TSTP Solution File: SWW482_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWW482_5 : TPTP v8.1.2. Released v6.0.0.
% 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 : Tue Apr 30 17:35:21 EDT 2024
% Result : Theorem 12.16s 2.08s
% Output : Refutation 12.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 79
% Syntax : Number of formulae : 188 ( 48 unt; 51 typ; 0 def)
% Number of atoms : 309 ( 174 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 270 ( 98 ~; 117 |; 24 &)
% ( 14 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 5 ( 4 usr)
% Number of type conns : 31 ( 17 >; 14 *; 0 +; 0 <<)
% Number of predicates : 36 ( 34 usr; 5 prp; 0-4 aty)
% Number of functors : 17 ( 17 usr; 5 con; 0-4 aty)
% Number of variables : 221 ( 182 !; 0 ?; 221 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
real: $tType ).
tff(type_def_9,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
inverse_divide:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
abs_abs:
!>[X0: $tType] : ( X0 > X0 ) ).
tff(func_def_2,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_4,type,
bit0: int > int ).
tff(func_def_5,type,
bit1: int > int ).
tff(func_def_6,type,
pls: int ).
tff(func_def_7,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_8,type,
root: nat > fun(real,real) ).
tff(func_def_9,type,
sqrt: fun(real,real) ).
tff(func_def_10,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_11,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_12,type,
fFalse: bool ).
tff(func_def_13,type,
fTrue: bool ).
tff(func_def_14,type,
y: real ).
tff(func_def_15,type,
sK8:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
field:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
division_ring:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
comm_semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
comm_monoid_mult:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
field_inverse_zero:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ring_n68954251visors:
!>[X0: $tType] : $o ).
tff(pred_def_18,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_19,type,
divisi14063676e_zero:
!>[X0: $tType] : $o ).
tff(pred_def_20,type,
linord1117847801e_zero:
!>[X0: $tType] : $o ).
tff(pred_def_21,type,
iszero:
!>[X0: $tType] : ( X0 > $o ) ).
tff(pred_def_22,type,
pp: bool > $o ).
tff(pred_def_23,type,
sP0:
!>[X0: $tType] : ( ( int * X0 * X0 ) > $o ) ).
tff(pred_def_24,type,
sP1:
!>[X0: $tType] : $o ).
tff(pred_def_25,type,
sP2:
!>[X0: $tType] : ( ( int * X0 * X0 ) > $o ) ).
tff(pred_def_26,type,
sP3:
!>[X0: $tType] : $o ).
tff(pred_def_27,type,
sP4:
!>[X0: $tType] : ( ( X0 * int * X0 ) > $o ) ).
tff(pred_def_28,type,
sP5:
!>[X0: $tType] : $o ).
tff(pred_def_29,type,
sP6:
!>[X0: $tType] : ( ( X0 * int * X0 ) > $o ) ).
tff(pred_def_30,type,
sP7:
!>[X0: $tType] : $o ).
tff(f36302,plain,
$false,
inference(avatar_sat_refutation,[],[f1002,f1153,f1160,f2257,f36273]) ).
tff(f36273,plain,
spl9_33,
inference(avatar_contradiction_clause,[],[f36272]) ).
tff(f36272,plain,
( $false
| spl9_33 ),
inference(subsumption_resolution,[],[f36271,f2072]) ).
tff(f2072,plain,
( ( pls != bit0(bit1(pls)) )
| spl9_33 ),
inference(avatar_component_clause,[],[f2071]) ).
tff(f2071,plain,
( spl9_33
<=> ( pls = bit0(bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).
tff(f36271,plain,
pls = bit0(bit1(pls)),
inference(subsumption_resolution,[],[f36194,f594]) ).
tff(f594,plain,
aa(real,real,sqrt,number_number_of(real,bit0(bit0(bit1(pls))))) != abs_abs(real,number_number_of(real,bit0(bit1(pls)))),
inference(backward_demodulation,[],[f360,f422]) ).
tff(f422,plain,
! [X0: real] : ( abs_abs(real,X0) = aa(real,real,sqrt,power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) ),
inference(cnf_transformation,[],[f155]) ).
tff(f155,plain,
! [X0: real] : ( abs_abs(real,X0) = aa(real,real,sqrt,power_power(real,X0,number_number_of(nat,bit0(bit1(pls))))) ),
inference(rectify,[],[f18]) ).
tff(f18,axiom,
! [X6: real] : ( aa(real,real,sqrt,power_power(real,X6,number_number_of(nat,bit0(bit1(pls))))) = abs_abs(real,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_real__sqrt__abs) ).
tff(f360,plain,
aa(real,real,sqrt,number_number_of(real,bit0(bit0(bit1(pls))))) != aa(real,real,sqrt,power_power(real,number_number_of(real,bit0(bit1(pls))),number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f148]) ).
tff(f148,plain,
aa(real,real,sqrt,number_number_of(real,bit0(bit0(bit1(pls))))) != aa(real,real,sqrt,power_power(real,number_number_of(real,bit0(bit1(pls))),number_number_of(nat,bit0(bit1(pls))))),
inference(flattening,[],[f147]) ).
tff(f147,negated_conjecture,
( ~ aa(real,real,sqrt,number_number_of(real,bit0(bit0(bit1(pls))))) = aa(real,real,sqrt,power_power(real,number_number_of(real,bit0(bit1(pls))),number_number_of(nat,bit0(bit1(pls))))) ),
inference(negated_conjecture,[],[f146]) ).
tff(f146,conjecture,
aa(real,real,sqrt,number_number_of(real,bit0(bit0(bit1(pls))))) = aa(real,real,sqrt,power_power(real,number_number_of(real,bit0(bit1(pls))),number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f36194,plain,
( ( aa(real,real,sqrt,number_number_of(real,bit0(bit0(bit1(pls))))) = abs_abs(real,number_number_of(real,bit0(bit1(pls)))) )
| ( pls = bit0(bit1(pls)) ) ),
inference(superposition,[],[f4424,f2031]) ).
tff(f2031,plain,
! [X0: int] :
( ( bit0(X0) = times_times(int,bit0(bit1(pls)),X0) )
| ( pls = X0 ) ),
inference(forward_demodulation,[],[f2030,f418]) ).
tff(f418,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(cnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: int] : ( number_number_of(int,X0) = X0 ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X5: int] : ( number_number_of(int,X5) = X5 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_number__of__is__id) ).
tff(f2030,plain,
! [X0: int] :
( ( pls = X0 )
| ( bit0(X0) = times_times(int,number_number_of(int,bit0(bit1(pls))),X0) ) ),
inference(duplicate_literal_removal,[],[f2029]) ).
tff(f2029,plain,
! [X0: int] :
( ( pls = X0 )
| ( pls = X0 )
| ( bit0(X0) = times_times(int,number_number_of(int,bit0(bit1(pls))),X0) ) ),
inference(forward_demodulation,[],[f2026,f410]) ).
tff(f410,plain,
pls = zero_zero(int),
inference(cnf_transformation,[],[f56]) ).
tff(f56,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_Pls__def) ).
tff(f2026,plain,
! [X0: int] :
( ( pls = X0 )
| ( zero_zero(int) = X0 )
| ( bit0(X0) = times_times(int,number_number_of(int,bit0(bit1(pls))),X0) ) ),
inference(resolution,[],[f2016,f486]) ).
tff(f486,plain,
! [X1: $tType,X2: X1,X3: X1,X0: int] :
( ~ sP0(X1,X0,X2,X3)
| ( zero_zero(X1) = X2 )
| ( times_times(X1,number_number_of(X1,X0),X2) = X3 ) ),
inference(cnf_transformation,[],[f332]) ).
tff(f332,plain,
! [X0: int,X1: $tType,X2: X1,X3: X1] :
( ( sP0(X1,X0,X2,X3)
| ( ( zero_zero(X1) != number_number_of(X1,X0) )
& ( zero_zero(X1) = X2 ) )
| ( ( times_times(X1,number_number_of(X1,X0),X2) != X3 )
& ( zero_zero(X1) != X2 ) ) )
& ( ( ( ( zero_zero(X1) = number_number_of(X1,X0) )
| ( zero_zero(X1) != X2 ) )
& ( ( times_times(X1,number_number_of(X1,X0),X2) = X3 )
| ( zero_zero(X1) = X2 ) ) )
| ~ sP0(X1,X0,X2,X3) ) ),
inference(rectify,[],[f331]) ).
tff(f331,plain,
! [X3: int,X0: $tType,X1: X0,X2: X0] :
( ( sP0(X0,X3,X1,X2)
| ( ( zero_zero(X0) != number_number_of(X0,X3) )
& ( zero_zero(X0) = X1 ) )
| ( ( times_times(X0,number_number_of(X0,X3),X1) != X2 )
& ( zero_zero(X0) != X1 ) ) )
& ( ( ( ( zero_zero(X0) = number_number_of(X0,X3) )
| ( zero_zero(X0) != X1 ) )
& ( ( times_times(X0,number_number_of(X0,X3),X1) = X2 )
| ( zero_zero(X0) = X1 ) ) )
| ~ sP0(X0,X3,X1,X2) ) ),
inference(flattening,[],[f330]) ).
tff(f330,plain,
! [X3: int,X0: $tType,X1: X0,X2: X0] :
( ( sP0(X0,X3,X1,X2)
| ( ( zero_zero(X0) != number_number_of(X0,X3) )
& ( zero_zero(X0) = X1 ) )
| ( ( times_times(X0,number_number_of(X0,X3),X1) != X2 )
& ( zero_zero(X0) != X1 ) ) )
& ( ( ( ( zero_zero(X0) = number_number_of(X0,X3) )
| ( zero_zero(X0) != X1 ) )
& ( ( times_times(X0,number_number_of(X0,X3),X1) = X2 )
| ( zero_zero(X0) = X1 ) ) )
| ~ sP0(X0,X3,X1,X2) ) ),
inference(nnf_transformation,[],[f312]) ).
tff(f312,plain,
! [X3: int,X0: $tType,X1: X0,X2: X0] :
( sP0(X0,X3,X1,X2)
<=> ( ( ( zero_zero(X0) = number_number_of(X0,X3) )
| ( zero_zero(X0) != X1 ) )
& ( ( times_times(X0,number_number_of(X0,X3),X1) = X2 )
| ( zero_zero(X0) = X1 ) ) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
tff(f2016,plain,
! [X0: int] :
( sP0(int,bit0(bit1(pls)),X0,bit0(X0))
| ( pls = X0 ) ),
inference(superposition,[],[f1178,f666]) ).
tff(f666,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = X0 ),
inference(forward_demodulation,[],[f664,f418]) ).
tff(f664,plain,
! [X0: int] : ( times_times(int,number_number_of(int,bit1(pls)),X0) = X0 ),
inference(resolution,[],[f446,f376]) ).
tff(f376,plain,
number_ring(int),
inference(cnf_transformation,[],[f111]) ).
tff(f111,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f446,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
inference(cnf_transformation,[],[f250]) ).
tff(f250,plain,
! [X0: $tType] :
( ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X1) = X1 ) ),
inference(rectify,[],[f63]) ).
tff(f63,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X10: X0] : ( times_times(X0,number_number_of(X0,bit1(pls)),X10) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_mult__numeral__1) ).
tff(f1178,plain,
! [X0: int,X1: int] :
( sP0(int,bit0(X0),X1,bit0(times_times(int,X0,X1)))
| ( pls = X1 ) ),
inference(superposition,[],[f949,f540]) ).
tff(f540,plain,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
inference(cnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: int,X1: int] : ( times_times(int,bit0(X1),X0) = bit0(times_times(int,X1,X0)) ),
inference(rectify,[],[f29]) ).
tff(f29,axiom,
! [X4: int,X5: int] : ( times_times(int,bit0(X5),X4) = bit0(times_times(int,X5,X4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_mult__Bit0) ).
tff(f949,plain,
! [X0: int,X1: int] :
( sP0(int,X0,X1,times_times(int,X0,X1))
| ( pls = X1 ) ),
inference(forward_demodulation,[],[f932,f410]) ).
tff(f932,plain,
! [X0: int,X1: int] :
( sP0(int,X0,X1,times_times(int,X0,X1))
| ( zero_zero(int) = X1 ) ),
inference(superposition,[],[f564,f418]) ).
tff(f564,plain,
! [X1: $tType,X2: X1,X0: int] :
( sP0(X1,X0,X2,times_times(X1,number_number_of(X1,X0),X2))
| ( zero_zero(X1) = X2 ) ),
inference(equality_resolution,[],[f489]) ).
tff(f489,plain,
! [X1: $tType,X2: X1,X3: X1,X0: int] :
( sP0(X1,X0,X2,X3)
| ( zero_zero(X1) = X2 )
| ( times_times(X1,number_number_of(X1,X0),X2) != X3 ) ),
inference(cnf_transformation,[],[f332]) ).
tff(f4424,plain,
! [X0: int] : ( abs_abs(real,number_number_of(real,X0)) = aa(real,real,sqrt,number_number_of(real,times_times(int,X0,X0))) ),
inference(superposition,[],[f421,f1734]) ).
tff(f1734,plain,
! [X0: int,X1: int] : ( times_times(real,number_number_of(real,X0),number_number_of(real,X1)) = number_number_of(real,times_times(int,X0,X1)) ),
inference(resolution,[],[f447,f377]) ).
tff(f377,plain,
number_ring(real),
inference(cnf_transformation,[],[f140]) ).
tff(f140,axiom,
number_ring(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber__ring) ).
tff(f447,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ number_ring(X0)
| ( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1)) ) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) = number_number_of(X0,times_times(int,X2,X1)) ) ),
inference(rectify,[],[f33]) ).
tff(f33,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X14: int,X16: int] : ( times_times(X0,number_number_of(X0,X16),number_number_of(X0,X14)) = number_number_of(X0,times_times(int,X16,X14)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_arith__simps_I32_J) ).
tff(f421,plain,
! [X0: real] : ( abs_abs(real,X0) = aa(real,real,sqrt,times_times(real,X0,X0)) ),
inference(cnf_transformation,[],[f154]) ).
tff(f154,plain,
! [X0: real] : ( abs_abs(real,X0) = aa(real,real,sqrt,times_times(real,X0,X0)) ),
inference(rectify,[],[f39]) ).
tff(f39,axiom,
! [X6: real] : ( abs_abs(real,X6) = aa(real,real,sqrt,times_times(real,X6,X6)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_real__sqrt__abs2) ).
tff(f2257,plain,
( spl9_21
| ~ spl9_28
| ~ spl9_33 ),
inference(avatar_contradiction_clause,[],[f2256]) ).
tff(f2256,plain,
( $false
| spl9_21
| ~ spl9_28
| ~ spl9_33 ),
inference(subsumption_resolution,[],[f2117,f2255]) ).
tff(f2255,plain,
( ! [X0: real,X1: real] : ( X0 = X1 )
| spl9_21
| ~ spl9_28
| ~ spl9_33 ),
inference(subsumption_resolution,[],[f2238,f2205]) ).
tff(f2205,plain,
( ! [X0: real] : ( zero_zero(real) = X0 )
| spl9_21
| ~ spl9_28
| ~ spl9_33 ),
inference(subsumption_resolution,[],[f2197,f965]) ).
tff(f965,plain,
( ( zero_zero(real) != number_number_of(real,bit1(pls)) )
| spl9_21 ),
inference(avatar_component_clause,[],[f964]) ).
tff(f964,plain,
( spl9_21
<=> ( zero_zero(real) = number_number_of(real,bit1(pls)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
tff(f2197,plain,
( ! [X0: real] :
( ( zero_zero(real) = number_number_of(real,bit1(pls)) )
| ( zero_zero(real) = X0 ) )
| ~ spl9_28
| ~ spl9_33 ),
inference(backward_demodulation,[],[f1152,f2195]) ).
tff(f2195,plain,
( ! [X0: real,X1: real] : ( zero_zero(real) = inverse_divide(real,X1,X0) )
| ~ spl9_33 ),
inference(forward_demodulation,[],[f2194,f642]) ).
tff(f642,plain,
! [X0: real] : ( zero_zero(real) = times_times(real,zero_zero(real),X0) ),
inference(resolution,[],[f457,f397]) ).
tff(f397,plain,
mult_zero(real),
inference(cnf_transformation,[],[f138]) ).
tff(f138,axiom,
mult_zero(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Rings_Omult__zero) ).
tff(f457,plain,
! [X0: $tType,X1: X0] :
( ~ mult_zero(X0)
| ( zero_zero(X0) = times_times(X0,zero_zero(X0),X1) ) ),
inference(cnf_transformation,[],[f260]) ).
tff(f260,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = times_times(X0,zero_zero(X0),X1) )
| ~ mult_zero(X0) ),
inference(ennf_transformation,[],[f179]) ).
tff(f179,plain,
! [X0: $tType] :
( mult_zero(X0)
=> ! [X1: X0] : ( zero_zero(X0) = times_times(X0,zero_zero(X0),X1) ) ),
inference(rectify,[],[f76]) ).
tff(f76,axiom,
! [X0: $tType] :
( mult_zero(X0)
=> ! [X10: X0] : ( zero_zero(X0) = times_times(X0,zero_zero(X0),X10) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mult__zero__left) ).
tff(f2194,plain,
( ! [X0: real,X1: real] : ( inverse_divide(real,X1,X0) = times_times(real,zero_zero(real),inverse_divide(real,X1,times_times(real,zero_zero(real),X0))) )
| ~ spl9_33 ),
inference(forward_demodulation,[],[f2116,f616]) ).
tff(f616,plain,
zero_zero(real) = number_number_of(real,pls),
inference(resolution,[],[f443,f377]) ).
tff(f443,plain,
! [X0: $tType] :
( ~ number_ring(X0)
| ( zero_zero(X0) = number_number_of(X0,pls) ) ),
inference(cnf_transformation,[],[f247]) ).
tff(f247,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f38]) ).
tff(f38,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_number__of__Pls) ).
tff(f2116,plain,
( ! [X0: real,X1: real] : ( inverse_divide(real,X1,X0) = times_times(real,number_number_of(real,pls),inverse_divide(real,X1,times_times(real,number_number_of(real,pls),X0))) )
| ~ spl9_33 ),
inference(backward_demodulation,[],[f592,f2073]) ).
tff(f2073,plain,
( ( pls = bit0(bit1(pls)) )
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f2071]) ).
tff(f592,plain,
! [X0: real,X1: real] : ( inverse_divide(real,X1,X0) = times_times(real,number_number_of(real,bit0(bit1(pls))),inverse_divide(real,X1,times_times(real,number_number_of(real,bit0(bit1(pls))),X0))) ),
inference(equality_resolution,[],[f553]) ).
tff(f553,plain,
! [X2: real,X0: real,X1: real] :
( ( inverse_divide(real,X1,X0) = times_times(real,number_number_of(real,bit0(bit1(pls))),X2) )
| ( inverse_divide(real,X1,times_times(real,number_number_of(real,bit0(bit1(pls))),X0)) != X2 ) ),
inference(cnf_transformation,[],[f357]) ).
tff(f357,plain,
! [X0: real,X1: real,X2: real] :
( ( ( inverse_divide(real,X1,times_times(real,number_number_of(real,bit0(bit1(pls))),X0)) = X2 )
| ( inverse_divide(real,X1,X0) != times_times(real,number_number_of(real,bit0(bit1(pls))),X2) ) )
& ( ( inverse_divide(real,X1,X0) = times_times(real,number_number_of(real,bit0(bit1(pls))),X2) )
| ( inverse_divide(real,X1,times_times(real,number_number_of(real,bit0(bit1(pls))),X0)) != X2 ) ) ),
inference(nnf_transformation,[],[f230]) ).
tff(f230,plain,
! [X0: real,X1: real,X2: real] :
( ( inverse_divide(real,X1,times_times(real,number_number_of(real,bit0(bit1(pls))),X0)) = X2 )
<=> ( inverse_divide(real,X1,X0) = times_times(real,number_number_of(real,bit0(bit1(pls))),X2) ) ),
inference(rectify,[],[f70]) ).
tff(f70,axiom,
! [X21: real,X7: real,X8: real] :
( ( inverse_divide(real,X7,times_times(real,number_number_of(real,bit0(bit1(pls))),X21)) = X8 )
<=> ( times_times(real,number_number_of(real,bit0(bit1(pls))),X8) = inverse_divide(real,X7,X21) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_eq__divide__2__times__iff) ).
tff(f1152,plain,
( ! [X0: real] :
( ( number_number_of(real,bit1(pls)) = inverse_divide(real,X0,X0) )
| ( zero_zero(real) = X0 ) )
| ~ spl9_28 ),
inference(avatar_component_clause,[],[f1151]) ).
tff(f1151,plain,
( spl9_28
<=> ! [X0: real] :
( ( number_number_of(real,bit1(pls)) = inverse_divide(real,X0,X0) )
| ( zero_zero(real) = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
tff(f2238,plain,
( ! [X0: real,X1: real] :
( ( zero_zero(real) != aa(real,real,sqrt,X1) )
| ( X0 = X1 ) )
| spl9_21
| ~ spl9_28
| ~ spl9_33 ),
inference(backward_demodulation,[],[f550,f2205]) ).
tff(f550,plain,
! [X0: real,X1: real] :
( ( aa(real,real,sqrt,X0) != aa(real,real,sqrt,X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f356]) ).
tff(f356,plain,
! [X0: real,X1: real] :
( ( ( aa(real,real,sqrt,X0) = aa(real,real,sqrt,X1) )
| ( X0 != X1 ) )
& ( ( X0 = X1 )
| ( aa(real,real,sqrt,X0) != aa(real,real,sqrt,X1) ) ) ),
inference(nnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: real,X1: real] :
( ( aa(real,real,sqrt,X0) = aa(real,real,sqrt,X1) )
<=> ( X0 = X1 ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X7: real,X8: real] :
( ( aa(real,real,sqrt,X8) = aa(real,real,sqrt,X7) )
<=> ( X7 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_real__sqrt__eq__iff) ).
tff(f2117,plain,
( ( aa(real,real,sqrt,number_number_of(real,bit0(pls))) != abs_abs(real,number_number_of(real,pls)) )
| ~ spl9_33 ),
inference(backward_demodulation,[],[f594,f2073]) ).
tff(f1160,plain,
spl9_27,
inference(avatar_contradiction_clause,[],[f1159]) ).
tff(f1159,plain,
( $false
| spl9_27 ),
inference(subsumption_resolution,[],[f1158,f367]) ).
tff(f367,plain,
field_inverse_zero(real),
inference(cnf_transformation,[],[f128]) ).
tff(f128,axiom,
field_inverse_zero(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield__inverse__zero) ).
tff(f1158,plain,
( ~ field_inverse_zero(real)
| spl9_27 ),
inference(subsumption_resolution,[],[f1157,f403]) ).
tff(f403,plain,
number(real),
inference(cnf_transformation,[],[f143]) ).
tff(f143,axiom,
number(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Int_Onumber) ).
tff(f1157,plain,
( ~ number(real)
| ~ field_inverse_zero(real)
| spl9_27 ),
inference(resolution,[],[f1149,f492]) ).
tff(f492,plain,
! [X0: $tType] :
( sP1(X0)
| ~ number(X0)
| ~ field_inverse_zero(X0) ),
inference(cnf_transformation,[],[f314]) ).
tff(f314,plain,
! [X0: $tType] :
( sP1(X0)
| ~ number(X0)
| ~ field_inverse_zero(X0) ),
inference(definition_folding,[],[f292,f313,f312]) ).
tff(f313,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] :
( ( inverse_divide(X0,X2,X1) = number_number_of(X0,X3) )
<=> sP0(X0,X3,X1,X2) )
| ~ sP1(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
tff(f292,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] :
( ( inverse_divide(X0,X2,X1) = number_number_of(X0,X3) )
<=> ( ( ( zero_zero(X0) = number_number_of(X0,X3) )
| ( zero_zero(X0) != X1 ) )
& ( ( times_times(X0,number_number_of(X0,X3),X1) = X2 )
| ( zero_zero(X0) = X1 ) ) ) )
| ~ number(X0)
| ~ field_inverse_zero(X0) ),
inference(flattening,[],[f291]) ).
tff(f291,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] :
( ( inverse_divide(X0,X2,X1) = number_number_of(X0,X3) )
<=> ( ( ( zero_zero(X0) = number_number_of(X0,X3) )
| ( zero_zero(X0) != X1 ) )
& ( ( times_times(X0,number_number_of(X0,X3),X1) = X2 )
| ( zero_zero(X0) = X1 ) ) ) )
| ~ number(X0)
| ~ field_inverse_zero(X0) ),
inference(ennf_transformation,[],[f205]) ).
tff(f205,plain,
! [X0: $tType] :
( ( number(X0)
& field_inverse_zero(X0) )
=> ! [X1: X0,X2: X0,X3: int] :
( ( inverse_divide(X0,X2,X1) = number_number_of(X0,X3) )
<=> ( ( ( zero_zero(X0) = X1 )
=> ( zero_zero(X0) = number_number_of(X0,X3) ) )
& ( ( zero_zero(X0) != X1 )
=> ( times_times(X0,number_number_of(X0,X3),X1) = X2 ) ) ) ) ),
inference(rectify,[],[f54]) ).
tff(f54,axiom,
! [X0: $tType] :
( ( number(X0)
& field_inverse_zero(X0) )
=> ! [X23: X0,X20: X0,X11: int] :
( ( number_number_of(X0,X11) = inverse_divide(X0,X20,X23) )
<=> ( ( ( zero_zero(X0) = X23 )
=> ( number_number_of(X0,X11) = zero_zero(X0) ) )
& ( ( zero_zero(X0) != X23 )
=> ( times_times(X0,number_number_of(X0,X11),X23) = X20 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_eq__divide__eq__number__of) ).
tff(f1149,plain,
( ~ sP1(real)
| spl9_27 ),
inference(avatar_component_clause,[],[f1147]) ).
tff(f1147,plain,
( spl9_27
<=> sP1(real) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
tff(f1153,plain,
( ~ spl9_27
| spl9_28 ),
inference(avatar_split_clause,[],[f1132,f1151,f1147]) ).
tff(f1132,plain,
! [X0: real] :
( ( number_number_of(real,bit1(pls)) = inverse_divide(real,X0,X0) )
| ~ sP1(real)
| ( zero_zero(real) = X0 ) ),
inference(resolution,[],[f485,f944]) ).
tff(f944,plain,
! [X0: real] :
( sP0(real,bit1(pls),X0,X0)
| ( zero_zero(real) = X0 ) ),
inference(superposition,[],[f564,f665]) ).
tff(f665,plain,
! [X0: real] : ( times_times(real,number_number_of(real,bit1(pls)),X0) = X0 ),
inference(resolution,[],[f446,f377]) ).
tff(f485,plain,
! [X0: $tType,X2: X0,X3: int,X1: X0] :
( ~ sP0(X0,X3,X1,X2)
| ( inverse_divide(X0,X2,X1) = number_number_of(X0,X3) )
| ~ sP1(X0) ),
inference(cnf_transformation,[],[f329]) ).
tff(f329,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] :
( ( ( inverse_divide(X0,X2,X1) = number_number_of(X0,X3) )
| ~ sP0(X0,X3,X1,X2) )
& ( sP0(X0,X3,X1,X2)
| ( inverse_divide(X0,X2,X1) != number_number_of(X0,X3) ) ) )
| ~ sP1(X0) ),
inference(nnf_transformation,[],[f313]) ).
tff(f1002,plain,
~ spl9_21,
inference(avatar_contradiction_clause,[],[f1001]) ).
tff(f1001,plain,
( $false
| ~ spl9_21 ),
inference(subsumption_resolution,[],[f987,f976]) ).
tff(f976,plain,
( ! [X0: real] : ( zero_zero(real) = X0 )
| ~ spl9_21 ),
inference(superposition,[],[f971,f634]) ).
tff(f634,plain,
! [X0: real] : ( zero_zero(real) = inverse_divide(real,X0,zero_zero(real)) ),
inference(resolution,[],[f425,f363]) ).
tff(f363,plain,
divisi14063676e_zero(real),
inference(cnf_transformation,[],[f125]) ).
tff(f125,axiom,
divisi14063676e_zero(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Odivision__ring__inverse__zero) ).
tff(f425,plain,
! [X0: $tType,X1: X0] :
( ~ divisi14063676e_zero(X0)
| ( zero_zero(X0) = inverse_divide(X0,X1,zero_zero(X0)) ) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType] :
( ! [X1: X0] : ( zero_zero(X0) = inverse_divide(X0,X1,zero_zero(X0)) )
| ~ divisi14063676e_zero(X0) ),
inference(ennf_transformation,[],[f158]) ).
tff(f158,plain,
! [X0: $tType] :
( divisi14063676e_zero(X0)
=> ! [X1: X0] : ( zero_zero(X0) = inverse_divide(X0,X1,zero_zero(X0)) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X0: $tType] :
( divisi14063676e_zero(X0)
=> ! [X10: X0] : ( zero_zero(X0) = inverse_divide(X0,X10,zero_zero(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_divide__zero) ).
tff(f971,plain,
( ! [X0: real] : ( inverse_divide(real,X0,zero_zero(real)) = X0 )
| ~ spl9_21 ),
inference(backward_demodulation,[],[f904,f966]) ).
tff(f966,plain,
( ( zero_zero(real) = number_number_of(real,bit1(pls)) )
| ~ spl9_21 ),
inference(avatar_component_clause,[],[f964]) ).
tff(f904,plain,
! [X0: real] : ( inverse_divide(real,X0,number_number_of(real,bit1(pls))) = X0 ),
inference(subsumption_resolution,[],[f894,f366]) ).
tff(f366,plain,
field(real),
inference(cnf_transformation,[],[f141]) ).
tff(f141,axiom,
field(real),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_RealDef_Oreal___Fields_Ofield) ).
tff(f894,plain,
! [X0: real] :
( ( inverse_divide(real,X0,number_number_of(real,bit1(pls))) = X0 )
| ~ field(real) ),
inference(resolution,[],[f481,f377]) ).
tff(f481,plain,
! [X0: $tType,X1: X0] :
( ~ number_ring(X0)
| ( inverse_divide(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ field(X0) ),
inference(cnf_transformation,[],[f286]) ).
tff(f286,plain,
! [X0: $tType] :
( ! [X1: X0] : ( inverse_divide(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0)
| ~ field(X0) ),
inference(flattening,[],[f285]) ).
tff(f285,plain,
! [X0: $tType] :
( ! [X1: X0] : ( inverse_divide(X0,X1,number_number_of(X0,bit1(pls))) = X1 )
| ~ number_ring(X0)
| ~ field(X0) ),
inference(ennf_transformation,[],[f202]) ).
tff(f202,plain,
! [X0: $tType] :
( ( number_ring(X0)
& field(X0) )
=> ! [X1: X0] : ( inverse_divide(X0,X1,number_number_of(X0,bit1(pls))) = X1 ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X0: $tType] :
( ( number_ring(X0)
& field(X0) )
=> ! [X10: X0] : ( inverse_divide(X0,X10,number_number_of(X0,bit1(pls))) = X10 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_divide__numeral__1) ).
tff(f987,plain,
( ( zero_zero(real) != aa(real,real,sqrt,number_number_of(real,bit0(bit0(bit1(pls))))) )
| ~ spl9_21 ),
inference(backward_demodulation,[],[f594,f976]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW482_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Apr 30 03:11:11 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % (3476)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (3479)WARNING: value z3 for option sas not known
% 0.13/0.37 % (3481)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)
% 0.13/0.37 % (3478)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (3480)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (3482)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)
% 0.13/0.37 % (3483)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)
% 0.13/0.37 % (3479)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)
% 0.13/0.37 % (3477)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (3483)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.38 % Exception at run slice level
% 0.13/0.38 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39 % (3484)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.13/0.39 % (3485)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)
% 0.13/0.39 % (3484)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.39 % (3485)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.39 % Exception at run slice level
% 0.13/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.39 % (3486)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)
% 0.18/0.40 % (3487)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)
% 12.02/2.07 % (3486)First to succeed.
% 12.16/2.08 % (3486)Refutation found. Thanks to Tanya!
% 12.16/2.08 % SZS status Theorem for theBenchmark
% 12.16/2.08 % SZS output start Proof for theBenchmark
% See solution above
% 12.16/2.08 % (3486)------------------------------
% 12.16/2.08 % (3486)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 12.16/2.08 % (3486)Termination reason: Refutation
% 12.16/2.08
% 12.16/2.08 % (3486)Memory used [KB]: 12388
% 12.16/2.08 % (3486)Time elapsed: 1.686 s
% 12.16/2.08 % (3486)Instructions burned: 3812 (million)
% 12.16/2.08 % (3486)------------------------------
% 12.16/2.08 % (3486)------------------------------
% 12.16/2.08 % (3476)Success in time 1.728 s
%------------------------------------------------------------------------------