%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS126+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n009.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 05:13:26 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 34
% Syntax : Number of formulae : 82 ( 20 unt; 0 typ; 0 def)
% Number of atoms : 441 ( 0 equ)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 670 ( 346 ~; 234 |; 17 &)
% ( 67 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 35 ( 35 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 179 ( 143 !; 23 ?; 179 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px2_type,type,
ra_Px2: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_2_type,type,
tptp_fun_Y0_2: $i > $i ).
tff(i2003_11_14_17_22_23554_type,type,
i2003_11_14_17_22_23554: $i ).
tff(cd1_type,type,
cd1: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(cd1xcomp_type,type,
cd1xcomp: $i > $o ).
tff(tptp_fun_Y_3_type,type,
tptp_fun_Y_3: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) )
<=> ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )),
( ( ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
& ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ( ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
& ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) )),
rewrite(( ( ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
& ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) )),
( ( ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
& ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
& ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i] :
( cd1(X)
<=> ? [Y0: $i] : ra_Px2(X,Y0) )
<=> ! [X: $i] :
( cd1(X)
<=> ? [Y0: $i] : ra_Px2(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [X: $i] :
( cd1(X)
<=> ? [Y0: $i] : ra_Px2(X,Y0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_7) ).
tff(10,plain,
! [X: $i] :
( cd1(X)
<=> ? [Y0: $i] : ra_Px2(X,Y0) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
& ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cd1(X)
| ra_Px2(X,tptp_fun_Y0_2(X)) )
| ~ ( cd1(X)
| ! [Y0: $i] : ~ ra_Px2(X,Y0) ) )
| ~ ( ~ ( ~ cd1(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) )
| ~ ( cd1(i2003_11_14_17_22_23554)
| ! [Y0: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
~ ( ~ ( ~ cd1(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) )
| ~ ( cd1(i2003_11_14_17_22_23554)
| ! [Y0: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y0) ) ),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ( ~ cd1(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) )
| ~ ( cd1(i2003_11_14_17_22_23554)
| ! [Y0: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y0) )
| ~ cd1(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ~ cd1(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
( cUnsatisfiable(i2003_11_14_17_22_23554)
<=> cUnsatisfiable(i2003_11_14_17_22_23554) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
cUnsatisfiable(i2003_11_14_17_22_23554),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_11) ).
tff(20,plain,
cUnsatisfiable(i2003_11_14_17_22_23554),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
^ [X: $i] :
refl(( ( cd1(X)
| ~ cUnsatisfiable(X) )
<=> ( cd1(X)
| ~ cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) )
<=> ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) )
<=> ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
=> cd1(X) )
<=> ( cd1(X)
| ~ cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
=> cd1(X) )
<=> ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,axiom,
! [X: $i] :
( cUnsatisfiable(X)
=> cd1(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_3) ).
tff(27,plain,
! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[29,22]) ).
tff(31,plain,
( ( ~ ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) )
| cd1(i2003_11_14_17_22_23554)
| ~ cUnsatisfiable(i2003_11_14_17_22_23554) )
<=> ( ~ ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) )
| cd1(i2003_11_14_17_22_23554)
| ~ cUnsatisfiable(i2003_11_14_17_22_23554) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) )
| cd1(i2003_11_14_17_22_23554)
| ~ cUnsatisfiable(i2003_11_14_17_22_23554) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [X: $i] :
( cd1(X)
| ~ cUnsatisfiable(X) )
| cd1(i2003_11_14_17_22_23554)
| ~ cUnsatisfiable(i2003_11_14_17_22_23554) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
cd1(i2003_11_14_17_22_23554),
inference(unit_resolution,[status(thm)],[33,30,20]) ).
tff(35,plain,
( ~ ( ~ cd1(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) )
| ~ cd1(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) ),
inference(tautology,[status(thm)],[]) ).
tff(36,plain,
( ~ ( ~ cd1(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) )
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) ),
inference(unit_resolution,[status(thm)],[35,34]) ).
tff(37,plain,
ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)),
inference(unit_resolution,[status(thm)],[36,17]) ).
tff(38,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ~ cd1xcomp(X)
| ! [Y: $i] : ~ ra_Px2(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ~ cd1xcomp(X)
| ! [Y: $i] : ~ ra_Px2(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(43,plain,
( ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[42]) ).
tff(44,plain,
( ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) )
<=> ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )),
( ( ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ( ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) )),
rewrite(( ( ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) )),
( ( ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(46,plain,
( ! [X: $i] :
( ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px2(X,tptp_fun_Y_3(X))
| cd1xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ( ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [X: $i] :
( ( ra_Px2(X,tptp_fun_Y_3(X))
| cd1xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) )
<=> ! [X: $i] :
( ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(50,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px2(X,Y)
<=> ~ ? [Y: $i] : ra_Px2(X,Y) )),
( ( cd1xcomp(X)
<=> ~ ? [Y: $i] : ra_Px2(X,Y) )
<=> ( cd1xcomp(X)
<=> ~ ? [Y: $i] : ra_Px2(X,Y) ) )),
rewrite(( ( cd1xcomp(X)
<=> ~ ? [Y: $i] : ra_Px2(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) ) )),
( ( cd1xcomp(X)
<=> ~ ? [Y: $i] : ra_Px2(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) )
<=> ~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) ) )),
( ( cd1xcomp(X)
<=> ~ ? [Y: $i] : ra_Px2(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [X: $i] :
( cd1xcomp(X)
<=> ~ ? [Y: $i] : ra_Px2(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,axiom,
! [X: $i] :
( cd1xcomp(X)
<=> ~ ? [Y: $i] : ra_Px2(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_8) ).
tff(53,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px2(X,Y)
<=> cd1xcomp(X) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
! [X: $i] :
( ( ra_Px2(X,tptp_fun_Y_3(X))
| cd1xcomp(X) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ),
inference(skolemize,[status(sab)],[54]) ).
tff(56,plain,
! [X: $i] :
( ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
& ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[55,48]) ).
tff(57,plain,
! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[56,46]) ).
tff(58,plain,
! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px2(X,Y)
| ~ cd1xcomp(X) ) ),
inference(modus_ponens,[status(thm)],[57,44]) ).
tff(59,plain,
! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ~ cd1xcomp(X)
| ! [Y: $i] : ~ ra_Px2(X,Y) ) ),
inference(modus_ponens,[status(thm)],[58,39]) ).
tff(60,plain,
( ~ ! [X: $i] :
~ ( ~ ( cd1xcomp(X)
| ra_Px2(X,tptp_fun_Y_3(X)) )
| ~ ( ~ cd1xcomp(X)
| ! [Y: $i] : ~ ra_Px2(X,Y) ) )
| ~ ( ~ ( cd1xcomp(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y_3(i2003_11_14_17_22_23554)) )
| ~ ( ~ cd1xcomp(i2003_11_14_17_22_23554)
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
~ ( ~ ( cd1xcomp(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y_3(i2003_11_14_17_22_23554)) )
| ~ ( ~ cd1xcomp(i2003_11_14_17_22_23554)
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) ) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ ( cd1xcomp(i2003_11_14_17_22_23554)
| ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y_3(i2003_11_14_17_22_23554)) )
| ~ ( ~ cd1xcomp(i2003_11_14_17_22_23554)
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) )
| ~ cd1xcomp(i2003_11_14_17_22_23554)
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(63,plain,
( ~ cd1xcomp(i2003_11_14_17_22_23554)
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
^ [X: $i] :
refl(( ( cd1xcomp(X)
| ~ cUnsatisfiable(X) )
<=> ( cd1xcomp(X)
| ~ cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) )
<=> ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) )
<=> ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
^ [X: $i] :
rewrite(( ( cUnsatisfiable(X)
=> cd1xcomp(X) )
<=> ( cd1xcomp(X)
| ~ cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
=> cd1xcomp(X) )
<=> ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [X: $i] :
( cUnsatisfiable(X)
=> cd1xcomp(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_2) ).
tff(70,plain,
! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
( ( ~ ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) )
| cd1xcomp(i2003_11_14_17_22_23554)
| ~ cUnsatisfiable(i2003_11_14_17_22_23554) )
<=> ( ~ ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) )
| cd1xcomp(i2003_11_14_17_22_23554)
| ~ cUnsatisfiable(i2003_11_14_17_22_23554) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) )
| cd1xcomp(i2003_11_14_17_22_23554)
| ~ cUnsatisfiable(i2003_11_14_17_22_23554) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [X: $i] :
( cd1xcomp(X)
| ~ cUnsatisfiable(X) )
| cd1xcomp(i2003_11_14_17_22_23554)
| ~ cUnsatisfiable(i2003_11_14_17_22_23554) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
cd1xcomp(i2003_11_14_17_22_23554),
inference(unit_resolution,[status(thm)],[76,73,20]) ).
tff(78,plain,
( ~ ( ~ cd1xcomp(i2003_11_14_17_22_23554)
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) )
| ~ cd1xcomp(i2003_11_14_17_22_23554)
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(79,plain,
( ~ ( ~ cd1xcomp(i2003_11_14_17_22_23554)
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) )
| ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y) ),
inference(unit_resolution,[status(thm)],[78,77]) ).
tff(80,plain,
! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y),
inference(unit_resolution,[status(thm)],[79,63]) ).
tff(81,plain,
( ~ ! [Y: $i] : ~ ra_Px2(i2003_11_14_17_22_23554,Y)
| ~ ra_Px2(i2003_11_14_17_22_23554,tptp_fun_Y0_2(i2003_11_14_17_22_23554)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,80,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KRS126+1 : TPTP v9.0.0. Released v3.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n009.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 19:11:18 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.36 % SZS status Unsatisfiable
% 0.19/0.36 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------