,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(32,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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,Y0)
| ~ rinvR(X,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)],[31]) ).
tff(33,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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,Y0)
| ~ rinvR(X,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(transitivity,[status(thm)],[32,30]) ).
tff(34,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,Y0)
| ~ rinvR(X,Y1) )
| ~ 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)
| ~ ( ~ 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) ) ) )
<=> ( ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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) ) ) ) )),
rewrite(( ( ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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,Y0)
| ~ rinvR(X,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) ) ) )
<=> ~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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(35,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,Y0)
| ~ rinvR(X,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)],[34]) ).
tff(36,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(37,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)],[36]) ).
tff(38,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(39,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(40,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)],[39]) ).
tff(41,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(42,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)],[41,40]) ).
tff(43,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)],[42,38]) ).
tff(44,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)],[43]) ).
tff(45,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)],[44,37]) ).
tff(46,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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)],[45,35]) ).
tff(47,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax4(X)
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,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)],[46,33]) ).
tff(48,plain,
! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,28]) ).
tff(49,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) )
| ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [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))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) )
| ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [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))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,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_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)))
| ( 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)) ) )
| ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y)
| ~ ca_Vx5(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) ) ) ) )
<=> ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [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))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) )
| ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y)
| ~ ca_Vx5(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) )
| ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [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))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ) ) ) ),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) )
| ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y)
| ~ ca_Vx5(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) ) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) )
| ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [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))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ) ) ) ),
inference(transitivity,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) )
| ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [Y: $i] :
( ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y)
| ~ ca_Vx5(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(54,plain,
( ~ ! [X: $i] :
~ ( ~ ( 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)
| ~ ( ~ rinvR(X,tptp_fun_Y_6(X))
| ~ ca_Vx5(tptp_fun_Y_6(X))
| ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(X,Y0)
| ~ rinvR(X,Y1) ) ) ) )
| ~ ( ~ ( 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_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)))
| ( 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)) ) )
| ! [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))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ) ) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,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_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)))
| ( 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)) ) )
| ! [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))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ) ),
inference(unit_resolution,[status(thm)],[54,48]) ).
tff(56,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_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)))
| ( 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)) ) )
| ! [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))
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) )
| ~ ca_Ax4(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(57,plain,
( ~ ca_Ax4(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,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] :
( ~ 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(59,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)],[58]) ).
tff(60,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(61,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)],[60]) ).
tff(62,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(transitivity,[status(thm)],[61,59]) ).
tff(63,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] :
( ~ 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) ) ) )
<=> ( ( ~ 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) ) ) ) )),
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) ) ) ) )),
( ( ( ~ 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(64,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)],[63]) ).
tff(65,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(66,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)],[65]) ).
tff(67,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(68,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(69,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)],[68,67]) ).
tff(70,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)],[69]) ).
tff(71,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)],[70,66]) ).
tff(72,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)],[71,64]) ).
tff(73,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)],[72,62]) ).
tff(74,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) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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] :
( ~ rr(X,Y)
| ~ ca_Ax4(Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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(75,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] :
( ~ rr(i2003_11_14_17_21_262,Y)
| ~ ca_Ax4(Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_262,Y)
| ~ ca_Ax3(Y) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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(76,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) ) ) )
| ~ ( ~ ( ~ 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] :
( ~ rr(i2003_11_14_17_21_262,Y)
| ~ ca_Ax4(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] :
( ~ rr(X,Y)
| ~ ca_Ax4(Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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)],[75]) ).
tff(77,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) ) ) )
| ~ ( ~ ( ~ 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] :
( ~ rr(i2003_11_14_17_21_262,Y)
| ~ ca_Ax4(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] :
( ~ rr(X,Y)
| ~ ca_Ax4(Y) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax3(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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)],[76,74]) ).
tff(78,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) ) ) )
| ~ ( ~ ( ~ 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] :
( ~ rr(i2003_11_14_17_21_262,Y)
| ~ ca_Ax4(Y) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_262,Y)
| ~ ca_Ax3(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,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) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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)],[78,77]) ).
tff(80,plain,
~ ( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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)],[79,73]) ).
tff(81,plain,
( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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)
| ~ ( ~ 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))
| ~ ca_Ax4(tptp_fun_Y_0(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(82,plain,
( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(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)],[81,80]) ).
tff(83,plain,
( cUnsatisfiable(i2003_11_14_17_21_262)
<=> cUnsatisfiable(i2003_11_14_17_21_262) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,axiom,
cUnsatisfiable(i2003_11_14_17_21_262),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(85,plain,
cUnsatisfiable(i2003_11_14_17_21_262),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)) ) )
| ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(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(87,plain,
( ~ ( ~ cUnsatisfiable(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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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))
| ~ ca_Ax4(tptp_fun_Y_0(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)],[86,85]) ).
tff(88,plain,
~ ( ~ 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))
| ~ ca_Ax4(tptp_fun_Y_0(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)],[87,82]) ).
tff(89,plain,
( ~ 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))
| ~ ca_Ax4(tptp_fun_Y_0(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)) ),
inference(tautology,[status(thm)],[]) ).
tff(90,plain,
ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ ( ~ ca_Ax4(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) )
| ~ ca_Ax4(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(92,plain,
( ~ ( ~ ca_Ax4(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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) )
| ~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ) ),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
~ ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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))) ),
inference(unit_resolution,[status(thm)],[92,57]) ).
tff(94,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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)))
| 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(95,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)],[94,93]) ).
tff(96,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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)))
| ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) ) ),
inference(tautology,[status(thm)],[]) ).
tff(97,plain,
! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) ),
inference(unit_resolution,[status(thm)],[96,93]) ).
tff(98,plain,
^ [X: $i,Y: $i] :
refl(( ( rinvR(X,Y)
<=> rr(Y,X) )
<=> ( rinvR(X,Y)
<=> rr(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(99,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)],[98]) ).
tff(100,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(101,axiom,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_10) ).
tff(102,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(skolemize,[status(sab)],[102]) ).
tff(104,plain,
! [X: $i,Y: $i] :
( rinvR(X,Y)
<=> rr(Y,X) ),
inference(modus_ponens,[status(thm)],[103,99]) ).
tff(105,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(106,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)],[105,104]) ).
tff(107,plain,
( ~ 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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(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(108,plain,
rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[107,88]) ).
tff(109,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(110,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)],[109,108]) ).
tff(111,plain,
rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),i2003_11_14_17_21_262),
inference(unit_resolution,[status(thm)],[110,106]) ).
tff(112,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ 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)))
| ( 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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ 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)))
| ( i2003_11_14_17_21_262 = tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(113,plain,
( ( ( 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),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),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)))
| ( i2003_11_14_17_21_262 = tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ( 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),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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ 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)))
| ( i2003_11_14_17_21_262 = tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) ) ) ),
inference(monotonicity,[status(thm)],[113]) ).
tff(115,plain,
( ( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ( 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),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),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ 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)))
| ( i2003_11_14_17_21_262 = tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) ) ) ),
inference(transitivity,[status(thm)],[114,112]) ).
tff(116,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ( 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),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(117,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ 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)))
| ( i2003_11_14_17_21_262 = tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) ) ),
inference(modus_ponens,[status(thm)],[116,115]) ).
tff(118,plain,
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)],[117,111,97,95]) ).
tff(119,plain,
tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262)) = i2003_11_14_17_21_262,
inference(symmetry,[status(thm)],[118]) ).
tff(120,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)],[119]) ).
tff(121,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)],[120]) ).
tff(122,plain,
( ~ 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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,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)) ),
inference(tautology,[status(thm)],[]) ).
tff(123,plain,
rs(i2003_11_14_17_21_262,tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[122,88]) ).
tff(124,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)],[123,121]) ).
tff(125,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(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)) ) ) )
<=> ! [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)],[125]) ).
tff(127,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(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)) ) ) )
<=> ! [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)],[127]) ).
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)) ) ) )
<=> ! [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)],[128,126]) ).
tff(130,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(131,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)],[130]) ).
tff(132,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(133,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(134,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)],[133]) ).
tff(135,axiom,
! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( rs(X,Y)
=> cp(Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_9) ).
tff(136,plain,
! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) ),
inference(modus_ponens,[status(thm)],[135,134]) ).
tff(137,plain,
! [X: $i] :
( ca_Vx5(X)
<=> ! [Y: $i] :
( cp(Y)
| ~ rs(X,Y) ) ),
inference(modus_ponens,[status(thm)],[136,132]) ).
tff(138,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)],[137]) ).
tff(139,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)],[138,131]) ).
tff(140,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)],[139,129]) ).
tff(141,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(142,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)],[141,140]) ).
tff(143,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(144,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)],[143,142]) ).
tff(145,plain,
( ~ ! [Y0: $i,Y1: $i] :
( ( Y0 = Y1 )
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y0)
| ~ rinvR(tptp_fun_Y_0(i2003_11_14_17_21_262),Y1) )
| ~ ca_Vx5(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)))
| ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))) ),
inference(tautology,[status(thm)],[]) ).
tff(146,plain,
ca_Vx5(tptp_fun_Y_6(tptp_fun_Y_0(i2003_11_14_17_21_262))),
inference(unit_resolution,[status(thm)],[145,93]) ).
tff(147,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(148,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)],[147,146]) ).
tff(149,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)],[148,144]) ).
tff(150,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(151,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(152,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)],[151,150]) ).
tff(153,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)],[152,149]) ).
tff(154,plain,
cp(tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[153,124]) ).
tff(155,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(156,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)],[155,154]) ).
tff(157,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_1(i2003_11_14_17_21_262),Y),
inference(unit_resolution,[status(thm)],[156,26]) ).
tff(158,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(159,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)],[158]) ).
tff(160,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(161,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)],[160]) ).
tff(162,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)],[161,159]) ).
tff(163,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(164,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)],[163]) ).
tff(165,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(166,axiom,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_4) ).
tff(167,plain,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[166,165]) ).
tff(168,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)],[167]) ).
tff(169,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)],[168,164]) ).
tff(170,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)],[169,162]) ).
tff(171,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(172,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)],[171,170]) ).
tff(173,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(174,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)],[173,172]) ).
tff(175,plain,
^ [X: $i] :
refl(( ~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) )
<=> ~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ) )),
inference(bind,[status(th)],[]) ).
tff(176,plain,
( ! [X: $i] :
~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) )
<=> ! [X: $i] :
~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ) ),
inference(quant_intro,[status(thm)],[175]) ).
tff(177,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ( cqxcomp(X)
& cpxcomp(X) )
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) )),
( ( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) )
<=> ( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) ) )),
rewrite(( ( ca_Ax3(X)
<=> ~ ( ~ cpxcomp(X)
| ~ cqxcomp(X) ) )
<=> ~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ) )),
( ( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) )
<=> ~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ) )),
rewrite(( ~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) )
<=> ~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ) )),
( ( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) )
<=> ~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ) )),
inference(bind,[status(th)],[]) ).
tff(178,plain,
( ! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) )
<=> ! [X: $i] :
~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ) ),
inference(quant_intro,[status(thm)],[177]) ).
tff(179,plain,
( ! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) )
<=> ! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(180,axiom,
! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(181,plain,
! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) ),
inference(modus_ponens,[status(thm)],[180,179]) ).
tff(182,plain,
! [X: $i] :
( ca_Ax3(X)
<=> ( cqxcomp(X)
& cpxcomp(X) ) ),
inference(skolemize,[status(sab)],[181]) ).
tff(183,plain,
! [X: $i] :
~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ),
inference(modus_ponens,[status(thm)],[182,178]) ).
tff(184,plain,
! [X: $i] :
~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) ),
inference(modus_ponens,[status(thm)],[183,176]) ).
tff(185,plain,
( ~ ! [X: $i] :
~ ( ( ~ cpxcomp(X)
| ~ cqxcomp(X) )
<=> ca_Ax3(X) )
| ~ ( ( ~ 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)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(186,plain,
~ ( ( ~ 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)) ),
inference(unit_resolution,[status(thm)],[185,184]) ).
tff(187,plain,
( ~ 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))
| ~ ca_Ax4(tptp_fun_Y_0(i2003_11_14_17_21_262))
| ~ rr(i2003_11_14_17_21_262,tptp_fun_Y_0(i2003_11_14_17_21_262))
| ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(tautology,[status(thm)],[]) ).
tff(188,plain,
ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[187,88]) ).
tff(189,plain,
( ( ( ~ 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)) )
| ~ ca_Ax3(tptp_fun_Y_1(i2003_11_14_17_21_262)) ),
inference(tautology,[status(thm)],[]) ).
tff(190,plain,
( ( ( ~ 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(unit_resolution,[status(thm)],[189,188]) ).
tff(191,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)],[190,186]) ).
tff(192,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(193,plain,
cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_262)),
inference(unit_resolution,[status(thm)],[192,191]) ).
tff(194,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(195,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)],[194,193]) ).
tff(196,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)],[195,174]) ).
tff(197,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(198,plain,
$false,
inference(unit_resolution,[status(thm)],[197,196,157]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KRS114+1 : TPTP v9.0.0. Released v3.1.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n011.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 19:11:41 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38 % SZS output start Proof
% See solution above
% 0.19/0.42 % E exiting
%------------------------------------------------------------------------------