%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CSR059+4 : TPTP v9.0.0. Released v3.4.0.
% 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 05:01:38 AM UTC 2025
% Result : Theorem 11.06s 11.24s
% Output : Proof 11.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 52 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 236 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 300 ( 133 ~; 112 |; 16 &)
% ( 29 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 17 ( 17 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 84 ( 74 !; 0 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
tff(borderson_type,type,
borderson: ( $i * $i ) > $o ).
tff(c_georegion_l4_x57_y47_type,type,
c_georegion_l4_x57_y47: $i ).
tff(c_georegion_l4_x56_y47_type,type,
c_georegion_l4_x56_y47: $i ).
tff(mtvisible_type,type,
mtvisible: $i > $o ).
tff(c_tptpgeo_spindlecollectormt_type,type,
c_tptpgeo_spindlecollectormt: $i ).
tff(c_tptpgeo_member5_mt_type,type,
c_tptpgeo_member5_mt: $i ).
tff(genlmt_type,type,
genlmt: ( $i * $i ) > $o ).
tff(1,plain,
( ~ borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47)
<=> ~ borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( mtvisible(c_tptpgeo_spindlecollectormt)
=> borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) )
<=> ~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( mtvisible(c_tptpgeo_spindlecollectormt)
=> borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query209) ).
tff(4,plain,
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
~ borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [X: $i,Y: $i] :
refl(( ( ~ borderson(X,Y)
| borderson(Y,X) )
<=> ( ~ borderson(X,Y)
| borderson(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [X: $i,Y: $i] :
rewrite(( ( borderson(X,Y)
=> borderson(Y,X) )
<=> ( ~ borderson(X,Y)
| borderson(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i,Y: $i] :
( borderson(X,Y)
=> borderson(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [X: $i,Y: $i] :
( borderson(X,Y)
=> borderson(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+3.ax',ax3_43084) ).
tff(13,plain,
! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) )
| ~ borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47)
| borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) )
| ~ borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47)
| borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) )
| ~ borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47)
| borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [X: $i,Y: $i] :
( ~ borderson(X,Y)
| borderson(Y,X) )
| ~ borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47)
| borderson(c_georegion_l4_x57_y47,c_georegion_l4_x56_y47) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47),
inference(unit_resolution,[status(thm)],[19,16,6]) ).
tff(21,plain,
( mtvisible(c_tptpgeo_spindlecollectormt)
<=> mtvisible(c_tptpgeo_spindlecollectormt) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
mtvisible(c_tptpgeo_spindlecollectormt),
inference(or_elim,[status(thm)],[4]) ).
tff(23,plain,
mtvisible(c_tptpgeo_spindlecollectormt),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [SPECMT: $i,GENLMT: $i] :
refl(( ( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
<=> ( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
<=> ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [SPECMT: $i,GENLMT: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
<=> ~ ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
( ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
<=> ~ ~ ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
rewrite(( ~ ~ ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) )
<=> ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
( ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
<=> ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
( ( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) )
<=> ( mtvisible(GENLMT)
| ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
rewrite(( ( mtvisible(GENLMT)
| ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) )
<=> ( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) )),
( ( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) )
<=> ( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) )),
inference(bind,[status(th)],[]) ).
tff(27,plain,
( ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) )
<=> ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) )
<=> ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
^ [SPECMT: $i,GENLMT: $i] :
rewrite(( ( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
=> mtvisible(GENLMT) )
<=> ( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [SPECMT: $i,GENLMT: $i] :
( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
=> mtvisible(GENLMT) )
<=> ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,axiom,
! [SPECMT: $i,GENLMT: $i] :
( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
=> mtvisible(GENLMT) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+3.ax',ax3_44208) ).
tff(32,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(modus_ponens,[status(thm)],[32,28]) ).
tff(34,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ),
inference(modus_ponens,[status(thm)],[34,27]) ).
tff(36,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ),
inference(modus_ponens,[status(thm)],[35,25]) ).
tff(37,plain,
( genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt)
<=> genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+3.ax',ax3_11126) ).
tff(39,plain,
genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( mtvisible(c_tptpgeo_member5_mt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) )
<=> ( mtvisible(c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member5_mt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt) ) ),
inference(monotonicity,[status(thm)],[41]) ).
tff(43,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member5_mt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt) ) ),
inference(transitivity,[status(thm)],[42,40]) ).
tff(44,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member5_mt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member5_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member5_mt) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
mtvisible(c_tptpgeo_member5_mt),
inference(unit_resolution,[status(thm)],[45,39,36,23]) ).
tff(47,plain,
( ( ~ mtvisible(c_tptpgeo_member5_mt)
| borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47) )
<=> ( ~ mtvisible(c_tptpgeo_member5_mt)
| borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( mtvisible(c_tptpgeo_member5_mt)
=> borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47) )
<=> ( ~ mtvisible(c_tptpgeo_member5_mt)
| borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
( mtvisible(c_tptpgeo_member5_mt)
=> borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47) ),
file('/export/starexec/sandbox/benchmark/Axioms/CSR002+3.ax',ax3_6006) ).
tff(50,plain,
( ~ mtvisible(c_tptpgeo_member5_mt)
| borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
( ~ mtvisible(c_tptpgeo_member5_mt)
| borderson(c_georegion_l4_x56_y47,c_georegion_l4_x57_y47) ),
inference(modus_ponens,[status(thm)],[50,47]) ).
tff(52,plain,
$false,
inference(unit_resolution,[status(thm)],[51,46,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : CSR059+4 : TPTP v9.0.0. Released v3.4.0.
% 0.08/0.12 % 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 12:45:48 EDT 2025
% 0.11/0.33 % CPUTime :
% 11.06/11.24 % SZS status Theorem
% 11.06/11.24 % SZS output start Proof
% See solution above
% 12.03/12.23 % E exiting
%------------------------------------------------------------------------------