%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : KRS123+1 : TPTP v9.0.0. Released v3.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.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 0.11s 0.36s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 36
% Syntax : Number of formulae : 87 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 502 ( 0 equ)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 765 ( 395 ~; 241 |; 27 &)
% ( 99 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 45 ( 45 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 176 ( 140 !; 23 ?; 176 :)
% Comments :
%------------------------------------------------------------------------------
tff(ra_Px1_type,type,
ra_Px1: ( $i * $i ) > $o ).
tff(tptp_fun_Y0_1_type,type,
tptp_fun_Y0_1: $i > $i ).
tff(i2003_11_14_17_22_02803_type,type,
i2003_11_14_17_22_02803: $i ).
tff(cdxcomp_type,type,
cdxcomp: $i > $o ).
tff(cc_type,type,
cc: $i > $o ).
tff(cd_type,type,
cd: $i > $o ).
tff(cUnsatisfiable_type,type,
cUnsatisfiable: $i > $o ).
tff(tptp_fun_Y_0_type,type,
tptp_fun_Y_0: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) )
<=> ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )),
( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
rewrite(( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
( ( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [X: $i] :
( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
<=> ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) )
<=> ! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
tff(10,plain,
! [X: $i] :
( cdxcomp(X)
<=> ? [Y0: $i] : ra_Px1(X,Y0) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [X: $i] :
( ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
& ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ~ ! [X: $i] :
~ ( ~ ( ~ cdxcomp(X)
| ra_Px1(X,tptp_fun_Y0_1(X)) )
| ~ ( cdxcomp(X)
| ! [Y0: $i] : ~ ra_Px1(X,Y0) ) )
| ~ ( ~ ( ~ cdxcomp(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) )
| ~ ( cdxcomp(i2003_11_14_17_22_02803)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y0) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
~ ( ~ ( ~ cdxcomp(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) )
| ~ ( cdxcomp(i2003_11_14_17_22_02803)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y0) ) ),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
( ~ ( ~ cdxcomp(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) )
| ~ ( cdxcomp(i2003_11_14_17_22_02803)
| ! [Y0: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y0) )
| ~ cdxcomp(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ~ cdxcomp(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
^ [X: $i] :
refl(( ~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) )
<=> ~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) )
<=> ! [X: $i] :
~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ( cc(X)
& cd(X) )
<=> ~ ( ~ cc(X)
| ~ cd(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) )
<=> ( cUnsatisfiable(X)
<=> ~ ( ~ cc(X)
| ~ cd(X) ) ) )),
rewrite(( ( cUnsatisfiable(X)
<=> ~ ( ~ cc(X)
| ~ cd(X) ) )
<=> ~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) )
<=> ~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ) )),
rewrite(( ~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) )
<=> ~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ) )),
( ( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) )
<=> ~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ) )),
inference(bind,[status(th)],[]) ).
tff(21,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) )
<=> ! [X: $i] :
~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) )
<=> ! [X: $i] :
( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
tff(24,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [X: $i] :
( cUnsatisfiable(X)
<=> ( cc(X)
& cd(X) ) ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [X: $i] :
~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [X: $i] :
~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ~ ! [X: $i] :
~ ( ( ~ cc(X)
| ~ cd(X) )
<=> cUnsatisfiable(X) )
| ~ ( ( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803) )
<=> cUnsatisfiable(i2003_11_14_17_22_02803) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
~ ( ( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803) )
<=> cUnsatisfiable(i2003_11_14_17_22_02803) ),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
( cUnsatisfiable(i2003_11_14_17_22_02803)
<=> cUnsatisfiable(i2003_11_14_17_22_02803) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
cUnsatisfiable(i2003_11_14_17_22_02803),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_12) ).
tff(32,plain,
cUnsatisfiable(i2003_11_14_17_22_02803),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803) )
<=> cUnsatisfiable(i2003_11_14_17_22_02803) )
| ~ ( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803) )
| ~ cUnsatisfiable(i2003_11_14_17_22_02803) ),
inference(tautology,[status(thm)],[]) ).
tff(34,plain,
( ( ( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803) )
<=> cUnsatisfiable(i2003_11_14_17_22_02803) )
| ~ ( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803) ) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
~ ( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803) ),
inference(unit_resolution,[status(thm)],[34,29]) ).
tff(36,plain,
( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803)
| cc(i2003_11_14_17_22_02803) ),
inference(tautology,[status(thm)],[]) ).
tff(37,plain,
cc(i2003_11_14_17_22_02803),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
^ [X: $i] :
refl(( ( cdxcomp(X)
| ~ cc(X) )
<=> ( cdxcomp(X)
| ~ cc(X) ) )),
inference(bind,[status(th)],[]) ).
tff(39,plain,
( ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
^ [X: $i] :
rewrite(( ( cc(X)
=> cdxcomp(X) )
<=> ( cdxcomp(X)
| ~ cc(X) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [X: $i] :
( cc(X)
=> cdxcomp(X) )
<=> ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,axiom,
! [X: $i] :
( cc(X)
=> cdxcomp(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
tff(44,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(skolemize,[status(sab)],[45]) ).
tff(47,plain,
! [X: $i] :
( cdxcomp(X)
| ~ cc(X) ),
inference(modus_ponens,[status(thm)],[46,39]) ).
tff(48,plain,
( ( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(i2003_11_14_17_22_02803)
| ~ cc(i2003_11_14_17_22_02803) )
<=> ( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(i2003_11_14_17_22_02803)
| ~ cc(i2003_11_14_17_22_02803) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(i2003_11_14_17_22_02803)
| ~ cc(i2003_11_14_17_22_02803) ),
inference(quant_inst,[status(thm)],[]) ).
tff(50,plain,
( ~ ! [X: $i] :
( cdxcomp(X)
| ~ cc(X) )
| cdxcomp(i2003_11_14_17_22_02803)
| ~ cc(i2003_11_14_17_22_02803) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
cdxcomp(i2003_11_14_17_22_02803),
inference(unit_resolution,[status(thm)],[50,47,37]) ).
tff(52,plain,
( ~ ( ~ cdxcomp(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) )
| ~ cdxcomp(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
( ~ ( ~ cdxcomp(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) )
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) ),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)),
inference(unit_resolution,[status(thm)],[53,17]) ).
tff(55,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [X: $i] :
refl(( ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(58,plain,
( ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
^ [X: $i] :
rewrite(( ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
^ [X: $i] :
trans(monotonicity(rewrite(( ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) )
<=> ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )),
( ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
rewrite(( ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
( ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(63,plain,
( ! [X: $i] :
( ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(quant_intro,[status(thm)],[62]) ).
tff(64,plain,
^ [X: $i] :
rewrite(( ( ( ra_Px1(X,tptp_fun_Y_0(X))
| cd(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ( ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) )),
inference(bind,[status(th)],[]) ).
tff(65,plain,
( ! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_0(X))
| cd(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) )
<=> ! [X: $i] :
( ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
^ [X: $i] :
trans(trans(monotonicity(rewrite(( ~ ? [Y: $i] : ra_Px1(X,Y)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )),
( ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ) )),
rewrite(( ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) )),
( ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) )),
rewrite(( ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) )),
( ( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) )),
inference(bind,[status(th)],[]) ).
tff(68,plain,
( ! [X: $i] :
( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) )
<=> ! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,axiom,
! [X: $i] :
( cd(X)
<=> ~ ? [Y: $i] : ra_Px1(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
tff(70,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ),
inference(modus_ponens,[status(thm)],[69,68]) ).
tff(71,plain,
! [X: $i] :
~ ( ? [Y: $i] : ra_Px1(X,Y)
<=> cd(X) ),
inference(modus_ponens,[status(thm)],[70,66]) ).
tff(72,plain,
! [X: $i] :
( ( ra_Px1(X,tptp_fun_Y_0(X))
| cd(X) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(skolemize,[status(sab)],[71]) ).
tff(73,plain,
! [X: $i] :
( ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
& ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(modus_ponens,[status(thm)],[72,65]) ).
tff(74,plain,
! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(modus_ponens,[status(thm)],[73,63]) ).
tff(75,plain,
! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ! [Y: $i] : ~ ra_Px1(X,Y)
| ~ cd(X) ) ),
inference(modus_ponens,[status(thm)],[74,61]) ).
tff(76,plain,
! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) ),
inference(modus_ponens,[status(thm)],[75,56]) ).
tff(77,plain,
( ~ ! [X: $i] :
~ ( ~ ( cd(X)
| ra_Px1(X,tptp_fun_Y_0(X)) )
| ~ ( ~ cd(X)
| ! [Y: $i] : ~ ra_Px1(X,Y) ) )
| ~ ( ~ ( cd(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y_0(i2003_11_14_17_22_02803)) )
| ~ ( ~ cd(i2003_11_14_17_22_02803)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
~ ( ~ ( cd(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y_0(i2003_11_14_17_22_02803)) )
| ~ ( ~ cd(i2003_11_14_17_22_02803)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ ( cd(i2003_11_14_17_22_02803)
| ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y_0(i2003_11_14_17_22_02803)) )
| ~ ( ~ cd(i2003_11_14_17_22_02803)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) )
| ~ cd(i2003_11_14_17_22_02803)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(80,plain,
( ~ cd(i2003_11_14_17_22_02803)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) ),
inference(unit_resolution,[status(thm)],[79,78]) ).
tff(81,plain,
( ~ cc(i2003_11_14_17_22_02803)
| ~ cd(i2003_11_14_17_22_02803)
| cd(i2003_11_14_17_22_02803) ),
inference(tautology,[status(thm)],[]) ).
tff(82,plain,
cd(i2003_11_14_17_22_02803),
inference(unit_resolution,[status(thm)],[81,35]) ).
tff(83,plain,
( ~ ( ~ cd(i2003_11_14_17_22_02803)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) )
| ~ cd(i2003_11_14_17_22_02803)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) ),
inference(tautology,[status(thm)],[]) ).
tff(84,plain,
( ~ ( ~ cd(i2003_11_14_17_22_02803)
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) )
| ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y) ),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y),
inference(unit_resolution,[status(thm)],[84,80]) ).
tff(86,plain,
( ~ ! [Y: $i] : ~ ra_Px1(i2003_11_14_17_22_02803,Y)
| ~ ra_Px1(i2003_11_14_17_22_02803,tptp_fun_Y0_1(i2003_11_14_17_22_02803)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(87,plain,
$false,
inference(unit_resolution,[status(thm)],[86,85,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KRS123+1 : TPTP v9.0.0. Released v3.1.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Thu Jun 19 19:11:39 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.36 % SZS status Unsatisfiable
% 0.11/0.36 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------