%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS110+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:13:24 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 52
% Syntax : Number of formulae : 128 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 1485 ( 0 equ)
% Maximal formula atoms : 40 ( 11 avg)
% Number of connectives : 2783 (1498 ~;1036 |; 130 &)
% ( 116 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 72 ( 72 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-1 aty)
% Number of variables : 412 ( 356 !; 36 ?; 412 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(i2003_11_14_17_21_12565_type,type,
i2003_11_14_17_21_12565: $i ).
tff(cp_type,type,
cp: $i > $o ).
tff(tptp_fun_Y_2_type,type,
tptp_fun_Y_2: $i > $i ).
tff(rinvS_type,type,
rinvS: ( $i * $i ) > $o ).
tff(tptp_fun_Y_4_type,type,
tptp_fun_Y_4: $i > $i ).
tff(ca_Ax2_type,type,
ca_Ax2: $i > $o ).
tff(rs_type,type,
rs: ( $i * $i ) > $o ).
tff(cpxcomp_type,type,
cpxcomp: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_1_type,type,
tptp_fun_Y_1: $i > $i ).
tff(tptp_fun_Y0_3_type,type,
tptp_fun_Y0_3: $i > $i ).
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/sandbox2/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_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_2(tptp_fun_Y_0(i2003_11_14_17_21_12565))) )
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
~ ( ~ ( cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_2(tptp_fun_Y_0(i2003_11_14_17_21_12565))) )
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_2(tptp_fun_Y_0(i2003_11_14_17_21_12565))) )
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) )
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(26,plain,
( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(28,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[27]) ).
tff(29,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
<=> ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) ) )),
rewrite(( ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) )
<=> ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) )),
rewrite(( ( ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) )),
( ( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [X: $i] :
rewrite(( ( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) )
<=> ( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [X: $i] :
( ca_Ax2(X)
<=> ( cp(X)
& ? [Y: $i] :
( rinvS(X,Y)
& cp(Y) ) ) )
<=> ! [X: $i] :
( ca_Ax2(X)
<=> ( cp(X)
& ? [Y: $i] :
( rinvS(X,Y)
& cp(Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [X: $i] :
( ca_Ax2(X)
<=> ( cp(X)
& ? [Y: $i] :
( rinvS(X,Y)
& cp(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
tff(38,plain,
! [X: $i] :
( ca_Ax2(X)
<=> ( cp(X)
& ? [Y: $i] :
( rinvS(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [X: $i] :
( ( ~ ca_Ax2(X)
| ( cp(X)
& rinvS(X,tptp_fun_Y_4(X))
& cp(tptp_fun_Y_4(X)) ) )
& ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
~ ( rinvS(X,Y)
& cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[40,33]) ).
tff(42,plain,
! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) ),
inference(modus_ponens,[status(thm)],[41,31]) ).
tff(43,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y)
| ~ cp(Y) ) ) )
<=> ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(45,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y)
| ~ cp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y)
| ~ cp(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ) ) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y)
| ~ cp(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ ca_Ax2(X)
| ~ ( ~ rinvS(X,tptp_fun_Y_4(X))
| ~ cp(tptp_fun_Y_4(X))
| ~ cp(X) ) )
| ~ ( ca_Ax2(X)
| ~ cp(X)
| ! [Y: $i] :
( ~ rinvS(X,Y)
| ~ cp(Y) ) ) )
| ~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) ) ),
inference(unit_resolution,[status(thm)],[48,42]) ).
tff(50,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( ~ cp(Y)
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) ),
inference(transitivity,[status(thm)],[57,55]) ).
tff(59,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
<=> ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) ) )),
trans(monotonicity(quant_intro(proof_bind(^ [Y: $i] :
trans(monotonicity(rewrite(( ( rs(X,Y)
& ca_Ax2(Y) )
<=> ~ ( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) )),
( ~ ( rs(X,Y)
& ca_Ax2(Y) )
<=> ~ ~ ( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) )),
rewrite(( ~ ~ ( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
<=> ( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) )),
( ~ ( rs(X,Y)
& ca_Ax2(Y) )
<=> ( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ))),
( ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
<=> ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )),
rewrite(( ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )),
( ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) )
<=> ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) )),
rewrite(( ( ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) )),
( ( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
^ [X: $i] :
rewrite(( ( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,plain,
( ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) )
<=> ! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( rs(X,Y)
=> cpxcomp(Y) ) ) )
<=> ( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( rs(X,Y)
=> cpxcomp(Y) ) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( rs(X,Y)
=> cpxcomp(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(67,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( ? [Y: $i] :
( rs(X,Y)
& ca_Ax2(Y) )
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [X: $i] :
( ( ~ cUnsatisfiable(X)
| ( rs(X,tptp_fun_Y_0(X))
& ca_Ax2(tptp_fun_Y_0(X))
& ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
& ( cUnsatisfiable(X)
| ! [Y: $i] :
~ ( rs(X,Y)
& ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ),
inference(modus_ponens,[status(thm)],[70,60]) ).
tff(72,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) )
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) ) ) ),
inference(modus_ponens,[status(thm)],[71,58]) ).
tff(73,plain,
! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) ),
inference(modus_ponens,[status(thm)],[72,53]) ).
tff(74,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_12565,Y)
| ~ ca_Ax2(Y) ) ) )
<=> ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_12565,Y)
| ~ ca_Ax2(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ) ) ) ),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_12565,Y)
| ~ ca_Ax2(Y) ) ) ) )
<=> ( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ) ) ) ),
inference(transitivity,[status(thm)],[76,74]) ).
tff(78,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) ) )
| ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ rs(i2003_11_14_17_21_12565,Y)
| ~ ca_Ax2(Y) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(79,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cUnsatisfiable(X)
| ~ ( ~ rs(X,tptp_fun_Y_0(X))
| ~ ca_Ax2(tptp_fun_Y_0(X))
| ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(X,Y) ) ) )
| ~ ( cUnsatisfiable(X)
| ~ ( cpxcomp(tptp_fun_Y_1(X))
| ~ rs(X,tptp_fun_Y_1(X)) )
| ! [Y: $i] :
( ~ rs(X,Y)
| ~ ca_Ax2(Y) ) ) )
| ~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ) ) ),
inference(modus_ponens,[status(thm)],[78,77]) ).
tff(80,plain,
~ ( ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ) ),
inference(unit_resolution,[status(thm)],[79,73]) ).
tff(81,plain,
( ~ ( cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( cpxcomp(tptp_fun_Y_1(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_1(i2003_11_14_17_21_12565)) )
| ! [Y: $i] :
( ~ ca_Ax2(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) )
| ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(82,plain,
( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ),
inference(unit_resolution,[status(thm)],[81,80]) ).
tff(83,plain,
( cUnsatisfiable(i2003_11_14_17_21_12565)
<=> cUnsatisfiable(i2003_11_14_17_21_12565) ),
inference(rewrite,[status(thm)],[]) ).
tff(84,axiom,
cUnsatisfiable(i2003_11_14_17_21_12565),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
tff(85,plain,
cUnsatisfiable(i2003_11_14_17_21_12565),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) )
| ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(87,plain,
( ~ ( ~ cUnsatisfiable(i2003_11_14_17_21_12565)
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) )
| ~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ),
inference(unit_resolution,[status(thm)],[86,85]) ).
tff(88,plain,
~ ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ),
inference(unit_resolution,[status(thm)],[87,82]) ).
tff(89,plain,
( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565)) ),
inference(tautology,[status(thm)],[]) ).
tff(90,plain,
ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565)),
inference(unit_resolution,[status(thm)],[89,88]) ).
tff(91,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(92,plain,
( ~ ( ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) )
| ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ) ),
inference(unit_resolution,[status(thm)],[91,90]) ).
tff(93,plain,
~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ),
inference(unit_resolution,[status(thm)],[92,51]) ).
tff(94,plain,
( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ cp(tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| ~ rinvS(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y_4(tptp_fun_Y_0(i2003_11_14_17_21_12565)))
| cp(tptp_fun_Y_0(i2003_11_14_17_21_12565)) ),
inference(tautology,[status(thm)],[]) ).
tff(95,plain,
cp(tptp_fun_Y_0(i2003_11_14_17_21_12565)),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) )
| ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ),
inference(tautology,[status(thm)],[]) ).
tff(97,plain,
( ~ ( ~ cp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) )
| ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y) ),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y),
inference(unit_resolution,[status(thm)],[97,26]) ).
tff(99,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(100,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)],[99]) ).
tff(101,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(102,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)],[101]) ).
tff(103,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)],[102,100]) ).
tff(104,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(105,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)],[104]) ).
tff(106,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(107,axiom,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
tff(108,plain,
! [X: $i] :
( cpxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,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)],[108]) ).
tff(110,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)],[109,105]) ).
tff(111,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)],[110,103]) ).
tff(112,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_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(113,plain,
~ ( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y0) ) ),
inference(unit_resolution,[status(thm)],[112,111]) ).
tff(114,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) )
| ~ ( cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y0: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y0) )
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ),
inference(tautology,[status(thm)],[]) ).
tff(115,plain,
( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ),
inference(unit_resolution,[status(thm)],[114,113]) ).
tff(116,plain,
( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565))
| rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ),
inference(tautology,[status(thm)],[]) ).
tff(117,plain,
rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)),
inference(unit_resolution,[status(thm)],[116,88]) ).
tff(118,plain,
( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| ~ ca_Ax2(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ) ),
inference(tautology,[status(thm)],[]) ).
tff(119,plain,
! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) ),
inference(unit_resolution,[status(thm)],[118,88]) ).
tff(120,plain,
( ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) )
<=> ( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(121,plain,
( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
( ~ ! [Y: $i] :
( cpxcomp(Y)
| ~ rs(i2003_11_14_17_21_12565,Y) )
| cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ~ rs(i2003_11_14_17_21_12565,tptp_fun_Y_0(i2003_11_14_17_21_12565)) ),
inference(modus_ponens,[status(thm)],[121,120]) ).
tff(123,plain,
cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565)),
inference(unit_resolution,[status(thm)],[122,119,117]) ).
tff(124,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) )
| ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ),
inference(tautology,[status(thm)],[]) ).
tff(125,plain,
( ~ ( ~ cpxcomp(tptp_fun_Y_0(i2003_11_14_17_21_12565))
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) )
| ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ),
inference(unit_resolution,[status(thm)],[124,123]) ).
tff(126,plain,
ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))),
inference(unit_resolution,[status(thm)],[125,115]) ).
tff(127,plain,
( ~ ! [Y: $i] : ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),Y)
| ~ ra_Px1(tptp_fun_Y_0(i2003_11_14_17_21_12565),tptp_fun_Y0_3(tptp_fun_Y_0(i2003_11_14_17_21_12565))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,126,98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS110+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n001.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 19:15:19 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------