TSTP Solution File: DAT153^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT153^1 : TPTP v8.2.0. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n024.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 : Mon May 20 19:51:39 EDT 2024
% Result : Theorem 0.21s 0.51s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 145
% Syntax : Number of formulae : 192 ( 30 unt; 138 typ; 0 def)
% Number of atoms : 474 ( 81 equ; 0 cnn)
% Maximal formula atoms : 3 ( 8 avg)
% Number of connectives : 44 ( 18 ~; 26 |; 0 &; 0 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 264 ( 263 >; 1 *; 0 +; 0 <<)
% Number of symbols : 135 ( 132 usr; 3 con; 0-6 aty)
% Number of variables : 130 ( 0 ^ 45 !; 0 ?; 130 :)
% ( 85 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
itself: $tType > $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_7,type,
int: $tType ).
thf(type_def_8,type,
stream: $tType > $tType ).
thf(type_def_9,type,
extended_enat: $tType ).
thf(type_def_10,type,
nat: $tType ).
thf(type_def_11,type,
set: $tType > $tType ).
thf(type_def_12,type,
a: $tType ).
thf(func_def_0,type,
extended_enat: $tType ).
thf(func_def_1,type,
stream: $tType > $tType ).
thf(func_def_2,type,
set: $tType > $tType ).
thf(func_def_3,type,
nat: $tType ).
thf(func_def_4,type,
int: $tType ).
thf(func_def_5,type,
itself: $tType > $tType ).
thf(func_def_6,type,
a: $tType ).
thf(func_def_7,type,
zero:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_8,type,
field:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_9,type,
mult_zero:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_10,type,
semiring_1:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_11,type,
semiring_char_0:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_12,type,
division_ring:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_13,type,
semigroup_mult:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_14,type,
comm_semiring_1:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_15,type,
linordered_idom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_16,type,
linordered_ring:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_17,type,
linordered_field:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_18,type,
ab_semigroup_mult:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_19,type,
linordered_semidom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_20,type,
linord581940658strict:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_21,type,
archim1727834104eiling:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_22,type,
semiri1193490041visors:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_23,type,
linord20386208strict:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_24,type,
archim1804426504_field:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_25,type,
canoni770627133id_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_26,type,
linord893533164strict:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_27,type,
semiri1923998003cancel:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_28,type,
archimedean_ceiling:
!>[X0: $tType] : ( X0 > int ) ).
thf(func_def_29,type,
coindu1365464361scount:
!>[X0: $tType] : ( ( stream(X0) > $o ) > stream(X0) > extended_enat ) ).
thf(func_def_30,type,
coindu76177514sfirst:
!>[X0: $tType] : ( ( stream(X0) > $o ) > stream(X0) > extended_enat ) ).
thf(func_def_31,type,
extended_enat2: nat > extended_enat ).
thf(func_def_32,type,
extended_case_enat:
!>[X0: $tType] : ( ( nat > X0 ) > X0 > extended_enat > X0 ) ).
thf(func_def_33,type,
extended_rec_enat:
!>[X0: $tType] : ( ( nat > X0 ) > X0 > extended_enat > X0 ) ).
thf(func_def_34,type,
extended_size_enat: extended_enat > nat ).
thf(func_def_35,type,
extend1396239628finity:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
extended_the_enat: extended_enat > nat ).
thf(func_def_37,type,
inverse_inverse:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_38,type,
finite_card:
!>[X0: $tType] : ( set(X0) > nat ) ).
thf(func_def_39,type,
times_times:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_40,type,
zero_zero:
!>[X0: $tType] : X0 ).
thf(func_def_41,type,
if:
!>[X0: $tType] : ( $o > X0 > X0 > X0 ) ).
thf(func_def_42,type,
nat2: int > nat ).
thf(func_def_43,type,
linear1341015445_UNTIL:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) > $o ) ).
thf(func_def_44,type,
linear1386806755on_alw:
!>[X0: $tType] : ( ( stream(X0) > $o ) > stream(X0) > $o ) ).
thf(func_def_45,type,
linear505997466_on_ev:
!>[X0: $tType] : ( ( stream(X0) > $o ) > stream(X0) > $o ) ).
thf(func_def_46,type,
linear1335279038n_wait:
!>[X0: $tType] : ( ( stream(X0) > $o ) > stream(X0) > nat ) ).
thf(func_def_47,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
thf(func_def_48,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
thf(func_def_49,type,
nat_tr1645093318rphism:
!>[X0: $tType,X1: $tType] : ( ( X0 > X1 ) > ( X0 > $o ) > $o ) ).
thf(func_def_50,type,
ord_less:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
type:
!>[X0: $tType] : itself(X0) ).
thf(func_def_52,type,
collect:
!>[X0: $tType] : ( ( X0 > $o ) > set(X0) ) ).
thf(func_def_53,type,
sdrop:
!>[X0: $tType] : ( nat > stream(X0) > stream(X0) ) ).
thf(func_def_54,type,
member:
!>[X0: $tType] : ( X0 > set(X0) > $o ) ).
thf(func_def_55,type,
p: stream(a) > $o ).
thf(func_def_56,type,
omega: stream(a) ).
thf(func_def_60,type,
vNOT: $o > $o ).
thf(func_def_61,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_62,type,
vOR: $o > $o > $o ).
thf(func_def_63,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_64,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_65,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_66,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_67,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_68,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_69,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_70,type,
vAND: $o > $o > $o ).
thf(func_def_71,type,
vIMP: $o > $o > $o ).
thf(func_def_72,type,
sP0: extended_enat > extended_enat > $o ).
thf(func_def_73,type,
sP1: extended_enat > extended_enat > $o ).
thf(func_def_74,type,
sP2: extended_enat > extended_enat > extended_enat > $o ).
thf(func_def_75,type,
sP3: extended_enat > extended_enat > extended_enat > $o ).
thf(func_def_76,type,
sP4: extended_enat > extended_enat > extended_enat > $o ).
thf(func_def_77,type,
sP5: extended_enat > extended_enat > extended_enat > $o ).
thf(func_def_78,type,
sP6: extended_enat > extended_enat > extended_enat > $o ).
thf(func_def_79,type,
sP7: extended_enat > extended_enat > extended_enat > $o ).
thf(func_def_80,type,
sP8: extended_enat > extended_enat > extended_enat > $o ).
thf(func_def_81,type,
sP9:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).
thf(func_def_82,type,
sK10: extended_enat > nat ).
thf(func_def_83,type,
sK11:
!>[X0: $tType] : ( X0 > nat ) ).
thf(func_def_84,type,
sK12:
!>[X0: $tType] : ( X0 > nat ) ).
thf(func_def_85,type,
sK13:
!>[X0: $tType] : ( X0 > X0 > nat ) ).
thf(func_def_86,type,
sK14:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_87,type,
sK15:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_88,type,
sK16: int > nat ).
thf(func_def_89,type,
sK17: extended_enat > nat ).
thf(func_def_90,type,
sK18: extended_enat > nat ).
thf(func_def_91,type,
sK19: extended_enat > nat ).
thf(func_def_92,type,
sK20: extended_enat > nat ).
thf(func_def_93,type,
sK21: extended_enat > nat ).
thf(func_def_94,type,
sK22: ( nat > $o ) > nat ).
thf(func_def_95,type,
sK23: ( extended_enat > $o ) > extended_enat ).
thf(func_def_96,type,
sK24: ( nat > $o ) > nat ).
thf(func_def_97,type,
sK25: ( extended_enat > $o ) > nat ).
thf(func_def_98,type,
sK26: ( nat > $o ) > nat ).
thf(func_def_99,type,
sK27: nat > extended_enat > nat ).
thf(func_def_100,type,
sK28: extended_enat > nat ).
thf(func_def_101,type,
sK29: extended_enat > nat ).
thf(func_def_102,type,
sK30: extended_enat > nat ).
thf(func_def_103,type,
sK31: extended_enat > nat ).
thf(func_def_104,type,
sK32: extended_enat > nat ).
thf(func_def_105,type,
sK33: extended_enat > nat ).
thf(func_def_106,type,
sK34: extended_enat > nat ).
thf(func_def_107,type,
sK35: extended_enat > nat ).
thf(func_def_108,type,
sK36: extended_enat > nat ).
thf(func_def_109,type,
sK37: extended_enat > nat ).
thf(func_def_110,type,
sK38: extended_enat > nat ).
thf(func_def_111,type,
sK39: extended_enat > nat ).
thf(func_def_112,type,
sK40: extended_enat > nat ).
thf(func_def_113,type,
sK41:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_114,type,
sK42:
!>[X0: $tType] : ( nat > ( X0 > extended_enat ) > X0 ) ).
thf(func_def_115,type,
sK43:
!>[X0: $tType] : ( ( X0 > extended_enat ) > X0 ) ).
thf(func_def_116,type,
sK44:
!>[X0: $tType] : ( ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_117,type,
sK45:
!>[X0: $tType,X1: $tType] : ( ( X1 > X0 ) > ( X1 > X0 ) > X1 ) ).
thf(func_def_118,type,
sK46:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_119,type,
sK47:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_120,type,
sK48:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_121,type,
sK49:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_122,type,
sK50:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_123,type,
sK51:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_124,type,
sK52:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_125,type,
sK53:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_126,type,
sK54:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_127,type,
sK55:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_128,type,
sK56:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_129,type,
sK57:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_130,type,
sK58:
!>[X0: $tType] : ( ( stream(X0) > $o ) > ( stream(X0) > $o ) > stream(X0) ) ).
thf(func_def_131,type,
sK59: extended_enat > nat ).
thf(func_def_132,type,
sK60: extended_enat > nat ).
thf(f3219,plain,
$false,
inference(trivial_inequality_removal,[],[f3218]) ).
thf(f3218,plain,
$true = $false,
inference(forward_demodulation,[],[f3216,f3193]) ).
thf(f3193,plain,
$false = vAPP(stream(a),$o,p,omega),
inference(trivial_inequality_removal,[],[f3192]) ).
thf(f3192,plain,
( ( $true = $false )
| ( $false = vAPP(stream(a),$o,p,omega) ) ),
inference(forward_demodulation,[],[f3191,f2044]) ).
thf(f2044,plain,
! [X0: extended_enat] : ( $false = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),X0),zero_zero(extended_enat)) ),
inference(trivial_inequality_removal,[],[f2043]) ).
thf(f2043,plain,
! [X0: extended_enat] :
( ( $true != $true )
| ( $false = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),X0),zero_zero(extended_enat)) ) ),
inference(superposition,[],[f1332,f297]) ).
thf(f297,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1332,plain,
! [X0: extended_enat] : ( $true != vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),X0),zero_zero(extended_enat)) ),
inference(cnf_transformation,[],[f823]) ).
thf(f823,plain,
! [X0: extended_enat] : ( $true != vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),X0),zero_zero(extended_enat)) ),
inference(flattening,[],[f533]) ).
thf(f533,plain,
! [X0: extended_enat] : ( $true != vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),X0),zero_zero(extended_enat)) ),
inference(fool_elimination,[],[f532]) ).
thf(f532,plain,
! [X0: extended_enat] : ~ vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),X0),zero_zero(extended_enat)),
inference(rectify,[],[f17]) ).
thf(f17,axiom,
! [X5: extended_enat] : ~ vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),X5),zero_zero(extended_enat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_not__iless0) ).
thf(f3191,plain,
( ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),zero_zero(extended_enat)) )
| ( $false = vAPP(stream(a),$o,p,omega) ) ),
inference(duplicate_literal_removal,[],[f3190]) ).
thf(f3190,plain,
( ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),zero_zero(extended_enat)) )
| ( $false = vAPP(stream(a),$o,p,omega) )
| ( $false = vAPP(stream(a),$o,p,omega) ) ),
inference(superposition,[],[f1983,f1630]) ).
thf(f1630,plain,
! [X0: $tType,X2: stream(X0),X1: stream(X0) > $o] :
( ( zero_zero(extended_enat) = vAPP(stream(X0),extended_enat,vAPP(sTfun(stream(X0),$o),sTfun(stream(X0),extended_enat),coindu76177514sfirst(X0),X1),X2) )
| ( $false = vAPP(stream(X0),$o,X1,X2) ) ),
inference(equality_proxy_clausification,[],[f1629]) ).
thf(f1629,plain,
! [X0: $tType,X2: stream(X0),X1: stream(X0) > $o] :
( ( $false = vAPP(stream(X0),$o,X1,X2) )
| ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),vEQ(extended_enat),zero_zero(extended_enat)),vAPP(stream(X0),extended_enat,vAPP(sTfun(stream(X0),$o),sTfun(stream(X0),extended_enat),coindu76177514sfirst(X0),X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f1396]) ).
thf(f1396,plain,
! [X0: $tType,X2: stream(X0),X1: stream(X0) > $o] : ( vAPP(stream(X0),$o,X1,X2) = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),vEQ(extended_enat),zero_zero(extended_enat)),vAPP(stream(X0),extended_enat,vAPP(sTfun(stream(X0),$o),sTfun(stream(X0),extended_enat),coindu76177514sfirst(X0),X1),X2)) ),
inference(cnf_transformation,[],[f607]) ).
thf(f607,plain,
! [X0: $tType,X1: stream(X0) > $o,X2: stream(X0)] : ( vAPP(stream(X0),$o,X1,X2) = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),vEQ(extended_enat),zero_zero(extended_enat)),vAPP(stream(X0),extended_enat,vAPP(sTfun(stream(X0),$o),sTfun(stream(X0),extended_enat),coindu76177514sfirst(X0),X1),X2)) ),
inference(fool_elimination,[],[f606]) ).
thf(f606,plain,
! [X0: $tType,X1: stream(X0) > $o,X2: stream(X0)] :
( ( zero_zero(extended_enat) = vAPP(stream(X0),extended_enat,vAPP(sTfun(stream(X0),$o),sTfun(stream(X0),extended_enat),coindu76177514sfirst(X0),X1),X2) )
= vAPP(stream(X0),$o,X1,X2) ),
inference(rectify,[],[f22]) ).
thf(f22,axiom,
! [X0: $tType,X6: stream(X0) > $o,X7: stream(X0)] :
( ( vAPP(stream(X0),extended_enat,vAPP(sTfun(stream(X0),$o),sTfun(stream(X0),extended_enat),coindu76177514sfirst(X0),X6),X7) = zero_zero(extended_enat) )
= vAPP(stream(X0),$o,X6,X7) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_sfirst__eq__0) ).
thf(f1983,plain,
( ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) )
| ( $false = vAPP(stream(a),$o,p,omega) ) ),
inference(backward_demodulation,[],[f1976,f1339]) ).
thf(f1339,plain,
! [X0: $tType,X1: stream(X0)] : ( vAPP(stream(X0),stream(X0),vAPP(nat,sTfun(stream(X0),stream(X0)),sdrop(X0),zero_zero(nat)),X1) = X1 ),
inference(cnf_transformation,[],[f829]) ).
thf(f829,plain,
! [X0: $tType,X1: stream(X0)] : ( vAPP(stream(X0),stream(X0),vAPP(nat,sTfun(stream(X0),stream(X0)),sdrop(X0),zero_zero(nat)),X1) = X1 ),
inference(rectify,[],[f5]) ).
thf(f5,axiom,
! [X0: $tType,X10: stream(X0)] : ( vAPP(stream(X0),stream(X0),vAPP(nat,sTfun(stream(X0),stream(X0)),sdrop(X0),zero_zero(nat)),X10) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_sdrop_Osimps_I1_J) ).
thf(f1976,plain,
( ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) )
| ( vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega)) = $false ) ),
inference(backward_demodulation,[],[f1973,f1188]) ).
thf(f1188,plain,
zero_zero(extended_enat) = vAPP(nat,extended_enat,extended_enat2,zero_zero(nat)),
inference(cnf_transformation,[],[f18]) ).
thf(f18,axiom,
zero_zero(extended_enat) = vAPP(nat,extended_enat,extended_enat2,zero_zero(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_zero__enat__def) ).
thf(f1973,plain,
( ( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) = $true )
| ( vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega)) = $false ) ),
inference(not_proxy_clausification,[],[f1970]) ).
thf(f1970,plain,
( ( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) = $true )
| ( $true = vAPP($o,$o,vNOT,vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega))) ) ),
inference(binary_proxy_clausification,[],[f1185]) ).
thf(f1185,plain,
vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) != vAPP($o,$o,vNOT,vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega))),
inference(cnf_transformation,[],[f798]) ).
thf(f798,plain,
vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) != vAPP($o,$o,vNOT,vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega))),
inference(flattening,[],[f299]) ).
thf(f299,plain,
vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) != vAPP($o,$o,vNOT,vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega))),
inference(fool_elimination,[],[f298]) ).
thf(f298,plain,
( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) != ~ vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega)) ),
inference(rectify,[],[f295]) ).
thf(f295,negated_conjecture,
( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) != ~ vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega)) ),
inference(negated_conjecture,[],[f294]) ).
thf(f294,conjecture,
( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) = ~ vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f3216,plain,
$true = vAPP(stream(a),$o,p,omega),
inference(trivial_inequality_removal,[],[f3215]) ).
thf(f3215,plain,
( ( zero_zero(extended_enat) != zero_zero(extended_enat) )
| ( $true = vAPP(stream(a),$o,p,omega) ) ),
inference(superposition,[],[f1631,f3200]) ).
thf(f3200,plain,
zero_zero(extended_enat) = vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega),
inference(trivial_inequality_removal,[],[f3197]) ).
thf(f3197,plain,
( ( $true = $false )
| ( zero_zero(extended_enat) = vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega) ) ),
inference(backward_demodulation,[],[f2319,f3193]) ).
thf(f2319,plain,
( ( zero_zero(extended_enat) = vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega) )
| ( $true = vAPP(stream(a),$o,p,omega) ) ),
inference(trivial_inequality_removal,[],[f2308]) ).
thf(f2308,plain,
( ( $true = $false )
| ( $true = vAPP(stream(a),$o,p,omega) )
| ( zero_zero(extended_enat) = vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega) ) ),
inference(superposition,[],[f1984,f1923]) ).
thf(f1923,plain,
! [X0: extended_enat] :
( ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),X0) )
| ( zero_zero(extended_enat) = X0 ) ),
inference(equality_proxy_clausification,[],[f1922]) ).
thf(f1922,plain,
! [X0: extended_enat] :
( ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),X0) )
| ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),vEQ(extended_enat),zero_zero(extended_enat)),X0) ) ),
inference(not_proxy_clausification,[],[f1918]) ).
thf(f1918,plain,
! [X0: extended_enat] :
( ( $true = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),X0) )
| ( $false = vAPP($o,$o,vNOT,vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),vEQ(extended_enat),zero_zero(extended_enat)),X0)) ) ),
inference(binary_proxy_clausification,[],[f1223]) ).
thf(f1223,plain,
! [X0: extended_enat] : ( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),X0) = vAPP($o,$o,vNOT,vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),vEQ(extended_enat),zero_zero(extended_enat)),X0)) ),
inference(cnf_transformation,[],[f333]) ).
thf(f333,plain,
! [X0: extended_enat] : ( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),X0) = vAPP($o,$o,vNOT,vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),vEQ(extended_enat),zero_zero(extended_enat)),X0)) ),
inference(fool_elimination,[],[f332]) ).
thf(f332,plain,
! [X0: extended_enat] :
( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),X0)
= ( zero_zero(extended_enat) != X0 ) ),
inference(rectify,[],[f14]) ).
thf(f14,axiom,
! [X5: extended_enat] :
( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),X5)
= ( zero_zero(extended_enat) != X5 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_i0__less) ).
thf(f1984,plain,
( ( $false = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) )
| ( $true = vAPP(stream(a),$o,p,omega) ) ),
inference(backward_demodulation,[],[f1975,f1339]) ).
thf(f1975,plain,
( ( $false = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),zero_zero(extended_enat)),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) )
| ( vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega)) = $true ) ),
inference(backward_demodulation,[],[f1972,f1188]) ).
thf(f1972,plain,
( ( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) = $false )
| ( vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega)) = $true ) ),
inference(not_proxy_clausification,[],[f1971]) ).
thf(f1971,plain,
( ( vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),ord_less(extended_enat),vAPP(nat,extended_enat,extended_enat2,zero_zero(nat))),vAPP(stream(a),extended_enat,vAPP(sTfun(stream(a),$o),sTfun(stream(a),extended_enat),coindu76177514sfirst(a),p),omega)) = $false )
| ( $false = vAPP($o,$o,vNOT,vAPP(stream(a),$o,p,vAPP(stream(a),stream(a),vAPP(nat,sTfun(stream(a),stream(a)),sdrop(a),zero_zero(nat)),omega))) ) ),
inference(binary_proxy_clausification,[],[f1185]) ).
thf(f1631,plain,
! [X0: $tType,X2: stream(X0),X1: stream(X0) > $o] :
( ( zero_zero(extended_enat) != vAPP(stream(X0),extended_enat,vAPP(sTfun(stream(X0),$o),sTfun(stream(X0),extended_enat),coindu76177514sfirst(X0),X1),X2) )
| ( $true = vAPP(stream(X0),$o,X1,X2) ) ),
inference(equality_proxy_clausification,[],[f1628]) ).
thf(f1628,plain,
! [X0: $tType,X2: stream(X0),X1: stream(X0) > $o] :
( ( $true = vAPP(stream(X0),$o,X1,X2) )
| ( $false = vAPP(extended_enat,$o,vAPP(extended_enat,sTfun(extended_enat,$o),vEQ(extended_enat),zero_zero(extended_enat)),vAPP(stream(X0),extended_enat,vAPP(sTfun(stream(X0),$o),sTfun(stream(X0),extended_enat),coindu76177514sfirst(X0),X1),X2)) ) ),
inference(binary_proxy_clausification,[],[f1396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : DAT153^1 : TPTP v8.2.0. Released v7.0.0.
% 0.03/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun May 19 23:30:22 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (20635)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (20638)WARNING: value z3 for option sas not known
% 0.21/0.38 % (20637)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (20639)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (20636)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (20638)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.21/0.38 % (20640)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.21/0.38 % (20641)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.21/0.38 % (20642)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.21/0.41 % (20642)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.43 % Exception at run slice level
% 0.21/0.43 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.45 % (20643)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.48 % (20643)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.49 % Exception at run slice level
% 0.21/0.49 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.50 % (20644)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.21/0.51 % (20641)First to succeed.
% 0.21/0.51 % (20641)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20635"
% 0.21/0.51 % (20641)Refutation found. Thanks to Tanya!
% 0.21/0.51 % SZS status Theorem for theBenchmark
% 0.21/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.51 % (20641)------------------------------
% 0.21/0.51 % (20641)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.21/0.51 % (20641)Termination reason: Refutation
% 0.21/0.51
% 0.21/0.51 % (20641)Memory used [KB]: 2735
% 0.21/0.51 % (20641)Time elapsed: 0.125 s
% 0.21/0.51 % (20641)Instructions burned: 279 (million)
% 0.21/0.51 % (20635)Success in time 0.146 s
%------------------------------------------------------------------------------