TSTP Solution File: CSR065+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR065+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 : Tue Sep 20 14:27:55 EDT 2022
% Result : Theorem 0.16s 0.38s
% Output : Proof 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 49
% Syntax : Number of formulae : 94 ( 24 unt; 12 typ; 0 def)
% Number of atoms : 432 ( 0 equ)
% Maximal formula atoms : 12 ( 5 avg)
% Number of connectives : 587 ( 267 ~; 232 |; 32 &)
% ( 46 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 5 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-1 aty)
% Number of variables : 103 ( 94 !; 0 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
tff(mtvisible_type,type,
mtvisible: $i > $o ).
tff(c_tptp_spindleheadmt_type,type,
c_tptp_spindleheadmt: $i ).
tff(c_tptp_member3993_mt_type,type,
c_tptp_member3993_mt: $i ).
tff(c_tptp_spindlecollectormt_type,type,
c_tptp_spindlecollectormt: $i ).
tff(tptpofobject_type,type,
tptpofobject: ( $i * $i ) > $o ).
tff(f_tptpquantityfn_13_type,type,
f_tptpquantityfn_13: $i > $i ).
tff(n_468_type,type,
n_468: $i ).
tff(c_tptpridgeline_topographical_type,type,
c_tptpridgeline_topographical: $i ).
tff(genlmt_type,type,
genlmt: ( $i * $i ) > $o ).
tff(c_cyclistsmt_type,type,
c_cyclistsmt: $i ).
tff(ridgeline_topographical_type,type,
ridgeline_topographical: $i > $o ).
tff(c_tptp_member235_mt_type,type,
c_tptp_member235_mt: $i ).
tff(1,plain,
( mtvisible(c_tptp_spindlecollectormt)
<=> mtvisible(c_tptp_spindlecollectormt) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( mtvisible(c_tptp_spindlecollectormt)
=> tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468)) )
<=> ~ ( ~ mtvisible(c_tptp_spindlecollectormt)
| tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( mtvisible(c_tptp_spindlecollectormt)
=> tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',query65) ).
tff(4,plain,
~ ( ~ mtvisible(c_tptp_spindlecollectormt)
| tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468)) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
mtvisible(c_tptp_spindlecollectormt),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
mtvisible(c_tptp_spindlecollectormt),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,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(8,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)],[7]) ).
tff(9,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(10,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)],[9]) ).
tff(11,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(12,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(13,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)],[12]) ).
tff(14,axiom,
! [SPECMT: $i,GENLMT: $i] :
( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
=> mtvisible(GENLMT) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just48) ).
tff(15,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ),
inference(modus_ponens,[status(thm)],[18,8]) ).
tff(20,plain,
( genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt)
<=> genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just8) ).
tff(22,plain,
genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| ~ mtvisible(c_tptp_spindlecollectormt)
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| ~ mtvisible(c_tptp_spindlecollectormt)
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt)
| ~ mtvisible(c_tptp_spindlecollectormt) )
<=> ( ~ mtvisible(c_tptp_spindlecollectormt)
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt)
| ~ mtvisible(c_tptp_spindlecollectormt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| ~ mtvisible(c_tptp_spindlecollectormt)
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt)
| ~ mtvisible(c_tptp_spindlecollectormt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| ~ mtvisible(c_tptp_spindlecollectormt)
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt)
| ~ mtvisible(c_tptp_spindlecollectormt) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| ~ mtvisible(c_tptp_spindlecollectormt)
| mtvisible(c_tptp_member3993_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member3993_mt) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
mtvisible(c_tptp_member3993_mt),
inference(unit_resolution,[status(thm)],[28,22,19,6]) ).
tff(30,plain,
( genlmt(c_tptp_member3993_mt,c_tptp_spindleheadmt)
<=> genlmt(c_tptp_member3993_mt,c_tptp_spindleheadmt) ),
inference(rewrite,[status(thm)],]) ).
tff(31,axiom,
genlmt(c_tptp_member3993_mt,c_tptp_spindleheadmt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just7) ).
tff(32,plain,
genlmt(c_tptp_member3993_mt,c_tptp_spindleheadmt),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_spindleheadmt)
| ~ genlmt(c_tptp_member3993_mt,c_tptp_spindleheadmt)
| ~ mtvisible(c_tptp_member3993_mt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_spindleheadmt)
| ~ genlmt(c_tptp_member3993_mt,c_tptp_spindleheadmt)
| ~ mtvisible(c_tptp_member3993_mt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_spindleheadmt)
| ~ genlmt(c_tptp_member3993_mt,c_tptp_spindleheadmt)
| ~ mtvisible(c_tptp_member3993_mt) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_spindleheadmt)
| ~ genlmt(c_tptp_member3993_mt,c_tptp_spindleheadmt)
| ~ mtvisible(c_tptp_member3993_mt) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( mtvisible(c_tptp_spindleheadmt)
| ~ mtvisible(c_tptp_member3993_mt) ),
inference(unit_resolution,[status(thm)],[35,32,19]) ).
tff(37,plain,
mtvisible(c_tptp_spindleheadmt),
inference(unit_resolution,[status(thm)],[36,29]) ).
tff(38,plain,
( genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt)
<=> genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just6) ).
tff(40,plain,
genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( mtvisible(c_tptp_member235_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt) )
<=> ( mtvisible(c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member235_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member235_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member235_mt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptp_member235_mt)
| ~ mtvisible(c_tptp_spindlecollectormt)
| ~ genlmt(c_tptp_spindlecollectormt,c_tptp_member235_mt) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
mtvisible(c_tptp_member235_mt),
inference(unit_resolution,[status(thm)],[46,40,19,6]) ).
tff(48,plain,
( ~ tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468))
<=> ~ tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468)) ),
inference(rewrite,[status(thm)],]) ).
tff(49,plain,
~ tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468)),
inference(or_elim,[status(thm)],[4]) ).
tff(50,plain,
~ tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468)),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
^ [INS: $i] :
refl(
( ( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) )
<=> ( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) )),
inference(bind,[status(th)],]) ).
tff(52,plain,
( ! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) )
<=> ! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) ),
inference(quant_intro,[status(thm)],[51]) ).
tff(53,plain,
^ [INS: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
<=> ~ ( ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) )),
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
<=> ~ ~ ( ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) )),
rewrite(
( ~ ~ ( ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) )
<=> ( ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) )),
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
<=> ( ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) )),
( ( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) )
<=> ( ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS)
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) ) )),
rewrite(
( ( ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS)
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) )
<=> ( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) )),
( ( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) )
<=> ( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) )),
inference(bind,[status(th)],]) ).
tff(54,plain,
( ! [INS: $i] :
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) )
<=> ! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [INS: $i] :
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) )
<=> ! [INS: $i] :
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(56,plain,
^ [INS: $i] :
rewrite(
( ( ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
=> tptpofobject(INS,f_tptpquantityfn_13(n_468)) )
<=> ( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [INS: $i] :
( ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
=> tptpofobject(INS,f_tptpquantityfn_13(n_468)) )
<=> ! [INS: $i] :
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,axiom,
! [INS: $i] :
( ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
=> tptpofobject(INS,f_tptpquantityfn_13(n_468)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just10) ).
tff(59,plain,
! [INS: $i] :
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
! [INS: $i] :
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
! [INS: $i] :
( ~ ( mtvisible(c_tptp_member235_mt)
& ridgeline_topographical(INS) )
| tptpofobject(INS,f_tptpquantityfn_13(n_468)) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ),
inference(modus_ponens,[status(thm)],[61,54]) ).
tff(63,plain,
! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) ),
inference(modus_ponens,[status(thm)],[62,52]) ).
tff(64,plain,
( ( ~ ! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) )
| tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(c_tptpridgeline_topographical) )
<=> ( ~ ! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) )
| tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(c_tptpridgeline_topographical) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) )
| tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(c_tptpridgeline_topographical) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [INS: $i] :
( tptpofobject(INS,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(INS) )
| tptpofobject(c_tptpridgeline_topographical,f_tptpquantityfn_13(n_468))
| ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(c_tptpridgeline_topographical) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ mtvisible(c_tptp_member235_mt)
| ~ ridgeline_topographical(c_tptpridgeline_topographical) ),
inference(unit_resolution,[status(thm)],[66,63,50]) ).
tff(68,plain,
~ ridgeline_topographical(c_tptpridgeline_topographical),
inference(unit_resolution,[status(thm)],[67,47]) ).
tff(69,plain,
( ( ridgeline_topographical(c_tptpridgeline_topographical)
| ~ mtvisible(c_cyclistsmt) )
<=> ( ridgeline_topographical(c_tptpridgeline_topographical)
| ~ mtvisible(c_cyclistsmt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( mtvisible(c_cyclistsmt)
=> ridgeline_topographical(c_tptpridgeline_topographical) )
<=> ( ridgeline_topographical(c_tptpridgeline_topographical)
| ~ mtvisible(c_cyclistsmt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
( mtvisible(c_cyclistsmt)
=> ridgeline_topographical(c_tptpridgeline_topographical) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just9) ).
tff(72,plain,
( ridgeline_topographical(c_tptpridgeline_topographical)
| ~ mtvisible(c_cyclistsmt) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
( ridgeline_topographical(c_tptpridgeline_topographical)
| ~ mtvisible(c_cyclistsmt) ),
inference(modus_ponens,[status(thm)],[72,69]) ).
tff(74,plain,
~ mtvisible(c_cyclistsmt),
inference(unit_resolution,[status(thm)],[73,68]) ).
tff(75,plain,
( genlmt(c_tptp_spindleheadmt,c_cyclistsmt)
<=> genlmt(c_tptp_spindleheadmt,c_cyclistsmt) ),
inference(rewrite,[status(thm)],]) ).
tff(76,axiom,
genlmt(c_tptp_spindleheadmt,c_cyclistsmt),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',just5) ).
tff(77,plain,
genlmt(c_tptp_spindleheadmt,c_cyclistsmt),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_cyclistsmt)
| ~ genlmt(c_tptp_spindleheadmt,c_cyclistsmt)
| ~ mtvisible(c_tptp_spindleheadmt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_cyclistsmt)
| ~ genlmt(c_tptp_spindleheadmt,c_cyclistsmt)
| ~ mtvisible(c_tptp_spindleheadmt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_cyclistsmt)
| ~ genlmt(c_tptp_spindleheadmt,c_cyclistsmt)
| ~ mtvisible(c_tptp_spindleheadmt) ),
inference(quant_inst,[status(thm)],]) ).
tff(80,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_cyclistsmt)
| ~ genlmt(c_tptp_spindleheadmt,c_cyclistsmt)
| ~ mtvisible(c_tptp_spindleheadmt) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
( mtvisible(c_cyclistsmt)
| ~ mtvisible(c_tptp_spindleheadmt) ),
inference(unit_resolution,[status(thm)],[80,77,19]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,74,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : CSR065+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.32 % Computer : n005.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue Aug 30 19:26:33 EDT 2022
% 0.10/0.33 % CPUTime :
% 0.10/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.10/0.33 Usage: tptp [options] [-file:]file
% 0.10/0.33 -h, -? prints this message.
% 0.10/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.10/0.33 -m, -model generate model.
% 0.10/0.33 -p, -proof generate proof.
% 0.10/0.33 -c, -core generate unsat core of named formulas.
% 0.10/0.33 -st, -statistics display statistics.
% 0.10/0.33 -t:timeout set timeout (in second).
% 0.10/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.10/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.10/0.33 -<param>:<value> configuration parameter and value.
% 0.10/0.33 -o:<output-file> file to place output in.
% 0.16/0.38 % SZS status Theorem
% 0.16/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------