TSTP Solution File: DAT239^1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : DAT239^1 : 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 : 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 : Mon May 20 19:51:54 EDT 2024
% Result : Theorem 2.41s 0.76s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 84
% Syntax : Number of formulae : 135 ( 31 unt; 75 typ; 0 def)
% Number of atoms : 464 ( 78 equ; 0 cnn)
% Maximal formula atoms : 3 ( 7 avg)
% Number of connectives : 70 ( 34 ~; 26 |; 1 &; 0 @)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 113 ( 112 >; 1 *; 0 +; 0 <<)
% Number of symbols : 77 ( 74 usr; 4 con; 0-6 aty)
% Number of variables : 100 ( 0 ^ 40 !; 0 ?; 100 :)
% ( 60 !>; 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,
num: $tType ).
thf(type_def_8,type,
nat: $tType ).
thf(type_def_9,type,
int: $tType ).
thf(func_def_0,type,
num: $tType ).
thf(func_def_1,type,
nat: $tType ).
thf(func_def_2,type,
int: $tType ).
thf(func_def_3,type,
itself: $tType > $tType ).
thf(func_def_4,type,
one:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_5,type,
zero:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_6,type,
numeral:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_7,type,
field:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_8,type,
neg_numeral:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_9,type,
group_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_10,type,
monoid_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_11,type,
preorder:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_12,type,
zero_neq_one:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_13,type,
semiring_char_0:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_14,type,
zero_less_one:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_15,type,
semiring_div:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_16,type,
division_ring:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_17,type,
semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_18,type,
semidom_divide:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_19,type,
linordered_idom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_20,type,
linordered_field:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_21,type,
ab_semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_22,type,
linordered_semidom:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_23,type,
semiring_div_parity:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_24,type,
cancel_semigroup_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_25,type,
semiring_numeral_div:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_26,type,
cancel1352612707id_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_27,type,
linord219039673up_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_28,type,
ordere779506340up_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_29,type,
linord1659791738miring:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_30,type,
canoni770627133id_add:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_31,type,
ordere236663937imp_le:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_32,type,
ordere516151231imp_le:
!>[X0: $tType] : ( itself(X0) > $o ) ).
thf(func_def_33,type,
one_one:
!>[X0: $tType] : X0 ).
thf(func_def_34,type,
plus_plus:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_35,type,
zero_zero:
!>[X0: $tType] : X0 ).
thf(func_def_36,type,
neg_numeral_dbl:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_37,type,
bit0: num > num ).
thf(func_def_38,type,
one2: num ).
thf(func_def_39,type,
numeral_numeral:
!>[X0: $tType] : ( num > X0 ) ).
thf(func_def_40,type,
ord_less:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_41,type,
ord_less_eq:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_42,type,
type:
!>[X0: $tType] : itself(X0) ).
thf(func_def_43,type,
divide_divide:
!>[X0: $tType] : ( X0 > X0 > X0 ) ).
thf(func_def_44,type,
na: nat ).
thf(func_def_48,type,
vOR: $o > $o > $o ).
thf(func_def_49,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_50,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_51,type,
sCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_52,type,
vAND: $o > $o > $o ).
thf(func_def_53,type,
vNOT: $o > $o ).
thf(func_def_54,type,
iCOMB:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_55,type,
cCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X1 > X2 ) > X1 > X0 > X2 ) ).
thf(func_def_56,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_57,type,
vIMP: $o > $o > $o ).
thf(func_def_58,type,
sP0:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > $o ) ).
thf(func_def_59,type,
sK1:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_60,type,
sK2:
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_61,type,
sK3: nat > ( nat > $o ) > nat ).
thf(func_def_62,type,
sK4: ( nat > $o ) > nat ).
thf(func_def_63,type,
sK5: ( nat > $o ) > nat ).
thf(func_def_64,type,
sK6: ( nat > $o ) > nat ).
thf(func_def_65,type,
sK7: ( nat > nat ) > nat ).
thf(func_def_66,type,
sK8: ( nat > nat ) > nat ).
thf(func_def_67,type,
sK9:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_68,type,
sK10:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_69,type,
sK11:
!>[X0: $tType] : ( ( X0 > nat ) > ( X0 > $o ) > X0 ) ).
thf(func_def_70,type,
sK12:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_71,type,
sK13:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > nat ) > X0 ) ).
thf(func_def_73,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(f11865,plain,
$false,
inference(trivial_inequality_removal,[],[f11864]) ).
thf(f11864,plain,
$true = $false,
inference(forward_demodulation,[],[f11863,f2099]) ).
thf(f2099,plain,
! [X0: nat] : ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ),
inference(trivial_inequality_removal,[],[f2098]) ).
thf(f2098,plain,
! [X0: nat] :
( ( $true != $true )
| ( $false = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ) ),
inference(superposition,[],[f1386,f304]) ).
thf(f304,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f1386,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ),
inference(cnf_transformation,[],[f902]) ).
thf(f902,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ),
inference(flattening,[],[f656]) ).
thf(f656,plain,
! [X0: nat] : ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0) ),
inference(fool_elimination,[],[f655]) ).
thf(f655,plain,
! [X0: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X0),
inference(rectify,[],[f107]) ).
thf(f107,axiom,
! [X2: nat] : ~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_106_less__irrefl__nat) ).
thf(f11863,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),zero_zero(nat)),
inference(forward_demodulation,[],[f11861,f2265]) ).
thf(f2265,plain,
zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2))),
inference(trivial_inequality_removal,[],[f2255]) ).
thf(f2255,plain,
( ( $true = $false )
| ( zero_zero(nat) = vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2))) ) ),
inference(superposition,[],[f2061,f2091]) ).
thf(f2091,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) = $false,
inference(trivial_inequality_removal,[],[f2090]) ).
thf(f2090,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) = $false ) ),
inference(superposition,[],[f1202,f304]) ).
thf(f1202,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) != $true,
inference(cnf_transformation,[],[f883]) ).
thf(f883,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) != $true,
inference(flattening,[],[f306]) ).
thf(f306,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) != $true,
inference(fool_elimination,[],[f305]) ).
thf(f305,plain,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))),
inference(rectify,[],[f302]) ).
thf(f302,negated_conjecture,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))),
inference(negated_conjecture,[],[f301]) ).
thf(f301,conjecture,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f2061,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
| ( zero_zero(nat) = X0 ) ),
inference(equality_proxy_clausification,[],[f2060]) ).
thf(f2060,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0) ) ),
inference(not_proxy_clausification,[],[f2056]) ).
thf(f2056,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) )
| ( $false = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) ) ),
inference(binary_proxy_clausification,[],[f1214]) ).
thf(f1214,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) ),
inference(cnf_transformation,[],[f314]) ).
thf(f314,plain,
! [X0: nat] : ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) = vAPP($o,$o,vNOT,vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),vEQ(nat),zero_zero(nat)),X0)) ),
inference(fool_elimination,[],[f313]) ).
thf(f313,plain,
! [X0: nat] :
( ( zero_zero(nat) != X0 )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X0) ),
inference(rectify,[],[f6]) ).
thf(f6,axiom,
! [X2: nat] :
( ( zero_zero(nat) != X2 )
= vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_neq0__conv) ).
thf(f11861,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) = $true,
inference(trivial_inequality_removal,[],[f11842]) ).
thf(f11842,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),na),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) = $true ) ),
inference(superposition,[],[f1383,f3515]) ).
thf(f3515,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),na),
inference(subsumption_resolution,[],[f3508,f1207]) ).
thf(f1207,plain,
na != one_one(nat),
inference(cnf_transformation,[],[f919]) ).
thf(f919,plain,
( ( na != one_one(nat) )
& ( na != zero_zero(nat) ) ),
inference(ennf_transformation,[],[f1]) ).
thf(f1,axiom,
~ ( ( na = one_one(nat) )
| ( na = zero_zero(nat) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_ns) ).
thf(f3508,plain,
( ( na = one_one(nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),na) ) ),
inference(trivial_inequality_removal,[],[f3494]) ).
thf(f3494,plain,
( ( $true != $true )
| ( na = one_one(nat) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),na) ) ),
inference(superposition,[],[f1423,f2979]) ).
thf(f2979,plain,
$true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),one_one(nat)),na),
inference(trivial_inequality_removal,[],[f2928]) ).
thf(f2928,plain,
( ( $true = $false )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),one_one(nat)),na) ) ),
inference(superposition,[],[f1407,f2106]) ).
thf(f2106,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) = $false,
inference(trivial_inequality_removal,[],[f2105]) ).
thf(f2105,plain,
( ( $true != $true )
| ( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) = $false ) ),
inference(superposition,[],[f1208,f304]) ).
thf(f1208,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) != $true,
inference(cnf_transformation,[],[f884]) ).
thf(f884,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) != $true,
inference(flattening,[],[f312]) ).
thf(f312,plain,
vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)) != $true,
inference(fool_elimination,[],[f311]) ).
thf(f311,plain,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)),
inference(rectify,[],[f2]) ).
thf(f2,axiom,
~ vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),na),one_one(nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_False) ).
thf(f1407,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(cnf_transformation,[],[f692]) ).
thf(f692,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(fool_elimination,[],[f691]) ).
thf(f691,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X0)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ),
inference(rectify,[],[f54]) ).
thf(f54,axiom,
! [X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X2),X1)
| vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_nat__le__linear) ).
thf(f1423,plain,
! [X0: nat,X1: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
| ( X0 = X1 )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(cnf_transformation,[],[f1122]) ).
thf(f1122,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(flattening,[],[f1121]) ).
thf(f1121,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) )
| ( X0 = X1 )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) ) ),
inference(ennf_transformation,[],[f710]) ).
thf(f710,plain,
! [X0: nat,X1: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1) )
=> ( ( X0 != X1 )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ) ),
inference(fool_elimination,[],[f709]) ).
thf(f709,plain,
! [X0: nat,X1: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X0),X1)
=> ( ( X0 != X1 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X0),X1) ) ),
inference(rectify,[],[f64]) ).
thf(f64,axiom,
! [X1: nat,X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less_eq(nat),X1),X2)
=> ( ( X1 != X2 )
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),X1),X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_le__neq__implies__less) ).
thf(f1383,plain,
! [X0: nat] :
( ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X0) )
| ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) ) ),
inference(cnf_transformation,[],[f1108]) ).
thf(f1108,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) )
| ( $true != vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X0) ) ),
inference(ennf_transformation,[],[f650]) ).
thf(f650,plain,
! [X0: nat] :
( ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X0) )
=> ( $true = vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) ) ),
inference(fool_elimination,[],[f649]) ).
thf(f649,plain,
! [X0: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X0)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X0),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) ),
inference(rectify,[],[f149]) ).
thf(f149,axiom,
! [X2: nat] :
( vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),one_one(nat)),X2)
=> vAPP(nat,$o,vAPP(nat,sTfun(nat,$o),ord_less(nat),zero_zero(nat)),vAPP(nat,nat,vAPP(nat,sTfun(nat,nat),divide_divide(nat),X2),vAPP(num,nat,numeral_numeral(nat),vAPP(num,num,bit0,one2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_148_div__2__gt__zero) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : DAT239^1 : TPTP v8.2.0. Released v7.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n009.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 23:28:37 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (25002)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (25005)WARNING: value z3 for option sas not known
% 0.14/0.39 % (25004)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39 % (25003)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39 % (25005)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)
% 0.14/0.39 % (25009)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)
% 0.14/0.39 % (25008)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)
% 0.14/0.39 % (25006)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.40 % (25007)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)
% 0.21/0.41 % (25009)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.42 % Exception at run slice level
% 0.21/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.42 % Exception at run slice level
% 0.21/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.42 % Exception at run slice level
% 0.21/0.42 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.43 % (25010)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.43 % (25011)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)
% 0.21/0.44 % (25012)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.21/0.46 % (25011)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46 % (25010)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.21/0.46 % Exception at run slice level
% 0.21/0.46 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.21/0.48 % (25013)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 2.41/0.75 % (25012)First to succeed.
% 2.41/0.75 % (25012)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25002"
% 2.41/0.76 % (25012)Refutation found. Thanks to Tanya!
% 2.41/0.76 % SZS status Theorem for theBenchmark
% 2.41/0.76 % SZS output start Proof for theBenchmark
% See solution above
% 2.41/0.76 % (25012)------------------------------
% 2.41/0.76 % (25012)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.41/0.76 % (25012)Termination reason: Refutation
% 2.41/0.76
% 2.41/0.76 % (25012)Memory used [KB]: 3564
% 2.41/0.76 % (25012)Time elapsed: 0.339 s
% 2.41/0.76 % (25012)Instructions burned: 1024 (million)
% 2.41/0.76 % (25002)Success in time 0.373 s
%------------------------------------------------------------------------------